Vibration Performance Analysis of a Mining Vehicle with Bounce and Pitch Tuned Hydraulically Interconnected Suspension
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Abstract
The current investigations primarily focus on using advanced suspensions to overcome the tradeoff design of ride comfort and handling performance for mining vehicles. It is generally realized by adjusting spring stiffness or damping parameters through active control methods. However, some drawbacks regarding control complexity and uncertain reliability are inevitable for these advanced suspensions. Herein, a novel passive hydraulically interconnected suspension (HIS) system is proposed to achieve an improved ride-handling compromise of mining vehicles. A lumped-mass vehicle model involved with a mechanical–hydraulic coupled system is developed by applying the free-body diagram method. The transfer matrix method is used to derive the impedance of the hydraulic system, and the impedance is integrated to form the equation of motions for a mechanical–hydraulic coupled system. The modal analysis method is employed to obtain the free vibration transmissibilities and force vibration responses under different road excitations. A series of frequency characteristic analyses are presented to evaluate the isolation vibration performance between the mining vehicles with the proposed HIS and the conventional suspension. The analysis results prove that the proposed HIS system can effectively suppress the pitch motion of sprung mass to guarantee the handling performance, and favorably provide soft bounce stiffness to improve the ride comfort. The distribution of dynamic forces between the front and rear wheels is more reasonable, and the vibration decay rate of sprung mass is increased effectively. This research proposes a new suspension design method that can achieve the enhanced cooperative control of bounce and pitch motion modes to improve the ride comfort and handling performance of mining vehicles as an effective passive suspension system.
Keywords
Hydraulically interconnected suspension Transfer matrix method Modal vibration analysis Ride comfort Handling performance Mining vehicle1 Introduction
Mining vehicles are an important underground device for the transportation of minerals and staff. Recently, higher requirements on their isolation vibration performance have been demanded. However, the vehicle body often experiences continuous and excessive vibrations owing to harsh working conditions. This can lead to discomfort and seriously affect the physical and mental health of staff [1]. Moreover, the long longitudinal distance between the axles and large load change in mining vehicles can aggravate the vehicle body pitch motion under continuous upslope and downslope roads in the mines. The severe pitch motion is the primary source of the longitudinal vibration to be experienced at points above the center of gravity (CG) of the vehicle body. Simultaneously, it intensifies the load transfer between the front and rear wheels, resulting in a safety accident. To improve the carrying capacity and reduce the maintenance cost, leaf spring suspension has been used as the typical suspension system for mining vehicles, but it cannot effectively suppress the vehicle body vibration.
It is known that the vehicle suspension system determines the full vehicle performances, such as ride comfort and handling safety [2]. Its properties can be described by using the combination of four suspension modes: bounce, pitch, roll, and warp [3]. For mining vehicles, the dynamic performance primarily depends on the coupled motion between the bounce and pitch modes. Thus, the reduction in vehicle body bounce and pitch motions is crucial to improve the ride comfort and stability of mining vehicles. However, the conventional suspension (CS) cannot well coordinate the bounce and pitch modes of the vehicle body. It is difficult to simultaneously obtain better ride comfort and handling performance by adjusting the suspension modal properties. To solve these problems, the remarkable advantages of active suspension (AS) have attracted the attention of researchers. Many control methods have been proposed to achieve the preferable vehicle performances, such as fuzzy logic control [4], optimal control [5], backstepping control [6], predictive control [7], and adaptive control [8]. Wu et al. [9] designed the active front steering (AFS) system by using the sliding mode control method to effectively improve vehicle handling and stability. Cheng et al. [10] proposed a human–machine cooperative-driving controller with a hierarchical structure to enhance vehicle dynamic stability effectively to ensure the driver’s intention. Li et al. [11] combined the adaptive square-root cubature Kalman filter with the integral correction fusion to acquire the slide-slip angle information for vehicle active safety control. Wong et al. [12] presented a novel integrated controller to coordinate the interactions among the AS, AFS, and direct yaw moment control (DYC), and it could effectively improve the lateral and vertical dynamics of the vehicle. Although these advanced control techniques can preferably solve the contradiction of vehicle performances, some drawbacks regarding control complexity, uncertain reliability, and high cost are inevitable.
To overcome these drawbacks of the CS and AS, a passive interconnected suspension (IS) system can be used alternatively owing to its simplicity, reliability, and zero energy consumption. The IS system between the individual wheel stations is typically realized through mechanical [13], hydraulic [14], and pneumatic [15] methods. The movement of any one of the wheels can generate the forces at other wheel stations. Its remarkable advantage is the passive decoupling of four suspension modes. In other words, this suspension can own the soft stiffness in the bounce and warp modes, and the stiff stiffness in the pitch and roll modes, simultaneously. In recent decades, many research efforts have been focused upon using interconnected suspension systems [16, 17]. Behave [18] developed a parametric study of the influence of pneumatic pitch-plane interconnection arrangements on vehicle ride performance. Yao et al. [19] designed a novel dual-mode interconnected suspension to optimize conflicting vehicle performance requirements by switching different modes. Guo et al. [20] devised a hydro–pneumatic interconnected suspension to enhance vehicle ride, traction ability, and trafficability. Zhang et al. [21] presented the research on the multibody system dynamics of vehicles fitted with HIS systems, and derived the impedance matrix of hydraulic subsystems for a roll-plane HIS system with linear parameters. Cao et al. [17] proposed interconnected hydro–pneumatic suspensions in roll planes and analyzed the dynamic characteristics of the HIS system at the full car level. Ding et al. [22] investigated the roll dynamics of a tri-axle truck model with the HIS system based on the established dynamic equations of motion for the coupled system. Zhu et al. [23] developed an investigation into the road-holding ability of a vehicle equipped with a hydraulically interconnected roll-plane suspension system. Zhou et al. [24] provided the parameter sensitivities of a half-car fitted with the HIS system using a global sensitivity analysis method. Wang et al. [25] proposed a new hydraulically interconnected inertia-spring-damper suspension to coordinate ride comfort and handling stability. The HIS used in the studies above has been proven capable of achieving good dynamic performances compared with the CS.
The vibration property of mining vehicles is easily subject to both the vertical bounce and pitch motions. Therefore, a suppression that can reduce bounce and pitch motions is essential for the suspension design of mining vehicles. A novel HIS system is proposed herein to effectively control the bounce and pitch motions to improve the ride comfort and handling performance. The remainder of the paper is organized as follows. Section 2 presents the description of a HIS-equipped vehicle. The modeling methodology is developed for deriving the dynamic equations of the HIS-equipped vehicle in Section 3. The modal analytical methods of vibration transmissibility and frequency response under stochastic road irregularity inputs are described in Section 4. Section 5 presents the comparative analyses of mining vehicles with the CS and HIS systems. Meanwhile, the sensitivity analysis of loss coefficient for damper valves is also given. Finally, the conclusions are drawn in Section 6.
2 Description of HIS-equipped Vehicles
The wheel assemblies are coupled to each other by the HIS system. In the body bounce motion shown in Figure 1, the top and bottom chambers are compressed and extended, respectively. Owing to the asymmetry of the hydraulic cylinders, every hydraulic circuit contains a small amount of fluid flowing into the accumulators. This leads to a small pressure change in the two hydraulic circuits. Thus, the actuators could generate an additional hydraulic force to restrict the bounce motion of the sprung mass relative to the unsprung mass. In the body pitch motion, all the front and rear suspensions are compressed and extended, respectively. The front and rear cylinder bodies move downward and upward relative to the piston rod, respectively. It reduces the volume of the front top and rear bottom chambers, and simultaneously increases the volume of the front bottom and rear top chambers. Thus, the fluid in circuit B flows into the corresponding accumulator B, and the fluid in the corresponding accumulator A flows into circuit A. Consequently, the pressures in circuits A and B are increased and decreased, respectively. It in return generates the large pitch restoring moment to prevent the vehicle body pitch motion relative to the unsprung mass.
3 Model Development of Vehicles with HIS
To obtain the motion properties of the mechanical–fluid coupled system in Eq. (1), the relationship between flow Q and pressure P of the fluid system must be derived. In this study, the transfer impedance matrix method is employed to describe the relationship between the flow rate Q and pressure P, given as Q = TP, where T is the impedance matrix of the hydraulic subsystem determined by the impedance matrices of the fluid components. As shown in Figure 2, the fluid components primarily include five types of components, namely hydraulic actuators, piston accumulators, three-way junctions, damper valves, and fluid pipelines. For the HIS system, the connection sections of different fluid components are marked by hai (i = 1, 2,…, 25) and hbi, respectively. The state vector composed of the pressure and flow rate (p and q) at the section hji (j = a, b) is defined as x_{ij} = [p q] _{ hij} ^{T} . The transmission matrix N^{k} is employed to describe the relationship between state vectors x_{ij} and x_{ij+1} of the two terminal sections for the kth component, given as x_{ji+1} = N^{k}x_{ji} (k = P,V), where the details of the transfer matrix N^{k} for these fluid components can be found in Ref. [21].
Similarly, the impedance matrix T_{A} of the hydraulic circuit A can also be obtained. Thus, the impedance matrices T_{A} and T_{b} can be combined and expressed as
In Eq. (16), Ĉ = C + C_{h} is the complex damping matrix. C_{h} = D_{1}A_{c}(T − D_{v})^{−1}A_{c}D_{2} is the damping contribution from hydraulic subsystem.
4 Vehicle Vibration Characteristics Analysis
As shown, the system modal characteristic matrix A(s) in Eq. (15) is frequency dependent and this matrix changes with the input frequency s. Based on the definition of the eigenvalue, solutions of the equation |det(A(s) − sI)| = 0 are the eigenvalues of A(s). Owing to the large numerical values of some of the parameters, the exact eigenvalues of A(s) are difficult to obtain by numerical means. Thus, the approximate roots are acceptable if the function J(s) = |det(A(s) − sI)| is approaching a local minimum value in the vicinity of s. To obtain the modal parameters, the Matlab optimization library function fminsearh was used to identify the real eigenvalues and eigenvectors according to the local minimum values.
5 Numerical Results and Discussions
Physical parameters of a seven-DOF vehicle model
Parameter | Value |
---|---|
Vehicle sprung mass m_{s} (kg) | 3860 |
Pitch moment inertia of sprung mass I_{x} (kg·m^{2}) | 8400 |
Roll moment inertia of sprung mass I_{y} (kg·m^{2}) | 1400 |
Distance from sprung mass CG to front axle a (m) | 1.64 |
Distance from sprung mass CG to rear axle b (m) | 1.49 |
Half width of front axle t_{f} (m) | 0.32 |
Half width of rear axle t_{r} (m) | 0.46 |
Front unsprung mass m_{uf} (kg) | 200 |
Rear unsprung mass m_{ur} (kg) | 260 |
Spring rate of front suspension k_{psf} (N/mm) | 265 |
Spring rate of rear suspension k_{psr} (N/mm) | 265 |
Damping coefficient of front suspension c_{psf} (N∙m/s) | 4880 |
Damping coefficient of rear suspension c_{psr} (N∙m/s) | 4880 |
Spring rate of front suspension k_{bsf} (N/mm) | 129.2 |
Spring rate of rear suspension K_{bsf} (N/mm) | 167.4 |
Vertical stiffness of tire k_{tf}/k_{tr} (N/mm) | 1172 |
Hydraulic system parameters
Parameter | Value |
---|---|
Hydraulic fluid density (kg/m^{3}) | 870 |
Bulk modulus (MPa) | 1400 |
Accumulator pre-charge gas volume (L) | 0.25 |
Accumulator pre-charge pressure (bar) | 10 |
Diameter of cylinder piston (m) | 0.05 |
Diameter of cylinder piston rod (m) | 0.036 |
Mean system pressure P_{0} (bar) | 23 |
Loss coefficient of cylinder valve R_{CV} (GPa∙s/m^{3}) | 1.5 |
Loss coefficient of hydraulic circuit valve R_{HCV} (GPa∙s/m^{3}) | 0.8 |
Loss coefficient of accumulator valve R_{AV} (GPa∙s/m^{3}) | 1.5 |
5.1 Dynamic Performance Evaluation
The identified natural frequencies, damping ratios, and corresponding mode shapes of VCS-EP and VHIS are presented in Table 5. As shown in Table 5, vehicle body–wheel motion-modes referring to the relative motion between body and wheels can be classified into seven modes in terms of the modal shapes. The normalized factor of the state vectors is used to distinguish seven modes. The motion corresponding to the maximum absolute value of the normalized factor in each modal shape represents one mode of the body-wheel motions. The values in the black bold font reveal that the first three mode shapes are called the body-dominated motion-modes, namely roll (1st), bounce (2nd), and pitch (3rd) motions of the sprung mass, and the following four mode shapes are called the wheel-dominated motion-modes, namely, the pitch (4th), bounce (5th), roll (6th), and warp (7th) motions of the unsprung mass. For the VCS-EP, the equivalent stiffness k_{psj} (j = fl, fr, rl, rr) is 265 N/mm. For the VHIS, the equivalent stiffness k_{bsi} (i = fl, fr) and k_{bsj} (j = rl, rr) are 129.2 N/mm and 167.4 N/mm, respectively. In Table 5, the HIS system can effectively increase the pitch mode (the 3rd mode) frequency (from 2.539 Hz/VCS-EP to 2.747 Hz/VHIS) of the sprung mass vibration, and reduce the bounce mode (the 2nd mode) frequency (from 2.351 Hz/VCS-EP to 1.906 Hz/VHIS). The result illustrates that the proposed HIS system can provide a higher pitch mode stiffness owing to the large fluids rapidly flowing into the accumulator in the pitch mode, and the lower bounce mode stiffness owing to the large fluids freely flowing in the hydraulic circuits. Owing to the soft mechanical suspensions, the body roll mode (the 1st mode) frequencies (1.286 Hz/VHIS) of the VHIS are lower than that of the VCS-EP. It is also observed that the proposed HIS system is unable to provide the extra roll mode stiffness.
Additionally, the HIS system can reduce the natural frequencies of the wheel-dominated motion-modes, involving the wheel pitch mode (the 4th mode in VHIS, 9.158 Hz), wheel bounce mode (the 5th mode in VHIS, 10.419 Hz), wheel roll mode (the 6th mode in VHIS, 11.226 Hz), and wheel warp mode (the 7th mode in VHIS, 12.530 Hz). In the previous study [23], it can be seen that the lower warp mode stiffness can improve the ground holding performance. From the comparisons of the mode shapes, the HIS system can decouple the body bounce and pitch modes, and intensify the coupling of wheel bounce and pitch modes, which is beneficial to balance the distribution of the front and rear tire forces. Furthermore, it is observed that the HIS system can increase the damping ratios corresponding to both the body modes (roll, bounce, and pitch) and wheel modes (bounce and pitch) of the integrated system, and the high damping can eliminate transient oscillations.
As shown in Figures 6 and 8, the peak values of the front suspension deflections and front tire dynamic forces are reduced by the HIS under the front wheel input. For the front suspension deflections of the VHIS, the frequency response lower than the natural vibration frequency is slightly enlarged, and that higher than the natural vibration frequency is unchanged; further, the HIS system reduces the transmissibility in high frequency ranges. For the front tire dynamic forces, the proposed HIS system maintains the same transmissibility located before the oscillation frequency, but slightly increases the transmissibility higher than the natural vibration frequency, and the frequency response is reduced in higher frequency ranges. Moreover, the frequency responses of the rear suspension deflections and rear tire dynamic forces under the left wheel input for the VHIS are much larger than those of the VCS-EP. This phenomenon illustrates that a mining vehicle with the HIS system transmits a greater degree of motion to the opposite wheels under the corresponding mode vibration. As shown, the frequency responses of the VHIS exhibit much broader peak ranges than the VCS-EP owing to the interconnection mechanism. For the VHIS, the additional excitation applied to the front or rear wheels can be transmitted much more efficiently to the opposite wheel through the hydraulic system. This result is helpful to balance the dynamic forces between the front and rear wheels, thus enhancing the ground holding performance.
RMS acceleration comparisons
Speed | Vertical acceleration (m/s^{2}) | Pitch angular acceleration (rad/s^{2}) | Roll angular acceleration (rad/s^{2}) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
20 | 30 | 40 | 50 | 20 | 30 | 40 | 50 | 20 | 30 | 40 | 50 | |
Medium-smooth road | ||||||||||||
VCS-EP | 0.783 | 1.515 | 1.621 | 1.610 | 0.399 | 0.482 | 0.871 | 1.245 | 1.712 | 1.087 | 1.214 | 2.00 |
VHIS | 0.614 | 0.886 | 1.102 | 1.260 | 0.274 | 0.410 | 0.612 | 0.833 | 1.101 | 0.873 | 1.454 | 2.100 |
Percentage | 21.58% | 41.52% | 32.02% | 21.74% | 31.33% | 14.94% | 29.74% | 33.09% | 35.69 | 19.69% | 19.77%↑ | 5%↑ |
Rough road | ||||||||||||
VCS-EP | 3.091 | 6.061 | 6.483 | 6.439 | 1.557 | 1.846 | 3.484 | 4.980 | 6.848 | 4.347 | 4.855 | 6.016 |
VHIS | 2.458 | 3.542 | 4.200 | 4.842 | 1.099 | 1.641 | 2.447 | 3.321 | 4.430 | 3.494 | 5.219 | 6.252 |
Percentage | 20.49% | 41.56% | 35.22% | 24.80% | 29.42% | 20.50% | 29.76% | 33.31% | 35.31% | 19.62% | 7.49%↑ | 3.92%↑ |
5.2 Parametric Sensitivity Analysis
Comparisons of natural frequency and damping ratio
R_{CV} (GPa∙s/m^{3}) | R_{HCV} (GPa∙s/m^{3}) | R_{AV} (GPa∙s/m^{3}) | |||||||
---|---|---|---|---|---|---|---|---|---|
1 | 1.5 | 2.5 | 0.4 | 0.8 | 1.6 | 0.1 | 1.5 | 2.5 | |
Roll mode | |||||||||
f_{d} (Hz) | 1.264 | 1.286 | 1.329 | 1.286 | 1.286 | 1.286 | 1.296 | 1.286 | 1.271 |
ξ | 0.077 | 0.097 | 0.117 | 0.097 | 0.097 | 0.097 | 0.097 | 0.097 | 0.099 |
Bounce mode | |||||||||
f_{d} (Hz) | 1.909 | 1.907 | 1.902 | 1.9125 | 1.907 | 1.890 | 1.909 | 1.907 | 1.901 |
ξ | 0.190 | 0.205 | 0.235 | 0.159 | 0.205 | 0.300 | 0.190 | 0.205 | 0.237 |
Pitch mode | |||||||||
f_{d} (Hz) | 2.741 | 2.747 | 2.761 | 2.732 | 2.747 | 2.796 | 2.714 | 2.747 | 3.083 |
ξ | 0.348 | 0.358 | 0.378 | 0.327 | 0.358 | 0.423 | 0.267 | 0.358 | 0.551 |
6 Conclusions and Future Work
A new HIS system to was proposed herein to improve the bounce and pitch motion performances for a mining vehicle. The integrated dynamic equations of the mechanical–hydraulic coupled system were derived using the impedance transfer matrix and free-body diagram methods. Based on the derived equations, the modal analysis method was employed to obtain the free vibration transmissibilities and force vibration responses under different road excitations. The dynamic characteristic comparisons between the VCS-EP and VHIS were presented to verify the prominent advantages of the HIS system. These results illustrated that the proposed HIS system could decouple the bounce and pitch modes, and intensify the coupling of wheel bounce and pitch modes to balance the distribution of tire dynamic forces. Furthermore, the HIS system could provide additional pitch stiffness to control the vehicle pitch motion, reduce the bounce stiffness to improve ride comfort, and increase the corresponding mode damping to eliminate transient oscillations in the lower frequency range.
Herein, the most obvious limitation is that the HIS system could not provide adequate roll stiffness to control the roll mode. Another limitation was that the modal analysis method was linear in this study. However, the suspension system and tire assembly often exhibit many nonlinearities for practical applications. Thus, the performances of the bounce, pitch, and roll modes would be considered for the passive HIS system, and the extension of the proposed methodology to a full nonlinear vehicle model must be explored in the future. Additionally, the semi-active or active control strategy for the HIS system must be considered as future works to improve the ride comfort and handling performance of the mining vehicle based on control theories.
Notes
Authors’ Contributions
JZ and YD was in charge of the whole trial; JZ wrote the manuscript; NZ, BZ, HQ and MZ assisted with sampling and laboratory analyses. All authors read and approved the final manuscript.
Authors’ Information
Jie Zhang, born in 1987, is currently a PhD candidate at State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, China. He received his bachelor degree from Yangtze University, China, in 2011. His research interests include control, modeling, and estimation of driver-vehicle system dynamics.
Yuanwang Deng, born in 1968, is currently an associate professor at College of Mechanical and Vehicle Engineering, Hunan University, China. He received his PhD degree from Huazhong University of Science and Technology, China, in 2002. His research interests include heat transfer theory, engine electronic control technology and mechanical system dynamics.
Nong Zhang, born in 1959, is currently a professor at Automotive Research Institute, Hefei University of Technology, China. He received his PhD degree from University of Tokyo, Japan, in 1989. His current research interests include dynamics and control of automotive systems.
Bangji Zhang, born in 1967, is currently a professor at State Key Laboratory of Advanced Manufacture and Design for Vehicle Body, Hunan University, China.
Hengmin Qi, born in 1990, is currently a PhD candidate at State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, China. He received his bachelor’s degree from China University of Petroleum, China, in 2012. His research interests include design and analysis of hydraulically interconnected suspension system and vehicle system dynamics.
Minyi Zheng, born in 1983, is currently a lecturer at School of Automotive and Transportation Engineering, Hefei University of Technology, China. He received his Ph.D. from Hunan University, China, in 2016 His research interests include vehicle dynamics and parameter identification.
Acknowledgements
The authors sincerely thanks to Assistant Professor Fei Ding of Hunan University for his critical discussion and reading during manuscript preparation.
Competing Interests
The authors declare no competing financial interests.
Funding
Supported by National Natural Science Foundation of China (Grant Nos. 51805155, 51675152), Foundation for Innovative Research Groups of National Natural Science Foundation of China (Grant No. 51621004), and Open Fund in the State Key Laboratory of Advanced Design and Manufacture for Vehicle Body (Grant No. 71575005).
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