SCHOOL OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEEERING PROJECT REPORT PROJECT TITLE SCREW JACK COURS CODE MENG 3161 PREPARED BY: SHUSHAY HAILU ID NO 4142/07 SECTION 2
SUBMITED TO INSTRACTOR: BERIHU SUBMITION DATE 30/08/2009E.C
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Table of content
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Acknowledgment…………………………………………………………………………………………………… 5 Abstract……………………………………………………………………………………………………………….… 6 Nomenclature……………………………………………………………………………………………………….. 7-9 4
Chapter1 Screw jack ………………………………………………………………………………………………………….…. 10 1.0 introduction……………………………………………………………………………………………………. .10 1.1Working principal …………………………………………………………………………………….... ..10-11 1.2 Problem statement ........................................................................................11-12 1.3 OBJECTIVE ……………………………………………………………………………………………… .…….12
1.4 methodology………………………………………………………………………………………………….12 1.5 design concepts…………………………………………………………………………………………….. .12-13 1.6 SCOPE AND LIMITION ……………………………………………………………………………… .……. 13-14
1.7 SCOPE OF THE PROJECT…………………………………………………………………………… …………14 CHAPTER TWO…………………………………………………………………………………………………………. 15 LITERATURE REVIEW………………………………………………………………………………………………. ..15 2.0 Introduction …………………………………………………………………………………………………. ..15 2.1 Operation …………………………………………………………………………………………… .15 2.2 Construction of a Screw Jack ………………………………………………………….… ...15 2.3 Advantages and Disadvantages of the Screw Jack ………………………………. 15 2.4 Mechanical Advantage (M.A) ………………………………………………………… .…...16 2.5 Common Types of Screw Jack…………………………………………………………….…. 16 CHAPTER 3…………………………………………………………………………………………………………………..1 9 MATERIALS SELECTION……………………………………………………………………………………………19 3.0 Introduction………………………………………………………………………………………………… ...…19 3.1 Engineering Materials for Components ………………………………………………...19 3.2 Steps for Selection of Materials for Components…………………………….….…19-20
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3.3 Components and their Specific Materials Selected ………………………….………….21
CLASSIFICATION OF SCREW THREADS ……………………………………………………….…….. 23 3.1 Introduction…………………………………………………………………………………………………..….23 3.1.1 Square Thread ……………………………………………………………………………………..……..…23
3.1.1.1 Nomenclature of Square Thread ………………………………………………………….23 3.1.1.2 Advantages of the Square Thread ………………………………........ .................23 3.1.1.3 Disadvantages of Square Thread …………………………………………………… ...…23 3.1.2 ISO Metric Trapezoidal Threads…………………………………………………...... .......24 3.1.2.1 Nomenclature of ISO Metric Trapezoidal Thread ………………………...….…24 3.1.2.2 Advantages of the Trapezoidal Thread ………………………………….….…..........24 3.1.2.3 Disadvantages of Trapezoidal Threads……………………………….…………….…24 3.3 Definition of Screw Thread Basic Terms ………………………………………………..…26 -27 3.4 Torque requirement lifting load…………………………………………………………... ....28 3.5 Torque requirement lowering the load…………………………………………….……...30 3.6 Over haling and self locking screw……………………………………………….. ............31 3.7 Efficiency of square treaded screw………………………………………………………..….33 3.8 Efficiency of self locking screws……………………………………………………………… ...35 3.9 Coefficient of friction……………………………………………………………………………… ...35 3.10 Buckling of columns……………………………………………………………………………… ...36 Chapter 4……………………………………………………………………………………………………… ..38 Designing procedure for the screw jack……………………………………………………… .…38 4.0 Introduction………………………………………………………………………………………………… .38 4.1 Design for Screw Shaft………………………………………………………………… ..38 4.1.1
Core Diameter……………………………………………………………… .38
4.1.2
Torque required to rotate the screw …………………………… .….39
4.1.3
Screw Stresses………………………………………………………………. .39
4.1.4
Principal Stresses…………………………………………………………… .40
4.2 Design for Nut………………………………………………………………………………. ..40
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4.2.2 Stresses in the Screw and Nut…………………………………………………..41 4.2.3 The outer diameter of Nut………………………………………………………..41 4.2.4 the outside diameter of Collar………………………………………………….41 4.2.5 Thickness of the Nut Collar…………………………………………………….…43 4.3 Designs for Head and Cup…………………………………………………………………… .43 4.3.2 Torque Required to Overcome Friction……………………………………………….45 4.3.3 Total Torque Subjected to the Handle………………………………………………..45 4.3.4 Diameter of Handle/Lever…………………………………………………………………..45 4.3.5 Height of Head……………………………………………………………………………………….46 4.3.6 Design Check against Instability/Buckling………………………………………………………47
4.4 Design of Body …………………………………………………………………………………………. 47 4.5 Dimensions for the body of the screw ……………………………………………………… .47
4.6 Efficiency of the Screw Jack ………………………………………………....51 4.7 Result and dissection ………………………………………………………... ..52 4.8CONCULUTION……………………………………………………………...53 4.9 Recommendation……………………………………………………………..………53 4.10 2D-drawing…………………………………………………………………54-55
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Acknowledgement I would like to acknowledge and appreciate the great guidance from my project supervisor, instructor berihu I would also like to thank my pare nts and classmates for their encouragement, understanding and support throughout the entire project. I would also like to thank the almighty God for bringing me this far and giving me the strength to c arry out the project. I would also like to thank my friend’s zemical and toweled.
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ABSTRACT a screw jack serves to give mechanical advantage advantage by changing changing rotational force to linear force thus allows one to lift a load and support it at a given height. The aim aim of the project project was to design design a screw jack that was raised 3500kg mass of car during maintenance and with a desired strength and mechanical properties that was free from any error. This case study is divided into various sections that describes c lassification of screw threads, design analysis ,result and dissection ,conclusion and recommendation parts of the screw jack and selection of materials used for construction that are in agreement with current industry practice of screw jack design. The design procedure adopted here is from design of machine elements 1 and 2 A factor of safety of 5 and above should be used in this design to reduce high chances of failure due to dynamic loadings and impact loadings. Dynamics loading is as a result of external inte rferences such as whirl wind, earth tremors and external forces while impact loading is such as load is applied suddenly with a 9
short time and results into high stresses w hich can cause failure hence these calls for a high factor of safety.
Nomenclature
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p - Pitch of screw thread (mm) n - Number of threads in contact with screwed spindle l - Lead of screw thread (mm) t - Thickness of screw d - Nominal diameter of screw (mm) d c - Core diameter of screw (mm) d m - Mean diameter of screw (mm) θ - Friction angle (degree) α - Helix angle of screw (degree) W- Load (kg) N - Normal reaction (Newton, N) μ − Coefficient of friction P - Effort (Newton, N) T - Torque (N. m) η − Efficiency (%) F load - The force the jack exerts on the load. (Newton, N) F effort - The rotational force exerted on the handle of the jack. (Newton, N) r-the length of the j ack handle (mm) M. A – A – Mechanical Mechanical advantage π = 3.141592654 BS – BS – British British standards σ c - Pure compression stress
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A c - Cross sectional area of the screw shaft σ c(max) -Maximum principal stress τ( max)- Maximum shear stress J - Polar moments P b - Bearing pressure on the nut t 1 - Thickness of nut collar h - Height of the nut D 1 - Outer diameter of nut collar D 2 - Outside diameter of nut collar σ t - Tearing strength of the nut σ c - Crushing strength of the nut τ (screw) -Shearing stress on the screw τ (nut) - Shearing stress on the nut Τ-Shearing stress of nut collar D 3 - Diameter of head on top of screw D 4 - Diameter of pin T-Total torque to which the handle is Subjected T 1 - Torque required rotating the screw T 2 –Torque required overcoming Friction T- Total torque subjected to handle σ y -Yield stress
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L – Length of the handle D - Diameter of handle M - Bending moment H - The height of head σ b - Bending stress L eff - Effective length of screw H 1 – Lift of screw W cr - Buckling or Critical load E – Young’s modulus or modulus of elasticity C - End fixity coefficient R- Slenderness ratio k - The radius of gyration HB – Hardness number I − Moment of inertia of the cross section. D 5 - Diameter of body at the top t 2 - Thickness of body t 3 - Thickness of base D 6 - Inner Diameter at the bottom D 7 - Outer Diameter at the bottom H b - Height of the body
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CHAPTER ONE SCREW JACK
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1.0 Introduction Screw jack is also called jack screw in other terms. A screw jack is an example of a power screw and referred to as a mechanical device that can increase the magnitude of an effort force. Screw jacks are used for raising and lowering platforms and they provide a high mechanical advantage in order to move moderately heavy and large weights with m inimum effort. They function byturning the lead screw when raising or lowering of loads. Screw jack is found everywhere is need to lift, position align and hold, to amplify force
1.1 Working principal A screw jack consists of a screw and a nut. The nut is fixed in a cast iron frame and remains stationary. The rotation of the nut inside the frame is prevented by pressing a set screw against it. The screw is rotated in the nut by means of a handle, which passes through a hole in the head of the screw. The head carries a platform, which supports the load and r emains stationary while the screw is being rot ated. A washer is fixed to the other end of the screw inside the frame, which prevents the screw from being completely turned out of the nut
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1.2 Problem statement There is one problem that the researcher observes in the environment .during tripe cars may reach the end life time their wheels at that time drivers need maintenance their cares . There for the researchers design is to lift 3500kg of car until the height of 200mm.
1.3 OBJECTIVE Objective of this design is to overcome the problem of statement.
1 General objective _to design and modal screw jack 2 specific objective _to designs _to select materials _to draw 2D and 3D _to outline dimensions
1.4 methodologies: I use books, like gupta Ashby,m.f 2005.material selection in mechanical designe.3 rd ed. New York Like bhandari,v.b., 2010.design of machine e lements. Like strength of material Like material science Like internet source
1.5 design concepts: I use the concepts cost, strength, mechanism, mechanical Properties, creep, fatigue, physical properties, thermal properties. There are different types of screw jack as shown blew
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but my design is most preferable one look the image blow
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1.6 SCOPE AND LIMITION Based on that design we are lifting only 3500kg .more than this mass is impossible The development of screw jack is only prototype not ready functioning as commercial. The developed screw jack is only for normal person. The developed screw jack is only operated on afloat surface.
1.7 SCOPE OF THE PROJECT The scope of the project is starting from acknowledgment, abstract, nomenclature, introduction to screw, litracher review, material selection, force analysis, design analyses, result and diction, conculition, recommendation.
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Collection of input data from research work. . Study of weight-dimensional parameters . Study of stresses, deformations in lift . Study of Vibration and impact resistance. . Study of Keeping of service life at different loading . Study of Reliable operation.
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CHAPTER 2
LITERATURE REVIEW 2.0 Introduction Screw jack is also called jack screw in other terms. A screw jack is an example of a power screw and referred to as a mechanical device that can increase the magnitude of an effort force. Screw jacks are used for raising and lowering platforms and they provide a high mechanical advantage in order to move moderately heavy and large weights with minimum effort. They function by turning the lead screw when raising or lowering of loads .
2.1 Operation The jack can be raised and lowered with a metal bar that is inserted into the jack. The operator turns the bar with his/her hands in a clockwise direction. This turns the screw inside the jack and makes it go up. The screw lifts the small metal cylinder and platform that are above it. As the j ack goes up, whatever is placed above it will raise as well, o nce the jack makes contact. The bar is turned until the jack is raised to the required level. To lower the jack the bar is turned in the opposite direction.
2.2 Construction of a Screw Jack A screw jack consists of a screw and a nut. The nut is fixed in a cast iron frame and remains stationary. The rotation of the nut inside the frame is prevented by pressing a set screw against it. The screw is rotated in the nut by means of a handle, which passes through a hole in the head of the screw. The head carries a platform, which supports the load and remains stationary while the screw is being rotated. A washer is fixed to the other end of the screw inside the frame, which prevents the screw from being completely turned out of the nut.
2.3 Advantages and Disadvantages of the Screw Jack 2.3.1 Advantages The load can be kept in lifted position since the screw jack is se lf-locking. This means it remains motionless where it was left when t he rotational force on the screw is withdrawn. It will not rotate backwards regardless of size of the weight. Screw jacks also lift or raise the moderate heavy weights against gravity and uses very small handle force that can be applied manually.
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2.3.2 Disadvantages The major disadvantage of the screw jack is that chances of dropping, tipping or slipping of the load are high and can cause serious accidents hence the device is termed as not safe fail. 5 Accidents caused by screw jack are due to the following reasons: (a) Improper securing of load on the jack. (b) Overloading. (c) Off center of axis of the jack with respect to center of gravity hence not ideal for side loads. (d) Placing the jack on a soft ground and unleveled surface. (e) Using the jack for wrong purpose instead of using it for the purpose for which it is designed. Precaution: Long lifts should be avoided since they can cause serious overheating and generate a large amount of heat. It should therefore be used under ambient temperatures with the use of the required lubricants. Design and manufacturer’s instructions such as speed, load capacity and recommended temperatures must be followed to avoid accidents. Always keep t he mating surfaces clean after use and check for wear and damage on the surfaces.
2.4 Mechanical Advantage (M.A) The mechanical advantage of a screw jack can be referred to as the ratio of the force the jack exerts on the load to the input force on the lever, neglecting friction. However, most screw jacks have large amounts of friction which increase the required input force , so the actual mechanical advantage is often only 30% to 50% of this figure (Bhandari, 2010). M. A = F load /F effort Where F load = The force the jack exerts on the load F effort = The rotational force exerted on the handle of the jack
2.5 Common Types of Screw Jack Commonly used screw jacks are as shown below
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(a)
(b)
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Figure 2.2: Examples of mechanical jacks (a) Floor Jack (b) Scissor jack A screw jack is a device that lifts heavy equipment. The most common form is a car jack, floor Jack or garage jack which lifts vehicles so that maintenance can be per formed. Car jacks usually use mechanical advantage to allow a human to lift a vehicle by manual force alone. Screw jacks are usually rated for maximum lifting capacity. There are several types of mechanical jacks: Scissor jack, floor jack, scaffolds, bottle jack etc. Advantages ü they are self-locking. ü They are simple to design. 24
ü They are cheap and affordable. ü They can lifts moderately loads like cars with very less force.
Disadvantages ü They should always be lubricated. ü They cannot be used to lift or support very heavy loads. 2.6 Factors to Consider in Selection of the Best Jack for Application Purposes 1. Consider the load carrying capacity of t he lifting screw (column load) when jacks are Loaded in compression. How high do you need to lift the load? One must choose a jack whose lifting screw is stout enough to handle the load at full rise. 2. Consider the travel speed of the dynamic load. The speed at which the load will be moved is a limiting factor. How fast do you need to move the load? Sometimes double lead machine screw jacks or ball screw jacks are a better choice in a given application. 3. How frequently will the jack need to move the load? Remember that he at builds up between the machine screws and nut during normal operation. Duty cycles for machine screw jacks must include periods of rest to dissipate that heat.
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HAPTER 3 MATERIALS SELECTION 3.0 Introduction Material selection is an important process in design processes. Sele cting materials is a process that is design-led in that the material selection process uses the design requirements as the input so as to come up with materials that have t he desired properties for the part to be designed to function well.
3.1 Engineering Materials for Components The common engineering materials used in making machine components include; Cast iron, Steel (all types of steel), Copper and its alloys, Aluminum and its alloys, Plastics.
Therefore, the right materials for the design of the screw jack parts should be selected. Selection requires one to consider the following factors which give the best material fit for the design job: a) Specific strength and mass. It is preferable to select a material of high yield stress with ability to carry external load without failure and low density in order to realize a screw shaft of high strength and low mass. Therefore, the material selection process should aim to maximize the quantity te rmed as the specific strength. 26
b) Resistance to abrasive wear.
Most of engineering materials in contact with one another are subjected to surface wear due to relative motion. It is therefore desirable to select a material from the candidate materials with low wear rate or capacity to resist abrasive wear at the thread surfaces. c) Resistance to buckling. Heavy loads may cause the screw to buckle once the critical load is exceeded. It is preferable to select a material with high resistance to buckling of t he screw, that is, excellent elasticity and deflection behavior in response to application of an external load. d) Availability, Cost and Affordability. It is also preferable to choose a material with the highest affordability rating. Relative cost o f the materials is used in finding or calculating the affordable rates. Therefore, t he availability of the material and the cost of processing the mat erial into the finished product need to be taken into account and considered as supporting information when making the final choice of the material. e) Heat transmission properties. As we know there always a relative motion between screw and nut, which cause a friction that generates heat which can cause change in the mechanical properties of the material. f) Other relevant properties include; resistance to corrosion, electrical and mechanical properties, heat transmission properties etc.
3.2 Steps for Selection of Materials for Components Selection of materials in engineering design involves the following steps: Translation of design requirements into specifications for a material. Screening out those materials that do not meet the specifications in order to leave only the viable candidates. Ranking of the surviving materials to identify those that have the greatest potential. Using supporting information to finally arrive at the choice of material to be used.
The first three steps involve mathematical analysis, use of various charts and graphs of specific property such as specific strength, wear resistance, buckling resistance and affordability. The materials are compared, ranked as per the indices of merit and available supporting information is used to reach the final decision (Ashby, 2005).
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In this project, information from case studies on previous designs of similar products is used in material selection for the screw jack components/parts. However, other factors such as availability of the candidate materials, purchase price of the candidate materials, m anufacturing processes and properties, forms and sizes in which the mate rials are available are also considered.
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3.3 Components and their Specific Materials Selected The goal of material selection is to c ome up with an appropriate material that best meet s the design requirements. The approach is to identify the connection between functional requirements and the material properties so as to help us reduce the number of candidate materials from which to select from. The following are components and materials required in the design of a power screw (screw jack):
3.3.1 Frame (Body) Most of the frames are in conical shape and hollow internally to accommodate both the nut and scre w assembly. The frame works to ensure that the screw jack is safe and has a complete rest on the ground. The purpose of the frame is to support the screw jack and enable it to withstand compressive load exerted on it. The frame is a bit complex and thus requires casting as a manufacturing process. For this reason, grey cast iron as a material is selected for the frame. This is also evident from the case study on previous design of the same product (Nyangasi, 18 Decem ber, 2006). Cast iron is cheap and it can give any complex shape without involving costly machining operations. Cast iron has higher compressive strength compared to steel. Therefore, it is technically and economically advantageous to use cast iron for the frame. Graphite flakes cast iron with an ultimate t ensile strength of 220MPa is considered suitable for the design of the frame. The graphite flakes improve the ability to resist compressive load. Mechanical properties
British Standard Specification
Tensile strength (MPa)
220
Compressive strength (MPa)
766
Shear strength (MPa)
284
Endurance limit (MPa)
96
Young’s modulus (GPa)
89 – 114
Modulus of rigidity (GPa)
36 – 45
Hardness number (HB)
196
Table3.1: Mechanical Properties of Cast iron – Appendix A (Marshek, 2012
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3.3.2 Screw The screw is subjected to tensional moment, compressive force and bending moment. The screw profile is square type because of its higher efficiency and self-locking but not compared to trapezoidal threads. Square threads are usually turned on lathes using a single point cutting tool also square threads are weak at the root and this leads to use of free cutting steel. Screws are usually made of steel where great resistance to weather or corrosion is required. Most fasteners close to 90% use carbon steel because steel has excellent workability, offers abroad range of attainable combinations of strength properties and it is less expensive. Medium plain carbon steel can be heat treated for the purpose of improving properties such as hardness, strength (tensile and yield), the desired results are therefore obtained (Fasteners, 2005). This leads to the use of plain carbon steels.
Table3.2: Mechanical Properties of Plain carbon steel – Appendix B ( Nyanja’s , 18 December, 2006)
3.3.3 Nut There exists a relative motion between the screw and the nut which causes friction, friction in turn causes wear of the material used for screw and nut. Therefore, it requires one of the two members to be softer. A suitable material for the nut is therefore phosphor bronze which is a copper alloy with small percentage of lead and has the following advantages; Good corrosion resistance. Low coefficient of friction. High tensile strength.
Bronze has 0.2% phosphor to increase te nsile strength and the yield stresses may be taken as; tension = 125MPa, compression = 150MPa, yield stress in shear = 105MPa with safe bearing pressure of 15MPa, ultimate tensile strength is 190MPa and a coefficient of friction of 0.1.
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Table3..3: Safe Bearing Pressures for Power screws – Appendix C (Nyangasi, 18 December, 2006) & (Gupta, 2005
3.3.4 Handle The handle is subjected to bending moments so plain carbon steel of BS 080M30 with yield strength of 385MPa can also be used. It has the same mechanical properties and process as in Table 3.2.
3.4.4 Cup Shape of cup is complex and thus re quires casting process. It also has the same properties as in Table3.1. Taking graphite flakes cast iron with an ultimate tensile strength of 200MPa. The graphite flakes improve the ability to resist compressive load.
3.4.5 Set Screw and Lock nut + Washer The purpose of the set screw is to resist motion of nut with screw. The lock nut + washer o n the other hand is used to provide uniform force by e nlarging the area under the action of the force. We can use plain carbon steel for both and they have the same manufacturing process and properties as in Table 3.2
CLASSIFICATION OF SCREW THREADS 3.1 Introduction Screw jacks commonly use various forms of threads, namely; square threads, ISO metric trapezoidal threads and buttress thread. 3.1.1 Square Thread As the name suggest, it has a square cross section of the thread. It is the most common form used by the screw jack and used especially in high load applications.
3.1.1.1 Nomenclature of Square Thread
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` Figure 3.1: Nomenclature of square thread
3.1.1.2 Advantages of the Square Thread The advantages of square threads are as follows: (i) They have high efficiency. (ii) They have lower friction coefficient hence less power loss in lifting the load. (iii)Motion of the nut is uniform since there is no side thrust and radial pressure on the nut.
3.1.1.3 Disadvantages of Square Thread The disadvantages of square threads are as follows: (i) The threads are usually turned on a lathe machine with a single point cutting tool hence e xpensive compared to machining with multi-point cutting tools. This makes them more difficult to manufacture. (ii) The strength of a screw depends upon the thread thickness at the core diameter. Square threads have less thickness at core diameter than trapezoidal threads. This reduces the load carrying capacity of the screw. (iii) It is not possible to compensate for wear in square threads since wear of the thread surface becomes a serious problem in the service life of the power screw. Therefore, replacement of the nut or the screw is required when worn out.
Applications: Square threads are used for screw-jacks and presses. 33
3.1.2 ISO Metric Trapezoidal Threads These are threads with trapezoidal outline profile. They are most commonly used for lead screws. They offer high strength and ease of manufacture.
3.1.2.1 Nomenclature of ISO Metric Trapezoidal Thread
Figure 3.2: Nomenclature of ISO metric trapezoidal thread
3.1.2.2 Advantages of the Trapezoidal Thread (i) They are cheap to manufacture as compared to square threads. Multi-point cutting tools are employed for machining compared to single point cutting tools that ar e used in machining square threads. (ii) The trapezoidal thread has greater t hickness at core diameter than that of the square thread. Therefore, a screw with trapezoidal threads is stronger than an equivalent screw with square threads. Such a screw has large load carrying capacity. (iii) The axial wear on the surface of the trapezoidal threads can be compensated by means of a splittype of nut. The nut is cut into two parts along the diameter. As we ar progresses, the looseness is prevented by tightening the two halves of the nut together. The split-type nut c an be used only for trapezoidal threads. It is used in lead-screw o f lathe to compensate wear at periodic intervals by tightening the two halves.
3.1.2.3 Disadvantages of Trapezoidal Threads The disadvantages of trapezoidal threads are as follows: (i) The efficiency of trapezoidal threads is less than that of square threads. 34
(ii) Trapezoidal threads result in side thrust or radial pressure o n the nut. The radial pressure or bursting pressure on the nut affects its performance.
Application: Trapezoidal and acme threads are used for le ad-screw and other power transmission devices in machine tools.
3.1.3 Buttress Thread
Figure 3.3: Nomenclature of buttress thread
3.1.3.1 Advantages of Buttress Thread The advantages of buttress threads are as follows: (i) It has higher efficiency compared to trapezoidal threads. (ii) It can be economically manufactured on a thre ad milling machine. (iii) The axial wear at the t hread surface can be compensated by means of split-type nut. (iv) A screw with buttress threads is stronger than equivalent screw with either square threads or trapezoidal threads. This is because of greater t hickness at the base of the thread.
3.1.3.2 Disadvantages of Buttress Thread The buttress threads have one disadvantage. They can transmit power and motion only in one direction as compared to square and ISO metric trapezoidal threads, which can transmit force and motion in both directions. Application: Buttress threads are used in vices, where force is applied only in one direction. 12
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3.2 Thread Series There are three standard thread series in the unified screw thread system; Fine series Coarse series Normal series
Fine thread series have more threads per axial distance and thus have a smaller pitch while coarse thread series have a large pitch (fewer threads per axial distance). This shows that fine series threads are stronger as compared to coarse thread series of the same dimensions (diameter) (Fasteners, 2005). Fine series has advantages over the other series, these are; They have large stress areas hence are strong in compression. They have a larger minor diameter which de velops higher tensional and shear strength. They have smaller helix angle therefore pe rmitting closer adjustment accuracy.
3.3 Definition of Screw Thread Basic Terms
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Figure 3.4: Screw Nomenclature (Bhandari, 2010
The terminologies of the screw thread are defined as follows (Gupta, 2005): (i) Pitch ()
The pitch is defined as the distance m easured parallel to the axis of the screw from a point on one thread to the corresponding point on the adjacent thread. (ii) Lead ()
The lead is defined as the distance measured parallel to the axis of the screw that the nut will advance in one revolution of the screw. For a single threaded screw = For a double threaded screw = (iii) Nominal or Outside Diameter ( ) 37
It is the largest diameter of the screw. It is also called major diameter. (iv) Core or Minor Diameter ()
It is the smallest diameter of the screw thread. =− (v) Mean Diameter ()
=(+)/2
=−0.5
(vi) Helix Angle()
It is defined as the angle made by the helix of the thread with a plane perpendicular to the axis of the screw. The helix angle is related to the lead and the mean diameter of the screw. Taking one thread of the screw and unwinding, one complete turn is developed. The thread will become the hypotenuse of a right-angled triangle with the base and height being equal to the lead .
Figure 3.5: Unwound thread
This right-angled triangle gives the relationship between the helix angle, mean diameter and lead, which can be expressed in the following form: Where
tan= /
= ℎ ℎ ℎ ℎ.
The following conclusions can be drawn on the basis of the development of thread: The screw can be considered as an inclined plane with as the angle of inclination. The load always acts in the vertical downward direction. When the load is raised, it moves up the inclined plane. When the load is lowered, it moves down the inclined plane.
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The load is raised or lowered by means of an imaginary force acting at the mean radius of the screw. The force multiplied by the mean radius ( /2) gives the torque required to raise or lower the load. Force is perpendicular to load .
3.4 Torque Requirement - Lifting Load The screw is considered as an inclined plane with inclination when the load is being raised. The following forces act at a point on this inclined plane:
Figure 3.6: Force diagram for lifting load
Load : It always acts in the vertical downward direction. Normal reaction : It acts perpendicular (normal) to the inclined plane. Frictional force : Frictional force acts opposite to the motion. Since the load is moving up the inclined plane, frictional force acts along the inclined plane in downward direction. Effort : The effort acts in a direction perpendicular to the load . It may act towards the right to overcome the friction and raise t he load. Resolving forces horizontally,
=cos+sin
(3.0)
Resolving forces vertically,
=cos−sin
(3.1)
Dividing equation (3.0) (3.1) we get:
=(cos+sin)(cos−sin)
(3.2)
Dividing the numerator and denominator of the right hand side of e quation (3.2) by we get:
=(+tan)(1−tan)
(3.3)
The coefficient of friction μ can be expressed as follows:
=tan
(3.4)
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Where
= the friction angle. Substituting (3.4) into equation (3.3),
=(tan+tan)/(1−tantan)
(3.5)
=tan(+)
(3.6)
The torque required to raise the load is given by: =×/2 Whence
=[tan(+)]/2
(3.7)
3.5 Torque Requirement - Lowering Load When the load is being lowered, the following forces act at a point on the inclined plane: Load : It always acts in the vertical downward direction. Normal reaction : It acts perpendicular (normal) to the inclined plane. Frictional force : Frictional force acts opposite to the motion. Since the load is moving down the inclined plane, frictional force acts along the inclined plane in the upward direction
Figure 3.7: Force diagram for lowering load
Effort : The effort acts in a direction perpendicular to the load . It should act towards left to overcome the friction and lower t he load. Resolving horizontally,
= −
(3.8)
Resolving vertically,
= +
(3.9) 40
Dividing expression (3.8) by (3.9) we get as follows:
=(cos−sin)/(cos+sin) (3.10) Dividing the numerator and denominator of the right hand side of e quation (3.10) by cos α:
=(−tan)/(1+tan) (3.11) Substituting equation (3.4) into Equation (3.11),
=(tan−tan)/(1+tantan) (3.12) Whence
= ( − )
(3.13)
The torque required to lower the load is given by, =×/2 Whence
=[tan(−)]/2 (3.14) 3.6 Over Hauling and Self-Locking Screws From equation (3.14), we know torque re quired to lower load is given by: =[tan(−)]/2 18
41
Case 1: When < The torque required to lower the load becomes negative. This indicates a condition that no force is required to lower the load and the load itself will begin to turn the screw and descend down, unless a restraining torque is applied. This condition is called overhauling of the screw. Case 2: When > The torque required to lower the load becomes positive. Under this condition, the load will not turn the screw and will not descend on its own unless effort is applied. This condition is called self- locking. The rule for self-locking screw states that: A screw will be self-locking if the coefficient of friction is equal to or greater than the tangent of the helix angle.
For self-locking screw, tan≥tan Or ≥/ Therefore, the following conclusion are made: (i) Self-locking of the screw is not possible when the coefficient of friction (μ) is low. The coefficient of friction between the surfaces of the screw and the nut is reduced by lubrication. Excessive lubrication may cause the load to descend on its own.
(ii) The self-locking property of the screw is lost when the lead is large. The le ad increases with number of starts. For double-start thread, lead is twice of the pitch and for t riple threaded screw, three times of pitch. Therefore, the single threaded screw is better than multiple threaded screws from self-locking considerations. Self-locking condition is essential in applications like screw jack (Naik, Apr 15, 2015).
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3.7 Efficiency of the Square Threaded Screw Referring to Figure 3.6: Force diagram for lifting the load , the output consists of raising the load if the load moves from the lower end to the upper end of the inclined plane. Therefore, = ℎ
= The input consists of rotating the screw by means of an effort P. =
ℎ = () The efficiency of the screw is given by,
=
(3.15b)
This equation can also be expressed as:
=l/()
(3.15c)
And tan=/ Therefore
=tanα/
(3.15d)
Substituting for =tan (+) we get;
=tan/tan (+)
(3.15e)
From the above equation, it is evident that the efficiency of the square threaded screw depends upon the helix angle and the friction angle. The following figure shows the variation of thefficiency of the square threaded screw against the helix angle for various values of the coefficient of friction. The graph is applicable when the load is being lifted
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44
3.8 Efficiency of Self-Locking Screw 45
The efficiency of square threaded screw is given by (From equation 3.15e):
=tan/tan(+) For self-locking screw ≥ Substituting the limiting value ( = ) into the equation above
≤tan/tan(+) (3.16a)
≤tan/tan(2) (3.16b) And from trigonometric identities tan2=2tan/1−2 Substituting for tan2 into the above expression,
≤tan/(1−2)tan(2) (3.16c) Simplifying
≤1/2(1−2)
(3.16d)
From the above expression we can deduce that the efficiency of self-locking square threaded power screw is less than 0.5 or 50%. If the efficiency is more than 50%, then the screw is said to be overhauling (Gupta, 2005).
3.9 Coefficient of Friction, It has been found that the coefficient of friction () at the thread surface depends upon the workmanship in cutting the threads and on the type of the lubricant used. It is practically independent of the load and dependent on rubbing velocity or materials. An average of 0.1 can be taken for the coefficient of friction when the screw is lubricated with mineral oil (Gupta, 2005
46
47
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Chapter 4 Designing procedure for the screw jack 4.0 introduction The generalized adopted design procedure for screw jack to rise a load of 3500kg, mini height=200mm, max height=400mm
4.1 Design for Screw Shaft Material specification selected for the screw shaft is plain carbon steel to British Standard specification BS 970 080M30, Hardened and Tempered, whose properties are as shown in Appendix B and the material yield strength is 700 MPa both in tension and pure compression and 450 MPa in shear.
4.1.1 Core Diameter The core diameter is determined by considering the screw to be under pure compression. That is;
W=cAc Where
c is pure compression stress=700mpa Ac is cross sectional area of screw shaft=/4(dc)2 Dc is core diameter
There for W=c/4(dc)2dc=(4W/c/) Taking factor of safety f.s=5 dc=(4W/c/5)dc=48583.75/700/5) dc=0.008835m=8.835mm For square threads of fine series, the following dimensions of screw are selected from Appendix D (Gupta, 2005) hence,, The core diameter dc=10mm,do=12mm,pitch p=l=2mm
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= tan=0.1, =5.71
Section of screw spindle
4.1.2 Torque required to rotate the screw When the torque required to rotate the screw is the same to torque required lift the load is given by
T1PdmWtandm dmdodc121011mm tanldm2110.05787 Then T1=(8583.75tan(3.312275.71)0.011)/2=7.496Nm
4.1.3 Screw Stresses Compressive stresses duo to axial loads using the new c ore diameter is
c=W/Ac=W/(dc2/4)=48583.75/0.012=109.29Mpa
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The shear stress due to this torque using the new core diameter is given
=T1dc/2J, where J is polar moments=dc4/32 =16T1/dc3=167.496/0.013=38.177Mpa 4.1.4 Principal Stresses Maximum principal stress is as follows:
c max=c(c)() c max=..43.7= cmax=121.3068Mpa And maximum shear stresses as follows:
max=c max=/2..=66.66Mpa Design value of is 450=90Mpa Cheek; those maximum shear and compressive stresses ar e less than the permissible stresses which is safe design.
4.2 Design for Nut 4.2.1 Height of the Nut We find the height of the nut (h) by considering the bearing pb on the nut
Pb=W/4dodcn, where n is number of treads in contact with screwed spindle Material specification for the nut is phosphor bronze which has tensile stress=150Mpa, compressive stress 125Mpa,shear stress=105Mpa specific bearing pressure not exceed 17Mpa and
=0.1
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17=... 17248.39nn14.6 Say n15 Then height of the nut is as fo llows; hnp152mm30mm Check: For a safe nut height ℎ ≤ 4dc40mm
4.2.2 Stresses in the Screw and Nut Shear stress in the screw is as follows
Screww/ndct
where t is thickness of screw p/22/21mm
Screw8583.75/150.010.00118.215Mpa 4.2.2 Stresses in the Screw and Nut Shear stress in the screw is as follow
NutW/ndot ,8583.75/150.0120.00115.179Mpa The given value of is 105/521Mpa
Check : These stresses are within permissible limit, hence, design for the nut is safe.
4.2.3 The outer diameter of Nut Outer diameter of D1 is found by considering the tearing strength of the nut
tW/4D12do2 t is tearing strength the nut Tensile stresst/f.s150/530Mpa Then we get D1 as follows 308583.75//4D12122 52
D122.097mm,say D123mm
4.2.4 The outside diameter of Collar Outside diameter D2 is found by considering the cr ashing strength of the nut collar
cW/4D22D12
where c is crushing strength of the nutcompressive strength
c125/525Mpa Then we get D2 as follow 258583.75/4D22232 D2 31.083mm,sayD232mm
53
4.2.5 Thickness of the Nut Collar The thickness of nut collar t1 is found by considering shearing strength of the nut color
54
T1 W/D1
is shearing strength of nut
collar105/521Mpa
T18583.75/23 215.656mm,say t16mm
4.3 Designs for Head and Cup
4.3.1 Dimensions of Diameter of Head on Top of Screw and for the Cup D3 ASSUMING D31.75do1.7512mm21mm
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The seat for the cup is made equal to the diameter of the head and then chamfered at the top the cup prevents the load from rotating and is fitted with pine of diameter D4D3/4 D45.25mm,say D46mm
Section of pin Take length of pin to be 9mm. Other dimensions for the cup are t aken as: Diameter at the top of the cup = Diameter of the head = 52mm Height of cup = 9mm Thickness of cup = 3mm Fillet radii = 1mm
Figure 5.4: Section of Cup
4.3.2 Torque Required to Overcome Friction We know that by assuming uniform pressure condition torque required to overcome friction is given as follows;
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T2WD3D4D32D42 Where D3diameter of head21mm D4diameter of pin6mm T20.18583.750.0210.0060.02120.006263.90Nm
4.3.3 Total Torque Subjected to the Handle Total torque to which the handle is subjected is given by TT1T2 T7.496Nm63.90Nm71.396
Activity
Professional use
Domestic use
Pushing
200N (20.4kg)
119N (12.1kg)
Pulling
145N (14.8kg)
96N (9.8kg)
Table 4.2: Maximal Isometric Force by General European Working Population for Whole Body Work in a Standing Posture
Therefore taking the force of 96N in domestic use (J.J. Fereira, 2004) then the length of the
handle required is TFLLTF LT/F71.396Nm/96N0.7437m743.7mm, say 744mm The length of the handle may be fixed by giving some allowance for gripping 70mm Therefore, the length of the handle/lever is 814mm Section of Lever 4.3.4 Diameter of Handle/Lever The diameter of the handle/lever, D may be obtained bending effects
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M32cD Whilebtc700/5140Mpa MForce appliedlength of lever M96N0.7437m71.395Nm 71.395 32140106D D0.0173m17.3mm,say D18mm
4.3.5 Height of Head The height of head is usually taken as t wice the diameter of handle. H2D H218mm
36mm
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4.3.6 Design Check against Instability/Buckling Effective length of screw, = + 1/2 ℎℎ
=1+ℎ/2
Leff 20030/2215mm
When the screw reaches the maximum lift, it can be regarded as strut whose lower end is fixed and the load end is free. Therefore, buckling or critical load for this given condition is as follows (Gupta, 2005
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WcrAc.yy4cELeff k
Wcr13199.04N W8583.75N
4.4 Design of Body 4.4.1 Dimensions for the body of the screw The dimension of the body may be fixed and given as in shown in the figure above (Gupta, 2005)
1. Diameter of the Body at the Top D51.5D2 D51.532mm48mm 60
2. Thickness of the body 3.
t20.25do,
t20.2512mm3mm
3Inside Diameter at the Bottom D62.25D2 D62.253272mm 4. Outer Diameter at the Bottom D71.75D6 D71.7572mm126 5. Thickness of Base t32t1, t326mm12mm 6. Height of the Body Height of the bodymax liftheight of nutextra50mm
200mm30mm70mm300mm Finally, the body is tapered in order to achieve stability of the jack.
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4.5 Efficiency of the Screw Jack Efficiency of screw jack is given as follows:
torque required to rotate screw with no frictiontorque required out put ToT But
To Wtandm/2 To8583.750.057870.0112 To2.732Nm
And T71.396Nm
To/T2.732/71.3960.0383.8
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4.6 result and dissection
the results I find from my project are listed as follows to design individual parts of the screw jack 1 to design body(frame) 2 to design nut 3 to design handl (Tommy bar) 4 to designs the cup 5 to design set screw 6 to design washer 7 to design screw Dissection
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RESULTES OF NUMERICAL VALUE OF THE DESIGNE
Dc
10mm
LPIN
9mm
D5 =48mm
12mm
D head
52mm
t2 =3mm
30mm
H cup
9mm
D6 =72mm
23mm
tcup
3mm
D7 =126mm
32mm
Filit raduis
1mm
t3 =12mm
6mm
Lhandl
814mm
Hbody
21mm
Dhandl
18mm
6mm
H head
36mm
Do H D1 D2 =300mm
t1 D3 D4
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4.7 CONCULUTION From my project I am concluded that from introduction part to design analysis we are seen clearly its working principle of the screw j ack and operation of the screw j ack, efficiency of this designed screw jack, methods of increasing efficiency of the screw jack. A screw jack is an example of a power screw and referred to as a mechanical device that can increase the magnitude of an effort force. Screw jacks are used for raising and lowering platforms and they provide a high me chanical advantage in order to move moderately heavy and large weights with minimum effort. Based on my calculations and assumptions the designed values are safe.
4.8 Recommendation From the case study, I concentrated on design of a simple mechanical screw jack where the nuts fixed in a cast iron frame and remains stationary while the spindle is being rotated by the lever. This design can only work for light loads hence when a screw jack is needed for heavy load application different designs required where the nut is rotated as the spindles moves. I therefore recommend design of a screw jack for the heavy loads. I recommended that the workshops and AutoCAD rooms open in order to practice more.
66
)
.1 Appendix A: Mechanical Properties of Cast Iron (Nyangasi, 18 December, 2006)
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6.2 Appendix B: Mechanical Properties of Steels (Nyangasi, 18 December, 2006) Maximum Materials
British
Production
section
standards
process
size, mm
Yield
Tensile
Strength
Strength,
MPa
MPa
215
430
0.20C
070M20
HR
152
254
200
400
20
CD
13
385
530
12
76
340
430
14
125
0.30C
080M30
HR
152
Hardness Elongation %
22
number, HB 126 – 179
116 – 170
245
154
490
20
143 – 192
134 –
254
230
460
19
CD
13
470
600
10
63
385
530
12
154
H&T
63
385
550 - 700
13
0.40C
080M40
HR
150
183
280
174
152 – 207 550
16
152 – 207
CD
63
430
570
10
H&T
63
385
625 - 775
16
165 179 – 229
0.50C
080M50
HR
150
310
620
14
179 – 229
68
CD
63
510
650
10
H&T
150
430
625 – 775
11
202 – 255 248 – 302
1Cr
530M40
H&T
100
29
680
850 - 1000
13
525
700 – 850
17
202 – 255
248 – 302
1.5MnMo
29
605M36
755
H&T
925 - 1075
150
12
525
700 – 850
17
202 – 255
269 – 331
1.25NiCr
640M40
H&T
152
102
585
770 – 930
15
525
700 – 850
17
202 – 255
223 – 277
64
680
850 - 1000
13
248 – 302
29
755
930 - 1080
12
3NiCr
653M31
H&T
64
269 – 331 755
930 1080
12
269 – 331
248 – -
680
850 – 000
12
302
Key: HR - Hot- Hot rolled and normalized
CD - Cold drawn H&T - Hardened and tempered 69
Appendix C: Safe Bearing Pressure for Power Screws (Gupta, 2005)
Type of power screw
Material
screw Hand press
Safe bearing
Rubbing speed
pressure,MPa
m/s
Nut Steel
Bronze
17.0-24.1
Low speed ,well lubricated
Screw jack
Steel
Cast Iron
12.0-17.0
Low speed < 2.5
Screw jack
Steel
Bronze
11.0-17.0
Low speed < 3
Hoisting screw
Steel
Cast Iron
4.0-7.0
Medium speed (6-12)
Hoisting screw
Steel
Bronze
5.5-10.0
Medium speed (6-12)
70
71
72
References 1. Ashby, M. F., 2005. Material Selection in Mechanical Design. 3rd ed. New York: Pergamon Press
. 2. Bhandari, V. B., 2010. Design of Machine Elements. Third Edition ed. New Delhi: Tata McGraw-
Hill Education. 3. Collection, J., 2015. hubpages.com › Autos › Automobile History. [Online] Available at:
https://www.history of screw jacks.com [Accessed 11 November 2015]. 4. Fasteners, C. o., 2005. Technical Reference Guide. Ninth Edition ed. Winona, Minnesota: Fastenal
Industrial & Construction Supplies. 5. Gupta, R. K. &. J., 2005. Theory of Machines. Revised Edition ed. Punjab, India: S. Chand and
Company
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“IF MECHANICAL AT REST WORLED BECOMS RUST”
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“MECHANICAL ENGINERING DEPARTMENT IS THE POWER OF THE WORLED” “ THE WORLED IS NULL WITH OUT MECHANICAL
ENGINEER”
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