analysis of the contact pressure between cams and roller

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SAE TECHNICAL 2011-36-0247 PAPER SERIES E

Analysis of the Contact Pressure between Cams and Roller

Philippe de Abreu Duque Mauro Moraes de Souza

Juliano Savoy Guilherme Valentina

Followers in Assembled Camshafts

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Copyright 2011 SAE International


2011-36-0247

Analysis of the Contact Pressure between Cams and Roller Followers in

Philippe de Abreu Duque Neumayer Tekfor Tech Center Brazil

Mauro Moraes de Souza Juliano Savoy

Guilherme Valentina Neumayer Tekfor Tech Center Brazil

Copyright 2011 SAE International

ABSTRACT This work presents the results of a simulation using the Finite Elements Method (FEM) to study the contact pressure between cams and followers in assembled camshafts. The geometry was chosen based on an iron casting camshaft from a commercial car in order to have a base to ensure that the assembled camshaft is a great solution to increase the performance and to reduce weight. Surfaces that are in contact with high levels of contact pressure can increase the wear and reduce the lifetime of the components. In contact stress analysis, the most critical modeling consideration is to choose the ideal meshing, so, as a preparatory step we summarized with some simulations, defined an acceptable model to run 3D finite elements analysis and calculated the contact pressure.

INTRODUCTION During the last 20 years, the automotive industry started to increase the application of the roller followers instead of the use of slider followers in valvetrains. The reason of that was the ongoing search of the fuel economy of the engine, due to the reduction of friction, the demand of high performance engine and the reduction of noise and CO2. Allied to these factors, the necessity of reducing costs and weight took the automotive industry to looking for alternatives of manufacturing camshafts over the conventional methods like casting, forging and machining [1]. The development of assembled camshafts showed up as an interesting and attractive solution to fill these gaps of performance [2]. According to [3], the roller follower reduces friction, due to its rolling nature. However, the geometry of roller followers dictates a reduction of the contact area which results in high contact pressure in the interface with the cam. This leads to the necessity of the use of alloy steel for the cam lobes [4]. Camshaft is one component of the internal combustion engine that engineers are always concerned about how to predict and extend the service life. Variables like lift profile and material of the cam, valvetrains configuration and manufacturing process are responsible for the fatigue performance of the

camshaft. High values of stress in the peak of the cam are the main responsible of cam damage according to [5]. The roller follower is the component of the valvetrain system that is direct in contact with the cam lobe. A car after 160.000 kilometers, will have submitted the camshaft to over 120 million cyclic revolutions, which takes the analysis of contact stress to an important level to be studied considering the wear mechanisms of the parts [6]. Figure 1 shows a schematic of the valvetrain components. Due to the wear mechanisms of these parts, the choice of the material of the cam lobes must be consider as one of the most important design factors, remembering that between gray cast iron, powder metal and forged steel cam lobes, the last one can withstand more compressive stresses than the others [7].

Figure 1 Valve and roller follower configuration [8].

Assembled Camshafts


in Figure 2, cases A and B, there is a stress concentration at the edges of the cylinders and the cylinder at the edge of the shortest length respectively due to a geometric singularity. For example C, the geometric singularity is removed by rounding radius so that there is a gradual relief in stress in this region. However, this relief will only be noticed for a rounding radius much larger than the width of the contact area.

In all previous examples the equations obtained by the Hertzs theory are only valid in regions far from the faces of the cylinders. More accurate results have to be obtained by using FEM (Finite Elements Methods).

FINITE ELEMENTS SIMULATION

The type, size and order of the element must be defined in advance to perform simulations of mechanical contact with finite element models. Due to the type and shape of both surfaces, that will be in contact during the analysis, we have to be careful to choose the appropriate settings that will define a reasonable discretization of the model and to reduce the computational effort of the calculation in the finite element software that will be used. Similar approach was done by [12] and [13].

First we did an experiment, called DOE (Design of Experiments), with a simplified model of a cylinder and a flat surface, to find a good combination of factors related to the finite elements settings, and then we compared with the theory of Hertz. Figure 3 shows the model of a cylinder and a flat surface that was used in the experiment, and Figure 4 shows the finite element model with a refined mesh in the region of the contact analysis. The aim of this experiment was not to have a full statistical understanding of all factors. Instead, it was only to have a good initial approach of the settings and then acceptable results compared with the theory of Hertz. The factors A, B, C and D of the Design Matrix are related to the contact region of the cylinder and the flat surface, and their levels (+ or -) and numbers of runs are described in Figure 5 (where HEXA = Hexahedral finite element and TETRA =Tetrahedral finite element). For this analysis, we choose the set surface-to-surface in our finite element software. This set uses the same principle described in case "C" of Figure 2, because it offers greater versatility in the simulations of contact between two bodies. Among these stand out: - no restriction to geometric surfaces; - improved numerical conditioning and numerical accuracy; - represents glued surfaces, rough and initial penetration

without increasing the numerical complexity of the problem; - allows to use elements with shape function of order higher

than quadratic; - allows the use of coarse meshes without loss of accuracy.

Figure 3 Model of a cylinder and flat plane [16].

Figure 4 Finite element model with mesh refinement in the contact region [16].

Figure 5 Design Matrix of the DOE [16].

As shown in the detailed view of Figure 3, we have a rounding radius at end of the cylinder, which can be compared to the case C of the Figure 2. We had already mentioned in the section Contact Analysis, that when we have a finite cylinder, the equations obtained by the Hertzs theory are only valid if we analyze the regions far from the faces of the cylinders. So, for the results of the finite elements simulation, that will be shown in the sequence, we separated only a small region between the faces of the cylinders, as shown in Figure 6-d), to compare with the results of the Hertzs theory. It is also possible to check that the distribution of pressure found in our finite element simulation, shown in Figure 6-c), is compatible with the distribution of pressure described in Figure 2 case C.


Figure 6 Detail of the finite element analysis result [16].

Rather than to calculate the equations of the Hertzs theory, described in [9], by hands, and also to facilitate our discussion, we used the Hertz Contact Calculator, an online calculator from the Tribology Laboratory of the University of Florida [17], that has a great interface and give us fast results and an useful graphic of the contact area. There we inserted our data: radius of cylinder = 5mm, radius of the flat surface = infinite radius, Youngs Modulus = 210 GPa and Poisons ratio = 0.30 of the both parts, and the load applied on the top of the cylinder = 100N/mm, and then got the results immediately, as shown in Figure 7.

Figure 7 Hertzs theory results [17].

Sixteen different configurations of parameters in the contact region were run, as mentioned in Figure 5, the data for material and geometry were the same as used for the calculations using the Hertzs theory. The results were plotted in the Figure 8 in a sequence from the lowest to the highest value of contact pressure.

The result of the Run 15 (R15) was chosen as the best result,

firstly because of the value of the contact pressure, and secondly because of its appearance that is closer to the result of the Hertzs theory and its contact width, not shown in the figure, but the value found was 0.15mm.

Figure 8 Summary of the results from the experiment [16].

Based in these results of the experiment, we ran an analysis using the same configuration of a cylinder, plan surface and element type, but with different sizes of mesh. The Figure 9 shows the evolution of the appearance of the contact pressure resulting from a finite element analysis and then compared to the result of theory. While a mesh size of 0.01mm generates a stress deviation of 1.7% and a good approximation of the theoretical contact pressure area, the mesh size of 0.05mm generates stress deviation of 7.0% and a regular approximation of the theoretical contact pressure area.

Figure 9 Evolution of the appearance contact pressure [16].

CAM LOBE AND ROLLER FOLLOWER This last simulation aims to focus in the analysis of the contact pressure between a cam lobe and a roller follower, with two different designs of camshaft. First we have the cast iron camshaft as shown in Figure 10 and then the assembled camshaft as shown in Figure 11. The properties of the materials used: Youngs Modulus = 210 GPa and Poisons ratio = 0.30 for the roller followers in both analyses, and for the tube and the cam of the assembled camshaft, and for the cast iron camshaft Youngs Modulus = 105 GPa and Poisons ratio = 0.29. Also for both analyses the load applied on the top of the cylinder was 1000N. Although the analysis with a cylinder in contact with a flat surface resulted in a best case the element size of 0.01mm, the size of the elements used in the contact region of the cam lobe and the roller follower was 0.05mm.


Figure 10 Finite elements model of a cast iron camshaft and roller follower. [16]

Figure 11 Finite elements model of an assembled camshaft and roller follower [16].

Here, there was a numerical and computational issue to be reported. In the cam lobe case, the refinement using a 0.01mm was so high that no computation resources were available for this analysis. This is something not unusual in daily tasks when dealing with finite element simulation that requires some attitude from the design engineer. Using 0.05mm for the element size in the contact region leads to expected results deviating approximately 7% from the theoretical expected values, which will be kept in mind in the analysis.

The result of the contact pressure from cast iron camshaft was lower than the value for the assembled camshaft, as expected due to the proprieties of the materials. These results are shown in Figure 12 and 13, respectively.

The maximal stress level resulting in the cast iron cam lobe amounts 997 MPa. Assuming +7.0% of variation, this leads to 1070 MPa of maximum value for application of this material. In the steel cam lobe amounts 1270 MPa or 1359MPa if ones considers +7.0% stress variation. Comparing these data with typical contact pressure values for different materials shown in Figure 14, one can conclude that while cast iron would fail, the steel cam lobe would withstand the applied loads, even if the simulation was led with 0.05mm element size.

Figure 12 Result of contact analysis of the cast iron camshaft [16].

Figure 13 Result of contact analysis of the assembled camshaft [16].


Figure 14 Contact pressure / cam lobe material [16].

These models fall outside the scope of Hertzs theory due to the geometry, stiffness and boundary conditions, as discussed before in the section Contact Analysis.

One can ask how the comparison of these finite elements results, with the Hertzs theory would be. The conclusions that will be presented here do not differ from previous results presented in this work for the cylinder/flat plane model.

Figures 16 and 18 show the finite elements results of the cast iron material and steel material, where we also separated only a small region far from the edges of the contact area to compare then with the Hertzs theory of Figures 15 and 17.

Figure 15 Hertzs theory result for Cast Iron material [17].

Figure 16 Detail of the finite element analysis of cast iron material [16].

Figure 17 Hertzs theory result for steel material [17].

Figure 18 Detail of the finite element analysis of steel material [16].

The deviation between the finite elements results and the Hertzs theory is now 10,6% for the cast iron material and 11,8% for the steel material. Two main effects are to be considered to explain the higher deviation of results when compared with the cylinder/flat plane model:

- contribution of the mesh characteristics here the best configuration from previous analysis was adopted. - the Hertzs theory for this case can only consider a cylinder contacting an infinite flat plane, while the finite element model take under consideration the influence of the geometry and the stiffness of the whole component, even if the simulated region shows a similar configuration as in the Hertzs model.

So, finite elements models allow one to assess situations that are outside the scope of the theory of Hertz in order to make a better judgment of real cases.

FINAL REMARKS

The lower the maximum contact pressure can be held, the less wear can be expected. The profile of the roller follower has a decisive influence on the maximum contact pressure [14].

What kind of issues related to the Contact Pressure can we have when changing from a cast iron camshaft to an assembled camshaft?

For a roller follower, the camshaft should be made of steel composite or steel, most often with induction hardened cams



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analysis of the contact pressure between cams and roller

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