Modelling the Valvetrain of the Car Engine to Study the Effects of Valve Rotation

Featured Application

The rotation motion of the valves is important because it ensures the good functioning of the gas exchange process and a longer life for the valve, the valvetrain mechanism and the engine, respectively. The results obtained in the study can be applied easily in engineering practice, particularly in the manufacture of internal combustion engines.

Abstract

The valve performs an alternating translational motion along its axis of symmetry, which is accompanied by a rotation about its own axis, possibly due the valve body’s cylindrical geometry and due to the conjugate element, the guide, which is also a cylindrically shape body. By ensuring this rotational motion of the valve, a number of advantages are obtained, mainly related to the increase of the operating period of the valve and implicitly of the engine. Following the critical analysis of the current state of research on the valvetrain systems and the rotational motion of the valves, the advantages and the disadvantages of valve rotation during engine operation were established. To this end, it has been established that, in addition to the theoretical approach to the problem, it is necessary to create a virtual model of the valvetrain mechanism to do a thorough analysis of the problem. Based on the model, the influence of the camshaft speed, temperature and lubricating oil pressure were monitored by changing the coefficient of friction, the influence of the cam position relative to the tappet and the influence of the valve spring. In this paper, the authors want to determine the rotational motion characteristics of internal combustion engine valves and to suggest measures that can be taken to ensure valve rotation at all operating modes without the use of auxiliary devices for generating rotational motion.

1. Introduction

One of the most important components of the valvetrain mechanism is the valve because it must ensure the optimal gas exchange process between the engine and the external environment by closing the intake and exhaust inlet, outlet ports on a certain time period. Thus, the valve performs an alternating translational movement along its axis of symmetry, a movement which is accompanied by a rotation about its own axis [1,2,3]. This rotation around its own axis of symmetry is possible because the valve stem is cylindrical and the translational motion performed by it takes place in a cylindrical guide [4,5,6]. By ensuring this rotational motion of the valve, a number of advantages are obtained, mainly related to the increase of the operation work period of the valve and implicitly of the engine [7,8,9].

Following a critical analysis of the current state of research on valvetrain systems and the rotational motion of the valves [10,11,12,13], the advantages and the disadvantages of valve rotation during engine operation were established. Analysing these results, it was concluded that an investigation of the rotation mechanism of the valves of internal combustion engines is absolutely necessary. For this purpose, it was established that in addition to the theoretical approach to the problem, it is necessary to make a virtual model of the valvetrain mechanism in order to analyse the effects of different factors on the rotation of the valve.

In recent years, due to the time reduction between the design phase and the manufacturing phase, the focus is to identify alternative solutions to the classic validation methods by test rig usage. One of the approaches is usage of simulation software for multibody analysis. Simplified models are defined using validated coefficients and parameters. Additionally, the evolution of these software products plus the computational power of new workstations has allowed researchers to obtain results that have a high degree of accuracy in a short period of time, results that have led to improvements in the process of design and the development of new engines [14,15].

This can determine the dynamic behaviour, forces and stresses that occur during the operation of the valvetrain system [16]. The development or optimization of a valvetrain system is often done starting from a simplified model of the valvetrain mechanism, a single valve, which is analysed from a kinematic and a dynamic point of view, after which a complex and complete model of the valvetrain mechanism is created [15].

Modelling can be done by using rigid or flexible bodies. The use of flexible bodies is more accurate, but it considerably increases the computation time, and the results are often not the best [17]. So, a middle way must be found to create a virtual model of the valvetrain system. In addition, the way in which the bodies are modelled and simplified has a great influence on the dynamic behaviour of the whole; and, as a result, there may be pronounced wear due to the high level of vibration and noise or undesirable phenomena such as the jump of the valve on its seat may be caused [18].

However, the biggest problem in this simulation software is the need to finally validate the model, with respective to the results, through experimental tests on the test stand [19].

This paper will analyse the most used type of cam mechanism, namely the valvetrain system with direct drive (Figure 1). The system is characterized by high rigidity because it has few components, and therefore it can be used in the case of engines running at high speeds. The role of the follower is to transform the rotational movement of the cam into a translational motion and to transmit it to the valve to take over by friction the lateral reaction produced by the cam and to take over the clearances from the valvetrain system. Increasing the operating period and evenly distributing wear on its surface can be achieved by ensuring a rotational motion. The hydraulic tappet has also been developed to reduce noise and cam wear [20,21,22].

Other problems involved by the rotation of the valve are presented in [23,24,25,26,27]. In this paper, the main goal of the authors was to obtain a 3D model, which reproduces as accurately as possible, the operation of the valvetrain mechanism in order to analyse the influence of certain functional and constructive factors on the rotational movement of the valves. In this sense, the influence of the camshaft speed, temperature and lubricating oil pressure were monitored by changing the coefficient of friction, the influence of the cam position with respect to the tappet, and the influence of the valve spring.

In conclusion, having a nonrotational movement of the valve during its main translational movement, opening–closing, will determine several disadvantages. One of the most important is related to wear of the valve head by the apparition of cracks [9,13,28]. In addition, when the valve rotates, a different contact point is then ensured between it and the valve seat, reducing the wear. A significant wear reduction is obtained between the valve stem and the guide. Finally, a uniform heat distribution on the valve head is ensured, a fact which will determine the avoidance of premature valve head deformation [23].

2. Multibody Model of the Valvetrain System

The first step in creating a virtual model of the valvetrain mechanism was to determine the dimensions of the components of the valvetrain mechanism directly and to make their three-dimensional models using the using LMS Virtual Lab v.10 software, which is based on the Catia v5 interface (Figure 2).

Thus, for each component, the geometry was determined and its 3D model was created. Particular attention was paid to the profile of the cam. The cam profile in the case of valvetrain systems can be determined by two methods: by determining the law of valve displacement based on the calculation of the cross-section or by making the cam profile according to the kinematic and dynamic requirements and experimentally and mathematically verifying the chronosection [20]. The cam profile must ensure an optimal opening and closing of the valve so that maximum filling or emptying of the cylinders is achieved. It must also ensure a low deceleration when the valve is approaching maximum lift and a low acceleration during the valve closing period so that springs with low rigidity can be used. So, the cam profile must be smooth and without steep curves so as not to induce high accelerations and inertia forces in the mechanism [28,29].

The cam size must also be as small as possible in order to meet a number of requirements. This reduces the sliding speed between the cam and the lug—the rocker arm, respectively, reduces wear and contact pressure between the two surfaces—the manufacturing cost decreases and last but not least the moment required to drive the camshaft has a low value [29,30].

Considering the cam profile, studies were performed comparing Kurz’s method of obtaining the cam profile starting from polynomial equations of degree 4, a method that has advantages and disadvantages, with the equations of hyperbolic spline curves of degree 4, a solution that determines a dynamic, behaviour-improved valvetrain mechanism [31]. Two cam profiles were also analysed; profiles between which there was a difference of 500μm and major differences in valve displacement, speed and acceleration were identified, including differences that influenced the contact forces [32].

The realization of the 3D cam that determines the rotation of the valve can be done starting from the valve stroke measured experimentally on the test stand or by measuring the cam profile of the valvetrain shaft of the studied mechanism [33,34,35,36]. Thus, the diameter of the basic circle of the cam was measured (34 mm), the width of the cam was determined (12.5 mm) and the maximum height of the cam was measured (42.8 mm), and the lift height of the valve was 8.8 mm. Based on these data and the graph of the valve lift, the cam profile was determined (Figure 3). Thus, the existence of ramps can be observed at the beginning of the valve lift and at the end of its closing, which has the role of reducing shock loads and maintaining a constant speed so that the transition from the base circle to the cam attack area is smooth, both when the valve is opened and when it is closed. Additionally, in this area are taken the games and deviations from the cam profile resulting from wear or manufacturing defects [22].

The next step was to assemble the components and constrain them so that the actual model of the valvetrain mechanism could be reproduced as accurately as possible.

The virtual model of the direct drive valvetrain mechanism comprised 14 bodies of which 13 were modelled as rigid bodies and one, the valve spring, was modelled as a flexible body to take into account the mass of the coils, respectively the inertia forces determined by these, and the contact that may occur between the spirals (Figure 4).

For the positioning of the elements in relation to the base reference frame, fixing couplings were used which cancelled all of the six degrees of freedom of the components. In this way it was fixed: the valve seat, the valve guide, the tapped guide and the cam bearing. Fixing couplings were also used in the case of the valve because it was divided into three components in order to more easily shape the existing contacts: valve head, valve rod and valve end.

The cam was fixed to the bearing by means of a rotation link, which allowed a single degree of freedom, the rotation about the X-axis. To obtain the rotational movement of the tappet or valve, it was necessary to use cylindrical links. These links allowed the existence of two degrees of freedom, translation and rotation around the Z axis.

The friction simulation of the two links was performed by introducing frictional forces inside them. Thus, a friction element was used which defined a static and a dynamic friction force based on the static and the dynamic coefficient of friction, respectively. This element also allowed the dimensions of the coupling to be defined so that the reaction forces occurring inside them could be determined.

The force acting in the cylindrical link represents the sum of the components on the three directions [34]:

$$N=\sqrt{F_x^2+F_y^2+F_z^2}$$

(1)

For the values of static and dynamic coefficients of friction, the values presented in

Table 1. Static and dynamic coefficients of friction.

Material 1	Material 2	Type of Contact	μ Static	μ Dinamic
Steel	Steel	dry-dry	0.7	0.57
Steel	Steel	lubricating-dry	0.23	0.16
Steel	Steel	Lubricating—lubricating	0.23	0.16

were considered [34,37,38].

The contact between the components was made by using the Cad Contact finite element. This element allows the Modelling and the simulation of contacts between rigid bodies with complex geometry. Thus, the use of this type of contact involves the selection of the two bodies between which the contact is to be defined, followed by their decomposition into triangles whose sizes and orientations are defined by the user. The coefficients that characterize the contact force are also defined: stiffness coefficient, damping coefficient, friction coefficient, etc.

The Modelling of contacts between rigid bodies required the definition of stiffness and damping coefficients for each body. Determining the stiffness coefficients of the parts can be determined by using the finite element method or by calculation [39], but the friction and damping coefficients are much more difficult to determine [14].

Thus, the damping coefficient was determined using the finite element analysis method using the ANSYS program (Figure 5). The analysis involved assigning a material to the part, acting on it with a certain force and determining the deformation value, knowing that the stiffness coefficient is the ratio between the deformation force and the deformation of the part.

The calculus of the damping coefficients was made starting from the hypothesis that the damping represents 2–3% of the critical damping coefficient [40,41]. Considering these, the critical damping coefficient was determined, considering two masses, $m_1$ and $m_2$, connected to each other by a spring-type element and a damping-type element. Thus, we can determine the following equations [41]:

-

Motion equation:

$$\ddot{y}+c\frac{\left(m_1+m_2\right)}{m_1{m}_2}\dot{y}+\frac{k\left(m_1+m_2\right)}{m_1{m}_2}y,$$

(2)

-

Natural frequency of the system:

$${\omega }_n=\sqrt{\frac{k\left(m_1+m_2\right)}{m_1{m}_2}},$$

(3)

-

Damping factor:

$$\zeta =\frac{c}{2}\sqrt{\frac{m_1+m_2}{k{m}_1{m}_2}},$$

(4)

-

Critical damping coefficient, considering ζ = 1:

$$c_r=2\sqrt{k\frac{m_1{m}_2}{m_1+m_2}},$$

(5)

The coefficients used to define the contacts between the components of the valvetrain system are presented in

Table 2. Coefficients of rigidity and damping.

Case No.	Bodies in Liaison	Rigidity [N/m]	Damping [Ns/m]
1	Camshaft–Outer tappet housing	7 × 107	420
2	Tappet Housing–Valve	4 × 107	250
3	Valve–Valve seat	10 × 107	520
4	Valve–Valve retainer	3 × 107	100
5	Valve retainer–Spring retainer	3 × 107	100
6	Spring washer–Valve guide	4 × 107	250

.

The next important element of the direct drive valvetrain mechanism is represented by the tappet. It is defined by the HLA (hydraulic lash adjuster), a hydraulic element, which allows the hydraulic system to model the properties of the oil, the oil pressure and the amount of air present in it [34]. The operation of this element is based on the force given by the pressure of the high-pressure oil chamber and the depreciation resulting from the leakage of the oil in the high-pressure chamber by the interstitis between the piston and the lower housing [34,40].

Modelling the spring as a flexible body is absolutely necessary because it has a very important role in the dynamics of the valvetrain mechanism. Thus, the first step in Modelling the spring was to determine its constructive characteristics and its elastic characteristic.

The valve springs are cylindrical in shape, its constructive characteristics being presented in

Table 3. Constructive characteristics of the valve spring.

Free height	Ho [mm]	44.5
Diameter	d [mm]	4
External diameter	D [mm]	28
Internal diameter	Di [mm]	20
Average diameter	Dm [mm]	24
The slope of the arch	α0 [°]	6
Number of spirals	nt	6.75

(Figure 6).

The elastic characteristic of the spring was determined using a spring test stand, Figure 7. The operation of the stand was based on the rotation of a crank through which a worm-driven gear was driven which caused the spring to act on a spring with a certain force corresponding to a weight whose value could be read on the graduated dial. Simultaneously, the value of the spring deformation corresponding to the applied weight could be read on the graduated ruler.

Thus, the springs corresponding to one cylinder were removed, two from the inlet valves and two from the exhaust valves, and their elastic characteristics were determined, entering in the table the values corresponding to the applied weights and their deformation (see

Table 4. Determination of the elastic characteristic of the valve spring.

Spring Length [mm]	Spring 1		Spring 2		Spring 3		Spring 4		Average Force [N]
	Mass [kg]	Force [N]	Mass [kg]	Force [N]	Mass [kg]	Force [N]	Mass [kg]	Force [N]
44.5	0	0	0	0	0	0	0	0	0
44	7	68.67	6	58.86	5.5	53.95	6.3	61.80	60.82
42	14	137.34	14	137.34	14	137.34	15	147.15	139.79
40	27.5	269.77	22.5	220.72	21	206.01	22.6	221.70	229.55
38	31	304.11	31.5	309.01	31.5	309.01	31	304.11	306.56
36	40.4	396.32	40	392.4	39.5	387.49	40	392.4	392.15
34	50	490.5	52.5	515.02	50.0	490.5	49	480.69	494.17
32	59.5	583.69	62.5	613.12	59.5	583.69	58.5	573.88	588.6
30	71	696.51	71	696.51	69.6	682.77	70	686.7	690.62
28	80.5	789.7	81	794.61	80	784.8	81	794.61	790.93
27	101	990.81	101	990.81	101	990.81	101	990.81	990.81

).

The elastic characteristic of the spring is determined by the relationship [42]:

$$c=\frac{F}{f},$$

(6)

Based on the calculations, an average elasticity resulted: c = 42,000 N/m (Figure 8).

The definition of the spring as a flexible body was achieved by using the PDS module (powertrain dynamic simulator) of the Virtual Lab program, which allowed Modelling of the engine or its components, models that could then be used accurately to determine their mechanical and dynamic performance [29,43,44].

Thus, the characteristics of the spring were defined in the PDS as: free length, diameter of the spiral, the number of segments into which the spring was divided, the characteristics of the material and the coordinates of equidistant points distributed along the spring, Figure 9. Using this model allowed for the detection of contact between the spiral of the spring using the inertia of each spiral. So, by Modelling the spring with this module, a behaviour close to reality was obtained [38].

3. Results

Following the development of the kinematic virtual model, Figure 10 and dynamic simulations were performed to determine whether the valve complied with the displacement law imposed by the cam [34]. Thus, it can be observed that the valve reached a maximum speed of 3 m/s and a maximum acceleration of 2620 m/s² for the considered maximum speed.

It can be seen in the kinematic analysis that the valve followed exactly the profile of the cam. This is because neither the forces in the system nor the inertia of the parts are taken into account in this analysis. The following behaviour is clear from the comparison of kinematic analysis with dynamic analysis at low operating speeds: the dynamic behaviour of the system remains unchanged, and at high speeds due to the influence of rigidity and body mass displacement, speed and acceleration have different values than those required, which is due to inertial forces and shock loads [45]. So, the dynamic behaviour of the components of the valvetrain system are more important at high speeds [40]. However, due to the way in which the contacts between the parts were modelled and due to the errors that may occur in determining the cam profile, small variations of the valve acceleration were obtained in the area of its maximum opening for the considered maximum camshaft speed. These variations can be seen more clearly when analysing the shocks in the valve.

Additionally, with the help of the virtual model it was possible to determine the values of the contact forces between the cam and the valve, respectively the valve and the valve or the valve and its seat. Thus, it can be seen that the force between the cam and the cleat is transmitted entirely to the valve, with the hydraulic cleat behaving like a pillow of oil of constant volume—more due to the way of defining contacts, approximation of surfaces with triangles, small variations of contact forces when opening and closing the valve, respectively (Figure 11).

The forces acting on the valve are influenced by the stiffness and the damping characteristics of the spring, with respective to the valve seat, but also by the geometry and the mass of the components. The type of lubrication and friction forces between the components in contact are other factors influencing these forces [32,46].

Additionally, contact between cam and tappet has a complex mechanism. This is due to variation in the type of lubrication during operation: elastohydrodynamic, mixed and hydrodynamic [47,48]. Linked to properties of this contact, it can also be said that during the cam rotation, the friction force between the cam and the tappet changes. So, when the cam acts on the tappet in the opening race we have friction by rolling, and when the top of the cam came into action we have slipping through sliding [47].

Validation of the virtual model was achieved by comparing its dynamic accelerations with those measured experimentally on the test stand. It can be seen in Figure 12, Figure 13 and Figure 14 that the difference between the two accelerations is below 5% and so the model can be considered valid.

Before presenting the results, it should be noted that the influence of the temperature and pressure in the combustion chamber as well as vibrations during the operation of the engine have not been considered. Additionally, the Virtual LAB program presents some limitations in terms of Modelling certain components. The valve spring considers some simplified behaviours. One important point is related to torque resulting during the compression, extension and movement of it. This torque could not be evaluated with high accuracy because it was not established if it was transmitted to the upper seating surface and the valve retaining ring, or the valve guide and one at the bottom. One example of this limitation is revealed in Figure 12, Figure 13 and Figure 14, where it can be observed that the bounce phenomenon of the valve upon its seat could not be reproduced, with values near 250 degrees of the crank angle.

In Figure 12 and Figure 13, the average difference is less than 5%, but some particulars areas occur with a higher variation mainly due to the CAD model definition and the contact between components. A fine mesh would lead us to a high computational time comparing with the improvement that could be obtained in the results. We use a middle approach in order to obtain the best ratio between the computational time and the accuracy of the results.

Another inconvenience was represented by how to achieve the hydraulic tappet. Using the HLA element did not allow for the reproduction of the relative rotation motion between the slaughter and the lower housing that is in contact with the end of the valve stem.

3.1. Influence of Camshaft Rotation Speed

The first factor analysed using the virtual model was the speed of the camshaft. The simulation of the influence of the camshaft speed on the rotational motion of the valve was performed by modifying the motion driver inserted in the rotating link of the cam.

Thus, the value of the angular rotation speed was set at 350 rpm, 750 rpm, 1000 rpm, 1250 rpm and 2000 rpm, and for each case an individual analysis was performed.

The results showed that in the case of changing the speed of the camshaft, an increase in the angle and the speed of rotation of the valve was obtained. As can be seen in Figure 15, the variation of the rotation angle is approximately linear. From the point of view of the rotational speed, it can be stated that with the increase of the speed of the camshaft, an increase is obtained, its variation being able to be approximated with a parabola (Figure 16).

So, by increasing the speed of the camshaft, an increase in the rotation angle of the valve was obtained without respecting the linearity. This was mainly due to the contact between the cam and the cleat, with sliding and rolling, but also to the slip that occurred when transmitting the moment from the cleat to the valve.

3.2. Influence of Friction Coefficient

As modelling in the virtual environment using LMS Virtual Lab v.10 [49] did not allow for the definition of the lubrication type and lubricant properties, in order to determine the influence of the conditions in which the contact between the parts took place on the rotation angle of the valves, three values of the dynamic coefficient were defined. Thus, the first value adopted, μ = 0.05, corresponded to an optimal level of lubrication of the components; the second, μ = 0.075, was assigned to a mixed lubrication regime; and the last value, μ = 0.1, corresponded to a limit lubrication level. The three values considered were used to define the contact forces and the frictional forces assigned to the cylindrical links between the stop and the guide, respectively the valve and the guide.

The results presented in Figure 17 and Figure 18 show that as the coefficient of friction increases, so do the friction forces, which causes a decrease in the rotation angle of the valve, with respective to the speed. It can also be seen that in the case of an increase in this coefficient, a linear dependence was maintained between the value of the rotation angle of the valve for all the cases considered.

Therefore, it can be stated that a high value of the coefficient of friction, as a result of insufficient lubrication, causes a decrease in the rotational motion of the valve for all speeds of the camshaft.

3.3. Influence of the Cam Position to the Axis of Symmetry of the Tappet

Another important factor in the dynamics of the rotation of the valve was considered to be the value of the eccentricity of the cam over the symmetry axis of the tappet. This parameter has been chosen because previous research revealed that the use of an increased eccentricity value causes an increase in the angle and the speed of the tappet rotation and thus an improvement in the rotation motion of the valve [47,50,51,52,53,54,55] can be achieved.

The results obtained from the simulations came to strengthen the above claim, so in both cases where the value of the eccentricity of the cam is increased, an amplification of the rotation angle and angular velocity of the valve was obtained (Figure 19). Additionally, if the value of the eccentricity was kept constant and the friction coefficient was varied, the rotation motion presented the same ascending trend (Figure 20).

So, it can be concluded that the eccentric positioning of the cam over the symmetry axis of the tappet obtained an improvement in the rotation movement of the valve for all five camshaft speeds. This is mainly due to the increase of the moment of rotation given by the eccentric contact between the cam and the tappet.

3.4. Influence of the Spring

The influence of the valve spring on the rotation motion was simulated by modifying its rigidity. This was considered to be the initial stiffness of 42 N/mm and two other rigidities of 36 N/mm and 48 N/mm, corresponding to a softer, more rigid spring (Figure 21).

In order to obtain these rigidities, the dimensional characteristics of the spring, the wire diameter and the average diameter of the spring were required, the rest of the characteristics remaining constant [56,57,58,59].

By modifying the stiffness of the valve spring, an important evolution of the rotation angle was achieved, with respective to the speed of rotation of the valve. Thus, a slight angle amplification, with respective to the velocity speed of the valve, was obtained. This increase was due to the reduction of the contact forces between the components, respectively the reactions in the valve and tappet guide (Figure 22).

When stiffness was increased, a double diminution of the dual rotation angle and speed was obtained. So, the interaction between the components and implicitly the friction forces that opposed to the rotation motion increased.

4. Conclusions

Based on the results obtained using the virtual model of the direct drive mechanism, several conclusions can be drawn. Thus, with the increase in the camshaft speed for all cases considered, there was an amplification of the rotation motion of the valves.

By increasing the value of the friction coefficient in kinematic pairs, a decrease in the rotation of the valve is obtained, with respective to the speed of rotation. This diminution is primarily due to the increase in friction forces that oppose the rotation, so an increase of the reaction forces in the guides.

Eccentric positioning of the cam over the symmetry axis of the hydraulic tappet has an important role in the rotation movement of the tappet with respective to the valve, once the increase of eccentricity produces an improvement in the rotation motion. Moreover, with an increase in the eccentricity, an angle of rotation is obtained that is up to 30% higher.

This considerable improvement is attributed to the momentum of rotation of the tappet, a moment due to the friction force and the arm created by the eccentric position of the cam over the symmetry axis of the tappet. So, by providing a pronounced rotation of the tappet it obtained a higher valve rotation angle.

The elastic spring feature is an important role in the dynamics of the valve rotation motion because if its value is diminished, an amplification of the angle of rotation is obtained and when it increases a decrease thereof. The variation of the rotation angle of the valve is due to the contact forces between the components, forces that decreased with the decreasing of stiffness of the valve spring rigidity.