Modelling of Cam-Follower Mechanism In Hyper-Works Using 3-D Contact and Curve-To-Curve Joint
Introduction: A cam is a rotating machine element which gives reciprocating or oscillating motion to another element known as follower. The cam and follower have a point or line contact constituting a higher pair. The contact between them is maintained by an external force which is generally provided by a spring or sometimes by the weight of the follower itself when it is sufficient. The cam converts rotary motion of one element into reciprocating (linear) motion or into oscillatory motion. The cam is the driver member and the follower is the driven member. The cam and follower mechanism is widely used for operating the inlet and exhaust valves of internal combustion engines. They are used in wall clocks and the feed mechanism of automatic lathe machines. They are also used in paper cutting machines and weaving textile machinery.
Using Altair Hyperworks, a type of cam known as the disc cam can be simulated. In the disc CAM, the working surface of the cam is designed such that follower moves in a plane perpendicular to the axis of the cam performing a reciprocating or oscillating motion. The type of follower used with this CAM is the roller-follower. The contact end of the follower is roller and the rolling motion exists between the cam and follower.
In this project, the CAM and follower mechanism was simulated using CVCV joint as well as using 3-D contacts. The displacement of the cam with respect to the follower is also compared between these two motion types. The CAM motion using 3-D contacts is demonstrated first.
CAM Follower Mechanism Using 3-D Contact:
MotionSolve contains a very sophisticated contact modeling capability that can handle complex contact scenarios between rigid bodies. Creating a contact is rather simple:
- You can identify geometries on one body that can contact a different set of geometries on a second body.
- You can also specify the contact material properties such as coefficient of restitution and friction.
• MotionSolve monitors the proximity of the specified geometries to each other. When any penetration between the two sets of geometries occurs, a force based on the defined contact properties is generated. This represents the contact force. Both normal as well as frictional forces are modeled.
• When the bodies separate, the force becomes zero.
Once the point of contact and surface normal vector are known, the normal force magnitudes are computed using Impact Method. The Impact model can be thought of as a non-linear spring-damper introduced when there is penetration.
The following parameters define the impact contact model:
• Stiffness- Non negative stiffness of the contact.
• Stiffness Exponent- Exponent of the force-deformation characteristic. Greater than 1:stiffening characteristic and value less than 1:softening characteristic.
• Maximum Damping: The maximum damping co-efficient.
• Penetration at Max Damping: The contact penetration at which the maximum damping is applied.
When the collision detection algorithm detects contact, the penetration depth, rate of penetration, and the above four parameters are sent to the MotionSolve IMPACT function where the normal force is calculated for each node.
Model-Building Process:-
1) The CAM geometry is imported into motion-view using the \'Import CAD or FE Using HyperMesh\' feature. The geometry is auto-meshed in Hypermesh which is then redirected to motion-view.
2) A point with co-ordinates (0,30,0) is added to create the follower-roller body and their associated graphics. The follower roller body was created and the Center of Mass Marker was asssigned to the associated point. A follower-roller cylinder graphic is then created which has the parent body associated to \'Follower roller point\' and aligned in global Z direction. The radii of the follower roller is 5mm with the length and offset being 7mm and -3.5mm respectively.
3) For the follower shaft a point with co-ordinates (0,67.5,0) is added. The shaft aligned in the global Y axis is then created which has a radii of 3mm, length 100mm and offset -38mm.
4) Next, a fixed rectangle graphic is created using its point co-ordinates (0,110,0). The type for the box graphic is chosen as center with parent body being the ground body as it will be fixed to the ground. The x,y,z length of the box is 10mm, 22mm and 10mm respectively.
5) After the geometry is complete, three joints are added. First is the Cam Pivot which is a revolute joint that provides one degree of rotational freedom. The joint is added to the CAM CG. The second joint is Follower Roller Joint which is also a revolute joint added at the roller\'s center. The last joint to be added is the translational joint which is associated with the follower shaft. This translational joint would allow the shaft to translate about global Y. A motion is also added to the CAM Pivot with the expression 10*Time using the expression builder tool.
6) 3-D rigid to rigid contact is established between the CAM and follower roller. Body I is assigned to the CAM Body and Body J to follower-roller. The parameters of the impact model are set to default initially to test how the mechanism performs. Dynamic Friction is applied between the contacting bodies.
7) Lastly, an output is created to measure the displacement of the follower shaft w.r.t CAM body. While adding 3-D contacts, motion-view automotically creates an output for the contact. Gravity is set to -9810mm/s^2 in Y-direction.
8) The CAM Follower model is then simulated with end time as 6.28 secs and Maximum step size as 0.001. Decreasing the maximum step size leads to prevention of integration error while running the simulation.
When modelling the 3-D contact between CAM and follower, the default parameters of the impact model were first selected. The graph above shows the contact force between the two bodies. For most part of the simulation, the follower tries to intermittently remain in contact with the CAM. However, the high value of stiffness (1000) and low value of damping (0.1) are unable to keep the follower in contact with the CAM profile. At 2.3 seconds, the follower experiences a high contact force which swings it in air. It tries to re-establish contact with the CAM only to be flung back again with force of much higher magnitude which eventually dies down. Towards the end we see that a negative contact force is generated between the two bodies. Since, this is an incorrect representation of the CAM Follower mechanism the parameters of the Impact Contact Model will have to be modified. The modification has been done on the basis of several iterations to arrive at the most optimal contact between the cam and follower.
It was observed that by reducing the stiffness parameter the sudden jerk being experienced by the follower is significantly reduced. Thus, the value of stiffness was brought down from 1000 to 175. Although the large contact force being experienced by the follower was considerably reduced, it still was unable to remain in contact with the CAM body throughout its motion. It was observed that by steadily increasing the value of damping, the follower was able to maintain a tangential contact with the CAM throughout its motion.
The above graph shows the contact force between the CAM and follower mechanism with the Impact Contact Model parameters modified. The graph is periodic in nature, however, the force experienced by the CAM is not constant, rather it keeps varying continously with each portion of the graph showing different peak contact force. If this graph is traced with the motion of the follower, the shaft gets raised only during the right half of each wave. The maximum force exerted by the follower on the CAM is approximately 130N.
CAM Follower Mechanism With CVCV Joint
CVCV Joint or curve-to-curve joint fall under the category of higher pair constraints. In this only one point or line is responsible to form a joint between two links. A CVCV Joint is useful for modeling cams where the point of contact between two parts changes during the motion of the system.
The curve-curve constraint removes three degrees of freedom (2 translational and 1 rotational) from the system.
When the body of the first curve is fixed in space, the second curve is allowed to move in three ways:
- It can slide along the first curve,
- roll on the first curve, and
- rotate about the common tangent at the point of contact.
Model-Building Process:
1) There are a few differences when it comes to modelling a CVCV joint from 3-D contact for a CAM and follower mechanism. In 3D contacts, the necessity to specify an advanced joint was not present. Only contacts had to be defined between the CAM and Follower. Here, under the \'Advanced Joint\' option, CVCV joint needs to be selected. But, before this step cam and follower markers need to be added. Also, a profile needs to be defined for the CAM and follower which would define their motion path.
2) A .csv file for the CAM profile is added under the \'Curves\' toolbar. The .csv file has 3 columns which contain data about the movement of CAM in x,y and z directions. Since a 2-D CAM is being modelled, the 3rd column for z-axis has zero values.
3) The profile for follower is created as a mathematical function in X,Y,Z directions. The function for x is 5*sin(2*pi*(0:1:0.01)), 5 being the radius of the follower roller. The function for y is 5*cos(2*pi*(0:1:0.01)).
4) Next, two markers namely CAM and Follower marker are created at the CAM pivot and follower roller center of mass respectively. These two markers would be referenced to the cam and follower when defining CVCV joint.
5) In the final step, a CVCV joint is added from the Advanced Joint toolbar. Curve 1 is assigned to the CAM profile and curve 2 to follower roller profile. Their respective markers are also assigned. A CVCV output is also created as an expression to measure the force between the follower and roller.
As with the case of CVCV joint too, we get a periodic curve where the follower shaft lifts during the left half of each wave instead. The magnitude of force experienced is very less for CVCV joint with peak force being 17.5N. The graph is pretty much uniform during each cycle. The sharp peak in each cycle is due to the follower roller reaching its original position with respect to the CAM.
COMPARISON OF FOLLOWER DISPLACEMENT W.R.T CAM BETWEEN 3D CONTACT AND CVCV JOINT:
The displacement of the follower roller shown below has been arrived after modifying the parameters of the Impact Contact Model. The mechanism when modelled using a CVCV joint gives the follower a very even movement throughout its cycle of 6.28 seconds. This is because when modelling a CVCV joint, the tangential point of contact between the follower and CAM is to be maintained during the entire simulation. The dynamics of the mechanism are not captured accurately using CVCV joint. A phenomenon known as lift-off where the follower partly loses contact with the cam occurs during its movement. This aspect of the mechanism is not captured with a CVCV joint. Thus a force based simulation i.e 3-D contact simulation is done to accurately capture the dynamics of the mechanism at the cost of computational time. The peaks shown below depict the upward displacement of follower. Where the follower smoothly traces the CAM while moving upward in a CVCV constraint, the upward displacement of the follower slightly reduces midway under 3-D contact simulation. The lift-off phenomenon has not been captured with great detail as the intent of modifying the parameters of the impact model was to get the follower to move as smoothly as possible along the CAM.
Another 3-D contact simulation was run to demonstrate the effect of lift-off. The value of damping was reduced from 2 to 0.06. From the video, it is evident how the follower roller is continuously lifting off instead of maintaining complete contact with the CAM. The graph for Y-displacement also shows the continuous rise and fall of the magnitude of follower displacement when the shaft moves upward.