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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 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
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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.
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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 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.
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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].
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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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