RIGID DYNAMICS ANALYSIS OF FOUR BAR MECHANISM IN ANSYS AND C ++ PROGRAMME

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1 International Journal of Mechanical and Production Engineering esearch and Development (IJMPED ) ISSN Vol.2, Issue 2 June 22-9 TJPC Pvt. Ltd., IGID DYNAMICS ANALYSIS OF FOU BA MECHANISM IN ANSYS AND C ++ POGAMME MANISH MEHTA P M GEOGE 2 esearch Scholar, SICAT, Vallabh Vidyanagar, Gujarat, India. 2 HOD, Mech. Engg, BVM (Engineering College), Vallabh Vidyanagar, India. ABSTACT In the present paper, a systematic approach is mention for dynamic force analysis of four bar linkage by considering rigid link. Of course, methods use for dynamic force analysis are important, not only because they introduce concepts and approaches that can be built upon and extended to none equilibrium situations. Program was developing for position analysis and force analysis of four bar mechanism in C language. Also result developed from this programme was compared with rigid dynamic analysis done in ANSYS Workbench for same linkage. KEY WODS: igid dynamics, ANSYS WB, Pin joint forces INTODUCTION Encyclopedia Britannica (98) defines kinematics as: Branch of physics and subdivision of classical mechanics, concerns the description of moton of objects without considering the forces that cause or result from the motion. It is an abstract study of motion that aims to provide a description of the spatial position of points in moving (velocity), and the rate at which their velocity is changing (acceleration). When the causative forces are disregarded, motion descriptions are possible only for points having constrained motion; i.e., moving on determine paths. In unconstrained or free motion the forces determine the shape of the main path. The study of mechanical systems has two distinct aspects: synthesis and analysis. The synthesis involves the prescription of sizes, shapes, materials, etc. so that the mechanism performs the functions for which it was designed. The analysis is the collection of scientific tools at the designer s disposal to analyze the suitability of the design. In this paper, the analysis of a four-bar mechanism is undertaken. The geometrical data of the mechanisre assumed to be known a priori. In the analysis and design of mechanisms, kinematic quantities such as velocities and accelerations are of great engineering importance. Velocities and displacements give an insight into the functional behavior of the mechanism. The accelerations, on the other hand, are related to forces by Newton s principle which themselves are related to stresses and deformations in the mechanism s components. In the kinematic analysis, the mechanism is assumed to be made up of rigid bodies.

2 Manish Mehta & P M George 2 Actually the machine member is moving and the applied forces are not always constant for different configurations of the machine, as in case of four bar mechanisms. However, these forces can be considered as constant forces acting on the respective links for a particular configuration. The force analysis is carried out with external forces acting on the machine members. However, since the machine members are dynamic, the additional forces due to their motion are to be taken into account. According to Newton s second law of motion if a body has linear or angular acceleration, there must be a force or couple acting on the body to cause the corresponding acceleration. In other words, the machine which drives its several members having a cyclic variation of acceleration required to supply more power than required for its purpose, the inertia forces become more prominent for higher speed of machine members. A combination of static and inertia force analysis leads to an important aspect of the estimation of the load carried by different links and pin joints force of the mechanism. For example, if a complete force analysis of a four bar mechanism is carried out in, 2 or degree intervals of the crank link in 6 rotation, important data, such as complete history of loading on the all the pin joints force can be obtained for design purposes. Further, such an analysis leads to an understanding of the actual type of input require for drive the mechanism. Fig. : The linkage and dimensions [2] The problem formulation given here for the mechanism in Fig., is based on the assumptions, that all parts of the mechanisre rigid and mechanism in a state of dynamic equilibrium. Specify the length of all the links and check for Groshof condition. Also specify the angular velocity and acceleration of actuator. Calculate the position of coupler and output link with respect to position of actuator. Once the position analysis is over next step is to calculate the acceleration of all links at CG of each link and angles. Force act at all pin joints as shown in Fig. 2. D Alembert s principle is used for force analysis

3 igid Dynamics Analysis of Four Bar Mechanism in ANSYS and C ++ Programme and torque. Write three equations for each moving link. It means total number of equation for the mechanism is nine and unknown parameters are also nine. These nine equations write in form of matrix and solve matrix for calculating the unknown parameters. METHODOLOGY Procedures for kinematic and dynamic analysis of a four bar mechanisre as follow. The angular velocities w and w of the coupler and rocker are obtained by eqn. and 2 are given below: w w aw2 sin( θ θ 2 ) =...() b sin( θ θ ) aw2 sin( θ 2 θ) = c sin( θ θ ).( 2) Fig. 2 : Free-body diagrams with notations [2] By differentiation of eqn. & 2 with respect to time, the angular accelerations α and α of the coupler and rocker respectively and given by eqn. & as follows: CD α = AF CE α = AE AF...() BD BF...() CD Where, A = c sin θ B = b sin θ

4 Manish Mehta & P M George C = a α2 sin θ2 + a w22 cos θ2 + b w2 cos θ - c w2 cos θ D = c cos θ F = a α2 cos θ2 - a w22 sin θ2 - b w2 sin θ + c w2 sin θ The angular accelerations of all the links are found than calculate the acceleration of any point on any link for any input position of the linkage by following eqn. The acceleration of point S on crank is As = S α2[-sin (θ2 + δ2)+j cos (θ2 + δ2)]-sw22[cos (θ2 + δ2)+j sin (θ2 + δ2)] The acceleration of point u on rocker or output link is Au = u α [-sin (θ + δ)+j cos (θ + δ)]-uw2 [cos (θ + δ)+j sin (θ + δ)] The acceleration of point p on coupler is Ap = AA + APA Where, AA = aα2 (-sin θ2+j cos θ2) aw22 ( cos θ2 +j sin θ2) Ap = p α [-sin (θ + δ)+j cos (θ + δ)]- pw2[ cos (θ + δ)+j sin (θ + δ)] Fig. : Free-body diagrams [2]

5 5 igid Dynamics Analysis of Four Bar Mechanism in ANSYS and C ++ Programme 2Y 2 X 2Y 2Y 2 X 2X Y Y X X Y X F F F F F F F F T 2 X 2Y 2 X 2Y X Y X Y 2 = I G α Gx G y I I G 2 G2x 2 G2 y G2 Px F F F Gx α Gx α T 2 Py Px Py + Py F Px DESIGN POBLEM A specification of four bar linkage for analysis is as follows: Parameters Fixed link () Crank (2) Coupler () Follower () Length (mm) C/S Area (mm2) - 8 Area moment of Inertia (mm) Modulus of Elasticity, E = 7. x MPa Density = 277 kg/m Crank speed = 2. rad/sec ESULTS AND CONCLUSIONS Program is run for given mechanism s parameter and calculates the angular velocity, angular acceleration of coupler link and output link and pin joints forces at different position of crank for one revolution. esult of the program or analysis of the mechanism saves in separate output file. Prepare a graph of angular velocity, angular acceleration of coupler link and pin joints forces versus time using output file generated by programme and M.S.Excel. Those graphs are representing in Fig. to Fig. 6. Same analysis has done in ANSYS Workbench software and results are plotted. esults of ANSYS are representing in Fig. 7 to Fig. 9. From both method results are same for angular velocity, angular acceleration of coupler link and output link. Some difference found in the result of pin joints force. Pattern of graph for pin joints are same. To create a model in ANSYS, at the ends of link eyes are required and due to this reason mass of links in ANSYS is more than mass calculate by density volume in C progamme.

6 Manish Mehta & P M George 6 Fig. Fig. 5 Fig. 6

7 7 igid Dynamics Analysis of Four Bar Mechanism in ANSYS and C ++ Programme Fig. 7 Fig. 8

8 Manish Mehta & P M George 8 Fig. 9 FUTUE SCOPE OF STUDY Fig. The present study is carried out by assuming links of mechanisre rigid. The links of mechanism can also be considered as a elastic for force analysis or stresses produce in links of mechanism.

9 9 igid Dynamics Analysis of Four Bar Mechanism in ANSYS and C ++ Programme EFEENCES For Book :. G.N.Sandor and A.G.Erdman; Advanced Mechanism Design;Vol.2, Prentice-Hall Inc. 2..L.Norton; Design of Machinery, McGraw-Hill International Editions.. Kreisig: Advanced Engineering Mathematics, PHI. Vicker J.J.,Pennock G.. and Shigley J.E.; Machines & Mechanism, Oxford University Press 5. David H. Myszka; Machines & Mechanism, Pearson Education Asia 6. E. Balaguruswami; Programming in ANSI C,Tata McGraw-Hill Publishing Company Limited. 7. Article in a Journal: 8. A.G.Erdman and G.N. Sandor; Kineto-Elastodynamics A review of the state of the art and trends, Mechanism & Machine Theory, Vol A. Midha, A.G.Erdman and D.A.Frohrlb; Finite element approach to mathematics modeling of highspeed Elastic linkages, Mechanism & Machine Theory, Vol... I.Imand G.N. Sandor; A general method of kineto-elastodynamic Design of High-speed Mechanisms, Mechanism & Machine Theory, Vol. 8.. Manish Mehta and Dr Anurag Verma, A study of physical parameter of links on pin joints forces in four bar linkage. National conference on Emerging trends in Mechanical Engineering (ETME 2) during 5th- 6th March 2, organized by G H Patel college of Engineering & Technology, V V Nagar 2. Manish Mehta and Dr Anurag Verma, Effect of physical parameters of actuator and coupler links on torque requirement of an actuator in four bar linkage. Journal of engineering & Technology, S P University, Vol. 22, December 29.