Asymmetric Single Point Incremental Forming of Sheet Metal J. Jeswiet1 (1), F. Micari2 (1), G. Hirt3, A. Bramley4 (1), J. Duflou5 (2), J. Allwood6 1
Queen’s University, Kingston, ON, Canada 2 University of Palermo, Palermo, Italy 3 University of Aachen, Germany 4 University of Bath, United Kingdom 5 Katholieke Universiteit Leuven, Belgium 6 University of Cambridge, Cambridge, England Abstract The use of computers in manufacturing has enabled the development of several new sheet metal forming processes, which are based upon older technologies. This paper describes modifications that have been made to traditional forming methods such as conventional spinning and shear forming, forming processes in which deformation is localized. Recent advances have enabled this localized deformation to be accurately controlled and studied. Current developments have been focused on forming asymmetric parts using CNC technology, without the need for costly dies. Asymmetric Incremental Sheet Forming has the potential to revolutionize sheet metal forming, making it accessible to all levels of manufacturing. This paper describes the genesis and current state-of-the-art of Asymmetric Incremental Sheet Forming.
Keywords: Forming, Rapid Prototyping, Sheet Metal
1 INTRODUCTION New methods of forming sheet metal are now at a stage where it is possible to make either custom manufactured parts or to manufacture small batch production quantities, with very short turn around times from design to manufacture. Schmoeckel [1] predicted in 1991 that with the increase in automation metal forming equipment would become more flexible. That has happened in this case. The idea of incrementally forming sheet metal with a single point tool, called ‘dieless forming’, was patented by Leszak [2] well before it was technically feasible. There have been many studies, which have lead to the present situation [3 – 8]. Today, there are new processes whereby sheet metal is plastically deformed at a local point enabling truly flexible production of complex sheet metal parts. This can be done in either small batch lots with short lead times, or in production of usable rapid prototypes within one day. The new processes are attractive because manufacturing sheet metal can be accomplished by any facility having a three-axis CNC mill. Inspiration for the emerging processes is usually found in traditional forming methods. These conventional processes are typically constrained as far as achievable part geometry is concerned and require dedicated tooling and dies. CNC hardware and software have reached a mature state of development enabling the development of new sheet metal forming processes. The new forming methods give the possibility to create flexible forming facilities, without dies, capable of producing complex shaped surfaces, while applying generic tooling. The ultimate goal is ‘dieless forming’. This paper will show how a product progresses from the design stage, to developing toolpaths for metal forming, to the final production process. Spinning is the forerunner of asymmetric incremental sheet metal forming. Hagan and Jeswiet [9] sketched a state-ofthe-art for a number of the newly emerging sheet metal forming processes, all having a genesis in spinning, and all having a potential for rapid prototyping applications with sheet metal.
2
A REVIEW OF SYMMETRIC INCREMENTAL SHEET METAL FORMING PROCESSES An in-depth discussion of spinning can be found in Brown [10, 11]. It can be broken down into the following three subgroups: 1) conventional spinning; 2) shear forming; 3) flow forming. Conventional spinning and shear forming will be discussed briefly. 2.1 Spinning and Shear Forming. Conventional spinning is performed through a series of sweeping strokes with a forming tool [12]. Figure 1 illustrates the movement of material from the original blank to the final conical shape using several passes. In shear forming, a roller tool is used and motion is programmed to follow the profile of the part surface [13]. In the ideal shear forming process no radial displacement of material occurs [14, 15]. Three types of computer-aided control are used in forming the sheet metal. CNC and numerical control (NC) systems and control type, programmable numerical control (PNC), which uses playback technology [16]. The final thickness of a shear formed part can be calculated using the sine law [13], where ti is the initial thickness, tf is the final thickness, and α is the spinning angle; see Figure 2. An element is shown for the wall and flange of a shear formed cone. There is no displacement of material in the flange region thus the wall deforms under pure shear and φ is defined as the draw angle. The plastic deformation forming limits in spinning can be determined by calculating spinnability [18, 19]. Kegg [18] defined spinnability as the maximum reduction of thickness, t, that a material, with initial thickness ti can achieve; see Figure 2. 2.2 Symmetric Incremental Forming Spinning without a mandrel showed dies are unnecessary with a single point forming tool. The work by Kitazawa [22, 23, 24, 25] showed controlled deformation is possible with a single point tool. Also, the techniques developed by Kitazawa [23] were a useful step toward multiple pass forming used in asymmetric incremental forming.
Formed cone
Formed Cone (one pass)
Rotating Mandrel
Rotating Mandrel
Initial Blank
Initial Blank
Shear forming
Conventional spinning
α
φ tf
ti ti
sine law: t f = t i sin α
h
before deformation
Figure 1. Conventional spinning and shear forming of a cone [9].
ellipsoid mandrel
spinnability: t −t %R = i ti
Figure 2. The spinning sine law [14] and the shear spinnability test designed by Kegg [18]. 3 ASYMMETRIC INCREMENTAL SHEET FORMING Several new metal forming techniques have been developed in the last few years due to advances in: 1) computer controlled machining; 2) symmetric single point forming (spinning); and 3) the development of toolpath postprocessors in CAD software packages. One significant outcome of this technology is the ability to form asymmetric shapes at low cost, without expensive dies. The asymmetric sheet metal incremental forming techniques discussed here can be divided into different categories. First is a method initially developed by Powell and Andrew [26], which was subsequently called the backward bulge method by Matsubara [27]. Bambach et al. are also active with this application [28]. Both symmetric and asymmetric shapes can be created using this process. See Figures 3 (c) and (d). The next class includes work by Jeswiet [29], Kim [30], Leach [31], and Felici [32], all of whom have studied the application of incremental CNC forming technology to asymmetric shapes. See Figure 3 (a). In this process, the blank remains stationary and forming occurs during CNC control of the tool in a CNC mill. The foregoing are discussed in the following sections. 3.1 Definition, making asymmetric shapes from sheet metal without dies Asymmetric incremental sheet forming (AISF) can be interpreted in different ways. Hence, a definition with Figures is included here, so that the process described cannot be confused with other incremental forming processes. Asymmetric Incremental Sheet Forming (AISF) is a process which: is a sheet metal forming process, has a solid, small-sized forming tool, does not have large, dedicated dies, has a forming tool which is in continuous contact with sheet metal,
has a tool that moves under control, in three dimensional space can produce asymmetric sheet metal shapes It is the last characteristic that separates symmetric spinning from AISF. AISF processes are purely a consequence of the introduction of CNC mills and CAD software with toolpath postprocessors. The idea was first introduced in a patent in 1967 [2], but the foregoing tools were not available at that time. The term ‘dieless’, as applied to this process, was first used in that patent. Asymmetric sheet metal parts can be made with either 1) a machine specifically designed for the process, or 2) a three-axis CNC mill, which most manufacturing facilities possess. Although machines have been designed specifically for this process AISF of sheet can be carried out by anyone having access to a three-axis CNC mill and off-the-shelf software, which generates machine toolpaths. Figure 3 shows the different configurations that are included in the group of asymmetric incremental sheet forming (ASIF) techniques. It can be seen that three of the processes meet the above criteria. The fourth, Figure 3(d), uses a full die and does not meet the “dieless” criteria. However, it is related directly to the other processes and it is being used successfully to make rapid prototype shapes. Hence it is included in the list of dieless forming techniques. The configurations shown in Figures 3(a) and (b) have a stationary sheet metal blankholder. The configurations shown in Figures 3(c) and (d) have a sheet blankholder that moves along a vertical axis, as the forming tool deforms the sheet, hence the vertical motion arrows shown. The configuration shown in Figures 3(c) and (d) are usually associated with machines dedicated to the incremental forming process, and those in Figures 3(a) and (b) are usually found in a CNC mill application. AISF includes two specific types of incremental forming: SPIF, single point incremental forming and TPIF, two point incremental forming. stationary blank holder sheet
forming tool
faceplate
(a) Single Point Incremental Forming; SPIF partial die
counter tool (b) Incremental Forming with counter tools
blankholder motion
(c) Two point incremental forming (partial die); TPIF
full die
(d) Two point incremental forming (full die); TPIF
Figure 3: Process principles of AISF. Four variations are shown [28]. 3.2 Common Types of Asymmetric Incremental Sheet Forming Asymmetric incremental sheet forming has four basic elements: 1) a sheet metal blank, 2) a blankholder, 3) a single point forming tool, 4) CNC motion. These basic
elements are illustrated in Figure 4; F is the metal forming force, v is the tool feed and ω is the spindle rpm. The two common types of AISF are Two Point Incremental Forming (TPIF), and Single Point Incremental Forming (SPIF). These are discussed in the chronological order in which they appeared, historically. In both cases there is a single forming tool whose motion is usually described in terms of Cartesian coordinates, with tool motion in the horizontal sheet plane labeled as the xaxis and y-axis, and the vertical z-axis being the direction in which deformation occurs.
of a series of incremental contours. Each toolpath profile consists of a contour at a constant depth, and the subsequent contours, in the z-axis direction, are at levels offset down by a ∆z increment. Sharp edges may be created in this process, depending upon the forming tool diameter used, since the tool follows the convex surface of the part during forming. Contours for a simple cone are shown in Figure 6. To form this shape the tool would follow the top contour, and then move incrementally downward along the z-axis, until finished. Shear forming theory can be applied. Experimental work with cones formed at various wall angles [27] shows measured thickness matches thickness calculated with the sine law. Because the flange material remains undeformed, the wall thickness can be easily calculated by the sine law, assuming a constant volume. Forming tool
blank Bushing
Figure 4. The basic elements needed for asymmetric Incremental Sheet Forming (AISF). Asymmetric Two Point Incremental Forming TPIF was introduced by Powell and Andrew [26] and used Matsubara [27] to meet the need for quick, inexpensive production of low volume asymmetric sheet metal parts. With the TPIF process, the metal blank moves vertically on bearings, which move on blankholder posts, along the zaxis, as the forming tool pushes into the sheet metal. This process has two points where the sheet metal is pressed, simultaneously, hence it is called Two Point Incremental Forming (TPIF) to differentiate it from Single Point Incremental Forming (SPIF) which has just one point at which force is applied. See Figures 3(c) and 3(d). The point where plastic deformation occurs is directly under the forming tool. When it is used in a CNC mill, it is mounted in the spindle. The forming tool pushes down on the sheet metal, causing plastic deformation at a point, while tracing a path, which is the outline of the shape being manufactured. In TPIF, the other point is a static post that creates an upward counter force on the sheet. One tool presses into the sheet and the other acts as a partial die. Because of the partial die, TPIF is not truly dieless, although it is often called that. The TPIF equipment, shown in Figure 5, consists of an apparatus, which clamps the sheet metal (blankholder), and allows for downward movement with toolpath increments in the z-axis direction. The centre of the blank is supported with a stationary post (a partial die) and a clamped perimeter (blankholder) that moves down on bushings as deformation of the sheet progresses. To prevent twisting of the shape about the partial die, and also provide a back pressure on the strip, there is a support plate underneath the blank. The partial die can be replaced by a shape that acts as a mould (full die) over which the sheet is formed incrementally by the single point. Both configurations are illustrated with details in Figure 3. The forming tool is a steel rod with a smooth, hemispherical tip, for instance a 12 mm diameter. The motion of this tool is controlled through CNC programming
Support Post
Figure 5. Backward bulge forming apparatus [27].
y x z
Figure 6. Toolpath contours for a cone [27]. Asymmetric Single Point Incremental Forming The asymmetric single point incremental forming (SPIF) research performed by Jeswiet [29], Leach [31] and Fratini [32] has shown the SPIF forming method can be performed on a standard three-axis CNC mill. This includes application of CAD/CAM software to plan the process toolpath allows for easy fabrication of complex parts. There is one major difference with respect to the apparatus shown in Figure 5 and that of Jeswiet [29] and Leach [31]. It is the lack of a partial or full die. In SPIF the back surface of the sheet being deformed is a “free”, unsupported surface. This creates different strain and stress patterns in the sheet as it is deformed, in comparison to TPIF. Chronologically, SPIF followed TPIF. It became apparent that any CNC milling machine, when used in conjunction with toolpath planning software, could be used to make sheet metal parts incrementally [29, 31, 32], as shown in Figure 3(a). It can be seen that this configuration is truly dieless forming as envisioned by Leszak [2]. It has been shown that shear forming can also be applied to this process [33]. Process Advantages and Limitations The advantages and disadvantages of SPIF are as follows [34]. Advantages:
Useable parts can be formed directly from CAD data with a minimum of specialized tooling. These can be either Rapid Prototypes or small volume production runs. The process does not require either positive or negative dies hence it is dieless. However it does need a backing plate to create a clear change of angle at the sheet surface. Changes in part design sizes can be easily and quickly accommodated, giving a high degree of flexibility. Making metal Rapid Prototypes is normally difficult, but easy with this process. The small plastic zone and incremental nature of the process contributes to increased formability, making it easier to deform low formability sheet. A conventional CNC milling machine or lathe can be used for this process. The size of the part is limited only by the size of the machine. Forces do not increase because the contact zone and incremental step size remain small. The surface finish of the part can be improved. The operation is quiet and relatively noise free. Disadvantages: The major disadvantage is the forming time is much longer than competitive processes such as deep drawing. As a result the process is limited to small size batch production. The forming of right angles cannot be done in one step, but requires a multi-step process. springback occurs, however algorithms are being developed to deal with this problem. 3.3 Forming Tool Spindle speeds One major difference between the different sheet incremental forming processes, described by Hagan [9] and other users of the process [29, 30, 31, 32], is the way the tool moves while deforming the sheet. In the case of SPIF the following have been done: 1) move the spindle without rotation, 2) move the spindle with the spindle rotating, at different spindle rotating speeds. In the second case the spindle rotates so that the forming tool rolls over the sheet surface. Controlling this variable controls the heating of the sheet during deformation. Reduced Friction Heating Speeds The forming tool has a hemispherical shape, which is pressed into the material to cause deformation as shown in Figure 9. The most obvious source of heating is friction. As the tool travels over the surface of the work piece it is also spinning at a certain number of revolutions per minute. If the tool is stopped it will slide along the surface of the material. In all cases heating will occur due to sliding friction. If the tool is rotated at a high speed, the tool surface will slide over the work piece much more often and there will be excessive heating. The relative motion of the surface of the tool, to the surface of the work piece, is directly proportional to the heat generated by sliding friction. If the relative motion between the tool surface and workpiece is small during forming (i.e. all friction is rolling friction, and not sliding friction) the heating is minimized. For the draw angle, φ, there will be a point where the sheet is tangent to the hemisphere. This is the location of the maximum diameter of contact (dmax). From then on the work piece is in contact with the tool down to the very bottom of the sphere, at which point the diameter of contact is zero. This is an assumption. The average diameter of contact is therefore half dmax, see Figure 7.
spindle speed ω , in terms of feed rate ν , tool radius r, and wall angle φ Invoking the cosine law where:
c 2 = a 2 + b 2 − 2ab o cos α
setting c = dmax ; a = b = r; β = 2 φ
d max = r 2(1 − cos β ) 1 (1 − cos β ) φ 2 d 1 d =r (1 − cos(2φ ) ; d = max 2 2 ω = spindle speed; ν = feed rate v v ω= ω= πd 1 π ⋅ r (1 − cos 2φ ) 2
forming tool
d =r
r
β
dmax
Figure 7. Tool geometry and spindle speeds. To keep friction heat minimal the tool must roll over the surface of the work piece as it is formed. This result requires that the distance traveled along the work piece (i.e. the feed rate) be equal to the average circumference of the tool in contact with the material multiplied by the spindle speed. The following equation, derived in Figure 7, describes this mathematically. Spindle speed and feed rate are represented by ω and ν respectively and the hemispherical tool radius is r.
ω=
v
(1)
1 π ⋅ r (1 − cos 2φ ) 2
Using Friction Heat Increased spindle rotational speed is used sometimes to increase Formability [35]. The Formability increase is due to both a local heating of the sheet and, what is more, a positive reduction of friction effects at the tool-sheet interface. Spindle, Free Rotation In a case study of manufacturing a solar oven cavity, the spindle could rotate freely in a CNC mill [36]. This allowed the friction at the tool/workpiece to cause the tool to rotate at a speed that automatically matched the spindle surface rotation speed. This method is also used by a machines specially built for Incremental Forming [37 38, 39, 40]. 3.4 Equipment used for Incremental Forming The total package needed to incrementally form sheet metal consists of a forming tool and the machinery that moves the forming tool in a controlled manner. These are discussed in the following. The main element is the single point forming tool. Solid hemispherical tools are usually used when plastically deforming sheet metal incrementally. A wide variety of solid tools is used, however, other types of tooling, such as water jets, are being investigated and these are reviewed. Tools are designed and made by the users, they are not yet part of an assortment made available in the market. Solid Forming tools A solid hemispherical head is generally used for asymmetric single point incremental forming; see Figure 8. This assures a continuous point contact between sheet and forming tool; see Figure 7. At very steep wall angles it
can become necessary to use a smaller tool shank than the sphere diameter. Contact between shank and sheet metal is avoided this way. This must be taken into account while generating the toolpath. Once a tool shape is established, usually a specific radius with a hemispherical ball-head, tool materials must be chosen. In most instances, the ball-head tools are made out of tool steel, which is suitable for most applications. To reduce friction, and to increase tool lifetime, the tool can be coated with or even be made out of cemented carbide; see Figure 8. For some tasks plastic tools are necessary to avoid chemical reactions with the sheet material and thus increase the surface quality. Wear of the tool can then become an important consideration. In addition, lubrication helps reduce the wear. Next the diameter of the ball-head must be chosen. A wide range of tool diameters is used, starting at small diameters of 6 mm and going up to large tool diameters of 100 mm for the manufacturing of large parts. These require much more power because of the much larger angle of contact involved. The diameter used depends upon the smallest concave radius required in the part. It also has an influence upon the surface quality and/or the manufacturing time. Furthermore small tools can reach their loading limit while forming materials like stainless steel or titanium. The most commonly used diameters are 12 mm and 12.5 mm [27, 28, 29, 30, 31, 32]. As indicated in section 3.2, special measures can be taken to reduce the friction between the tool and strip. Methods of controlling the relative velocity are discussed in the section on speeds used in forming. In addition to concern about friction heating, there is a concern about the surface roughness of the deformed sheet metal, which can be influenced by both the tool size and the friction. Where surface quality is a concern, the relative velocity can be controlled or a tool designed specifically for the deep rolling of surfaces can be used; see Figure 9. This tool consists of a ball supported by pressure fluid that can rotate freely in all directions and thus decreases friction on the sheet. Incremental forming and related flexible forming methods and their generic tooling Several other tool configurations are being investigated for their ability to plastically deform sheet metal at a local area. Some of these are based upon techniques that have been in existence for sometime, such as shot peening, and others are newer using much different deformation media, such as water jet forming and laser forming. In the case of shot peening, the sheet metal is hit repeatedly with a large number of small balls made of materials such as cast steel, glass, or ceramic. The size can vary from 0.125 mm to 5 mm in diameter. This process is used, traditionally, to create compressive stresses on the surface of bulk products. However, while shot peening has been used as a forming method since the 1950’s [41, 42, 43], recent work by Kopp [44] has demonstrated the possibility of creating both convex and concave shapes by simultaneously using double sided shot peening.
Figure 8: Cemented carbide tools with ∅ 6, 10, 30 mm, and a plastic tool (right) [37].
Sleeve, z-axis Socket (fixed) Flange (rotating collet)
Pressure fluid ca. 320 bar
Forming tool aperture
CBN-ball φ13 mm
Figure 9. A universal tool head [37]. This approach results in improved plastic deformation, while a well-chosen balance between the kinetic energy supplied from both sides allows a specified curvature of the work piece. Both convex and concave shapes can be achieved in this way. This effectively opens perspectives for a flexible forming tool for larger, single or double-curved surfaces, characterized by large radii of curvature. The potential for expanding the process window to generic part shapes, including strongly curved surfaces, has not yet been thoroughly researched. Therefore it has not been selected as an explicit focus point for this paper. Water jet forming is a relatively new process and also has potential as a SPIF tool. Water jet cutting has been used, successfully, in many cutting situations since its development in the early 1980’s. An attempt to apply water jet technology to incremental forming was carried out by Iseki [45], who explored the possibility to incrementally bulge a sheet metal. Subsequently Jurisevic et al. [46] analyzed the modifications that are necessary in order to utilize standard water jet cutting systems for incremental forming. They found water pressures up to 50 MPa are needed and with a higher water volume flow (up to 50 l/min) in comparison to cutting applications. The above mentioned researchers carried out their experiments on 0.5mm thick AA6082 sheets. Water jet forming is still at a very preliminary research stage and requires a wide research effort to investigate its possibilities and limitations. Laser forming is a new technology developed in the early 1990’s [47, 48, 49]. It also shows promise as a forming tool in the asymmetric incremental forming of sheet metal. In this technique a local area is heated repetitively, with a two phase heating and cooling process along a selected path. The sheet bends in a preferential direction, usually depending upon the resident stresses in the sheet. Research on laser forming has dealt with the analysis of process precision in order to obtain higher accuracy as required by the industrial applications [50]. Recently, closed loop control systems have been developed to improve the effectiveness of laser forming processes in the achievement of even complex 3-D shapes [51]. The investigation of laser forming to make complex industrial parts requires a further research. Male el al. [52] followed up on the laser forming techniques by using a plasma arc in place of a laser. The main reasoning given is less expense. Some shapes have been formed successfully, however, this is still in the embryonic stage. Blank holders and platforms Rigid blankholders are used to clamp the sheet. For SPIF, this is a rigid apparatus consisting of a metal plate on four posts, to which the sheet can be clamped. To achieve a high accuracy and to avoid an undesired draw-in of the sheet, different faceplates can be mounted on the apparatus.
Moveable blank holders are used to enable asymmetric TPIF with either partial or dedicated dies. In two point incremental forming, a vertically moveable blank holder is essential. In this case the manufacturing starts at the centre of the desired geometry. As the tool descends, gradually going down in small increments, the blank holder also descends as the forming process progresses; see Figures 3, 5 and 10. Forming Machinery In general all CNC-controlled three-axis CNC machines are suitable to perform ASIF. High speeds, large working volumes and sufficient stiffness are favourable. Milling machines are available in different designs, which differ in working volume, maximum feed rate, maximum load, stiffness and cost prices. The following includes machines, which can be used for AISF. In most cases they can be used for other machining processes, hence they are multi-purpose. Only three-axis mills have been used to date. One manufacturer makes a specially designed machine that is dedicated to incremental forming only [38]. Hence, it is less flexible according to the criteria set out by Schmoeckel [1]. A list of the types of machines available to do incremental forming is: CNC milling machines; Purpose built machines; Robots; Stewart platforms and Hexapods. Common, applicable, shop, CNC milling machines that can be used [53] are: Gantry milling machines; large working volume, high speed drives, high forces, expensive. Gateway milling machine; large working volume, high feed rates, high forces and stiffness, expensive. Bedplate type milling machines; large working volumes available, width is limited, low cost price, lower stiffness. Console milling machine; available in almost every workshop, low cost price, relatively small working volume. This is the only type of three-axis CNC mill used to date. A dedicated, single use, forming machine is commercially available. It has high feed rates, medium sized working volumes, and is equipped with a controlled movable blank holder. See Figure 11. It is based upon the technology developed by Matsubara [26] and Amino [36] including a patent by Aoyama [38].
Figure 10: Upgraded conventional milling machine with moveable blank holder [36].
Figure 11: A purpose built AISF machine [37].
Figure 12. One-off design by Allwood [40]. The concept of forming sheet metal incrementally with a single point has spawned other designs such as the purpose built, one-off design by Allwood [40] in Figure 12. A whole other class of potentially usable machines is available. Some can be used for re-entrant shapes. These are being tried currently as follows. Industrial robots have a large working volume, fast drives, low stiffness, and very low maximum allowable forces. Several institutes are trying to apply robots to incremental forming [54, 55, 56]. This method of forming is in the embryonic stage and looks promising. A special case of a robot application is, that in place of a continuously moving rigid tool, there is incremental forming by hammering. In this case, the tip of the forming tool has a fast oscillating movement beating the sheet into the desired form [55]. This device is especially suited for the application on an industrial robot because it partially compensates the lacking of stiffness of the robot arm. A Stewart Platform [57] offers infinite degrees of freedom. None are being used, but the potential is great, especially if compared to five-axis milling machines. Special tooling is also being developed. For instance, to reduce the tooling support effects in two point incremental forming, Iseki [58] has developed a set of universal roller punches on the opposite side of the universal forming tool to support the geometry to be formed. This multi-roller tool means more flexibility but has the disadvantage of requiring the numerical control of several tools. It has been shown that there is a wide diversity in the type of machine that can be used to achieve asymmetric Single Point Incremental forming. A manufacturer can choose between dedicated machines or flexible machines as envisaged by Schmoeckel [1].
4 MATERIAL PROCESS PARAMETERS Material process parameters and toolpath generation are at the heart of AISF. One of the first steps in a design is to create a CAD drawing of the part. For AISF processes the drawing may be designed in-house or be imported from third parties and modified as required. Fortunately, CAD drawings are usually made with a commercial package that allows the user to create a file in a neutral data format. This allows the CAD file to be exported easily into a CAM package. The procedure followed in making a part, from receiving a CAD model to generating a toolpath, is shown in Figure 14. The material parameter, draw angle φ, defined in Figure 2 is important in AISF. The largest design draw angle in the part, φd, must be less than the material parameter φmax, the maximum value of the draw angle, which is a material characteristic. An engineering designer can see from the CAD drawing if φmax has been reached and by making judicious choices when embedding the part in the sheet surface, φd can often be made smaller than φmax. Once a part has been embedded in the surface of the sheet metal the comparison between φd and φmax will show if the part can be made in one pass, two passes or several passes, after which toolpaths can be generated. 4.1 Formability Criteria for Incremental Forming The AISF process is characterized by increased material formability. Much higher strains than normally observed in deep drawing are observed in AISF, for instance strains can be well over 3. Recent studies have shown that the forming limit curve, which describes the formability in a minor-major strain plane, may be expressed as a straight line with a negative slope [32, 66, 67]. Bi-axial strains, in the deformed sheet, are measurable only during particular conditions, such as corners or plane intersections, with most strains localized close to the major strain axis, εmax. For this reason, material formability can be represented as an artificial index, which is the draw angle φ, as shown in Figures 2 and 15. AISF process mechanics are fully characterized by a small, localized plastic zone, which is limited to the small area between the tool and workpiece. Visioplastic evaluation shows the deformation mode is very close to plane strain deformation [60] and is almost pure stretching in the forming area [35]. Much higher strains are possible due to the presence of hydrostatic pressure caused by the elastic deformation of the area surrounding the confined plastic deformation zone [61]. Using a combination of φmax for a material at a specific thickness, and forming limit diagrams, an engineering designer can decide if a part can be made in one pass without tearing, or if a two pass or multiple pass sequence should be used. These are discussed in the following. 4.2 Maximum Draw Angle, φmax: a formability benchmark It is recognized that the material behaviour and maximum formability in AISF can be described by the maximum value of the draw angle φmax [32, 33, 60, 61, 62]. As φ increases the thickness reduction reaches a minimum value where fracture occurs as a consequence. This is related to the both the sine law and spinnability relation shown in Figure 2. Knowing the parameter φmax for a material at a specific thickness, a designer can take the first step in deciding if a sheet metal part can be made in one pass without tearing, or if a two pass or multiple pass sequence should be used; see Figure 14. Many parameters influence the process and have to be considered to fully understand the process mechanics and
formability results. For this reason, experimental investigations have been developed, taking into account a benchmark product. If the details of φmax, and formability are unknown then the cone shown in Figure 15 is used to conduct tests [35]. The benchmark cone base diameter, Do, is 72 mm with a height, H, equal to 40 mm. Tests are carried out at varying degrees of draw angle φ of the cone up to failure, which is defined as tearing in the specimen wall. Table 1 shows examples of material initial thickness and corresponding values of φmax that have been observed in AISF. The rule for spinning, in Figure 2, and the calculation for spinnability [18], both indicate that material thickness has an impact upon the formability of the material, and by simple geometry, see Figure 2, it can be seen that the
spinning angle and draw angle are related directly. CAD file arrives
Definitions: φd = largest draw angle in a CAD φmax = the maximum draw angle for a material Embed shape in the sheet metal surface; use minimum angles.
Check forming limit diagrams for formability.
Check for the largest φd ; if φd > φmax
List of materials available and their properties
Second check of forming limit diagrams for formability.
Check where the maximum φd occurs Choose a material. Find the maximum draw angle, φmax for that material.
Compare the maximum drawing angle to the largest forming angle expected: φd > φmax ; φd < φmax.
φd < φmax.
φd > φmax.
Generate toolpath Use ‘two pass method’
Use ‘one pass’ method
Figure 14. Procedure followed for making a part.
D0
φ
10 mm
H
Figure 15: Cone for testing forming parameters [35].
φmax
Material AA 1050-O
FLDo
67.5° 2.305
to , mm 1.21
Filice [31]
1.0
Micari [63]
AA 6114–T4
60°
Al 3003 – O
78.1°
2.1
Jeswiet [59]
Al 3003 – O
72.1°
1.3
Jeswiet [59]
Al 3003 – O
71°
1.21
Jeswiet [59]
Al 3003 – O
67°
0.93
Jeswiet [59]
Al 5754 – O
62°
1.02
Jeswiet [59]
Al 5182 – O
63°
0.93
Jeswiet [59]
AA 6111–T4P
53°
0.93
Jeswiet [59]
DC04, mild steel
65°
1.2
1.0
Hirt [65]
DDQ
70°
2.718
1.0
Micari [63]
HSS
65°
1.924
1.0
Micari [63]
Copper
65°
1.808
1.0
Micari [63]
Brass
40°
0.701
1.0
Micari [63]
0.841
3.0
Table 1: A list of materials with initial thickness and maximum draw angles. FLDo is the maximum major strain at a minor strain of zero.
to = 1.5mm α = 40°, t1 = 1.15mm α = 60°, t2 = 0.75mm
φ α
φ
to= 1.5mm
Figure 16: Asymmetric incremental forming of 1.5 mm thick DC04, into a pyramid with varying slope sides [60]. Using a pyramid shape, see Figure 16, Hirt [60] found the same result for material limits as Fratini [67]; that thinner sections occur with steeper sides and increasing φ. The process limit fracture is approximately 65o for AA 1100 aluminum and DC04 mild steel. Jeswiet et al [66] conducted a parametric study, aimed at determining the relation between material formability (measured to the maximum “safe” value of φmax) to sheet thickness. Testing two aluminium alloys gave: AA 3003–O
φmax = 8.5to + 60.7°
(2)
AA 5754–O φmax = 3.3to + 58.3° (3) The upper and lower limits to the linear function are defined by spinnabillity [18] and the sine law. Although the these linear functions have limitations, they are useful to the designer in giving choices for combinations of thickness and draw angle for single pass forming.
4.3 FLD’s and forming limits Forming limit diagrams are traditionally one of the tools used to decide if a material of a particular thickness can be formed by a deep drawing process. This has been applied to AISF. Work on AISF forming limit diagrams has been performed by Felice and Micari [32, 59], Hirt et al. [61] and Young and Jeswiet [62]. Micari used an agreed upon shape [59] to develop FLD’s while Hirt et al. [64] have used a pyramid with varying slopes and Young and Jeswiet [62] have used a grouping of five shapes for one FLD. These are all presented in the following. Traditional Forming Limit Diagrams The single point incremental forming of a cone, shown in Figures 15, 17 and 41, illustrates the use of FLD’s. The sequence of steps followed by the tool are shown. For the case shown, the ∆z incremental steps are labeled 5, 9, 13, etc. and the ∆x steps are labeled 4, 8, 12, etc. The hypotenuse of ∆x and ∆z is at the drawing angle φ. The four parameters usually of interest are: thickness of the sheet, size of the step down, ∆z, speed of deformation and size of the forming tool. Step down: The size of the step down, ∆z, (pitch) has a significant influence upon formability and surface roughness. With increasing ∆z the blank undergoes heavier deformation conditions. Micari [59] conducted step down tests on AA 1050-O, 1 mm thick sheets with a cone configuration as shown in Figure 15. It was found that sheet formability decreases as a direct consequence of increasing the tool pitch ∆z. The results are summarized by means of FLDo in Figure 18. A boundary area, which corresponds to the better choice for technological parameters, is highlighted. This has also been observed by Hirt et al. [60] and Hagan and Jeswiet [63]. Increasing spindle angular speed (spindle rpm) can increase formability [59]. The formability increase is due to both a local heating of the sheet and, what is more, a positive reduction of friction effects at the tool-sheet interface. There is a negative aspect in that the forming tool wears very quickly, plus lubricants tend to burn thereby creating safety and environmental problems. If the material, AA 1050-0 in this case, has a relatively lower formability, then a more formable material such as AA 8008-0 can be tried if lower spindle rpm is needed [36]. Forming tool diameter: An important role is played by the forming tool diameter where a small radius concentrates the strain at the zone of deformation in the sheet under the forming tool, while a larger radius tends to distribute the strains over a more extended area. As the forming tool radius increases the process becomes more similar to traditional stamping, thereby reducing formability limits. Micari [59] found decreasing tool size increased the forming limits; see Figure 18. Results found by Hirt [60], see Figure 19, show that as the tool diameter decreases from 30 mm to 6 mm, much higher strains and deformations can be achieved. It has been shown that sheet thickness has an effect upon the maximum draw angle. Hirt et al. [68] showed this to be true for forming limits with a study on DC04 taking into account three different sheet thickness’ while fixing the other experiment parameters. Similar trends were found by Kim and Park [70] with AA1050–O sheets. Their tests were carried out on very thin sheets (lower than 0.3 mm) with FLDo reductions from 1.2 to 0.92 for a sheet thickness decrease of 70 percent.
Figure 17: Single Point Incremental Forming of a cone.
3.5
Εmax, FLDo
3
Upper limit
2.5 2 1.5
Lower limit
1 0.5 0 0.00
1.00
2.00
3.00
4.00
Depth of step, ∆z, mm Figure 18: FLDo for different step sizes for AA 1050-0, with upper and lower bounds, with a 12 mm diameter tool [59].
2.0 1.8 1.6
6 mm tool
Major strain
1.4 1.2 1.0 0.8
10 mm tool 30 mm tool
3
1 2 4
x 2 x
1 x
x
3
Kim & Park [70] focused their attention on the influence of anisotropy on formability. For this purpose, a set of measurements of the major and the minor strains were carried out both along the rolling direction (RD) and the transverse one (TD). The tests were developed for pyramid specimens with a varying tool diameter. The material was the aluminium alloy 1050-O, with E = 70GPa, σο = 33MPa, R0 = 0.51, R45 = 0.75, R90 = 0.48. They concluded that formability along the transverse direction is greater when small diameter tools are utilized, while along the rolling direction it is larger with large diameter tools. In order to fully understand the increase in formability with AISF, a simple FEM was developed by Micari et al. [59] and Bambach et al. [69]. They found that with decreasing step size, ∆z, the strain increments imposed at each loop decrease and any point is overlapped other ‘active loops’, while strains increase with increasing wall angle. Also, from a stress point of view, a negative mean stress distribution is observed under the tool and in the nearby elements; in this way, the tool action postpones ductile fractures during the process, until the tool is out of contact with the sheet. Finally, at decreasing ∆z the stress value along the wall decreases too, so that a higher deformation can be imposed without tears occurring. Nontraditional Forming Limit Diagrams Forming limit diagrams usually have the dashed V-shape shown as FLC in conventional forming in Figure 20. However, extensive research has shown that not only are much higher strains achieved in this process, but the Forming Limit Curve (FLC) in SPIF has a negative slope as shown in Figure 20 [32, 62]. In one case, the maximum forming strains [32] were actually much higher because the AA 1050-0 sheet used in the experiments had been etched with a grid causing stress concentrations and hence premature failure to occur. Young and Jeswiet [62] used more than one shape to develop a composite FLD for 1.21 mm thick AA 3003-0. They used five different shapes with varying angles, and convex and concave curves. The shapes were: a dome, a cone, a hyperbola, a pyramid and a shape with both compressive and tensile stresses. These all have their own FLD, and when all placed in one, common FLD, they represent most combinations of shape found in a part. An example of their work is shown Figure 21. The boundary for safe forming, without any tearing, is shown by the dashed red line. It can be seen that both Filice [32] and Young [62] have the same slope for the boundary and that very high strains were achieved. It can be seen that the non-traditional FLD’s being developed [32, 62] provide the designer with an additional method of judging if a design can be made in one pass with AISF. FLC incremental forming
4
1.0 0.9
0.6 0.2 0
Scattering band for mild steel (t=1.5 mm) -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Minor strain
Figure 19: FLD for to = 1.5 mm DC04; influence of forming tool size upon forming limits [60]. Graph points x1 to x4 correspond to positions on the sheet marked by x.
Major strain, εmax
0.8
0.4
0.7 0.6 0.5 0.4 0.3 0.2 0.1
FLC conventional forming εmin
-0.2 -0.1 0
0.1 0.2 0.3 0.4 0.5 0.6
Figure 20: FLC for 1.21 mm thick AA 1050-0 forming of pyramids [32]. Both traditional and non-traditional curves.
εmax 2.5
ε min = −ε max + 3
2,5 2
2
1,5
1.5 1
1
0.5 -1.0
-0.5
major strain, εmax
3
3
0,5 0.5
1.0
0 εmin Figure 21: Composite FLD for five parts formed by asymmetric single point incremental forming of 1.21 mm thick AA 3003-0 [62]. Each colour a shape and each point represents a successfully formed shape. 4.4 Formability and material properties Materials all have different formabilities and Table 1 in section 4.2 shows how materials have a different maximum draw angle φmax. In most sheet metal operations, formability is limited by a local necking instability. Once a neck is initiated the high hydrostatic stress that develops within the neck leads to rapid void nucleation, growth and coalescence [60, 72]. However, in certain forming operations, such as bending and stretch flanging, necking is suppressed and formability is controlled by the evolution of void damage and shear band instability. If the strain is evenly distributed in the metal, as it is in SPIF, very large strains can be achieved due to the foregoing void damage and shear band instability. A comprehensive analysis was instigated to understand the correlations between material formability and other material properties [59]. The experimental campaign was developed with a set of different blank materials, typically utilized in the automotive and other sheet forming industries. The materials used and their main characteristics are summarized in the Table 2. As before, the formability results were formalized again through the FLDo values, while the testing parameters were fixed for all the experiments. An FLD of all the materials in table 2 is shown in Figure 22. An FLD does not give information on which material parameters predominate. Therefore a statistical analysis was carried out to determine the influence of the material properties in table 2. Five variables (K, n, Rn, UTS, A%) were chosen as inputs, each one with five replications with
0
-0,5
minor strain, εmin
-0,25 0 0,25 0,5 Copper HSS AA6114 Brass DDQ AA 1050 - O Figure 22: An FLD of the material parameters shown in Table 2 [59]. FLDo fixed as the output. The intention of the analysis was to determine how each input variable influenced the output parameter. The experimental results were analysed by a response surface statistical model where the qualitative influence of the predictors (pure linear terms and interactions among inputs, i.e. hybrid quadratic terms) on FLDo were reported. The results indicate the highest influence on material formability for AISF processes is the strain hardening coefficient, n. In addition, there is a high influence of a combined strength coefficient and strain hardening coefficient. Strength coefficient and elongation also have an influence upon the formability. The statistical analysis leads to a six dimension hyper-surface: FLDo = 8.64 - 36.2n - 0.00798K + 0.373Rn - 0.104A% + 0.0301K·n + 0.607n ·A% [59]. (4) Jeswiet et al. [66] also found that both strength coefficient and strain hardening coefficient had a major influence and that a more accurate model of the stress-strain condition could be obtained with a Voce model [71]. Verification of this can be found in work by Lievers et al. [72] who investigated three different automotive aluminum alloys in developing a model of stress strain characteristics: AA5182-0, AA5754-0 and AA6111-T4P. Their model shows the Hollomon-Ludwig [73] relationship fits the stress-strain curve at low values of strain, but at higher strains the plastic section of the curve was more accurate when fit to a Voce curve of the form: (5) σ M = σ s − σ s −σ y eq
(
where
)
( )
q = −α ε Mp
β
σM is the flow stress matrix and ε MP is the effective plastic strain. Young’s modulus, E, and Poisson’s ratio were taken to be 70 GPa and 0.3 respectively. σs is the saturation stress, σy is the yield stress, and both α and β are curve fit parameters. Material descriptions and fit parameters for the three materials are given in table 3.
Table 2: Materials and properties used to test correlations with formability by asymmetric incremental forming [59].
Specific materials and material properties Common sheet materials are employed in AISF with the most common being aluminium and steel. Aluminum and its alloys are used most frequently for AISF, mainly because of the reduced forming forces. The majority of the experiments with aluminium (AA 1100, AA 3003 and AA 1050) have been to investigate the formability and material properties of the material. Fratini et al. [67] and
t mm
α
β
MPa
σs
R
σy
MPa
AA5182-0
0.93
0.88
118
379
7.35
0.890
AA5754-0
1.02
0.76
93
298
7.48
0.844
AA6111-T4P
0.93
0.70
164
455
5.42
0.837
5050?m µm DC04, initial state
505 µm ?m o
DCO4, φ = 80 , ∆z = 1.75mm
Table 3: Material descriptions and fit parameters for the Voce curve for the three alloys [72]. Jeswiet et al. [66] focused on the investigation of material models for two common sheet materials, AA 1050 and AA 3003.They found appropriate material models for Aluminum, as follows: 1050-0, to = 1.0 mm, σ = 111ε
0.14
3003-0, to = 1.21 mm,
σ = 152ε
0.213
[67]
(6)
[76, 77]
(7)
Due to the higher forming forces required for the processing of steel materials, the sheet thickness spectrum investigated so far is smaller. Nevertheless, steel materials are used for the manufacturing of incrementally formed parts since they have an important role in the field of conventional sheet forming. Hence, there is a focus on the use of mild steel and stainless steels. Among the mild steel materials, DC04 is by far the most commonly used for incremental forming due to its high formability and its numerous applications in the field of sheet metal components. Amino et al [76] manufactured a fender and the inner of a car seat out of 0.8 mm DC04 sheets. Changes in a material’s microstructure induced by the incremental forming process have also been investigated [58]. The results of this investigation are displayed in Figure 23. This was done with common steel materials, DC04 and 1.4301. In both cases, the grains are significantly elongated due to the high strain. Besides mild steel, various kinds of stainless steel have been employed for incremental forming, but mainly for research purposes. Amino et al [76] have manufactured a stainless steel incubator bed and an exhaust part and Hirt et al. [78] have made various stainless steel demonstrator parts. Generally stainless steels are significantly more difficult than mild steels or aluminum when incrementally formed. This is mainly due to their high tensile strength, the high strain hardening coefficient and their distinct inclination to elastic spring back. Many other materials have been employed to perform experiments on incremental sheet forming. These include brass, copper, silver, gold, titanium and platinum. Because of its frequent application in the field of aircraft manufacturing, titanium occupies an important position among these. Some demonstrator parts have been formed successfully out of RT12S (Ti grade 1) [79], which is also suitable for deep-drawing. 4.5 Surface roughness Surface roughness is a major concern in a final product. In AISF the major factor in determining surface roughness is the incremental step size, ∆z [88, 89, 90]. Two examples are shown in Figure 24. In one in-depth study of the effect of pitch, ∆z, on surface roughness [88], the objective was to observe which surface roughness indicator was more useful. Figure 25 shows the 3D Figures for different pitch sizes. Figure 26 shows 2D profiles for three pitch sizes with the tool profile superimposed. At a pitch of 0.13 mm, when the pitch is 1 percent of the tool radius the ridging observed in Figure 25 virtually disappeared. It was also found that Rz, mean peak to valley height was a more useful measure.
100 µm 5 ?m 100? m 1.4301, initial state
505 µm ?m o
1.4301, φ = 80 , ∆z = 1.75mm
Figure 23: Change in steel microstructure with large angle of deformation in asymmetric single point incremental forming [59]. Junk et al also studied the effect of pitch ∆z, draw angle φ, and tool radius upon surface roughness [89]. They found that pitch size, tool radius, draw angle φ and surface roughness were interrelated as shown in Figure 27 and that with the right combination surface roughness due to pitch and draw angle can be eliminated. Spindle rpm has an effect upon maximum profile height [88] and an equation, which relates maximum profile height created by incremental forming to pitch size ∆z, can be developed. It has also been observed that surface roughness is higher in the case of non-rotating tools [88]. By decreasing the relative motion between tool and workpiece the surface roughness can be reduced. This will also reduce the incidence of spalling due to repeated stress over the same surface. There is an unwanted effect of which the designer should be aware. At high draw angles φ there is an orange peel effect [33, 61]. The size of the effect is influenced by the incremental step size, ∆x and ∆y, and the draw angle, φ. This effect occurs on free surfaces with very large plastic strains and is the result of texture and microstructural effects [75]. 4.6 Forces in Incremental Forming Potential users of incremental sheet forming processes are often concerned about the forces that are generated, especially if a CNC mill is the being used. Groups at KU Leuven and Queen’s University have designed special sensors specifically for this purpose, with the results being published recently [80, 81]. In one case, when measuring forces in SPIF, a force sensor design was based upon friction measurement work done with cantilever beams by Nyahumwa [82]. The cantilever sensor design shown in Figure 28 is a spindle mounted cantilever beam with strain gauged Wheatstone bridges. Each bridge is designed to measure one of three orthogonal forces: two bending directions, “Fr” and “Ft”, and one axial direction, “Fa”. An added attraction of this sensor is it can be used for friction measurement studies. The forces measured with the sensor shown in Figure 28 are for 1.21 mm thick AA 3003–0, being formed from flat sheet into a truncated pyramid shape. The force measurement results are shown in Figure 29. Snapshots are taken of the forces at percent completion of the part. These snapshots show how the forces vary at different points in the process. It can be seen the maximum forces encountered are around Fa = 450 N in the axial direction.
∆x2 ∆z2
φ
∆h2 ∆x1 material ridge
∆z1 φ
∆h1
Figure 24: An illustration of how the ridges occur due to pitch size, ∆z [89].
∆z = 1.27mm
∆z = 0.76mm
∆z = 0.51mm
∆z = 1.02mm
Figure 25: 3D Surface roughness for four pitch sizes, ∆z. Profiles were obtained by white light interferometry and are 3.6 mm x 4.6 mm [88]. The tool diameter is 12.5 mm.
1.78 mm ∆z 1.27 mm 0.51 mm
Profile height, mm 0.03 0.02 0.01
tool profile
-2.5 -2
0 -1.5 -1 -0.5 0 0.5 1 1.5 Distance Along Surface (mm)
2
2.5
Figure 26: 2D surface roughness profiles for three pitch sizes [88]. RZ [µm] 21,3
RZ [µm]
19,1
20 15 10 5 0
11,5
as received roughness 3,3 2,5 1,9 1,1 1,7 0,9
0.1
10,1 4,5 4,1 4,8 3,9
0.2 0.5 Pitch ∆z, mm
10,4
20 15 10 5
7,3
47° 65° m 47° 5m 65° mm m 1.0 15 ,m s u i Wall angle φ rad ol o T
Figure 27: The influence of pitch ∆z, draw angle φ, and tool size upon surface roughness Rz; 1.5 mm AA 1100 [89].
Most of the forming energy goes into pushing down shown by , Fa., the axial force, and that Fb, the resultant of Ft and Fr, is much lower than Fa. See Figure 28 for definitions. Forces were also measured in TPIF with a gauged partial die using a Poisson gauge configuration [80]. In forming cones, measurements were made at different draw angles, φ. The forces were averaged for each complete circuit around the partial die (called a profile #). Only peak values are of interest, therefore not all profile data points are o shown, for instance the points for a draw angle of φ = 60 are not all shown. The peak values for draw angles of φ = 30o, 45o and 60o are shown in Figure 30. The maximum values of force, experienced at a draw angle, φ, can simply be found by dividing by the cosine of the draw angle, φ. The maximum forces for both processes, measured by different sensors, can be seen to be close in magnitude. Aside from finding the maximum values of force, one o noticeable result is the large peak force at φ = 60 . This peak value is thought to indicate the sheet is approaching the maximum value of force that the sheet can sustain, similar to the ultimate tensile strength, σuts, observed in engineering stress-strain diagrams. Hence this could be used as an indicator of the approach of failure at the maximum draw angle, φmax. In the third case, Duflou et al. [81] conducted a series of experiments with a six-component force dynamometer mounted under a single point incremental forming rig and derived relations between forces and slope angle, tool diameter and incremental step size. The measurements were performed on the reference conical part described in Figure 15. Figures 31 and 32 provide an overview of the results for 1.21 mm thick AA 3003-0. Table 4 gives a summary of the results. In Table 4, Fp is the maximum force reached during the forming process for a given part, and Fs refers to the average force measured after a stable level is reached (excluding the transient behaviour interval and the peak force). It was concluded [81] that if the vertical step size ∆z, tool diameter or wall angle φ, are increased, the total forces on the forming tool, and thus the machine tool, also increase. For these three parameters, the vertical step size has the least significant impact and can therefore be increased without penalty, to reduce part production times. An increase in the tool diameter has a substantial impact on the magnitude of force required to form a given part. Although it can improve surface finish and reduce production time by allowing larger vertical step sizes without affecting surface quality, large increases in tool diameter result in much higher forces and could become a limiting factor. When the drawing angle φ increases the forming forces are much greater. Forces, that occur in deforming 1.21 mm thick AA 3003-0 sheet, have been measured successfully, with three separate sensor designs and for two separate types of AISF: SPIF and TPIF. Useful design/manufacturing information is: peak forces can be observed in the area where failure occurs at maximum draw angles, φmax, increasing the vertical step size ∆z increases forces, larger tool diameters increases forming forces. Wall Thinning The sine law, which is used in spinning [10, 13, 86], assumes a uniform wall thinning. This is true in low strain situations as shown by Matsubara [27], and Hagan [77].
Force Vector Sum, N
600 500 400
20° 30° 40° 50° 60°
300 200 100 0
750 500 1000 1250 Time, s Figure 31: Total force curves for conical parts with different drawing angles for a 0.5 mm vertical step size, 10 mm tool diameter, feed rate of 2000 mm/min [81].
Figure 28: Details of the Single Point Incremental Forming Sensor [80].
Fa: axial force on sensor Fr: radial, bending force on sensor Ft: tangential, bending force on sensor
500 450 400 350 300 250 200 150 100 50 0 - 50
Ft 10
20
80
30 40 50 60 70 Percentage Complete
Figure 29: Forces measured in forming a pyramid at o φ = 40 in SPIF of 1.21 mm thick AA 3003-0 [80].
Peak forces observed
N, ( lbf) 712, (160) 623, (140) 534, (120)
445 N
445, (100) 356, (80)
forming tool
o
a
60o b
45o
b
289 N
(60)
cone 30 cone 45
(40) (20) 0
F45o F60
30o 45o 60o
596 N
30o
b
cone 60 a
0
250
500
750 1000 1250 Time, s
Process parameter
F(N)
R2
Tool diameter Ø (in mm)
Fp=12.761 Ø +434.5 Fs=12.812 Ø +410.8
Part wall angle φ (in degrees)
Fp=6.793 Ø +210.4 0.9826 2 Fs=-0.2284 Ø +22.753 Ø 0.9919 47.0
Vertical step size ∆z (in mm)
Fp=151.58 ∆z +466.9 Fs=148.13 ∆z +447.17
0.9809 0.9884
0.9655 0.9725
Table 4. Experiment determined relation with total peak force Fp and average force Fs [81]. static tool post
Force
D of irec to tio ol n
Forces measured in TPIF of AA 3003-0
10.0 12.7 15.0 20.0 25.0
Figure 32: Force curves for parts formed with tools from a 10 mm to 25 mm diameter [81].
Ft
Fr
0
250
800 700 600 500 400 300 200 100 0
Fa
Fb
Fr β
tool path
Force, N
Forces measured in forming a pyramid.
Force Vector Sum, N
0
10 20 30 40 50 60 # of Profile from top to bottom
70 80
Figure 30: Force measurement data, measured with a gauged, static tool post, for three draw angles o o o φ = 30 , 45 and 60 , for 1.21 mm thick AA 3003-0 [80].
However, nonuniform wall thinning has been observed [35, 60, 77, 83]. Figure 33 is a typical example of wall thickness measurements for 30 and 70 degree cones in SPIF [83]. The initial sheet thickness was found to be 1.2069 mm +/0.0180 mm, The sheet thins until it stabilizes at an approximate thickness of 1.00 mm, and remains at this value for the remainder of the cone’s surface until it thins again slightly just below the apex of the cone. The uniform portion of the cone’s wall profile is thinner than the predicted sine law value of 1.10 mm, indicating that an over-spinning condition is occurring [18]. The initial deformation is due to bending with subsequent deformation being due to shear. The thinning zone shown as an inset in Figure 33 is a property of the process rather than of the particular geometry. Thinning is dramatic at high draw angles, and is a precursor of failure just after φmax. The sine law does not predict this band, and if the theory is solely followed, unexpected failures will occur in this location.
1.40 1.20
sine law, 30o
Thickness, mm
1.00 0.80 0.25 mm 0.37 mm
0.60 0.40
sine law, 70o
0.20 0.00 0
10
20 30
40
50 60
70 80 90
Distance Along Surface, mm
Figure 33: Single pass wall thickness profile for 30 and 70 degree cones. AA 3003-0, to = 1.21 mm [83].
forming tool offset
4.8 Toolpath Generation Once all the material characteristics are known a toolpath can be planned. There are several choices available for the forming toolpath shown in the following.
1.21 mm
bending applied force
0.65 mm
Figure 34: Detail of bending observed during first pass of a two-pass asymmetric incremental forming process [83].
4.7 Multiple pass asymmetric single point incremental forming To remedy thinning shown in the discrete zone in Figure 33, and to avoid failures, material available elsewhere in the part can be used to stop both thinning and failure. In their work on SPIF Kim and Yang [85] used a pre-form, or two-pass forming as a means of equalizing the strain distribution across the surface of a part. Jeswiet and Hagan [29], and Hirt et al [61] also used the same technique. This involves the creation of high strains in a pre-form at areas where low strains are present in the final geometry, and low strains at areas where high strains are present on the final geometry [83]. Pre-forms can then be designed to include a combination of wall angles and artificially large offsets from the backing plate. The hypothesis behind the steep wall angles and large offsets is that this encourages the undeformed sheet in the flange area to bend downwards over the backing plate and into the part. This presents a thick surface that is already inclined at a portion of the final angle desired in the finished geometry. When shear forming theory for preformed blanks is consulted, a two-pass sine law is employed [83, 84] as follows:
tf = tp
Sin (φ f ) Sin (φ p )
flange, then the wall thickness of a 70 degree cone would increase to 0.72 mm. The traditional sine law gives a prediction of 0.41 mm for the same 70 degree cone made in a single shear-forming pass. It is important to note that this increase in thickness will only occur in the area of the part that was affected by the bending of the flange. Unlike shear forming with a pressed pre-form of constant thickness, the pre-form of the first pass will vary in thickness from the thick bent flange area, to the remainder of the part that experiences normal thinning in the process; see Figures 33 and 35. Hence two-pass forming serves to alleviate the thinning band observed at high draw angles. The wall thickness of a multistage formed pyramid [61] shows thinning at the initial bend has been moved away from the initial bend; see Figure 35. This technique was put to good use in the SPIF of a rapid prototype for a car headlight reflector [29]. Four steps were needed to create the reflector surface; see Figure 36.
(7)
where: tf is the final wall thickness, tp is the wall thickness of the pre-form, φf is the final wall angle, φp is the wall angle of the pre-form. For example, if a pre-form could be designed to bend the flange inwards to a 55 degree angle while maintaining a sheet thickness which is the same as the undeformed
Contour milling toolpath is a finishing pass, typically defined by fixed ∆z increments between consecutive discrete contours. This is also the most common technique used. The disadvantage is it leaves marks at the transition point between layers and creates force peaks. Surface quality depends on tool radius, step size [29, 31, 32], and slope angle as well as lubrication system and spindle speed. A spiraling toolpath is continuous with incremental descent of the tool distributed over the complete contour of the part [32, 68]. The advantage is that no marks occur at step down. Multiple toolpath strategies include creating intermediate forms that are defined within the cavity of the final surface and are typically characterized by limited slope angles and curvature. This is comparable to a roughing step in milling, followed by a finishing pass that can be a conventional contour milling or spiral toolpath or a strategically chosen toolpath aiming at stretching out the cavity bottom and increasing part slope angles without causing excessive strains in the steeply sloped areas [83]. Both Figures 35 and 36 are examples. Contour toolpath generation Because it is the most common method used, this method is discussed in detail. First, the flat plane of the sheet is defined as the x-y plane before being deformed; see Figure 37. This is an artificial horizontal plane that acts as the original sheet reference when forming along the z-axis; the z-axis is equal to zero at this point. All portions of the required geometry must be at or below this plane. In the case of SPIF the forming tool moves from the outside edge, point a, toward the centre. In the case of TPIF this is reversed and the tool moves from the centre out. To make SPIF possible in one pass, a part should be first oriented so that steep walls (which means a draw angle φ equal to 65 degrees or greater) are reduced by rotating the part around the x and y axes. Then the steep walls will have a shallower angle relative to the z-axis, where possible. This initial manipulation greatly increases the ease with which the part can be formed successfully. Once the workplane is set, a modification to the required geometry is the addition of false surfaces to create an
Top surface Top radius RTop Flange Preform area
φα
sheet thickness t, mm
Blank Bottom radius RB 1.6 1.4 1.2 1.0 0.8 o sine law; Sine lawf = 45 0.6 o 1100-0 Material: Al99.5 sine law; f = 81 0.4 Thickness: to=1.5mm s0=1.5mm RR=15mm 0.2 Tool: TφT=15mm Angle: α=81 =° 81o 0.0 0 20 40 60 80 100 120 140 160 Rtop Top surface
Blank Rblank Preform area x- coordinate [mm]
Figure 38: Positioning of an irregular surface with support walls [29].
Flange
Figure 35: Thickness measurement for a multistage o formed pyramid; up to φ = 81 [61].
1
2
4
3
Figure 36: An example of using four stages to form a rapid prototype of a reflector surface for an automobile [29]. direction of forming tool, from outside edge to the centre a forming tool x-y plane of flat sheet
unbroken perimeter from the edges of the part up to the workplane. These surfaces support the part while it is being formed, and help to ensure that the desired geometry is obtained. The reflective lens shown in Figure 38 is an irregular shape that requires support surfaces. As these new surfaces will be removed once the part has been formed, their positioning and geometry is not critical, though the maximum draw angles of the process still apply. The support surfaces are shown as straight lines in Figure 38. In some cases this is called ‘lofting’. Wall angles of 40 to 55 degrees are recommended in the support surfaces where possible. This eliminates the chance of tears occurring in these sections during forming. The completed perimeter of the workplane is the outline that should be cut in the steel backing plate for the forming backplate. An offset of 1 mm is helpful to account for any minor misalignment of the forming rig during set-up on the milling machine traverse table. Once the CAD file has been modified, and ‘embedded’ in the sheet surface, the CNC toolpaths must be created for the milling machine to follow. Any available CAM software package can be used with equal success. Due to the range of packages available and the rate at which new software develops, only commands for a specific case will be discussed here. There are several choices for CNC control of the forming tool as shown in Figure 39. Commands vary with software package. Using of off-the-shelf CAM modules can be problematic because usually they are optimized for milling processes [34]. However the following strategies will show how this can be overcome.
1st contour
Figure 37: The asymmetric incremental forming of a reflective lens surface from sheet metal [29]. Green lines are the embedded shape.
Figure 39: Suitable toolpaths for SPIF [34].
Figure 40: Twisting observed in cones with TPIF [100]. The first step for the CAM portion is to check the CAD file visually for potential errors using a graphical interface, and then the toolpaths are created. Toolpaths may be set for either a roughing pass, or for a finishing pass. The difference between the two is that with the roughing process, commands are created to mill out all of the material as if the part is being milled from a solid block, while the finishing process only takes a fine, final cut around the surface of the geometry. CAM software is not designed for the incremental forming process, but by using the finishing pass commands, it will generate the proper CNC instructions when set to “cut” with an appropriately sized ball end mill. With the contour finishing pass toolpath selected, the remaining necessary machining parameters may be tailored to the forming process. These include feed rates, step-down, roll over all surfaces, filtering, and transitioning. Feed Rates: The feed rates for the forming process are much higher than typical machining feeds. As the tool is hemispherical, there is no concern about the amount of material cut per tooth per revolution, a critical factor in determining feed rates in conventional milling. Step-down: This factor controls the z-axis increments. In some cases an adjusted step-down for various wall angles has been used to maintain a constant traverse distance over the metal surface when manufacturing a range of pyramids and cones with different wall angles [59, 60]. This is more difficult with more complicated geometry containing different wall angles at different locations. Usually a constant diameter forming tool, with a standardized step-down is used. The step-down controls the surface finish. Keeping the same step-down with steep and shallow wall angles, can give a wavy surface on very shallow geometries. To correct this, a ‘shallow’ command can be selected to automatically reduce the step-down increments in these areas for a better finish. Roll over all surfaces: This setting is very important in the forming process. When a finish toolpath and a ball end mill are used together, the computer automatically begins the initial z-axis height at a level significantly below the metal sheet’s surface. This height is determined as the required z-axis position to contact the side of the ball with the steep wall geometry. Unfortunately, the steep wall geometry that the computer expects does not exist with forming, and the tip of the tool makes contact with the metal sheet long before the side of the ball contacts the theoretical steep wall. The overly large deformation on the first tracing of the part’s perimeter can lead to a premature failure of the metal sheet, so to avoid this, the “roll over all surfaces” feature is selected. This will have different command names, depending upon the software. This feature adjusts the initial toolpath so that the z-axis height begins with the tip of the ball in contact with the flat sheet metal blank. Filtering: The filtering command simply replaces the fine splines created by a software package with a series of arcs. Doing this significantly reduces the length of the CNC instruction file, and can allow very large metal forming toolpaths to fit on a standard computer floppy disk.
This method of data transmission is far superior to the alternative RS-232 serial cable compatible with the milling machines, and permits the use of a faster feed rate than would be possible with the serial cable. Care must be taken when using the filtering command to prevent the size of the replacement arcs from becoming coarse enough to affect the surface finish of the final part. Transitioning: The machining technique used in some cases is known as ‘2½ D’. The CNC code can be broken up into a z-axis traverse and then a simultaneous x and yaxis traverse. Problems arise when the transition is made between various z-axis levels unless care is taken to avoid them. The standard z-axis transition is a straight x-y axis traverse, then a plunge z-axis traverse. It is simple to program and does not affect the outcome of conventional machining processes. Unfortunately, an undesirable trait can occur when this transition is used in metal forming. When the z-axis plunge is performed at the same relative x-y co-ordinates for each pass of the forming process, the sheet metal can work harden to a point where this transition results in a visible flaw along the finished part, or even worse, it may lead to a fracture along this band of overly worked material. To correct this, a “ramp” transition can be selected, which breaks the large x-y axis and zaxis traverse up into a series of smaller traverses that occur incrementally along a specific length of the forming path. Subsequent transitions begin where the pervious one ended along the forming path, so in this fashion, the transitions are spaced equally around the perimeter of the part. Twisting of the sheet metal part, after forming, has been observed. This is due to the forming process and the path chosen as shown by Jadhav [100]; see Figure 40. The solution to this is to choose appropriate paths as indicated in Figure 39. Finally, the difference in toolpath planning between SPIF and TPIF is the tool moves from the outside inwards in SPIF and in TPIF it moves from the centre to the outside. Otherwise the planning for step increment, draw angle and tool size are generally the same. The end result is shown in Figure 37 where the inside of a cone with forming tool can be seen. The sequence of steps followed by the tool are also shown. The steps in Figure 17 correspond to those shown in Figure 37. For the case shown, the ∆z steps are labeled 5, 9, 13, etc. and the ∆x steps are labeled 4, 8, 12, etc. The hypotenuse of ∆x and ∆z is at the drawing angle φ. Spiral Toolpath A spiral trajectory is another way of controlling the surface roughness and also eliminating the mark left on the product surface by the previous method. The difference is that the path is given a pitch. Figure 38 shows the toolpath used by Filice [32]. The details of producing a toolpath, as discussed in the previous section, also apply to a spiral toolpath. However, CAM programs do not generally permit the use of spiral trajectories. Filice [32] solved the problem by using a simplified approach and did not utilize any particular CAM program. Instead they developed a spiral path inside EXCEL, thereby obtaining a large set of points that carefully defined the trajectory and gave it to the CNC milling machine. A couple of consecutive points were linked through linear interpolation. However, for complex, industrial parts it is necessary to use CAM programs that do not generally permit the use of spiral trajectories. Lubrication is one additional factor that must be taken into account. In all cases cited some form of lubrication is used. Bramley [103] conducted a set of tests to determine how much lubrication changes the surface roughness. The
upshot of the tests was the type of lubricant did not appear to be a factor, but lubrication is necessary to obtain a smooth surface. Table 5 shows results from some tests. Shape
lubrication
Spindle rpm 1000
Ra mm 9.42
Rt mm 74.73
sphere
none
pyramid
grease
1000
1.24
14.43
sphere
oil
20
0.538
5.09
pyramid
grease
20
0.564
5.43
Table 5: The effect of speed and lubrication on surface roughness [103].
Figure 41: Forming of a cone, showing the forming tool inside the cone and the outside surface of the cone. The steps shown are in sequential order and are for incremental, unidirectional steps [104].
Figure 42: The spiral toolpath used by Filice [32]. 4.9 Process Mechanics and FEA The knowledge of process mechanics is not only important with respect to the process limits, but the final properties of parts made by the new process are also of major importance with respect to details such as service life. As with most processes, a model can help explain/understand certain things such as the state of stress, strains and forming limits. In principle it is possible to model the AISF process, though at the moment experiments will usually be faster in forming small parts. There is a trade-off for large, complicated parts; it would not be economical to run many tests to verify if a shape can be made.
AISF is characterized by a cyclic, local plastic deformation of the sheet metal and has several peculiarities. It has been investigated mainly by simplified analytical deformation models and by full scale finite element analysis (FEA). The most prominent analytical model is the sine law [86], which is described in Figure 2. For single-step forming strategies that adhere to the zlevel type toolpath generation and for low draw angles φ, the sine law is in very good agreement with measured sheet thickness values, thus providing (in combination with the FLD for a given material) a quick estimation of the feasibility of designs. Kim [94] used the sine law to calculate the thickness distribution of a demonstrator part by means of a triangular mesh. In addition Iseki [95] proposed a plane strain deformation model, which assumes that the sheet metal in contact with the tool stretches uniformly. Unfortunately, analytical models are limited to the approximate prediction of strains. For further studies, the finite element method has been used. Micari [59], Hirt [68], Bambach [69], Ambrogio [91], He [107, 108] and Henrard [109] have been active in developing FEA models. Explicit FEA models developed by Hirt [68] give good results with respect to thinning and strains, however they are less accurate when predicting geometry and springback. Combining aspects such as alternating contact loci, large strain plasticity, high local field gradients and complex tool kinematics, make an FEA of the process a challenging task. Since asymmetric incremental sheet forming is a slow process with a time scale of minutes or hours, simulations with standard FEM systems and workstations can be expected to take much longer than the actual process. Two basic approaches are possible for the formulation and numerical solution of the governing equations of metal forming: implicit and explicit methods. There are advantages/disadvantages to either method. For instance, with explicit methods, the analysis of the springback phase often has a large computation time while with implicit codes, the springback phase can usually be performed in a few increments. Therefore, explicit finite element codes for sheet forming often use an implicit code to perform the springback analysis. Bambach et al. [93] did a benchmark analysis of AISF with implicit and explicit finite element models for a symmetric cup. The FEA used both ABAQUS/Standard and ABAQUS/Explicit. In both cases, the sheet is meshed with 2304 shell elements with nine through-the-thickness integration points. DC04 sheet is modeled as an elastoplastic material with isotropic hardening. The friction is assumed to be 0.05 between tool and sheet, and 0.15 between sheet and backing plate, which supports the part during forming. A fictitious time of 5.31 s is used for the process. This corresponds to the duration of the process in reality at full tool speed, i.e. if acceleration and deceleration are neglected. The result for the implicit FEA with respect to sheet thinning is given in Figure 43. For evaluation of the finite element calculations, the sheet thickness and the geometry are compared to experimental data along a radial section in positive x-direction for both the implicit and explicit FE models (Figure 44). To check the accuracy of the calculated geometry, the maximum normal distance dmax and the average normal distance dav between the experimental data and the FE results are determined. The prediction of sheet thickness is judged by means of the maximum deviation dth,max between the experimental data and the FEA. The implicit analysis provided very good results when compared to experimental data, however the time is large
Thinning [%] 60 50 40 30 20 10
Figure 43: Sheet thinning for a symmetric cup [93].
5 experiment explicit FEA implicit FEA
0 z [mm]
-5 -10 -15 -20 -25
0
10
20
30 40 x [mm]
50
60
70
Fig. 44: Comparison of calculated and measured part geometry [93]. FEA
Dt [s]
dmax mm
dav dth,max CPU mm [%] time [h]
implicit
0.004
1.09 0.59
11.7
7.32
explicit
0.0001 1.82 1.19
15.6
0.58
Table 6: Comparison of implicit and explicit FEA with experimental data [92]. sheet thickness [mm] 1.50 1.44 1.38 1.32 1.27 1.21 1.15 1.09 1.03 0.98 0.92 0.86 0.80
Figure 45: Calculated thickness distribution for the pyramidal frustum [93]. The tool outline is shown.
3 2 1 0 -1 -2 -3
ε pl, η
even for a small benchmark part and short toolpath, so that an implicit analysis cannot be used at present for toolpath optimisation. In contrast, the explicit analysis was performed in about 35 min on a 2.6 GHz Pentium IV single processor machine. Therefore, although the implicit FEA provides better results concerning geometry and thinning, the explicit FEA offers a reasonable accuracy with computation times that allow for a computer-based toolpath optimization. See table 6 for results. As reported earlier, the explicit method is generally considered to be ill-suited for the prediction of springback. Three types of springback can be defined in AISF: a continuous ‘local springback’ that occurs on every displacement of the tool, a global springback that occurs after the final unloading and dismounting from the clamps, a global springback after trimming (if done). If the last two types of springback are to be modeled, this can be performed by means of an implicit solution procedure that is employed after an explicit analysis step to analyze the forming process. However, the first type of springback as described in [69] cannot be modeled by means of a combination of explicit and implicit solution procedures as this would require a continuous interchange between the two codes. Since a purely implicit approach is not economically feasible for larger models, a viscous damping can be used [93] to improve the solution behavior of the explicit method for the prediction of springback for the single point forming of a pyramid frustum. The outcome of the FE analysis is given in Figure 45. Modeling the complete process (e.g. for a cone or a pyramid) using continuum elements is uneconomical. However, it is necessary to use continuum elements when the local stresses under the tool are of interest. For instance, shell elements based on Kirchhoff or MindlinReissner theory do not allow for a representation of the full 3D stress field. (Although they provide good results in the prediction of geometry and thickness.) Consequently, some researchers [69, 94] consider a strip of material that is meshed with brick elements. The strip can be thought of as a plane, side wall of a pyramidal frustum. The authors found that: the plastic strain increases stepwise under the action of the tool and each increase in plastic strain is accompanied by compressive stresses. This can be seen in Figure 46 where a plot of the equivalent plastic strain (blue curve) and the triaxiality ratio η (red curve) are given. Triaxiality is the ratio of the hydrostatic to the deviatoric stress. Figure 46 also shows that negative peaks in the course of the triaxiality coincide with and increase in plastic strain. Thus, compressive stresses are superimposed whenever the tool deforms the reference elements.
0.0
0.1 0.2 0.3 normalised process time
0.4
Figure 46: Equivalent plastic strain and triaxiality ratio [68]. These compressive stresses are thought to be the reason for the high forming limits observed experimentally. This assumption has been studied further [69, 72] using the Gurson-Tveergaard-Needleman (GTN) model to analyze the damage evolution during forming. Because of the stretching of the sheet, the damage evolution must be assumed to be anisotropic. Consequently, the isotropic GTN model cannot be used to quantitatively predict the damage evolution of the sheet. Despite these restrictions, the GTN model gives a good qualitative conformance to experimental results in that it predicts the amount of damage that occurs is increased when the size of the tools are increased.
For some part designs, a multi-stage SPIF procedure must be used for steep flanges [61, 83]. Starting with a shallow preform, the wall angle is increased in several stages to yield a final wall angle of 80-90°; see Figure 35. Multi-pass forming creates compressive stresses between the stages, and the sheet can wrinkle or fold under the action of the tool, e.g. when the increase in angle is too large between the stages. An initial investigation of the prediction of wrinkling has been successfully conducted [93], where an explicit code has been used to compare two variants of the multistage forming of an (almost) square box. The FEA is found to be in good qualitative conformance to experimental results, indicating that the material folds for one of the strategy variants, which can also be observed in the corresponding experiments. Furthermore, He et al [107] have used FEA to predict the forces acting on the tool during forming of an AA 3003 truncated cone. The simulated values overestimate the experimental ones by 30%. This may be due to the assumption of isotropic hardening. 4.10 Process Accuracy The importance of dimensional accuracy for sheet metal oriented rapid prototyping in general, and incremental forming processes specifically, is clearly illustrated by Allwood et al. in [99]. In the market study presented in this paper the process window for important process features is matched with the requirements for a significant number of potential part categories in demand by the market. The major shortcoming today for the asymmetric incremental forming methods can be situated at the achievable accuracy level: while most applications would impose a dimensional accuracy of less than 1 mm, and a significant number of part categories would require ±0.5mm as tolerance level, the accuracy levels reported by researchers typically exceed these limits. Bramley reports an accuracy of ±1.5 mm for symmetrical and ±2 mm for asymmetrical parts produced by SPIF using a toolpath from a milling oriented CAM module [103]. Along the outer edge of the workpiece, the deviations from the preset part geometry can be limited by the use of a support plate (see Figures 2 and 43). Otherwise this zone typically shows even larger deviations between the CAD geometry and the achieved part dimensions [91, 103]. The use of a support plate cannot eliminate similar problems due to strong, localized slope gradients at other locations in the workpiece. Reprocessing after reversal of the workpiece is suggested as a means to correct significant, unwanted deformation along the edge of the part in case no support plate is used [103, 105]. For TPIF of mild steel parts Hirt et al. [68] report deviations of order of magnitude ±2 to 3mm, depending on the part geometry, when using a straight forward toolpath as generated by standard CAM contouring algorithms. Besides the obvious machine tool inaccuracies, causes of deviation from the theoretical workpiece shape, that correspond to the programmed toolpath are: springback in the material, geometric distortion due to stress propagation (see Figure 47, point marked with A) and over-spinning effects that result in unwanted bulging [105]. When determining the process accuracy, the following typical features of asymmetric incremental forming need to be taken into account. The systematic thinning that characterizes the process can influence accuracy, since the dimensional errors induced by thinning are typically of the same order of magnitude as the imposed tolerances. This implies that accuracy should be determined for either the convex or concave face of the workpiece. Depending on the selected face, a toolpath should compensate for the anticipated thinning.
In contrast to conventional press work, the non-flatness of the blanks can be an important source of non-processrelated inaccuracy, since part coordinates are typically determined with the unprocessed blank surface as a datum plane.
Figure 47: Section view of the solar oven part, created without backing plate (above, shown in red) and with a backing plate (below, shown in blue). The CAD model is given in black and the preshape used in a double pass toolpath strategy that is explained later is in green [81]. (mm) Average Deviation
Test 1 Test 2
Absolute 1.327
Avg. Pos. Dev.
1.113
Test 3 Test 4
1.317
0.955
0.379
1.513
1.067
0.305
Avg. Neg. Dev.
-1.55
-0.58
-0.79
-0.47
Minimum
-4.47
-1.78
-2.75
-2.06
Maximum
4.137
5.398
4.223
0.980
Sigma (σ)
1.727
1.221
1.169
0.508
Table 7: Accuracy for different toolpath strategies [105].
Figure 48: Determination of virtual target part geometry based on measurement feedback [68]. The influence of different process parameters and toolpath strategies on part accuracy has been reported. Ambrogio et al. [91] demonstrate the positive influence of smaller tool diameters and pitch size on the geometric discrepancy between the workpiece and the target geometry. Duflou [105] compared different SPIF toolpath strategies for a given geometry. They concluded that double pass processing with an upward contour finishing pass provided the best overall accuracy (see Table 7). All test parts were AA 3003 with a tool with a diameter of 12.7 mm. The spindle speed was set so the tool rolls over the material and the feedrate was set to 2000 mm/min. Some corrective measures based on different feedback strategies have been proposed to improve part accuracy. Hirt et al. [68] proposed an iterative method in which the completed part is measured as a reverse engineering exercise, providing data for an adjusted toolpath generation. The proposed method is based on comparison of the actually formed part geometry with the target model, mirroring the measured points around the target geometry with a scale factor, and using these
points to generate new, virtual target geometry. This virtual part geometry forms the basis for the determination of an improved toolpath. Using a scale factor of 0.7 was found to provide optimal results for part made of DC04, 1.5 mm. Ambrogio et al. [106] use an in-process measurement system that allows the determination of deviation between the anticipated intermediate part geometry and the actually realized intermediate shape. Per layer (incremental toolpath contour) the observed deviations are measured to correct the toolpath geometry for the next contour. The proposed system has been tested with a discrete point contact measurement system, used interactively, thus simulating the availability of real in-process measurement equipment. The toolpath optimization algorithm has been tested with pyramid part geometry. The author claims significant accuracy improvements. No quantitative output is however available to evaluate the achievable dimensional accuracy. 5 EXAMPLES OF APPLICATIONS The major advantage of asymmetric incremental forming is it can be used to make asymmetric parts, quickly and economically, without using expensive dies. Shapes used to demonstrate the abilities of the process are shown in Table 8. Some of the shapes illustrated have been used to conduct springback experiments, and in determining the maximum draw angle φ, others are just for demonstration of process abilities. The asymmetric single and two point incremental forming processes are still in their infancy. Much research work remains to be done and to do this appropriate shapes are needed to develop: FLD’s, springback models and models to test accuracy. Standard shapes are used to determine what the draw angles should be for different materials and thickness. Standard shapes are needed to compare experimental results and for testing the process for maximum speeds of deformation. When testing materials for the maximum draw angle φ a truncated cone as shown in Figure 15 was agreed upon [59]. This shape has also been used by others [31, 32, 33, 59, 64, 66]. A pyramid shape has also been used on many occasions to demonstrate the asymmetric abilities of the new process plus it has become useful in determining the springback that occurs for different material thickness’ and for conducting pre and post process material tests [59, 64, 65, 67, 77]. Jadhav [100] has also used the pyramid to conduct studies of twisting in a shape once forming is completed. There is not agreement on which shape or shapes should be used to develop FLD’s for the new processes. Filice [32] and Hirt [78] have used a pyramid. Young is a proponent of using several shapes each of which has elements contained in most part shapes [62]. 5.1 Rapid Prototype Examples Making Rapid Prototypes, with sheet metal as the base material, giving a part that can be used directly in the function for which it is intended, is one of the major advantages of using this Incremental Forming process. The parts shown in table 9 are for designs that were made as Rapid Prototypes for the automotive industry. They are for the reflective surface of prototype headlights, for the first two cases. The third case is for a heat/noise shield, which is used over exhaust manifolds. Table 10 shows examples of rapid prototypes made for non-automotive applications. The first example is of a solar
Cross
Hexagon
5 lobe shape
Faceted cone
Multi-shaped surface
V shaped tub
Cone
Dome
Hyperbola
Truncated pyramid
Table 8: Shapes used to demonstrate the viability of the process and for experiments. oven cavity for use in developing country applications. The last two are for the same manufacturer of custom motorbikes; the first part is for a motorbike seat and the second is part of a gas tank. 5.2 Custom manufacture of a solar oven The SPIF process has made it possible to manufacture an aluminum solar oven cavity, economically without dies. The ability to make a sheet metal cavity, inexpensively, has allowed designers of the solar oven to redesign other parts of a product, thereby reducing the cost and labour in making a solar oven. A solar oven has been designed for export to developing countries. Originally the oven cavity was made from fibreglass, and painted black. The major drawback, was the fibreglass wall was 7 mm thick, heavy, time consuming to build, and labour intensive. The possibility of using dies to form sheet metal into solar cooking cavities was investigated and found to be very expensive. This lead to considering SPIF of sheet metal as a method of manufacture. Figure 49 shows how the assembled solar oven works. The red shape is the part which is formed by SPIF. A three dimensional model was made in a Unigraphics environment and Figure 50 shows the model and increment details. The total depth of the model is 74 mm. The downward step for each pass was set up differently for the two sections shown; ∆z = 0.4 mm from A to B, and ∆z =0.3 mm from B to C. The method of programming included a z-level profile following part contour, which is available in Unigraphics, was used. Details of the process set-up in Unigraphics are: Maximum drawing angle: set to 65o, everywhere. Forming tool: 25.4 mm diameter, highly polished. Forming speed (feedrate): 1125 mm/min. Additional note: the forming tool rotates freely, and is not matched to the machine feedrate. 1.3 mm thick AA 8008-0 Aluminum. The final, successful result is shown in table 10. Although the customer was unconcerned by springback, the crosssection was measured to find out how much springback actually occurred; see Figures 47 and 51.
z z
IGES file x
∆z = 0.4 mm
y 74 mm
C
2002 vehicle headlight
2002 vehicle headlight
Automotive heat/noise shield
y
A B
∆z = 0.3 mm
Figure 50. Illustration of the CAD and toolpath setup [ 36].
Finished part
inside
inside outside
aluminized Table 9: Rapid prototypes for automotive industries [29].
IGES file
Solar oven cavity.
Motorbike seat
Motorbike gas tank
Finished part inside
outside surface
outside
gl a
ss lid
Table 10: Non-automotive rapid prototype examples [104].
cooking cavity
side view - oven Figure 49: Assembled solar oven operation. The cooking cavity is shown in red [36].
Figure 51: The x-z profile of CAD file and formed product. The outside of the solar oven is shown as an inset. The springback can be observed [36]. 5.3 A Medical Application of SPIF The medical industry can benefit greatly by using the SPIF process to either produce Rapid Prototypes or one-off parts. The following is an application of asymmetric incremental forming of a customized medical product, i.e. an ankle support. The steps to go from the request for a part to the final manufacture are shown in Figure 52. The application addressed here represents a Reverse Engineering (RE) application; it permits the reproduction of high accuracy models called from complex geometries. By employing RE, it is possible to create lifelike 3D models representing many different objects including parts of a human body. In this application, SPIF was used to produce a part that is used as an ankle support. The process includes the following steps: first, the three-dimensional scanning of a human ankle with a laser (non contact inspection) is carried out in order to obtain the morphological and dimensional information of the object; next, once the data is available in a digital format, a ‘cloud of points’ is built, from which is possible to develop the surfaces that individualize the shape ankle; finally, through the application of CAD/CAM Systems, an ISO part program is generated. This is handed over to the numerical control machine, which carries out the Incremental Forming operation. Laser scanning is used because it has a large number of advantages, such as: low operation costs and easy acquisition; small dimensions; real time results. The application addressed here was carried out with a system that works according to triangulation principles. This permits the measurement of small objects, with a scan in six tenths of a second. The system permits recording of the object including surface features such as colour and luminosity. The next step is surface building or editing with software. This uses multiple observations during scanning, and since the object investigated is observed from many different angles markers are used on the surface. The software develops the parametric surfaces, which are used to obtain the solid model of the ankle.
CAD Model
Real Model
Laser Scanner
Virtual Model
Production
Request for an Ankle Support
CAD/CAM interface
shape embedding
````` Figure 52: The manufacture of an ankle support, from request, to scanning of a live subject (reverse engineering), to setting up a solid model and CAD drawing, to embedding the shape for toolpath planning, to creating a toolpath for manufacture, to checking for accuracy [59]. Strength coefficient
Hardening exponent
Anisotropy
Tensile Strength
Elongation %
K = 545 MPa
n = 0.27
ρν = 2.01
σR = 290 MPa
A% = 50
Table 11: Properties of deep drawing quality steel [59]. The ankle support was shaped starting from a surface slightly greater than the scanner recording, in order: a) to obtain a clearance between the instep and collar; b) to create space for an inside coating. At the end of this step a real curve grate, shape, is obtained. This is imported into a CAD/CAM system to develop the CAM step. The toolpath is compiled and generated in order to carry out the SPIF operation on a CNC milling machine. The ankle support is divided into two symmetrical parts, splitting the solid model and creating two separate part programs. The position of the model in the space is determined, with the specific aim of avoiding surface inclinations that go beyond the incremental forming limits in terms of the maximum drawing angle, φmax. Once the right positioning is found, the part program, is generated. A CNC, three-axis milling machine is used for the forming process. The work volume is 560X410X510. The program is loaded into the machine memory and the part is formed incrementally, making two matching, half ankle supports. The sheet material is DDQ (Deep Drawing Quality) steel, 1 mm thick. Its properties are shown in Table 11. The tool feed and rotating speed are 1000 mm/min, and 500 rev/min. The depth step, ∆z, is 0.5 mm, while the tool diameter is 11 mm. The forming time is half an hour. Figure 52, shows a completed DDQ steel half ankle. Process accuracy has been checked, by repeating the foregoing procedure, with a part formed by Incremental Forming. A laser scan of the part gives a new set of cloud points that can compared with the original surface part program. The results obtained show a maximum deviation error of 0.5 mm. 6 THE BUSINESS CASE FOR AISF As a relatively new process, AISF is not currently in regular commercial use, but all developers of the process have suggested potential application areas, and in some cases have made test products to demonstrate feasibility [31, 32, 33, 60]. Table 12 lists the range of applications that have been considered by developers which spans small to large products, and products with more or less complexity.
The most significant benefit from AISF arises in low volume production where existing processes require specialized tooling. The cost and lead time of tooling manufacture leads to very high component costs for small runs of new designs, and all developers of AISF have identified the attraction of AISF for prototyping or low volume manufacture. In order to provide more precise guidance on identification of candidate applications, two economic models have been developed to explore the trade off between fixed costs (particularly those associated with tooling) and direct costs. Hirt and Ames [97] consider the direct costs as comprising materials, labour and a machine overhead rate, with tooling as the fixed cost. Micari [59] uses more detail, with direct costs comprising materials, labour, power, two overhead rates and some batch setup costs, and fixed costs comprising tooling, NC programming and machine setup. Both authors find that AISF is likely to be attractive for production where new tooling would be required and total batch sizes are less than around 600. Such analysis gives a means to support decisions on investment in AISF. However, calculations of utility based on this form of cost model have some limits: the precise cost data required to apply the economic evaluation is often unavailable, except in very large companies. Even when it exists, it is unlikely to reflect true cost: labour costs may be higher or lower than a set rate depending on the capacity and utilisation rate at the factory; machine overhead rates are always estimates, as they can only be calculated accurately in arrears, once utilisation rates are known. the value of the ISF process is unlikely to be solely as a direct replacement for an existing process. Existing product designs and their associated process choices have been selected based on available production technology. The value of a novel technology such as ISF is likely to be achieved when product designs change to reflect the benefits and capability of the process. cost is not the only determinant of process selection. Constraints on tolerance, surface finish, sheet thickness and residual stress levels are equally important in determining process choice. These concerns are well known in more general analysis of investment in advanced manufacturing technology. They are discussed at more length by Ordoobadi and Mulvaney [98] who claim that purely economic assessments are generally pessimistic as they fail to capture the system wide benefits of the new technology. In an attempt to
provide a broader assessment of the value of AISF, Allwood, King and Duflou [98] have proposed an analysis of AISF based on product segmentation. They gathered a broad data set from 15 UK companies manufacturing products from sheet metal, considering a total of 28 products. The data was largely related to the product (or component or application) rather than the existing processes used to make it, and included Figures for direct costs and lead times, tooling costs and lead times, product design and quality specifications. The data set was plotted on a series of ‘segmentation charts’ which could also be used to display a process window for the capability of AISF. Analysis of the charts suggests that AISF is generally applicable for high value low volume products, and that the volume for which AISF is attractive increases with tooling costs. Generally, for batch sizes where AISF was economically attractive, it also showed a lead time advantage over conventional production. The product segmentation approach also allows validation of process capability. Of the products examined in the study, only one – a one-off cowling panel for a historic aeroplane – could be made by existing AISF techniques. However, if the AISF process window could be expanded by improving tolerance to around 0.3 mm, with feature definitions to 1 mm radius and allowing material thickness up to 3 mm, the process would be attractive for more than half of the applications considered. As AISF technology matures, and receives wider exposure, it can be considered by designers seeking the advantage of its unique features, and this will generate new applications. Furthermore, the avoidance of any significant tooling costs in AISF, and the relatively low asset value of the equipment suggests that AISF would be attractive for distributed manufacturing. This opens a further set of novel applications where supply chains that currently depend on stock-holding and mass distribution (such as the car body repairs and after-sales market) could be reorganised via a network of low cost AISF processes with distribution of data rather than material. This has obvious benefits both in reducing the economic and environmental burdens of distribution, and in offering increased customisation without additional cost. Clearly table 12 relates to actual applications – however the intention of table 12 is to include as the range of applications being considered is wider than the set of applications that have actually been tested. 7 RESEARCH OPPORTUNITIES AND CHALLENGES Many potential applications have been listed in the foregoing section. Nowadays, aspects such as aesthetics and ergonomic quality have on increasing importance. This gives rise to new products, which have always originated in a designer’s mind but have not always been economical to implement. Now, with AISF a design concept for a shape can be implemented, immediately and economically to give either a rapid prototype or a production part. Potential applications in markets that include insurance claims can be explored. For instance, sheet metal parts can be stored electronically and then made as required for automotive replacements, or parts can be reverse engineered and then made on a three-axis CNC mill. The architectural industry also has great promise for this application. Custom made sheet metal parts can be made with individualized patterns. Although AISF is now viable, many challenges remain. A set of useful guidelines now exist for the engineering designer when using this new process. However, these need to be expanded. The process is now established as a
useful tool for producing rapid prototypes which can be used in situ. One challenge is the issue of springback which keeps accuracy at 1.5 mm. Application areas: Automotive body panels (prototype, low-volume eg motorsport, and after-sales) Other automotive sheet metal parts – structural, or non-aesthetic Architectural – bespoke formwork, decorative panels Customized white goods Reflectors and casings for lighting Dental – bespoke dental crowns Housings and fairings for aerospace Ship hull plates Table 12: Potential applications areas for AISF [99]. Models that will allow a designer to achieve greater accuracy are needed. Another need is the development of Forming Limit Diagrams for different combinations of materials and sheet thickness. Both the Design Engineer and Manufacturing Engineer need these to determine if the process is applicable for a design. The challenge is to develop Forming Limit Diagrams, which can be used for many combinations, including: type of material, sheet thickness, forming tools and forming speeds. In addition, research work shows there is a relationship between maximum draw angle, φmax, and the major strain, εmax. Another challenge is to develop a comprehensive system, which gives an overview including shape prediction, FLD’s and φmax and compensates for springback. Traditional stamping processes will still be used for mass produced parts, for economic reasons. A challenge is to make asymmetric incremental forming more viable for mass production. With higher speeds and improvements in accuracy this new process can be an alternative to stamping especially with its flexibility. Modelling and on line control are challenges along with the development of algorithms which will compensate for springback. There are many areas of manufacturing in which asymmetric incremental sheet forming can be applied. One example is the Biomedical area for which an example has been given. For Biomedical applications it will be a challenge to find ways of manufacturing the part while meeting the clean room requirements of legal jurisdictions, as discussed by McAllister and Jeswiet [102]. In the end, all challenges are limited only to the imagination of the Design Engineer and the Manufacturing Engineer. 8 SUMMARY Asymmetric incremental sheet forming, with a single point doing the forming, is a viable process for making complicated shapes from sheet metal. It makes the forming of sheet metal a flexible operation and is an easy operation for all facilities having access to a three axis CNC mill. There are two variations to the process, one with a single point doing the forming and the other with two points where one point is either a partial or full die. The process has tremendous potential and there are many future possibilities where it can be used.
Guidelines have been established for designers and manufacturers who wish to form prototype sheet metal parts or run a low volume production runs. The parameters for which guidelines have been established are: thickness of the sheet metal relative to the maximum wall angle in a part (draw angle, φ), the size of the incremental step down, ∆z, the speed of deformation and size of the forming tool. Design and manufacturing guidelines Formability: Formability increases with higher sheet-to-workpiece relative velocities, with a trade-off of higher surface roughness. Formability decreases with thinner sheet. Smaller tool size gives increased formability. Anisotropy has an influence upon formability, with greater formability being achieved with smaller diameter tools in the transverse direction. Sheet formability decreases with increasing increment step size, ∆z. The effect of increment step size, ∆z: Large increment steps, ∆z, give a higher roughness. The increment step size, ∆z, can influence not only the surface roughness but also cause an orange peel effect. The size of the orange peel effect can be influenced by the incremental step size, ∆x and ∆y, and the draw angle. The effect of the draw angle φ: There is a limitation on the maximum draw angle φ that can be formed in one pass. With increasing draw angle φ, the sheet thickness reaches a minimum value where fracture occurs as a consequence. There is a strong dependence of the deformed sheet thickness on the draw angle φ, which can lead to inhomogeneous thickness distributions in the final part. Knowing the parameter φmax for a material at a specific thickness, a designer can take the first step in deciding if a sheet metal part can be made in one pass without tearing, or if a two pass or multiple pass sequence should be used. Plasticity: • Twisting can occur if forming is unidirectional. • Plastic strain increases in steps, with tool increments. • Each increase in plastic strain is accompanied by compressive stresses. Cyclic loading can produce residual stresses (due to repeated bending in combination with the Bauschinger effect). Springback is not any worse in this process compared to other sheet metal forming operations. Three types of springback can be defined in asymmetric incremental sheet forming: • A continuous local springback that takes places on every displacement of the forming tool, • A global springback that occurs after the final unloading and dismounting from the clamps, • A global springback after trimming (if done). Forces: Peak forces can be observed in the area where failure occurs at maximum draw angles, φmax, Increasing the vertical step size ∆z increases forces, Larger tool diameters increase forming forces. Increasing vertical step size ∆z has a much lower impact when compared to draw angle and tool size.
In addition, strategies need to be developed to increase accuracy. This work is ongoing by members of CIRP and will be reported in the future. In summary, the flexible forming system with short lead times envisioned by Schmoeckel [1] and the single point forming system patented by Leszak [2] are now a reality with the new ASIF processes that are now available. Guidelines now exist for the manufacturing designer and the new processes can be done by virtually any facility having access to a three-axis CNC mill. 9 ACKNOWLEDGEMENTS The authors are grateful to the UK EPSRC and the University of Bath Innovative Manufacturing Research Centre for the provision of funds to enable a workshop meeting to be held at the University of Cambridge in October 2004. The authors have also been supported by research grants in their individual countries and we wish to acknowledge their support: the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT); the Natural Sciences and Engineering Research Council of Canada. The information contained in this paper would not have been possible without our graduate students: G. Ambrogio, J. Ames, M. Bambach, E. Hagan, M. Ham, S. Jadhav, G. Owen, A. Szekeres, and D. Young. There are many others who have participated in seminars that have been held in preparation for this paper, many thanks to them. 10 [1] [2] [3]
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