Fundamental Issues in Suspension Design for Heavy Road Vehicles

Heavy road vehicles play an important role in the economy of many countries by providing an efficient means of transporting freight. Such vehicles can also have a significant impact on safety, the infrastructure and the environment. The design of the suspension affects the performance of the vehicle in terms of ride, infrastructure damage, suspension working space, energy consumption, rollover stability, yaw stability, braking and traction. The published literature on suspension design for heavy road vehicles is reviewed. It is found that extensive knowledge exists, but that there are areas where improved understanding is needed. Areas identified as fundamental issues requiring attention include ride discomfort criteria, secondary suspensions, and controllable suspensions. Two issues in particular are examined in detail: suspension tuning and suspension configuration. In the tuning of suspension parameter values for vibration performance, numerical optimisation techniques have been used extensively, but generic tuning strategies have not been widely developed. Modal analysis is proposed as a technique for gaining the insight into vehicle vibration behaviour necessary to enable tuning strategies to be devised. As an example, the technique is applied to the pitch-plane vibration of a tractor-semitrailer. In analyses of new suspension configurations or concepts, comparison with alternative concepts is not always made. Lack of such comparisons makes the selection of an optimum concept difficult. Analysis of alternative concepts using simple mathematical models, and comparison of their performance using common criteria, is advocated for enabling informed selection of an optimum. An example involving two alternative roll control systems is used to demonstrate the issue.     

Analysis and optimization of air suspension system with independent height and stiffness tuning

Suspensions play a crucial role in vehicle comfort and handling. Different types of suspensions have been proposed to address essential comfort and handling requirements of vehicles. The conventional air suspension systems use a single flexible rubber airbag to transfer the chassis load to the wheels. In this type of air suspensions, the chassis height can be controlled by further inflating the airbag; however, the suspension stiffness is not controllable, and it depends on the airbag volume and chassis load. A recent development in a new air suspension includes two air chambers (rubber airbags), allowing independent ride height and stiffness tuning. In this air suspension system, stiffness and ride height of the vehicle can be simultaneously altered for different driving conditions by controlling the air pressure in the two air chambers. This allows the vehicle’s natural frequency and height to be adjusted according to the load and road conditions. This article discusses optimization of an air suspension design with ride height and stiffness tuning. An analytical formulation is developed to yield the optimum design of the new air suspension system. Experimental results verify the mathematical modeling and show the advantages of the new air suspension system.     

Heavy vehicle pitch dynamics and suspension tuning. Part I: unconnected suspension

The influence of suspension tuning of passenger cars on bounce and pitch ride performance has been explored in a number of studies, while only minimal efforts have been made for establishing similar rules for heavy vehicles. This study aims to explore pitch dynamics and suspension tunings of a two-axle heavy vehicle with unconnected suspension, which could also provide valuable information for heavy vehicles with coupled suspensions. Based on a generalised pitch-plane model of a two-axle heavy vehicle integrating either unconnected or coupled suspension, three dimensionless measures of suspension properties are defined and analysed—namely the pitch margin (PM), pitch stiffness ratio (PSR), and coupled pitch stiffness ratio (CPSR)—for different unconnected suspension tunings and load conditions. Dynamic responses of the vehicle with three different load conditions and five different tunings of the unconnected suspension are obtained under excitations arising from three different random road roughness conditions and a wide range of driving speeds, and braking manoeuvres. The responses are evaluated in terms of performance measures related to vertical and pitch ride, dynamic tyre load, suspension travel, and pitch-attitude control characteristics of the vehicle. Fundamental relationships between the vehicle responses and the proposed suspension measures (PM, PSR, and CPSR) are established, based on which some basic suspension tuning rules for heavy vehicles with unconnected suspensions are also proposed.     

Magneto-rheological suspensions for improving ground vehicle’s ride comfort,stability, and handling

ABSTRACT

A state-of-the-art discussion on the applications of magneto-rheological (MR) suspensions for improving ride comfort, handling, and stability in ground vehicles is discussed for both road and rail applications. A historical perspective on the discovery and engineering development of MR fluids is presented, followed by some of the common methods for modelling their non-Newtonian behaviour. The common modes of the MR fluids are discussed, along with the application of the fluid in valve mode for ground vehicles’ dampers (or shock absorbers). The applications span across nearly all road vehicles, including automobiles, trains, semi-trucks, motorcycles, and even bicycles. For each type of vehicle, the results of some of the past studies is presented briefly, with reference to the originating study. It is discussed that Past experimental and modelling studies have indicated that MR suspensions provide clear advantages for ground vehicles that far surpasses the performance of passive suspension. For rail vehicles, the primary advantage is in terms of increasing the speed at which the onset of hunting occurs, whereas for road vehicles – mainly automobiles – the performance improvements are in terms of a better balance between vehicle ride, handling, and stability. To further elaborate on this point, a single-suspension model is used to develop an index-based approach for studying the compromise that is offered by vehicle suspensions, using the H₂ optimisation approach. Evaluating three indices based on the sprung-mass acceleration, suspension rattlespace, and tyre deflection, it is clearly demonstrated that MR suspensions significantly improve road vehicle’s ride comfort, stability, and handling in comparison with passive suspensions. For rail vehicles, the simulation results indicate that using MR suspensions with an on-off switching control can increase the speed at which the on-set of hunting occurs by as much as 50% to more than 300%.     

Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.     

Optimal Linear Active Suspensions with Multivariable Integral Control

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

State observer-based sliding mode control for semi-active hydro-pneumatic suspension

This paper proposes an improved virtual reference model for semi-active suspension to coordinate the vehicle ride comfort and handling stability. The reference model combines the virtues of sky-hook with ground-hook control logic, and the hybrid coefficient is tuned according to the longitudinal and lateral acceleration so as to improve the vehicle stability especially in high-speed condition. Suspension state observer based on unscented Kalman filter is designed. A sliding mode controller (SMC) is developed to track the states of the reference model. The stability of the SMC strategy is proven by means of Lyapunov function taking into account the nonlinear damper characteristics and sprung mass variation of the vehicle. Finally, the performance of the controller is demonstrated under three typical working conditions: the random road excitation, speed bump road and sharp acceleration and braking. The simulation results indicated that, compared with the traditional passive suspension, the proposed control algorithm can offer a better coordination between vehicle ride comfort and handling stability. This approach provides a viable alternative to costlier active suspension control systems for commercial vehicles.     

A Two DOF Model for Jerk Optimal Vehicle Suspensions

Researchers have proposed various active suspension concepts to optimize the tradeoff between ride and handling in passenger vehicles. A few investigators suggested inclusion of the passenger jerk, the derivative of the passenger acceleration, as a measure of ride quality in the performance index. Minimization of a performance index then optimizes both the acceleration and jerk as well as other outputs representing handling quality and design constraints. This approach is called jerk optimal control.

This paper compares two different vehicle models of increasing complexity (the one and two DOF quarter car) using jerk optimal control. Different aspects of suspension performance are investigated, including the structure of the system transfer functions, the structure of the force control laws, and the tradeoffs between the various root mean square (rms) outputs defining system ride and handling performance. Tables compare the numerical results of the two models, allowing predictions of actual vehicle performance.

The results of the two models show the same basic trend for the tradeoff between ride and handling quality: at a constant level of rms passenger acceleration the rms passenger jerk can be reduced significantly, but only at a cost of increased rms tire deflections. In physical terms, a softer ride results in degraded handling performance. For a chosen level of ride improvement, the more realistic two DOF quarter car model predicts more severe degradation of handling. The latter nevertheless predicts a substantial increase in vehicle ride quality is possible through a 55% reduction in jerk. It is expected that actual suspensions could also produce significant increases in ride quality through jerk reduction. Jerk optimal suspensions could find use both in higher end passenger vehicles and in transports for vibration sensitive cargo.     

DISCUSSION NOTE on Karnopp's article “Active Damping in Road Vehicle Suspension Systems”

SUMMARY

In this paper, an optimal suspension system is derived for a quarter-car model using multivariable integral control. The suspension system features two parts. The first part is an integral control acting on suspension deflection to ensure zero steady-sate offset due to body and maneuvering forces as well as road inputs. The second is a proportional control operating on the vehicle system states for vibration control and performance improvement. The optimal ride performance of the active suspensions based on linear full-state feedback control laws with and without integral control together with the performance of passive suspensions are compared.     

Roll- and pitch-plane-coupled hydro-pneumatic suspension. Part 2: dynamic response analyses

In the first part of this study, the potential performance benefits of fluidically coupled passive suspensions were demonstrated through analyses of suspension properties, design flexibility and feasibility. In this second part of the study, the dynamic responses of a vehicle equipped with different configurations of fluidically coupled hydro-pneumatic suspension systems are investigated for more comprehensive assessments of the coupled suspension concepts. A generalised 14 degree-of-freedom nonlinear vehicle model is developed and validated to evaluate vehicle ride and handling dynamic responses and suspension anti-roll and anti-pitch characteristics under various road excitations and steering/braking manoeuvres. The dynamic responses of the vehicle model with the coupled suspension are compared with those of the unconnected suspensions to demonstrate the performance potential of the fluidic couplings. The dynamic responses together with the suspension properties suggest that the full-vehicle-coupled hydro-pneumatic suspension could offer considerable potential in realising enhanced ride and handling performance, as well as improved anti-roll and anti-pitch properties in a very flexible and energy-saving manner.     

Stochastic Optimal Control of Highway Tractors with Active Suspensions

Stochastic optimal control and estimation theories are used to design an active suspension system for a cab ride in a tractor-semitrailer vehicle. A discrete-continuous vehicle model with eleven degrees of freedom is augmented by a stochastic road excitation model and a human perception of vibration shape filter. Both perfect measurement and estimated state cases are considered. The impact of the measurement noise on the design of the optimal controller is demonstrated. The performance of the optimally controlled system is compared with an optimal passive system. It is shown that significant improvements in ride comfort can be achieved through the use of actively controlled cab suspensions.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

重型商用车驾驶室悬置结构对平顺性影响的试验研究

以某重型商用车驾驶室悬置系统为例,通过实车道路试验,研究了四弹簧,四气囊悬置减振系统的振动特性在A级路面和B级路面对车辆行驶平顺性的影响规律。试验结果表明,四气囊驾驶室悬置系统的平顺性整体优于四弹簧驾驶室悬置结构。     

Using the lead vehicle as preview sensor in convoy vehicle active suspension control

Both ride quality and roadholding of actively suspended vehicles can be improved by sensing the road ahead of the vehicle and using this information in a preview controller. Previous applications have used look-ahead sensors mounted on the front bumper to measure terrain beneath. Such sensors are vulnerable, potentially confused by water, snow, or other soft obstacles and offer a fixed preview time. For convoy vehicle applications, this paper proposes using the overall response of the preceding vehicle(s) to generate preview controller information for follower vehicles. A robust observer is used to estimate the states of a quarter-car vehicle model, from which road profile is estimated and passed on to the follower vehicle(s) to generate a preview function. The preview-active suspension, implemented in discrete time using a shift register approach to improve simulation time, reduces sprung mass acceleration and dynamic tyre deflection peaks by more than 50% and 40%, respectively. Terrain can change from one vehicle to the next if a loose obstacle is dislodged, or if the vehicle paths are sufficiently different so that one vehicle misses a discrete road event. The resulting spurious preview information can give suspension performance worse than that of a passive or conventional active system. In this paper, each vehicle can effectively estimate the road profile based on its own state trajectory. By comparing its own road estimate with the preview information, preview errors can be detected and suspension control quickly switched from preview to conventional active control to preserve performance improvements compared to passive suspensions.     

An investigation into the effect of suspension configurations on the performance of tracked vehicles traversing bump terrains

This is a theoretical investigation into the effect of various suspension configurations on a tracked vehicle performance over bump terrains. The model developed is validated using published experimental data of the modal characteristics of the vehicle. The desired performance is based on ride comfort via the mixed objective function (MOF), which combines the crest factor of bounce acceleration, bounce displacement, angular acceleration, and pitch angle. The optimisation process involves evaluating the MOF for different numbers and locations of dampers and under different rigid bump road conditions and speeds. The system responses of the selected suspension configurations in the time and frequency domains are compared against the undamped suspension. The results show that the suspension configurations have a significant effect on the vehicle mobility over bump road profiles. For a five-road–wheel half model of a tracked vehicle, the maximum number of dampers to use for ride comfort over these road bumps is three with the dampers located at wheel positions 1, 2 and 5. This confirms the current practice for many tracked vehicles with 10 road wheels. However, it is further shown that the suspension fitted with two dampers at the extreme road wheels offer the best performance over various rigid bump terrains.     

Performance evaluation and parameter sensitivity of energy-harvesting shock absorbers on different vehicles

Traditional shock absorbers provide favourable ride comfort and road handling by dissipating the suspension vibration energy into heat waste. In order to harvest this dissipated energy and improve the vehicle fuel efficiency, many energy-harvesting shock absorbers (EHSAs) have been proposed in recent years. Among them, two types of EHSAs have attracted much attention. One is a traditional EHSA which converts the oscillatory vibration into bidirectional rotation using rack-pinion, ball-screw or other mechanisms. The other EHSA is equipped with a mechanical motion rectifier (MMR) that transforms the bidirectional vibration into unidirectional rotation. Hereinafter, they are referred to as NonMMR-EHSA and MMR-EHSA, respectively. This paper compares their performances with the corresponding traditional shock absorber by using closed-form analysis and numerical simulations on various types of vehicles, including passenger cars, buses and trucks. Results suggest that MMR-EHSA provides better ride performances than NonMMR-EHSA, and that MMR-EHSA is able to improve both the ride comfort and road handling simultaneously over the traditional shock absorber when installed on light-damped, heavy-duty vehicles. Additionally, the optimal parameters of MMR-EHSA are obtained for ride comfort. The optimal solutions (‘Pareto-optimal solutions’) are also obtained by considering the trade-off between ride comfort and road handling.     

Overturning Stability of Three Wheeled Motorized Vehicles

Three wheeled motorized vehicles are a major mode of public transport in many countries. These vehicles are prone to overturning even during normal turning and obstacle avoidance maneuvers. This paper presents a parametric analysis of a mathematical model of the vehicle and evolves guidelines for improving the overturning stability in terms of vehicle geometry and suspension properties.

Differential equations governing the dynamic behavior of the vehicle are derived on the basis of a six degree of freedom model. The vehicle response to variations in steering, engine power and braking inputs is then numerically simulated. The effects of vehicle geometry and elasto-damping suspension coefficients on the vehicle stability are presented. The results indicate an optimum position of the center of gravity where the vehicle is most stable. While stiffer suspensions favour stability, there exists an optimum value of suspension damping for which the minimum wheel load is a maximum.     

A Procedure for Optimization of Truck Suspensions

The purpose of this paper is to develop a procedure based on covariance analysis and nonlinear programming techniques which can be used for the parameter selection of optimum truck suspensions. The procedure is applied to explore the differences in parameter selection caused by the changes in the frequency content of the road input or by changes in the criteria for optimization. The equations of motion for a tractor-semitrailer truck are cast in state space form. The road excitations are represented by the output of a white noise excited shaping filter taking into consideration the time delays between the different vehicle axles. Shape filters to represent human perception of vibration in both the vertical and longitudinal directions in the time domain are presented and realized in terms of state variables. The suspension parameters of the road-vehicle-human body system are optimized using a direct search algorithm.     

Directional performance issues in evaluation and design of articulated heavy vehicles

This review of the dynamics of heavy road-vehicle systems emphasizes directional performance. The review presents information on the following topics: why are articulated vehicles used; units, hitches, and combination vehicles; multiple axle suspensions and steering systems; important performance issues; models and simulation tools; and controlling directional performance. The concluding section summarizes the material presented and provides ideas regarding the application of vehicle system dynamics concepts in developing controllers for road trains.