A novel optimization technique for optimizing the damper top mount characteristics to improve vehicle ride comfort and harshness is developed. The proposed optimization technique employs a new combined objective function based on ride comfort, harshness, and impact harshness evaluation. A detailed and accurate damper top mount mathematical model is implemented inside a validated quarter vehicle model to provide a realistic simulation environment for the optimization study. The ride comfort and harshness of the quarter vehicle are evaluated by analyzing the body acceleration in different frequency ranges. In addition, the top mount deformation is considered as a penalty factor for the system performance. The influence of the ride comfort and harshness weighting parameters of the proposed objective function on the optimal damper top mount characteristics is studied. The dynamic stiffness of the damper top mount is used to describe the optimum damper top mount characteristics for different optimization case studies. The proposed optimization routine is able to find the optimum characteristics of the damper top mount which improve the ride comfort and the harshness performances together.
Damper top mounts are used in the vehicles not only to provide ideal Noise-Vibration-Harshness (NVH) performance but also to improve ride comfort, driving safety, and handling. The ride comfort and harshness can be considered as the vibration response of the vehicle body at different frequency ranges. Vehicle ride comfort can be evaluated by using vertical acceleration of the body up to 20 Hz while the harshness can be considered as the body vertical acceleration in the frequency range over 20 Hz until 100 Hz [
The driver and the passengers are always in contact with different parts of the vehicle chassis during the operation of the vehicle. Therefore, it is expected that reducing the acceleration response of the vehicle body will improve ride comfort and harshness. Some previous studies have shown that the ride comfort and harshness performance of the vehicle can be improved by optimizing the characteristics of the suspension system components [
A numerical procedure for finding the optimum values of the vehicle suspension system parameters has been studied by Pintado and Benitez [
An efficient methodology for the determination of the gradient information, while performing gradient based optimization of an off-road vehicle’s suspension system, has been proposed by Thoresson et al. [
The impact harshness performance of a vehicle is as important as the ride comfort and handling. In a recent study, Aydın and Ünlüsoy [
In this study, a new optimization technique for damper top mount characteristics is presented to improve the ride comfort and harshness performance of a vehicle. A new combined objective function involving ride comfort, harshness, and impact harshness evaluation is proposed, and it is used within an evolutionary optimization routine. The detailed mathematical damper top mount model of [
In this study, a generic quarter vehicle suspension model including a detailed damper top mount model is used. The vehicle is modeled as a two-degree-of-freedom system consisting of two masses which represent the body and wheel. The damper and top mount weights are neglected. The suspension between body mass and wheel mass is modeled using a linear spring and a viscous damper in series with a rubber top mount as shown in Figure
Quarter vehicle model.
The dynamic equations of motion for the quarter vehicle model are written as follows:
Quarter vehicle model parameters.
Parameter | Value | Unit |
---|---|---|
Body mass | 270.8 | kg |
Wheel mass | 46.5 | kg |
Spring stiffness | 32 | kN/m |
Tire stiffness | 320 | kN/m |
Tire damping | 200 | Ns/m |
A detailed damper top mount model developed by the authors is used for the optimization analysis in this study [
Damper top mount model.
As shown in Figure
Measured and simulated time histories of the damper top mount force for a stochastic excitation.
The dynamic stiffness is a commonly used rubber mount characteristic, which describes the change of rubber mount behaviour with the excitation frequency. A comparison between the measured and the simulated dynamic stiffness of the damper top mount is shown in Figure
Measured and simulated damper top mount dynamic stiffness.
The detailed top mount model presented in the previous section can be used to analyze the effect of damper top mount characteristics on the vertical dynamics of a vehicle. However, since the damper top mount operates in series to the damper, that is, transmits the damper force to chassis, the damper top mount model should be combined with a detailed damper model. Therefore, in the quarter vehicle model, the detailed top mount model is used together with the IAE nonlinear damper model [
Combined top mount and damper model.
The damper top mount and the combined top mount-damper models are verified through physical tests performed on a hydraulic component test rig. Figures
Components test rig setup: (a) top mount and (b) top mount together with damper.
The time history of the simulated and the measured damper forces and the damper top mount displacements for a stochastic excitation are plotted in Figures
Comparison of measured and simulated damper top mount behavior: (a)-(b) top mount displacement and (c)-(d) damper force.
The quarter vehicle simulation model is validated through laboratory tests performed using the quarter vehicle test rig shown in Figure
(a) Quarter vehicle test rig at IAE and (b) quarter vehicle model verification.
A comparison of the measured and simulated transfer function magnitudes between body and road accelerations, which are obtained by using a real measured road profile as the excitation, is presented in Figure
Two types of road inputs are used for the ride comfort and harshness optimization analysis. The first type of input is a real road profile selected from the road profile measurement database available of the IAE [
Road inputs: (a) random road and (b) triangle cleat.
The IH events are usually evaluated under specific forward velocities without applying any steering input. In order to evaluate IH performance of a vehicle through computer analysis, the mathematical model of the vehicle can be simulated using a triangle road cleat as the road input. Typical forward speed range for the analysis of IH events is around 60 kph [
As a preparation to the optimization analysis, the authors have performed a parametric study to analyze the influence of the top mount characteristics on vehicle ride comfort and harshness [
Regarding the effect of damper top mount stiffness on vehicle vertical dynamics, a conflict exists between the low frequency ride comfort and the high frequency harshness objectives. The results of the parametric study showed that high top mount stiffness is preferable for improved ride comfort at low frequencies while lower stiffness values provide improved harshness performance during high frequency excitations. As a result of this fact, the dynamic stiffness, which describes the stiffness of the top mount as function of the excitation frequency, can be regarded as the most important characteristic of a top mount. A similar conflict has also been observed during the impact harshness analysis. In order to reduce the magnitude of the first peak of the body acceleration after a triangle cleat input, the top mount stiffness should be low; however, secondary peaks attain higher values in this case.
Following the concluding remarks of the parametric analysis in [
As the first stage of the optimization analysis, the influence of the weighting parameters of the proposed objective function on the optimum damper top mount characteristics, and consequently on the trade-off between the vehicle ride comfort and harshness performance, is investigated. The aim of the optimization process is to improve the ride comfort and harshness by reducing the vertical acceleration of the vehicle body at different frequency ranges, while keeping the damper top mount deformation within the allowable limits. The proposed optimization routine is shown in Figure
The proposed optimization process for damper top mount characteristics.
In the optimization analysis, the weighting parameters of the proposed objective function
In the following sections, first the effect of the ride comfort and harshness weighting factors on the calculated optimal dynamic stiffness of the damper top mount is analyzed. Then, the optimal dynamic stiffness of the damper top mount together with the corresponding body vertical acceleration and top mount deformation is compared for three different optimization cases: optimal ride comfort, optimal harshness, and combined optimal performance.
The dynamic stiffness is a commonly used rubber mount characteristic which describes the relationship between the stiffness and the excitation frequency. The ride comfort and harshness performance of a vehicle are evaluated at different excitation frequency ranges. Therefore, the dynamic stiffness, which defines the change of rubber mount characteristics with frequency, is used to present the calculated optimal characteristics of the damper top mount.
Figure
Change of top mount dynamic stiffness with ride comfort weighting.
Figure
Change of top mount dynamic stiffness with harshness weighting.
A comparison between each set of weighting parameters in terms of body vertical acceleration and damper top mount deformation is provided in Table
Body vertical acceleration and damper top mount deformation during ride comfort and harshness optimization parameter variation.
Optimization |
RMS |
RMS |
Peak-to-Peak B.Acc. (m/s2) |
Peak-to-Peak TMD (m) |
---|---|---|---|---|
Nominal | 1.4333 | 0.00233 | 13.5064 | 0.0152 |
|
1.3946 | 0.00086 | 13.5949 | 0.0070 |
|
1.3979 | 0.00086 | 13.5371 | 0.0071 |
|
1.3992 | 0.00082 | 13.4852 | 0.0073 |
|
1.4021 | 0.00080 | 13.4470 | 0.0073 |
|
1.4055 | 0.00079 | 13.4024 | 0.0074 |
|
1.4296 | 0.00186 | 13.6331 | 0.0133 |
|
1.4221 | 0.00174 | 13.6344 | 0.0115 |
|
1.4189 | 0.00155 | 13.6350 | 0.0109 |
|
1.4130 | 0.00138 | 13.6353 | 0.0102 |
|
1.4088 | 0.00102 | 13.6360 | 0.0091 |
The results presented above suggest that the body vertical acceleration RMS in the harshness optimization (with weighting factors
As mentioned before, three different optimization cases for ride comfort, harshness, and combined ride comfort and harshness have been studied. The optimum ride comfort is obtained by setting the ride comfort weighting parameter
Normalized optimum top mount characteristics.
Optimization set |
|
|
|
|
|
---|---|---|---|---|---|
Nominal | 1.0000 | 1.0000 | 1.0000 | 1.0000 | 1.0000 |
Optimum ride | 1.9691 | 1.0612 | 0.5875 | 1.9672 | 1.3372 |
Optimum harshness | 1.2712 | 1.4456 | 1.7284 | 0.7313 | 0.5158 |
Combined optimum | 1.2281 | 1.8306 | 0.6942 | 0.5180 | 0.8663 |
Figure
Dynamic stiffness of the damper top mount for different optimization cases.
Table
Body vertical acceleration and damper top mount deformation for optimization cases.
Optimization |
RMS |
RMS |
Peak-to-Peak B.Acc. (m/s2) |
Peak-to-Peak TMD (m) |
---|---|---|---|---|
Nominal | 1.4333 | 0.00233 | 13.5064 | 0.0152 |
Optimum Ride | 1.3946 | 0.00086 | 13.5949 | 0.0070 |
Optimum harshness | 1.4296 | 0.00186 | 13.6331 | 0.0133 |
Combined optimum | 1.4314 | 0.00177 | 13.1920 | 0.0118 |
Body vertical acceleration in the ride comfort frequency range for different optimization cases.
Body vertical acceleration in the harshness frequency range for different optimization cases.
Figures
Deformation of the top mount must be constrained due to the space limitations of the vehicle suspension system. Low top mount stiffness values imposed by the optimization process can lead to high peaks in top mount deformation, especially around the body and wheel natural frequencies, which might violate the design constraints. The PSD of the damper top mount deformation in ride and harshness frequency ranges are presented in Figures
Damper top mount deformation in the ride comfort frequency range for different optimization cases.
Damper top mount deformation in the harshness frequency range for different optimization cases.
As the vehicle crosses over the triangle road cleat presented in the previous sections, oscillations are observed in the body acceleration and the damper top mount deformation. The performance of the suspension can be evaluated by considering the magnitudes of the acceleration peaks as the indication of the impact harshness. In addition to this, the peaks in damper top mount displacement are critical due to the space limitations. Therefore, the metric for the evaluation of IH is selected as the peak-to-peak values of body acceleration and damper top mount deformation. In order to improve the IH, the sum of these two performance metrics (
Figure
Body acceleration and damper top mount deformation during impact harshness event for different optimization cases.
The deformation of the damper top mount is expected to decrease with increasing top mount stiffness. As shown in Figure
In this study, a new optimization methodology for optimizing the damper top mount characteristics to improve the vehicle ride comfort and harshness is presented. A combined objective function including the ride comfort, harshness, and impact harshness evaluations is developed and used within the optimization routine. Furthermore, a detailed damper top mount mathematical model is implemented inside a quarter vehicle model to provide accurate simulation results for the optimization study.
As the first stage of the optimization study, the influence of ride comfort and harshness weighting parameters of the objective function on the calculated optimal damper top mount characteristics is studied. The optimal damper top mount characteristics have been presented using dynamic stiffness curves. Furthermore, the influence of the objective function weighting parameters on vehicle ride comfort, harshness, and impact harshness is shown by using the RMS and peak-to-peak values of the vertical acceleration and damper top mount deformation. It is observed that increasing the ride comfort weighting parameter increases the calculated dynamic stiffness of the top mount. Contrarily, lower dynamic stiffness is obtained by using higher harshness weighting parameter. This suggests that a ride comfort oriented performance optimization leads to harder top mount characteristics, while softer damper top mount characteristics are imposed as a result of the harshness optimization.
The optimization results obtained by using the combined objective function with equal ride comfort and harshness weighting factors showed that the combined optimal top mount characteristics are closer to the optimum harshness characteristics. This is mainly due to the structure of the combined objective function proposed in this study. The combined objective function, with all weighting parameters set to one, includes only one ride comfort related component (0–20 Hz acceleration RMS) but three harshness related components (20–50 Hz and 50–80 Hz acceleration RMS, and peak-to-peak body acceleration). The idea behind having higher number of harshness performance components in the objective function is related to the roles of the damper and the damper top mount in the suspension system. The top mount is mainly responsible for isolating the body from high frequency excitations while the damper is responsible for the low frequency isolation. The task of the ride comfort component included in the proposed objective function is to guarantee that the selected top mount does not deteriorate the ride comfort. On the other hand, the three harshness related components in the objective function are related to the main task of the top mount in the suspension system.
Body acceleration
Cost function for the ride comfort and harshness
Cost function for the impact harshness
Tire damping coefficient
Top mount deformation
Damping force of the top mount
Damper force
Elastic force of the top mount
Friction force of the top mount
Maximum friction force of the top mount
The reference value of the state
Top mount force subjected to the vehicle body
Total force generated from the damper and top mount combination
Viscous force of the top mount
Impact harshness
Spring stiffness of the Maxwell element of the top mount
Stiffness coefficients of the nonlinear elastic element of the top mount
Spring stiffness
Tire stiffness
Body mass
Wheel mass
The overall objective function
Power spectral density
Optimization weighting parameters
Weighting parameters normalization factors
Normalized weighting parameters
Root mean square
Ride comfort and harshness
Power spectral density of the top mount deformation
Power spectral density of the body vertical acceleration
The reference value of the state
Vehicle body displacement
Maximum positive peak of the body vertical acceleration over triangle road cleat
Minimum negative peak of the body vertical acceleration over triangle road cleat
Maximum positive peak of the top mount deformation over triangle road cleat
Minimum negative peak of the top mount deformation over triangle road cleat
Displacement inside the Maxwell element of the top mount
Damper displacement
The parameter which determines how fast the friction force develops in relation to the displacement
Damper connection displacement
Top mount displacement
Road input displacement
Wheel displacement
The ratio between the friction force and the maximum friction force.
The authors declare that there is no conflict of interests regarding the publishing of this paper.