RD-E: 2100 Cam

The modeling of a camshaft, which takes the engine's rotary motion and translates it into linear motion for operating the intake and exhaust valves, is studied.

A cam can be considered as a device that translates motion from circular to linear. The camshaft of a car takes the rotary motion of the engine and translates it into the linear motion required for operating the intake and exhaust valves. The purpose of this example is to illustrate the capacity of Radioss to simulate the dynamic behavior and the kinematic motion of a cam-valve system. The smooth motion of the valve can be simulated using an adequate and accurate contact model having contact algorithms with quadratic surfaces without any gaps.

rad_ex_21_cam
Figure 1.

Options and Keywords Used

  • Rigid bodies: In order to apply a constant angular velocity to the cam, a rigid body is created over the internal nodes, as shown in Figure 2. The master node is moved to the camshaft axis.
    To attach the valve head to the spring, another rigid body is created to distribute the internal spring force over several nodes.

    rad_ex_fig_21-4
    Figure 2. Rigid Body Cam
  • Boundary conditions:
    • Master node of the cam is blocked, except when rotating around Y.
    • Master node of the valve is blocked, except when translating around Z.
    • One extremity of the spring is fixed to the valve, while the other is blocked.

      rad_ex_fig_21-5
      Figure 3. Boundary Condition on Valve
  • Imposed velocity: A rotational velocity of 314 rad/s is imposed on the master node of the rigid body. This velocity is activated by a temporal sensor, with a short activation delay (Tdelay =0.0002s). This sensor is necessary to avoid applying the initial and imposed velocities at the same time.

    rad_ex_fig_21-6
    Figure 4. Imposed Velocity
  • Initial velocity:
    An initial rotational velocity is applied to all the cam's nodes, including the master node of the rigid body. You must define the origin (center of rotation) and the orientation vector.

    rad_ex_fig_21-7
    Figure 5. Initial Velocity
  • Interfaces: The TYPE16 interface simulates a contact between a quadratic master surface and a group of nodes. In the case of contact between a curved and a plane surface, the curved surface is defined as the master surface and the nodes of the plane part are slave.

    rad_ex_fig_21-8
    Figure 6. Interface TYPE6
    The TYPE7 interface works either with Penalty or with Lagrange multipliers. In its basic formulation, the interface simulates contact between two facetisated surfaces. The use of the Lagrange Multipliers method enables to precisely satisfy the kinematic contact without introducing a gap.

    rad_ex_fig_21-9
    Figure 7. Interface TYPE7

Input Files

The input files used in this example include:
Interface 16:
Fine mesh
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface16/fine_mesh/I16S16FM*
Coarse mesh
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface16/coarse_mesh/I16S16CM*
Interface 7:
Penalty method
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface7/penalty/slave_cam/I7PMCAM*
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface7/penalty/slave_valve/I7PMVALVE*
Lagrange multipliers
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface7/lagrange/slave_cam/I7LMCAM*
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface7/lagrange/slave_valve/I7LMVALVE*
Friction
<install_directory>/hwsolvers/demos/radioss/example/21_Cam/interface7/friction/I7PFMCAM*

Model Description

Modeling a contact between a plane and a curved surface uses a faceted curved surface. Interfaces 7 and 16 are compatible with the geometry of the problem and the faceting, are described and compared.

This problem demonstrates a cam rotating with an angular velocity of 314 rad/s, which interacts and triggers off the translation of a valve tied to two springs. The superposed springs have varying stiffness (spring 1: 30000 N/m and spring 2: 15000 N/m). The springs control the higher and lower rotary frequencies.
  • The cam is 36 mm in length, with a maximum width of 14 mm and a thickness of 18 mm.
  • The valve is 44 mm in diameter, with a thickness of 3 mm (Figure 8).
  • The spring is 40 mm in length.

The following system is used: mm, s, kg, mN , KPa.

The material used for the cam and the valve is steel. It is characterized by the isotropic elasto-plastic material (/MAT/LAW2) and the Johnson-Cook plasticity model, with the following properties:
Material Properties
Initial density
7.8 x 10-06 Mkg/l
Young's modulus
2.1 x 10+08 KPa
Poisson ratio
0.3
Yield stress
20000 KPa
Hardening parameter
40000 KPa
Hardening exponent
0.5

rad_ex_fig_21-1
Figure 8. Geometry of the Problem

Model Method

The problem raised in this example is the modeling of an interface between a plane and a curved surface. In this case, using quadratic elements is the most appropriate.

A TYPE16 interface with 16-node shell elements for both the valve and the cam should be chosen first for the modeling. 20-node brick elements are used for the mesh inside the cam (Figure 9).

rad_ex_fig_21-2
Figure 9. BRIC20 and SHEL16 Mesh
Another model using linear elements is studied. Contact between the cam and valve is defined by a TYPE7 interface. In order to satisfy the closed contact between parts, the Lagrange Multipliers method is selected.

rad_ex_fig_21-3
Figure 10. BRICK Elements Mesh
The springs are modeled using Radioss TYPE4 springs. The stiffness is linear and defined by the following functions. Damping is neglected.
l-l0 (mm) -40 0 50
Fspring 1 (mN) -1.5 e+06 -0.3 e+06 1.2 e+06
Fspring 2 (mN) -0.75 e+06 -0.15 e+06 0.6 e+06

Results

At first, you are interested by the kinematics of the problem. The results obtained for velocity and acceleration at the master node of the rigid body's valve are thus compared.

The graphs in Figure 11 provide the velocity of the valve's master node when a TYPE7 interface is used with the Penalty method. The raw results obtained are noisy due to the fact that the Penalty method applies discontinued forces. The smooth velocity curve is obtained by using a low pass CFC 180 (3db) filter. Figure 12 shows the acceleration of the same master point.

rad_ex_fig_21-10
Figure 11. Vertical Velocity of the Master Node Valve for a TYPE7 Interface, using the Penalty Method
Attention should be paid to the use of filters. The filtered curves are in fact generally affected by a border effect. Filtering induces an error in the beginning and end parts of the curves (for this example, take the intervals of 0 < t < 0.002 and 0.038 < t < 0.04).

rad_ex_fig_21-11
Figure 12. Vertical Acceleration of the Master Node Valve for a TYPE7 Interface, using the Penalty Method

The filtering quality depends on the number of samples which, in this case is the number of points computed by Radioss for each curve. Therefore, a low value for the /TFILE parameter in the Engine file (*_0001.rad) is used to obtain good results, especially for the acceleration curve.

In the following sections, only the filtered curves are represented in order to the compare different models.

Comparison of Interfaces

Figure 13 and Figure 14 represent velocity and acceleration curves for a model using a TYPE7 interface with the Penalty method. As for the master and slave part definition, the results are slightly different.

Figure 15 and Figure 16 give velocity and acceleration curves for TYPE7 interface using the Lagrange Multipliers method.

rad_ex_fig_21-12
Figure 13. Vertical Velocity of the Valve's Master Node for a TYPE7 Interface, using the Penalty Method

rad_ex_fig_21-13
Figure 14. Vertical Acceleration of the Valve's Master Node for a TYPE7 Interface, using the Penalty Method
For both Figure 15 and Figure 16, the model using slave nodes on the cam and a master surface on the valve seems to be the most realistic.

rad_ex_fig_21-14
Figure 15. Vertical Velocity of the Valve's Master Node for a TYPE7 Interface, using the Lagrange Multipliers Method

rad_ex_fig_21-15
Figure 16. Vertical Acceleration of the Valve's Master Node for a TYPE7 Interface, using the Lagrange Multipliers Method

Even if using a TYPE7 interface with the Penalty or the Lagrange Multipliers method good results can be achieved, a quadratic mesh with the TYPE16 interface will enable the reduction of oscillations, due to facetisation.

Figure 17 and Figure 18 compare the results for models using TYPE7 and TYPE16 interfaces.

rad_ex_fig_21-16
Figure 17. Vertical Velocity of the Valve's Master Node

rad_ex_fig_21-17
Figure 18. Vertical Acceleration of the Valve's Master Node

Comparison of Meshes

Considering a contact modeled with a TYPE16 interface, the influence of the mesh density is studied using two relatively coarse and fine meshes.
Fine Mesh:
Cam
200 external SHEL16 elements, 250 internal BRIC20 elements
Valve
88 SHEL16 elements
Coarse Mesh:
Cam
40 SHEL16 elements
Valve
12 SHEL16 elements

rad_ex_fig_21-18
Figure 19. Vertical Velocity of the Valve's Master Node

rad_ex_fig_21-19
Figure 20. Vertical Acceleration of the Valve's Master Node

Although the coarser mesh amplifies the facetisation of the curved surfaced, the mesh density does not influence the results for velocity after filtering. However, the fine mesh provides better results for acceleration, having limited parasite oscillations for each node/surface contact.

Friction

An option in interface TYPE7 using the Penalty method allows you to add friction to the model. Several friction models are available. The Coulomb friction model is used here. A comparison is made between models with and without friction.

rad_ex_fig_21-20
Figure 21. TYPE7 Interface using Penalty and Friction

rad_ex_fig_21-21
Figure 22. Vertical Velocity of the Valve's Master Node for a TYPE7 Interface, using the Penalty Method

rad_ex_fig_21-22
Figure 23. Vertical Acceleration of the Valve's Master Node for a TYPE7 Interface, using the Penalty Method
Table 1. CPU and Time Step Comparison
Simulation CPU (normalized) Time Step
TYPE16 interface with fine mesh 22,50 0.8365 x 10-7
TYPE16 interface with coarse mesh 1 0.207 x 10-6
TYPE7 interface with Penalty method

(slave nodes on cam and master surface on valve)

 1.65 0.2133 x 10-6
TYPE7 interface with penalty method

(slave nodes on valve and master surface on cam)

 1.75 0.2117 x 10-6
TYPE7 interface with Lagrange multipliers method

(slave nodes on cam and master surface on valve)

 1.68 0.2133 x 10-6
TYPE7 interface with Lagrange multipliers method

(slave nodes on valve and master surface on cam)

 1.69 0.2126 x 10-6
TYPE7 interface with Penalty method and friction

(slave nodes on cam and master surface on valve)

 1.66 0.2133 x 10-6
TYPE7 interface with Penalty method and friction

(slave nodes on valve and master surface on cam)

 1.65 0.2126 x 10-6

Conclusion

This example illustrated the ability of Radioss to model mechanisms, particularly in the case of this contact mechanism. Interface TYPE16 and TYPE7 can be used to model contact between plane and curved surfaces. The TYPE16 interface enables you to simulate contact between quadratic surfaces without using a gap and provides accurate results within a reasonable computation time. The TYPE7 interface allows a frictional modeling of the contact, needing little computation time and provides good simulation results.