FEA of Single Spring Mass System Using ANSYS 5.4

FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER \u2013 I

AIM OF PROJECT

Today's industries growing as a dynamics sector aheading with the competitive environment. Industries are emphasizes under recent concepts such as TQM, preplanning because of less time huge competition and will to establish as a better one. Machine should be stand in much overloading condition so it must be supreme in design. Spring is the elastic bodies are displaced from the equilibrium position by the application of the external forces and thus released they execute a vibratory motions. Intimacy in the irrelevant vibration motion with the machine element creates the problem although their should be breakage in the machines element. Hence analysis in the spring part is very important. This constraint component must be analised for better performance of the machines. FEM is the sophisticated tool which is the very helpful in the comparative result making. For the so many method of FEM today's software is the very systematic and gives earliest way for result making with reduction in the complicated calculation. Hence readily available software such as ANSYS and PROE gives a readymade result in that work.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER \u2013 II

INTRODUCTION Vibration :- When elastic bodies such as spring, a beam and a shaft are displace from its

equilibrium position by the application of external forces and then release they execute a vibratory motion. Generally three types of vibration found in machinery some times these may be free or natural vibration ( i.e. Due to its own weight ) or may be force vibration. 1. Longitudinal Vibration 2. Transverse vibration 3. Torsional vibration To avoid failure of machine component in working condition due to vibration we can analyese the vibration in machine component at design stages. And if necessary we can improve the design giving strength to the machine component to reduce the vibration. Types of Analysis :-

Structural Analysis :- Structural analysis probably the most common application of the finite element method. The term structural implies not only civil engineering structures such as bridges and building, but also, aeronautical and mechanical structure such as ship hulls, air craft bodies and machine housings, as well as mechanical components such as pistons, machine parts and tools. Types of Structural Analysis :

a) Stastic Analysis b) Modal Analysis c) Harmonic Analysis C.O.E. & T., Akola

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FEA of Single Spring Mass System Using ANSYS 5.4

d) Transient Dynamics Analysis e) Spectrum Analysis f) Buckling Analysis g) Explicit Dynamics Analysis. Following are some types of Analysis other than structural analysis which comes under F.E.A. \ u e 0 0 0

Thermal Analysis

\ u e 0 0 0

Magnetic field Analysis

\ u e 0 0 0

Fluid Analysis

FOR CALCULATION OF FREQUENCY WE USED MODAL ANALYSIS.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER – III

ROLE OF VIBRATION When the elastic bodies such as spring, a beam and a shaft are displace from its equilibrium position by the application of external forces and then release they execute a vibratory motion. This is due to the reason that when a body displaced, the internal forces in the form of elastic or strain energy are present in the body. At release these forces bring the body to its original position. When the body reaches the equilibrium position, the whole of the elastic or strain energy is converted in to kinetic energy due to which the body continues to move in the opposite direction. The whole of the kinetic energy is again converted in to strain energy due to which the body again returns to the equilibrium position. In this way the vibratory motion is repeated indefinitely. Definition related with vibratory motion :

Free or Natural Vibration :- When no external force act on the body, after giving it an initial displacement, then the body is said to be under free or natural vibration and frequency is free or natural frequency. Force Vibration :- When the body vibrates under the influence of external force, then the body is said to be under forced vibration. The external force applied to the body is a periodic disturbing force created by unbalance. The vibrations have the same frequency as the applied force. Machines are mainly composed of two parts viz. stationary parts and moving parts. ( i.e. transverse movements or rotary movements )

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In moving parts some times vibrations are necessary. The parts where forces and stresses are developed in such cases vibrations are necessary to relieves that stresses e.g. shock up of two wheelers, suspension systems in four wheelers. In short the components of elements which acts like springs, vibrations are necessary whereas the rigid parts or stationary parts should be avoided from vibrations e.g. bed base of lathe machine, gig and fixtures. When no external force act on body, after giving it an initial displacement. Then the body is said to be under free or natural vibration and the frequency is free or natural frequency. And when the frequency of external force is same as that of natural frequency, resonance takes place. Necessary to calculate natural frequency.

Suppose a propeller shaft transferring the rotary motion ( in four wheelers) then it will have its own natural frequency. When engine supply power to rotate the shaft, it causes rotary motion due to external sources of energy. Due to the forced vibrations, force frequency is generated within shaft. This frequency should not match with natural frequency of shaft. If it matches then resonance phenomenon takes places due to which the shaft may bend. So it is necessary to determine natural frequency of shaft at design stage. Another Example :- In two wheelers there are shock absorber which are vibrates with its own frequency, when vehicle is in running condition.

Due to road irregularities in

vehicles forced vibration is created which act on shock up, the frequency of forced vibration is matched with natural frequency of spring a resonance phenomenon will occur C.O.E. & T., Akola

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and the spring may get break, so here it is important to determined the natural frequency of shock up (Spring). Types of Vibrations.

1. Longitudinal Vibration :- When the particles of the shaft or mass move parallel to the axis of the shaft or spring then vibration are known as longitudinal vibration. 2. Transverse Vibration :- When the particles of the shaft or disk move approximately perpendicular to the axis of the shaft or spring element, then the vibration are known as transverse vibration. 3. Torsional vibration :- When the particles of the spring element move in circle about the axis of the shaft, then the vibration are known as torsional vibration. Vibration of tuning :-

The terms tune relates with any part with which it says its intimacy. Machine build with the different component, one component related to other component in various form such as constraint motion, vibration motion, kinetic energy, potential energy etc. Spring part and their motion is consumed for shock absorbing spring energy and releasing energy. There determined or undetermined frequencies and machine vibration which is an external unbalance force if tune with each other, there is perfect possibilities of breaking either spring on damages in the machine parts. Hence care should be taken on not to match their frequency with machine vibrations. This concept of vibration of tuning in modern long bridge engineering is avoided by specifying the speed limit of car by traveling on the bridge as it coupled with a spring trust.

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Manual Technique to calculate Natural frequency. (fn.)

First we should have to familiar with the term time period, natural frequency. Time period : It is the time interval after which the motion is repeated itself. The period of vibration is usually expressed in seconds. It is denoted by Tr. Frequency :- It is the no. of cycles expressed in one second. In SI unit it is expressed in Hertz (Hz). Natural Frequency :- The frequency of free or natural vibration is called natural frequency. It is denoted by fn. 1) Natural frequency of free longitudinal vibration.

There are three method to calculate natural frequency of free longitudinal vibrations. a) Equilibrium Method. By this method. Time period tp =π2

m s

m = mass of body. s = stiftness of constraint

1 Natural frequency fn = 2π

g s

Where, g = acceleration due to gravity. S = static deflection of spring due to weight W. We can also calculate the tp and fn by using same formula given above by using energy method and Raybeigh's method instead of equilibrium method.

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II) Natural frequency of free transverse vibration.

Now to calculate the natural frequency of free transverse vibration, the same procedure as per free longitudinal vibration. III) Natural frequency of free Torsional Vibration :-

To calculate the time period and natural frequency, we use following formula in manual method. π2 a) Time period tp =

J q

Where, J – Mass moment inertia of disk = w/g Q = Torsional stiffness of the shaft. 1 q b) Natural frequency fn = 2π J where, q=

CJ l

C – modulas of rigidity j - Polar modulus of inertia l - length of shaft.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER – IV

ISSUE OF ANALYSIS Conventional analytical methods for solving stresses and strain become very complex and almost impossible when the part geometry is intricate as such cases finite element modeling (F.E.M.) becomes a very convenient means to carry out the analysis. The finite element analysis ( F.E.M.) is a very powerful analysis tool which can be applied to a range of engineering problems. The finite element modeling ( F.E.M.) process allows for discrediting the intricate geometries in to small fundamental volumes called finite elements it is then possible to write the governing equations and material properties for these element. These equations are then assembled by taking proper care of the constraints and loading which results in a set of equations. These equations when solved gives the results that describe the behavior of the original complex body being analyzed. A large amount of commercial as well as free software for the application of finite element is available. computes is needed.

Generally to solve complex problem a very powerful

However with the developments in Pentium processors, it is

possible to carryout such analysis in most of the present day desk-top computers with the FEM soft ware it is possible to try a number of alternative designs before actually going to a prototype manufacture. After analyzing the design we will get some results, which will be get in working conditions, so on the basis of these result we can modify the design to make it optimum. Modal Analysis.

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We use modal analysis to determine the vibration characteristics ( i.e. natural frequency and mode shapes ) of structure or a machine component while it is being designed. It can also a starting point for another more detailed dynamic analysis such as transient dynamic analysis, a harmonic response analysis or a spectrum analysis. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions. They are also required if we want to do a spectrum analysis or a mode super position harmonic or transient analysis. We can do model analysis on a pretressed structure such as a spinning turbine blade. Another useful feature is modal cyclic symmetry, which allows to review the mode shapes of a cyclic symmetric structure by modeling fact a sector of it.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER – V

MODAL ANALYSIS Main aim of modal analysis to determine the natural frequency and mode of modal analysis. We can find the natural frequency by analytical method by using equations and formula developer by considering theoretical and practical aspect, by study behavior of machine under working condition. We improved this analytical method by ANSYS software. Steps in Modal Analysis Procedure for a Modal Analysis consist of four main steps – 1. Build the model 2. Apply loads and obtain the solution 3. Expand the modes 4. Review the results. 1) Build the model :-

In this step, specify the job name and analysis title and then define the element type, element real constants, material property and model geometry. Before the model developed following points are important. 1. Only linear behavior is valid in a Modal Analysis, if we use specify non-linear elements, they are treated as linear. 2. Material property can be linear, isotropic or orthotropic and constant or temperature dependent.

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2. Apply loads and obtain the solution.

After the building the model, the next process is to apply load. This load are as per design constraint. In this step, we use the solution processor to define the analysis type and analysis option, apply load, specify load step, option and initiate the finite element solution. The word loads, as used in this manual includes boundary conditions as well as other externally and internally applied loads. The most of these loads either on solid model or finite element model. Another term in load applied are load step and set up. A load step is simply a configuration of loads for which you obtain a solution. After applying load obtained a solution by using ANSYS software. 3. Expand Modes.

Expand means reduced solution is usually termed as Degree of freedom. The term expansion to mean writing a model shaped to results files, expanding the model applies not just to reduced mode shapes from the reduced mode shaped from the reduced mode extraction method, but to full mode shape from the other mode extraction method as well. Thus, if we want to review mode shape in post processor, we must expand them. 4. Review the Results :-

Once the solutions has been calculated, use the ANSYS postprocessor. The general postprocessor, to review the result at one sub step over the entire model or selected portion of model. By obtains contour displace, deformed shape and tabular listing to review and interpret the result of analysis, it also include error estimation, load case combination, calculation among result data and path operation.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER – VI

FINITE ELEMENT METHOD Introduction :

In the field of Engineering Design we come across many complex problems, the Mathematical Formulation of which is tedious and usually not possible by analytical methods. At such instants we resort to the use of Numerical techniques. Here lies the importance of FEM, which is a very powerful tool for getting the Numerical solution of a wide range of Engineering problems. The basic concept is that a body or structure may be divided in to smaller elements of finite dimensions called as “Finite Elements”. The original body or structure is then considered as an assemblage of these elements connected at a finite number of joints called as “Nodes” or “Nodal Points”.

The

properties of the elements are formulated and combined top obtain the properties of the entire body. The equations of equilibrium for the entire structure or body are then obtained by combining the equilibrium equation of each element such that the continuity is ensured at each node. The necessary boundary conditions are then imposed and the equations of equilibrium are the solved to obtain the required variables such as Stress, Strain, Temperature Distribution or Velocity Flow depending on the application. Thus instead of solving the problem for the entire structure or body in one operation, in the method attention is mainly devoted to the formulation of properties of the constituent elements. A common procedure is adopted for combining the elements,

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solution of equations and evaluation of the required variables in all fields. Thus the modular structure of the method is well exploited in various disciplines of Engineering. History :

Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems. Shortly in 1956 Turner introduced, the first treatment of two-dimensional elements. They derived stiffness matrices for truss elements, beam elements and two-dimensional triangular and rectangular elements in plane stress and outlined the procedure commonly known as the direct stiffness method for obtaining the total structure stiffness matrix. Along with the development of high-speed digital computer in the early 1950s, the work of turner prompted further development of finite element stiffness equations expressed in matrix notation. By the early 70’s, FEA was limited to expensive mainframe computers generally owned by the aeronautics, automotive, defense, and nuclear industries, and the scope of analyses were considerably limited. Finite Element technology was further enhanced during the 70’s by such people as Zeinkiewicz & Cheung, when they applied the technology to general problems described by Laplace & Poisson’s equations. Mathematicians were developing better solution algorithms, the Galerkin, Ritz & Rayleigh-Ritz methods emerged as the optimum solutions for certain categories of general type problems. Later, considerable research was carried out into the modeling & solution of non linear problems, Hinton & Crisfield being major contributors.

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Stepwise Approach for FEM and underlying principle :

The most fundamental underlying concept of finite element method (FEM), or finite element analysis (FEA), is the piecewise approximation of solution of a known geometry for which the characteristics are well established. Thus, the first requirement of FEM approach is descritization of the physical domain for which appropriate type of element is required to be selected. 1) Domain Descritization for a field problem :

This is also referred to as finite mesh generation step.

Here the domain of

problem addressed is divided into a number of geometrically simple subdomains termed as finite elements with certain nodal points being associated with each element. In the process, data concerning nodal coordinates, node numbers, element numbers, and connectivity is generated. Following figure provides examples of elements employed in one, two and three dimensions. FEM Classification

Various element geometries

1D element or 2D element or Area element

Triangular

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Rectangular

3 D element Line element or volume element

Tetrahedron

Hexahedron

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3 noded triangle

4 noded tetrahedron

6 noded triangle

10 noded tetrahedron

4 noded quadrilateral

8 noded brick

8 noded quadrilateral

20 noded brick

Figure : FEM – Element classification 2) Discretization of problem :

Element equations : The next step is to develop equations to approximate the solutions for each element. This involves two steps. First, we choose an appropriate function with unknown coefficients that will used to approximate the solution. Second, evaluating the coefficients so that the function approximates the solution in an optimal fashion. 3) Optimal fit :

The element equation is an approximate solution.

In this step the attempt to

minimize the error of fitting the solution over the element domain is made using celebrated methods like direct approach method, the method of weighted residuals, and the variational approach. 4) Assembly to obtain global system of equations from element equations : After the individual element equations are derived, they must be linked together or assembled to characterize the unified behavior of the entire system. The assembly process is governed by the concept of continuity. That is, the solutions for contiguous C.O.E. & T., Akola

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elements are matched so that the unknown values at their common nodes are equivalent. Thus, the total solution will be continuous. 5) Boundary Conditions : The nodes on the boundary of domain subjected to known conditions are considered to take effect in assembled set of equations. 6) Solution :

Now the number of unknowns in the equations’ set is equal to number of equations, which could be solved using Gaussian elimination equation or other suitable algorithm. 7) Post processing :

Upon obtaining a solution, it can be output in tabular form or displayed graphically.

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FEA of Single Spring Mass System Using ANSYS 5.4 CHAPTER – VII

FEA OF SPRING MASS SYSTEM ANSYS finite element analysis software enables engineers to perform the following tasks.

Build computer models or transfer ( AD models of structure, product, componen or system.

Apply operating loads or other design performance condition. Study physical response, such as stress level, temperature distribution or impact of electromagnetic field.

Optimize a design in the development process to reduce production cost. An ANSYS program has a comprehensive graphical user interface (GUI) that gives uses easy, interactive access to program function, commands, documentation and reference material. An intuitive menu system helps uses navigate through the ANSYS program. Users can input data using a mouse, a keyboard, or a combination of both. ANSYS 5.4 FOR FEA :

ANSYS is a general purpose finite element modeling package for numerically solving a wide variety of mechanical problems. These problems include : static/dynamic structural analysis ( both linear and non-linear ), heat transfer and fluid problems, as well as acoustic and electro-magnetic problems. Summary of steps :

1. Preprocessing : defining the problem :

The major steps in prepossessing are given below :

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Define job name db. Specify the title and set up the structural preferences. Define the keypoints/lines/areas/volumes. Define element type, options and material/geometric properties. Mesh lines/areas/volumes as required. The amount of detail required will depends on the dimensionality of the analysis ( i.e. 1D, 2D, axi-symmetric, 3D).

Save the database. 2) Solution : assigning loads, constraints and solving :

Apply Loads : Here we specify the loads ( point or pressure )

Apply constraints : Here we specify the constraints ( translational and rotational ).

Obtain Solution : And finally solve the resulting set of equations. 3) Post processing : Further processing and viewing of the results :

In this stage one may wish to sec :

Review Results Enter the general postprocessor and read in the results. Plot the deformed shape Lists of nodal displacement Element forces and moments C.O.E. & T., Akola

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Deflection plots Stress contour diagrams Animations for stress plots and deflection plots. List the reaction solution Exit the ANSYS program.

Diagram of Spring Mass System :

Test Case :

An instrument of weight W is set on a rubber mount system having a stiffness K. Determine its natural frequency of vibration f. Material Properties

Loading

K = 48 lb/in

g = 386 in/sec2

W = 2.5 lb Y

2

k

1

MDOF

w

2

1

x Problem model

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The procedure for determining the natural frequency of spring mass system by ANSYS 5.4 software is discuss below. ANSYS software have provision for modeling of simple geometrical parts. By using the commands given in preprocessor we have prepared a model of spring mass system. Before applying load firstly we have define the material properties. The part (1) in diagram have given the properties of spring and part (2) has given the properties of mass. In this problem no external force is applied. The vibration creates in spring is due to the weight of mass. With the help of solve option we have given solving command. The ANSYS software selfly solve the problem and find out the solution. Lastly by postprocessor we can review the result by giving different commands. The software have provision to show the behavior of spring under working condition by simulation. Finally, we found the natural frequency of spring mass system is 13.701 Hz.

Result of ANSYS

The results obtained by post processor are displaced on screen of computer. ANSYS have ability to show the result in various ways.

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Figure 1

The representation of this diagram involves nine colours. This is a steady diagram. In this spring is divided into a nodes ( parts ) on each part the natural frequency obtained is different. It increases from bottom to top. On bottom part the frequency is lowest and on top part the frequency is highest. In this way ANSYS software shows the behavior of each part ( i.e. frequency at node ) under applied load. Figure 2

This is a simulation type representation of spring mass system. In this fig. The behaviour of spring from bottom to top under applied load is shown by different colour i.e. in working conditions the colour changes. From this we can predict the behaviour of spring under working condition. Figure 3

This representation separate each nodes from other by using two colours. At bottom the colour of node is white then the next node is blue in colour as so on. Alternately vary and at the end the top node colour is white. The extension of spring due to load is shown by simulation in blue colour. Figure 4

This is a simple representation in a only single blue colour showing only the elongation of spring under applied forces. In this spring mass system the force or load applied is the of weight of mass attached to spring at the top most position. C.O.E. & T., Akola

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Manual Process Results :

Problem : An instrument of weight 2.5 lb is set on a rubber mount system having a stiffness 48 lb/in. Determine its natural frequency of vibration. Data :-

Stiffness – K = 98 lb/in

Weight - W = 2.5 lb - g = 386 in/sec2

Load

Solution :- Natural frequency fn =

1 tp

Where, tp – time period

tp = 2π

∴

fn =

=

1

K

2π

M

1

Kg

2π

w

M=

M K

w g

w = kS

⇒

⇒

1

M

S=

f

= W K

=

w

2.5 4.8

S = 0.05208 =

1

K .g

2π

K .S

1

=

2π

g

δ

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=

1

386

2π

0.05208

fn = 13.701 Hz Comparision of ANSYS result with Analytical Method.

Although there is a various methods in the FEA analyze is "ANSYS Software" is very implemented solution to it. In this analysis stepping goes through model design, dividing it into nodes ( or parts ) applying mathematical calculation by providing varieties up to breakage condition and obtain a optimum design. As the various critical calculation, considering a variable parameter at a time is done by it in fraction of time hence it is superior than any other method. There comparision are as follows. i) In ANSYS, frequency at each node on spring mass system is calculated but in analytical method we can calculate natural frequency, but it will gives result at only a single node ( i.e. at the end point ) hence calculation at intermediate node is not there. ii) In ANSYS accuracy is more than analytical method with fast processing. iii) In ANSYS actual simulation is seen with a various colours. iv) Analytical method required large time durations for mathematical data collection, but ANSYS made by feeding data in memory, various formula by expert of FEA, hence its valuable as a in build software. v) Also the ANSYS software is self guide, self evaluation system technique as it direct evaluate and verify result. These facility is not there in any other system.

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In our spring mass analysis Natural frequency obtained is 13.701 Hz which match with a frequency obtain by analytical method.

CHAPTER – VIII

SUGGESTION FOR IMPROVEMENT In large profit earning, modern automatic industries, machines, implemented with a FEA method as a in built software. The modern design software C A D, and PRO-E engineering which practices in a design engineering for long duration of time.

ANSYS is a recent FEA method for

Analysis in which analysis is a core thing. i) Exchange of Data between software terminals is preferred so that model in any software must be exchange with ANSYS and analysis should be carried out frequently. ii) In ANSYS, model creation is complicated so as it occupied large space of memory in analysis work, it should also made used friendly with this criteria. iii) Text writing command is difficult to understand, it should be made easy. iv) If we made spring mass system in combination with different component such as joints, rivets, etc. while analysis it takes as a line diagram and analysis with a line diagram only. It would be along with line diagram it also analysis with actual model so that it is easily understandable. v) If any model is analysis independently we known the limitation of design. If we want assembled it for application purpose it does not give the geometrical guide line for perfect fits. C.O.E. & T., Akola

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vi) Now a days ANSYS is available with license copy. It is very costly and not easily available. It should be made easily available and economical for purchase.

CHAPTER – IX

CONCLUSION Determination of natural frequency is important for knowing the resonance phenomenon which occur when the force vibration comes in context with the natural frequency. By performing model analysis of spring mass system, we will create a solid design of any machine component assembled with a spring as an element. There is natural frequency related to each past which is very important to calculate. In this way, natural frequency and forced vibration frequency will match the resonance phenomenon occur and it will cause vibration with maximum amplitude which is undesirable and cause a failure of component in machine so avoiding the matching of both frequency with each other. In this way we optimized the design in the development process to reduce the production cost for a particular product, calculating the natural frequency with ANSYS software by breaking the object in the parts as one of the FEA method, ANSYS gives various methods in which modal analysis works on model, breaking them in to parts and obtained the result by providing variable to it. In addition to this, analytical method also gives the same result as in ANSYS software.

Thus by we will safe our design in various loading conditions, avoiding

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machine breakage, minimize the machine failure and making the design as a resistance proof in any circumstances.

BIBLIOGRAPHY 1.

CAD/CAM

by P.N. Rao.

2.

Theory of Machine

by R.S. Khurmi by Balaney

3.

modalanalysis.com

4.

www.google.com

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INDEX

Sr. No. 1 2 3 4 5 6 7 8 9

C.O.E. & T., Akola

Particulars

Aim of Project Introduction Role of Vibration Issue of Analysis Modal Analysis Finite Element Method FEA of Spring Mass System Suggestion for Improvement Conclusion Bibliography

Page No. 1 2 4 9 11 13 18 29 30 31

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FEA of Single Spring Mass System Using ANSYS 5.4

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