Week 7-Long Piston With Cam

OBJECTIVE

To perform a transient analysis on a piston and cam mechanism for the following three cases:

1. Contact between Cam & follower is Frictionless.
2. Contact between Cam & follower is Frictional with coefficient of friction of 0.1.
3. Contact between Cam & follower is Frictional with coefficient of friction of 0.2.

From the simulation results, find out the Equivalent Stress, Directional Deformation and Equivalent Elastic Strain and compare them for all the three cases. Also, give an inference as to why the results vary between cases.

INTRODUCTION

Transient Analysis: It is technique used to determine the response of a structure under the action of loads which are dependent on the time. It is also known as time-history analysis. This type of analysis is used to determine the time-varying displacements, strains, stresses, and forces in a structure as it responds to any transient loads. Here inertial or damping effects are important consideration.

In the following Simulation, motion of barrel cam and follower is analysed for transient loads. Geometry consisting of a barrel, follower and cam is pre-processed. Here Rotation, which is given as boundary condition to cam, is acting as transient load. It constrains the follower to follow in the grooved portion and hence cause it to oscillate in the barrel. This whole motion is simulated in following analysis for three different cases in which the frictional nature of the contacting surfaces is changed.

1. Frictionless contact
2. Frictional contact with 0.1 as coefficient of friction
3. Frictional contact with 0.2 as coefficient of friction

From the simulation, time dependent structural responses (i.e. displacements, strains, stresses) are noted. Here follower is considered as the point of interest and results are presented for the following in the report.

ANALYSIS PROCEDURE

1. Material Selection

Structural Steel is assigned to all the components in the geometry.

Properties of Structural Steel

2. Geometry

Geometry consisting of a barrel, cam and follower is directly imported in the workbench from the available sources.

Fig. Geometry

3. Meshing

Components are meshed with program-controlled mesh with mesh element size of 6 mm. However regions of particular interest i.e. contacting surfaces between follower and cam is meshed using face sizing with mesh element size of 2 mm.

Statistics

Total No. of Nodes: 6402

Total No. of Elements: 2626

Avg. Element Quality: 0.9123

Fig. Meshed Geometry

4. Setup

• Stiffness Behaviour

Since our point of interest is on follower, therefore in order to simply the model Rigid Stiffness behaviour is imposed on Cam and Barrel bodies. This will simplify our model by concentrating the body mass about its centroid.

• Contacts

1. In the first case, Frictionless contact is established between all the contacting interfaces.
2. For the second case, Frictional contact is established with 0.1 as coefficient of friction.
3. In third case same frictional contact is established but value of coefficient of friction is changed to 0.2.

Fig. Frictionless contact between Barrel & Cam follower

Fig. Frictionless contact between Cam Follower & Cylindrical Cam

Similarly, frictional contact is established between the contacting interfaces for different values of coefficient of friction.

• Joints

1. Revolute Joint is assigned to the cylindrical cam relative to ground hence allowing only axial rotation.

Fig. Revolute Joint

2. Translational Joint is assigned to the follower relative to the barrel so that follower can move axially inside the barrel.

Fig. Translational Joint

3. Fixed Joint is given to the barrel relative to the ground in order to hold it steady.

Fig. Fixed Joint

• Boundary Condition

In Boundary condition, time-dependent rotation is provided to the cylindrical cam.

Fig. Boundary Condition- Rotation( in degree)

• Analysis Setting

Following changes have been made to save computational time and ease convergence of solution.

1. Auto-time Stepping is enabled to proceed the solving in small time increment steps.
2. Weak Spring and Large Deflection options are also enable to aid in solving.
3. Stabilization option is switched to constant and 0.1 is provided as Energy Dissipation ratio.

Fig. Analysis Settings

RESULTS AND DISCUSSION

Results are presented at the end of 9th sec.

1. Equivalent Stress

Case 1. Frictionless Contact

Fig. Equivalent Stress distribution in the follower with Max. Equ. Stress(MPa) vs Time(sec.) Graph

At the end of 9th sec.

Maximum Equivalent Stress = 2703.2 MPa

Case 2. Frictional Contact with f.c.=0.1

Fig. Equivalent Stress distribution in the follower with Max. Equ. Stress(MPa) vs Time(sec.) Graph

At the end of 9th sec.

Maximum Equivalent Stress = 2848.3 MPa

Case 3. Frictional Contact with f.c.=0.2

Fig. Equivalent Stress distribution in the follower with Max. Equ. Stress(MPa) vs Time(sec.) Graph

At the end of 9th sec.

Maximum Equivalent Stress = 3054.8 MPa

From the results, we can observe that Equivalent stress is varying more or less in a sinusoidal manner w.r.t time. This is attributed to the fact that with the rotation of cylindrical cam the contacting surface between follower and cylindrical cam changes which changes the direction of force reaction during the course. Because of the particular grooved path, initially force reaction acts from right side on the follower and with time as follower moves further this reactive force acts from the left side. Along with force direction, its magnitude is also changing in similar fashion i.e. increasing at the beginning & then decreasing with time. This will become clearer from the force reaction results of the simulation.

Fig. Graph between Force reaction(N) on follower end along X-axis & Time(sec.)

Now, after comparing the three cases we can see that as the frictional coefficient is changed from zero in frictionless contact to a value of 0.2 in third case, magnitude of Equivalent Stress developed is increasing. This variation is quite expected since with increase in frictional coefficient between surfaces more resistance is developed during the motion of follower and hence force is acting on follower, which causes development of higher stresses.

2. Directional Deformation

Case 1. Frictionless Contact

Fig. Shows Directional Deformation along the X-axis i.e. along Barrel axial direction and shows the graph between Max. Directional Deformation(mm) vs Time(sec.)

At the end of 9th sec.

Max. Directional Deformation (along X-axis) = 11.278mm

Case 2. Frictional Contact with f.c.=0.1

Fig. Shows Directional Deformation along the X-axis i.e. along Barrel axial direction and shows the graph between Max. Directional Deformation(mm) vs Time(sec.)

At the end of 9th sec.

Max. Directional Deformation (along X-axis) = 11.327mm

Case 3. Frictional Contact with f.c.=0.2

Fig. Shows Directional Deformation along the X-axis i.e. along Barrel axial direction and shows the graph between Max. Directional Deformation vs Time(sec.)

At the end of 9th sec.

Max. Directional Deformation (along X-axis) = 11.382mm

Since there is no change in the path of the follower, therefore similar results are obtained for Directional Deformation.

3. Equivalent Elastic Strain

Case 1. Frictionless Contact

Fig. Shows Equivalent Elastic Strain Distribution in Follower and shows the graph between Max. EES(mm/mm) vs Time(sec.)

At the end of 9th sec.

Max. Equivalent Elastic Strain = 0.01354

Case 2. Frictional Contact with f.c.=0.1

Fig. Shows Equivalent Elastic Strain Distribution in Follower and shows the graph between Max. EES(mm/mm) vs Time(sec.)

At the end of 9th sec.

Max. Equivalent Elastic Strain = 0.014263

Case 3. Frictional Contact with f.c.=0.2

Fig. Shows Equivalent Elastic Strain Distribution in Follower and shows the graph between Max. EES(mm/mm) vs Time(sec.)

At the end of 9th sec.

Max. Equivalent Elastic Strain = 0.015339

Similar to the Equivalent Stress results, same observation is seen in Equivalent Elastic Strain results. Strain is varying in sinusoidal manner w.r.t time & with increase in frictional coefficient between the interacting surfaces Strain developed is also increasing.

ANIMATION