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Abstract:The solid model of a vehicular double wishbone type front suspension was established. After achieving the data of key points, the kinematics simulation analysis of simplified model was carried out. The change of the alignment parameters under the condition of steering and bouncing was analyzed. The results met the requirement of front suspension.
Keywords：Double wishbone type suspension; Solid model; Kinematics analysis
I.INTRODUCTION
Front suspension system is an important part of the car system, which have a critical impact on automotive handling stability and ride quality. By studying the wheel alignment of double wishbone front suspension when certain vehicle steering and bouncing, you can accurately grasp the suspension characteristics and provide a reference basis for improved design
II. SOLID MODEL
Take the double-wishbone type front suspension of certain pickup as an example. Build the three-dimensional models of various parts. Then assemble them to get the solid model of the double-wishbone front suspension. Due to bilateral symmetry，we just take half of it into research，as shown in Figure 1.
Figure 1 1/2 Solid Model of double wishbone type front suspension
III. KINEMATIC MODEL OF DOUBLE-WISHBONE FRONT SUSPENSION
Regard the kingpin, the steering knuckle and the wheel as a whole. The single-sided double-wishbone suspension actually consists of the upper arm, the lower arm, the steering knuckle (kingpin) and the frame. It is a spatial four-bar linkage of two-degree-of-freedom. The length of the upper and lower arm is unequal. And the hinges joined the arms and the frame are not on the same plane.All of these lead to the results of the kingpin inclination and the caster angle. Its kinematic diagram is shown in Figure 2.
Figure 2 1/2 Kinematic Model of double wishbone type front suspension
A: Oscillation Centre of Upper Arm
B: Oscillation Centre of Lower Arm
C:Intersection Point of Kingpin Axis and Knuckle Axis
D:Upper Ball Joint Centre of Kingpin
E: Lower Ball Joint Centre of Kingpin
F:Ball Joint Centre of Steering Knuckle Arm
G:Wheel Centre
H:Steering Trapezium Break-point
To simplify the calculation, the coordinate of each space point could be used to calculate the camber angle, the kingpin inclination, the caster angle and toe-in.
IV. VIRTUAL PROTOTYPE
In the actual vehicle, the upper arm, the lower one and the steering knuckle could bear extremely static load and dynamic load. The strength and stiffness of it are also considerable excellent. So, in this article, the upper and lower arm together with the steering knuckle are regarded as rigid and the actual shape of them are not been taken into consideration. Meanwhile the wheel is treated as rigid as well, which means that the elastic deformation of it should not be considered, to make the calculation simpler.
When the virtual prototype is been build, regard the connecting center of the left and right upper arm’s oscillation center on the front suspension as the coordinate origin. 3D coordinate of several key points could be measured. They are shown in the following table.
TABLE 1COORDINATE OF KEY POINTS
KEY POINT
COORDINATE X Y Z
Inner end point of left upper arm 345.75 0.0 0.0
Outer end point of left upper arm 568.75 0.0 0.0
Inner end point of left lower arm 245 -238.5 10.7
Outer end point of left lower arm 604.9 -246.9 10.7
Inner end point of left tie rod 250.0 -163.0 303.0
Outer end point of left tie rod 549.7 -170.5 139.0
The 1/2 suspension model could be established according to the data in the table above. Due to the bilateral symmetry, the coordinate of the key points in the suspension on the right side could be calculated to known. Thus the model of the front suspension could be built, as shown in figure 3. In order to simulate the actual motion, the constraints added to it are supposed to be:
4 Revolute Joints
8 Spherical Joints
3 Translational Joints
4 Fixed Joints
2 Inplane Primitive Joints
There are 15 moving parts in total. According to Gruebler rule, the model’s degrees of freedom are obtained by calculation as: DOF=15*6-4*5-8*3-4*5-4*6-2*1=5
So, in the model built above, only the rotation of the wheel is restrained, while the other five motions are not.
Figure 3 Virtual Prototype of the double wishbone type front suspension
V. WHEEL ALIGNMENT PARAMETERS
The caster angle of the front wheel can provide stable self- aligning torque, which can ensure the straight driving of the vehicle. However, this torque should not be too large in case of the result of hard steering. Generally,the caster angle of FF vehicle is 0～3°,that of FR is 3～10°. Due to the air pressure of tire decreasing and the elasticity increasing of Modern high speed vehicle, the stabilizing moment increase. So, the caster angle could decrease close to zero, even to a negative value.
To ensure the proper self- aligning torque of the vehicle, the kingpin inclination of the front wheel should be designed, which will contribute to the good handling stability. The angle should not be too large, otherwise, when turning,which increase the friction resistance between the tire and the road. And these not only cause hard steering, but also lead to accelerate the wear of the tire.
The camber angle of the front wheel has the function of location, which makes the tire wear harmonious and also reduce the load of the outer bearing on the hub. Besides, it matches the arched road very well. Generally, take the camber angle to be 1°。 When the vehicle is driving in the straight direction, the wheel bouncing may be caused by the rough road surface. If the change of the camber angle is relatively violent during the high speed driving, it will result the shimmy of the front wheel. And this will reduce the stability of the vehicle when driving at a high speed. The suitable change relative to the frame ranges from -2°to +0.5°/50mm when jumping in general.
The toe-in and the camber angle of the front wheel work together to remove the fact that the wheel is rolling together with dragging due to the outward separation of the wheel. Thus it guides the front wheel driving in the straight direction. The toe-in is 0～12mm in general. However, the toe-in ranges from 0 to -0.5°/50mm when the front wheel jumps.
VI.SIMULATION ANALYSIS
1.Parallel jump of both sides of the wheel
Add a drive to each wheel in the built virtual prototype. The displacement function of the wheel is 50*sin(360d*time). Therefore, the added model has 3 DOF due to the added motivation, which means adding a constraint to it. Because of the consistency of the wheel motivation and the symmetry of the suspension, taking single-side wheel into research is enough.
Figure 4 Variation curve of the caster angle when the wheel jumps.
Figure 5 Variation curve of the kingpin inclination when the wheel jumps.
Figure 6 Variation curve of the camber angle when the wheel jumps.
Figure 7 Variation curve of the toe-in when the wheel jumps.
From the figures above, what we can see is that when the wheel within the bounce limit of 100mm, the caster angle ranges from 1.3° to 3.3°, variable quantity is about 2°; The kingpin inclination ranges from 8.58° to 9.03°, with mean variable quantity of 0.5°; the camber angle ranges from 0.21° to 0.65°, with meaning variable quantity of 0.44°; toe-in ranges 2.11mm to 4.11mm. The changes met the requirement of front suspension, and does not make a difference to the handling. Thus, it guarantees the straight-line running of vehicle.
2.Steering
In the virtual prototype built above (shown in figure 3), alternate the direction of the translational joint between the wheels and the platform to be horizontal. Meanwhile add steering actuation to the translational joint which represents the motion of rack and pinion steering gear. The displacement function is 30.0 * sin(360d*time). The DOF of the modified model is 4.
Figure 8 Variation curve of the kingpin inclination when the wheel steers.
Figure 9 Variation curve of the caster angle when the wheel steers.
Figure 10 Variation curve of the camber angle when the wheel steers.
What can be seen from the figure 8, 9 and 10 is that, with the change of the turning angle of the wheel, the kingpin inclination ranges from 8.32°to 8.35°,the caster angle ranges from 2.44°to 2.54°， the camber angle ranges from -0.72°to 1.22°.The variable quantity is relatively large, which will lead to the wear of the tire.
VII. CONCLUSION
The solid model of a double wishbone type front suspension was established. After achieving the data of key points, the kinematics simulation analysis of simplified model was carried out.
Due to the kinematics simulation analysis, we can come to a conclusion that The change of the alignment parameters under the condition of steering and bouncing is less, which is able to ensure the vehicle to has the good handling stability
REFERENCES:
[1] CHENLi-qing， WANGQi-rui, CHENWu-wei， SHI Pei-cheng.Analysis of handling stability of torsion-bar double wishbone independent suspension based on ADAMS software Journal of Hefei University of Technology (Natural Science) 2005,(4).
[2] Tan Yong-gang Motion Character Analysis of Double-Wishbone Suspension. SHANGHAI AUTO,2006,(01).
[3] Chen Jia-rui. Car Structure（Second Edition,Rudin）.
[4] Automotive Engineering Manuals Editorial Committee. Automobile Engineering Manual. Beijing: China communications press, 2001.
(编辑：WYQ)
Keywords：Double wishbone type suspension; Solid model; Kinematics analysis
I.INTRODUCTION
Front suspension system is an important part of the car system, which have a critical impact on automotive handling stability and ride quality. By studying the wheel alignment of double wishbone front suspension when certain vehicle steering and bouncing, you can accurately grasp the suspension characteristics and provide a reference basis for improved design
II. SOLID MODEL
Take the double-wishbone type front suspension of certain pickup as an example. Build the three-dimensional models of various parts. Then assemble them to get the solid model of the double-wishbone front suspension. Due to bilateral symmetry，we just take half of it into research，as shown in Figure 1.
Figure 1 1/2 Solid Model of double wishbone type front suspension
III. KINEMATIC MODEL OF DOUBLE-WISHBONE FRONT SUSPENSION
Regard the kingpin, the steering knuckle and the wheel as a whole. The single-sided double-wishbone suspension actually consists of the upper arm, the lower arm, the steering knuckle (kingpin) and the frame. It is a spatial four-bar linkage of two-degree-of-freedom. The length of the upper and lower arm is unequal. And the hinges joined the arms and the frame are not on the same plane.All of these lead to the results of the kingpin inclination and the caster angle. Its kinematic diagram is shown in Figure 2.
Figure 2 1/2 Kinematic Model of double wishbone type front suspension
A: Oscillation Centre of Upper Arm
B: Oscillation Centre of Lower Arm
C:Intersection Point of Kingpin Axis and Knuckle Axis
D:Upper Ball Joint Centre of Kingpin
E: Lower Ball Joint Centre of Kingpin
F:Ball Joint Centre of Steering Knuckle Arm
G:Wheel Centre
H:Steering Trapezium Break-point
To simplify the calculation, the coordinate of each space point could be used to calculate the camber angle, the kingpin inclination, the caster angle and toe-in.
IV. VIRTUAL PROTOTYPE
In the actual vehicle, the upper arm, the lower one and the steering knuckle could bear extremely static load and dynamic load. The strength and stiffness of it are also considerable excellent. So, in this article, the upper and lower arm together with the steering knuckle are regarded as rigid and the actual shape of them are not been taken into consideration. Meanwhile the wheel is treated as rigid as well, which means that the elastic deformation of it should not be considered, to make the calculation simpler.
When the virtual prototype is been build, regard the connecting center of the left and right upper arm’s oscillation center on the front suspension as the coordinate origin. 3D coordinate of several key points could be measured. They are shown in the following table.
TABLE 1COORDINATE OF KEY POINTS
KEY POINT
COORDINATE X Y Z
Inner end point of left upper arm 345.75 0.0 0.0
Outer end point of left upper arm 568.75 0.0 0.0
Inner end point of left lower arm 245 -238.5 10.7
Outer end point of left lower arm 604.9 -246.9 10.7
Inner end point of left tie rod 250.0 -163.0 303.0
Outer end point of left tie rod 549.7 -170.5 139.0
The 1/2 suspension model could be established according to the data in the table above. Due to the bilateral symmetry, the coordinate of the key points in the suspension on the right side could be calculated to known. Thus the model of the front suspension could be built, as shown in figure 3. In order to simulate the actual motion, the constraints added to it are supposed to be:
4 Revolute Joints
8 Spherical Joints
3 Translational Joints
4 Fixed Joints
2 Inplane Primitive Joints
There are 15 moving parts in total. According to Gruebler rule, the model’s degrees of freedom are obtained by calculation as: DOF=15*6-4*5-8*3-4*5-4*6-2*1=5
So, in the model built above, only the rotation of the wheel is restrained, while the other five motions are not.
Figure 3 Virtual Prototype of the double wishbone type front suspension
V. WHEEL ALIGNMENT PARAMETERS
The caster angle of the front wheel can provide stable self- aligning torque, which can ensure the straight driving of the vehicle. However, this torque should not be too large in case of the result of hard steering. Generally,the caster angle of FF vehicle is 0～3°,that of FR is 3～10°. Due to the air pressure of tire decreasing and the elasticity increasing of Modern high speed vehicle, the stabilizing moment increase. So, the caster angle could decrease close to zero, even to a negative value.
To ensure the proper self- aligning torque of the vehicle, the kingpin inclination of the front wheel should be designed, which will contribute to the good handling stability. The angle should not be too large, otherwise, when turning,which increase the friction resistance between the tire and the road. And these not only cause hard steering, but also lead to accelerate the wear of the tire.
The camber angle of the front wheel has the function of location, which makes the tire wear harmonious and also reduce the load of the outer bearing on the hub. Besides, it matches the arched road very well. Generally, take the camber angle to be 1°。 When the vehicle is driving in the straight direction, the wheel bouncing may be caused by the rough road surface. If the change of the camber angle is relatively violent during the high speed driving, it will result the shimmy of the front wheel. And this will reduce the stability of the vehicle when driving at a high speed. The suitable change relative to the frame ranges from -2°to +0.5°/50mm when jumping in general.
The toe-in and the camber angle of the front wheel work together to remove the fact that the wheel is rolling together with dragging due to the outward separation of the wheel. Thus it guides the front wheel driving in the straight direction. The toe-in is 0～12mm in general. However, the toe-in ranges from 0 to -0.5°/50mm when the front wheel jumps.
VI.SIMULATION ANALYSIS
1.Parallel jump of both sides of the wheel
Add a drive to each wheel in the built virtual prototype. The displacement function of the wheel is 50*sin(360d*time). Therefore, the added model has 3 DOF due to the added motivation, which means adding a constraint to it. Because of the consistency of the wheel motivation and the symmetry of the suspension, taking single-side wheel into research is enough.
Figure 4 Variation curve of the caster angle when the wheel jumps.
Figure 5 Variation curve of the kingpin inclination when the wheel jumps.
Figure 6 Variation curve of the camber angle when the wheel jumps.
Figure 7 Variation curve of the toe-in when the wheel jumps.
From the figures above, what we can see is that when the wheel within the bounce limit of 100mm, the caster angle ranges from 1.3° to 3.3°, variable quantity is about 2°; The kingpin inclination ranges from 8.58° to 9.03°, with mean variable quantity of 0.5°; the camber angle ranges from 0.21° to 0.65°, with meaning variable quantity of 0.44°; toe-in ranges 2.11mm to 4.11mm. The changes met the requirement of front suspension, and does not make a difference to the handling. Thus, it guarantees the straight-line running of vehicle.
2.Steering
In the virtual prototype built above (shown in figure 3), alternate the direction of the translational joint between the wheels and the platform to be horizontal. Meanwhile add steering actuation to the translational joint which represents the motion of rack and pinion steering gear. The displacement function is 30.0 * sin(360d*time). The DOF of the modified model is 4.
Figure 8 Variation curve of the kingpin inclination when the wheel steers.
Figure 9 Variation curve of the caster angle when the wheel steers.
Figure 10 Variation curve of the camber angle when the wheel steers.
What can be seen from the figure 8, 9 and 10 is that, with the change of the turning angle of the wheel, the kingpin inclination ranges from 8.32°to 8.35°,the caster angle ranges from 2.44°to 2.54°， the camber angle ranges from -0.72°to 1.22°.The variable quantity is relatively large, which will lead to the wear of the tire.
VII. CONCLUSION
The solid model of a double wishbone type front suspension was established. After achieving the data of key points, the kinematics simulation analysis of simplified model was carried out.
Due to the kinematics simulation analysis, we can come to a conclusion that The change of the alignment parameters under the condition of steering and bouncing is less, which is able to ensure the vehicle to has the good handling stability
REFERENCES:
[1] CHENLi-qing， WANGQi-rui, CHENWu-wei， SHI Pei-cheng.Analysis of handling stability of torsion-bar double wishbone independent suspension based on ADAMS software Journal of Hefei University of Technology (Natural Science) 2005,(4).
[2] Tan Yong-gang Motion Character Analysis of Double-Wishbone Suspension. SHANGHAI AUTO,2006,(01).
[3] Chen Jia-rui. Car Structure（Second Edition,Rudin）.
[4] Automotive Engineering Manuals Editorial Committee. Automobile Engineering Manual. Beijing: China communications press, 2001.
(编辑：WYQ)