Analysis of the Contact Pressure Between Cams and Roller - [PDF Document] (2025)

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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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2011-36-0247

Analysis of the Contact Pressure between Cams and RollerFollowers 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 usingthe Finite Elements Method (FEM) to study the contact pressurebetween cams and followers in assembled camshafts. The geometry waschosen based on an iron casting camshaft from a commercial car inorder to have a base to ensure that the assembled camshaft is agreat solution to increase the performance and to reduce weight.Surfaces that are in contact with high levels of contact pressurecan increase the wear and reduce the lifetime of the components. Incontact stress analysis, the most critical modeling considerationis to choose the ideal meshing, so, as a preparatory step wesummarized with some simulations, defined an acceptable model torun 3D finite elements analysis and calculated the contactpressure.

INTRODUCTION During the last 20 years, the automotive industrystarted to increase the application of the roller followers insteadof the use of slider followers in valvetrains. The reason of thatwas the ongoing search of the fuel economy of the engine, due tothe reduction of friction, the demand of high performance engineand the reduction of noise and CO2. Allied to these factors, thenecessity of reducing costs and weight took the automotive industryto looking for alternatives of manufacturing camshafts over theconventional methods like casting, forging and machining [1]. Thedevelopment of assembled camshafts showed up as an interesting andattractive solution to fill these gaps of performance [2].According to [3], the roller follower reduces friction, due to itsrolling nature. However, the geometry of roller followers dictatesa reduction of the contact area which results in high contactpressure in the interface with the cam. This leads to the necessityof the use of alloy steel for the cam lobes [4]. Camshaft is onecomponent of the internal combustion engine that engineers arealways concerned about how to predict and extend the service life.Variables like lift profile and material of the cam, valvetrainsconfiguration and manufacturing process are responsible for thefatigue performance of the

camshaft. High values of stress in the peak of the cam are themain responsible of cam damage according to [5]. The rollerfollower is the component of the valvetrain system that is directin contact with the cam lobe. A car after 160.000 kilometers, willhave submitted the camshaft to over 120 million cyclic revolutions,which takes the analysis of contact stress to an important level tobe studied considering the wear mechanisms of the parts [6]. Figure1 shows a schematic of the valvetrain components. Due to the wearmechanisms of these parts, the choice of the material of the camlobes must be consider as one of the most important design factors,remembering that between gray cast iron, powder metal and forgedsteel cam lobes, the last one can withstand more compressivestresses than the others [7].

Figure 1 Valve and roller follower configuration [8].

Assembled Camshafts

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

In all previous examples the equations obtained by the Hertzstheory are only valid in regions far from the faces of thecylinders. 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 inadvance to perform simulations of mechanical contact with finiteelement models. Due to the type and shape of both surfaces, thatwill be in contact during the analysis, we have to be careful tochoose the appropriate settings that will define a reasonablediscretization of the model and to reduce the computational effortof the calculation in the finite element software that will beused. 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 agood combination of factors related to the finite elementssettings, and then we compared with the theory of Hertz. Figure 3shows the model of a cylinder and a flat surface that was used inthe experiment, and Figure 4 shows the finite element model with arefined mesh in the region of the contact analysis. The aim of thisexperiment was not to have a full statistical understanding of allfactors. Instead, it was only to have a good initial approach ofthe settings and then acceptable results compared with the theoryof Hertz. The factors A, B, C and D of the Design Matrix arerelated to the contact region of the cylinder and the flat surface,and their levels (+ or -) and numbers of runs are described inFigure 5 (where HEXA = Hexahedral finite element and TETRA=Tetrahedral finite element). For this analysis, we choose the setsurface-to-surface in our finite element software. This set usesthe same principle described in case "C" of Figure 2, because itoffers greater versatility in the simulations of contact betweentwo bodies. Among these stand out: - no restriction to geometricsurfaces; - 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 lossof accuracy.

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

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

Figure 5 Design Matrix of the DOE [16].

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

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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 theTribology Laboratory of the University of Florida [17], that has agreat interface and give us fast results and an useful graphic ofthe 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 loadapplied on the top of the cylinder = 100N/mm, and then got theresults immediately, as shown in Figure 7.

Figure 7 Hertzs theory results [17].

Sixteen different configurations of parameters in the contactregion were run, as mentioned in Figure 5, the data for materialand geometry were the same as used for the calculations using theHertzs theory. The results were plotted in the Figure 8 in asequence from the lowest to the highest value of contactpressure.

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

firstly because of the value of the contact pressure, andsecondly because of its appearance that is closer to the result ofthe 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 analysisusing the same configuration of a cylinder, plan surface andelement type, but with different sizes of mesh. The Figure 9 showsthe evolution of the appearance of the contact pressure resultingfrom a finite element analysis and then compared to the result oftheory. While a mesh size of 0.01mm generates a stress deviation of1.7% and a good approximation of the theoretical contact pressurearea, the mesh size of 0.05mm generates stress deviation of 7.0%and a regular approximation of the theoretical contact pressurearea.

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

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

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

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

Here, there was a numerical and computational issue to bereported. In the cam lobe case, the refinement using a 0.01mm wasso high that no computation resources were available for thisanalysis. This is something not unusual in daily tasks when dealingwith finite element simulation that requires some attitude from thedesign engineer. Using 0.05mm for the element size in the contactregion leads to expected results deviating approximately 7% fromthe theoretical expected values, which will be kept in mind in theanalysis.

The result of the contact pressure from cast iron camshaft waslower than the value for the assembled camshaft, as expected due tothe proprieties of the materials. These results are shown in Figure12 and 13, respectively.

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

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

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

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

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

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

Figures 16 and 18 show the finite elements results of the castiron material and steel material, where we also separated only asmall region far from the edges of the contact area to compare thenwith 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 ironmaterial [16].

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

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

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

- contribution of the mesh characteristics here the bestconfiguration from previous analysis was adopted. - the Hertzstheory for this case can only consider a cylinder contacting aninfinite flat plane, while the finite element model take underconsideration the influence of the geometry and the stiffness ofthe whole component, even if the simulated region shows a similarconfiguration as in the Hertzs model.

So, finite elements models allow one to assess situations thatare outside the scope of the theory of Hertz in order to make abetter judgment of real cases.

FINAL REMARKS

The lower the maximum contact pressure can be held, the lesswear can be expected. The profile of the roller follower has adecisive influence on the maximum contact pressure [14].

What kind of issues related to the Contact Pressure can we havewhen changing from a cast iron camshaft to an assembledcamshaft?

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

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