MacPherson Strut Research Articles

Kinematic Analysis of MacPherson Strut Mechanism

In this paper, we derive the closed-loop equations of the MacPherson strut mechanism as the spatial six-link mechanism of two degrees of freedom. With given values of steering and strut displacements, the formulas for analyzing the attitude of the strut are established. The results of analysis are verified experimentally. The static analysis is done under the several conditions, for example, the angle of the lower arm and the position of the steering rack are varied. By this analysis, it can be shown how the force transmitted through the rod is needed to steer the tires. From the results of analysis, we can know how the force preventing the smooth sliding of the strut occurs. We analyzed the sensitivities to show how the error of the assembling and processing had an effect on the kinematics of this mechanism. The sensitivities can be derived from partially differentiating the closed-loop equations with respect to the kinematic constants. A few of them are verified experimentally. Comparing with result of static analysis, we investigate if the cause of error involve in transmissibility.

Uncertainty modelling of a suspension unit

Many organizations are increasingly relying on design simulation rather than expensive and time-consuming prototype testing for product evaluation. However, uncertainties in analytical and computational methods need to be understood in order to improve confidence in their use, and models need to be validated. This paper presents a case study of a MacPherson strut automotive suspension analysis, and evaluates the uncertainties in the modelling of this complex dynamic problem using a simplified analytical model and a complex computational model. In both cases, variability in design variables is characterized using probabilistic design methods. As a first step, the model variables are described by assumed datasets, which are collated from several sources such as tolerances specified in drawings, expert opinion, published data, etc. Measurement of the properties of the suspension system components is then performed (spring stiffness, damping coeffcient, etc.), and the statistical parameters so obtained are used in probabilistic calculations for specified time sequences from measured test track road load data. The results are used to accumulate evidence of uncertainties in analytical and computational methods, to correlate predicted results to experimental data for vehicle chassis top mount force, and to derive sensitivity measures. A response surface function is approximated which is useful for parametric studies for new variants of the system studied. Sources of uncertainty in this case study and methods for improving the correlations are then suggested.

Analytical Approach for Strongly Coupled Vibration System Composed of Two Substructures (1st Report, Theory and Its Application to Vibration of Vehicle Suspension)

This paper deals with a forced vibration of strongly coupled subsystems. A theoretical and practical approach is proposed to obtain targets of the subsystem's vibration properties which fulfill the target of whole system. The approach is an application of transfer function synthesis method and provides a procedure to analyze the compliance of subsystems at connecting points for setting the natural frequency and reducing the internal forces. A new concept of kernel dynamic stiffness and kernel vector is introduced to understand vibration transmission in the analysis of the compliance at connecting points. This approach is applied to vehicle noise issue induced by road roughness (road noise) in the frequency range of 80 Hz and 150 Hz on macpherson strut type suspension. The results show effectiveness of this approach and present guideline of the suspension design for road noise.

車輪操舵・懸架機構の運動特性解析(S46-1 機構の開発とシミュレーション(I),S46 機構の開発とシミュレーション)

The independent suspension system is adopted in the automobiles to make the driving be comfortable and maneuverable. Especially, the MacPherson strut mechanism is the one of the most commonly used mechanisms in front suspension because of a small number of component parts. But that reduces parameters to draw the ideal trajectory of the wheel spindle and limit the freedom of design. It is difficult to estimate the trajectory of the wheel spindle comparing the ideal one in three dimensional space. In this paper, we derive the closed-loop equations of the MacPherson strut mechanism as the spatial six-link mechanism of two degrees of freedom. With given values of steering and strut displacements, the formulas for analyzing the attitude of the strut are established. And sensitivity analyses were done using the closed-loop equations with respect to the coordinets of the spherical pair connecting the strut and the frame. The results of analysis is verified experimentally.

An adaptive LQG control for semi-active suspension systems

In this paper, a road-adaptive LQG control for the semi-active Macpherson strut suspension system of hydraulic type is investigated. A new control-oriented model, which incorporates the rotational motion of the unsprung mass, is introduced. A semi-active suspension controller adapting to road variations is proposed. First, based on the extended least squares estimation algorithm, a LQG controller adapting to the estimated road characteristics is designed. Through the computer simulations, the performance of the proposed semi-active suspension is compared with that of a non-adaptive one. The results show better control performance of the proposed system over the compared one.

노면추정을 통한 반능동 현가시스템의 LQG 제어

A road-adaptive LQG control for the semi-active Macpherson strut suspension system of hydraulic type is investigated. A new control-oriented model, which incorporates the rotational motion of the unsprung mass, is used for control system design. First, based on the extended least squares estimation algorithm, a LQG controller adapting to the estimated road characteristics is designed. With computer simulations, the performance of the proposed LQC-controlled semi-active suspension is compared with that of a non-adaptive one. The results show better control performance of the proposed system over the compared one.

Dynamics of the macpherson strut motor-vehicle suspension system in point and joint coordinates

In this paper the dynamic analysis of the Macpherson strut motor-vehicle suspension system is presented. The equations of motion are formulated using a two-step transformation. Initially, the equations of motion are derived for a dynamically equivalent constrained system of particles that replaces the rigid bodies by applying Newton’s second law. The equations of motion are then transformed to a reduced set in terms of the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality. For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. For closed loops, suitable joints should be cut and few cut-joints constraint equations should be included for each closed chain. The chosen suspension includes open and closed loops with quarter-car model. The results of the simulation indicate the simplicity and generality of the dynamic formulation.

A Road-Adaptive LQG Control for Semi-Active Suspension Systems

In this paper, a road-adaptive LQG control for the semi -active Macpherson strut suspension system of hydraulic type is investigated. A new control-oriented model, which incorporates the rotational motion of the unsprung mass, is introduced. A semi-active suspension controller adapting to road variations is proposed. First, based on the extended least squares estimation algorithm, a LQG controller adapting to the estimated road characteristics is designed. Through the computer simulations, the performance of the proposed semi-active suspension is compared with that of a non-adaptive one. The results show better control performance of the proposed system over the compared one

Real-time Dynamic Simulation Using Multibody Vehicle Model

This paper presents a real-time multibody vehicle dynamic analysis method using recursive Kanes formulation and suspension composite joints. To shorten the computation time of simulation, relative coordinate system is used and the equations of motion are derived using recursive Kanes formulation. Typical suspension systems of vehicles such as MacPherson strut suspension system is modeled by suspension composite joints. The joints are derived and utilized to reduce the computation time of simulation without any degradation of kinematical accuracy of the suspension systems. Using the develop program, a multibody vehicle dynamic model is formed and simulations are performed. Accuracy of the simulation results is compared to the real vehicle field test results. It is found that the simulation results using the proposed method are very accurate and real-time simulation is achieved on a computer with single PowerPC 604 processor.

Modified Skyhook Control of Semi-Active Suspensions: A New Model, Gain Scheduling, and Hardware-in-the-Loop Tuning

In this paper, a road adaptive modified skyhook control for the semi-active Macpherson strut suspension system of hydraulic type is investigated. A new control-oriented model, which incorporates the rotational motion of the unsprung mass, is introduced. The control law extends the conventional skyhook-groundhook control scheme and schedules its gains for various road conditions. Using the vertical acceleration data measured, the road conditions are estimated by using the linearized new model developed. Two filters for estimating the absolute velocity of the sprung mass and the relative velocity in the rattle space are also designed. The hydraulic semi-active actuator dynamics are incorporated in the hardware-in-the-loop tuning stage of the control algorithm developed. The optimal gains for the ISO road classes are discussed. Experimental results are included.

A real-time multibody vehicle dynamic analysis method using suspension composite joints

This paper presents a real-time vehicle dynamic analysis method using suspension composite joints. Typical suspension systems of vehicles such as MacPherson strut, double wishbone, trailing arm and solid axle suspension systems are modelled by suspension composite joints. The joints are derived and utilised to reduce the computation time of simulation without any degradation of kinematical accuracy of the suspension systems. They are modelled using massless links on the suspension members that have small masses but have kinematical importance. Using the developed suspension composite joints, a multibody vehicle dynamic model is formed and simulations are performed. Accuracy of the simulation results is compared to the real vehicle field test results as well as to the simulation results with a full multibody vehicle model. It is found that the simulation results using the proposed method are very accurate and real-time simulation is achieved on a computer with single PowerPC 604 processor.

Dynamic Parameter Estimation of a MacPherson Strut Suspension

SUMMARY The dynamic parameters of a MacPherson strut suspension were estimated from the kinematic responses and measured external forces on the system. First, Lagrange equation was used to develop the equations of motion of the system, and then equations of motion were written as linear with respect to the dynamic parameters being estimated. The generalized coordinate partitioning technique was applied to create a reduced set of equations of motion of the constrained dynamic system. In this method only the measurements of positions and kinematic responses of the independent coordinates, and the external forces applied on the system are required as inputs. The rank deficient linear system was solved by QR decomposition. Good correlation was obtained between the actual parameters and the estimated parameters, by comparison between the simulated system response from the actual parameters and from the estimated parameters.

Use of Joint Geometric Conditions in Formulating Cartesian Constraint Equations

Basic constraint equations derived from orthogonality conditions between a pair of body-fixed vectors and a body-fixed vector or a vector between two bodies are reformulated by using geometric conditions built into each joint. Arithmetic numbers of operations required to compute derivatives of the constraint equations are drastically reduced. A mixed constraint formulation of relative and Cartesian coordinates is developed to further simplify derivatives of the constraints. Advantages and disadvantages of the new formulation are discussed. The kinematic analysis of a Macpherson strut suspension system is carried out to illustrate the use and efficiency of the new formulation.

The Nonlinear Behaviour of a MacPherson Strut Wheel Suspension

SUMMARY Three nonlinear models of a MacPherson strut wheel suspension have been studied. The nonlinearities considered are due to the nonlinear geometrical effects in the mechanism, the amplitude limitation due to the bumpstop, the progressive stiffness of the bumpstop and the different damping coefficients for the shock absorber in bump and rebound. The models have been derived according to physical parameter values of. the MacPherson strut wheel suspension of the car SAAB 9.000. The most suitable model was further studied with special attention to nonlinear phenomena. For harmonic forcing the system had phenomena such as multiple solutions and subharmonics. For some parameter values the solution was very sensitive to changes in the integration tolerances in the numerical integration routine. No chaotic steady state solutions were found for the parameter values studied.

Steering error optimization of the Macpherson strut automotive front suspension

A vehicle model is developed employing a detailed nonlinear kinematic representation of a MacPherson strut front independent automotive suspension with a rack and pinion steering system. The vehicle model is capable of front wheel steering motions as well as vehicle body rolling motions. The vehicle model is used to simulate steady-state turning maneuvers on a smooth, flat road. The model is employed in conjunction with a realistic set of constraints to optimize a representative suspension and steering system with respect to steering error for turn radii and body roll angles typical of highway driving. Improved suspension and steering geometries are presented for two optimization studies.

MacPherson strut kinematics

The MacPherson strut automotive suspension is modeled as a three-dimensional kinematic mechanism. Developed are a linearized position analysis and a nonlinear position analysis. The results of these analyses are compared for a representative geometry. Also developed for the mechanism are a velocity analysis and an acceleration analysis.

Resilient mounting means for MacPherson strut

The drawings illustrate a MacPherson strut-type concentric shock absorber and coil spring. A single elastomeric ring is preloaded between upper and lower retainer members, and suitable bearing means are mounted between the bottom portion of the elastomeric ring and a spring retainer flange for the upper end of the coil spring. The piston rod is secured within the center portion of the elastomeric ring. In this arrangement, the preloaded outer portion of the elastomeric ring is subjected to compression forces during jounce and rebound conditions, and the preloaded center portion of the ring is subjected to shear forces during such jounce and rebound conditions, thereby providing predetermined different stiffness characteristics for the shock absorber and the coil spring.

A Theoretical Analysis of the Lateral Properties of Suspension Systems

The suspension system of a vehicle interconnects its wheels and body and provides the means by which forces and movements are transferred from one to the other. The lateral properties of suspension systems are required for lateral handling and other suspension studies, and this paper contains a theoretical analysis of such properties for a range of suspension systems: viz. double wishbone, Macpherson strut, swing axle, beam axle, and beam axle-Panhard rod. The lateral motions of a wheel on a road, resulting from prescribed motions of the vehicle body, are derived for the range of suspension systems considered. Attention is concentrated on the two principal body motions of vertical and rolling velocity, and the resulting suspension movements are determined in terms of these suspension derivatives. In the case of the double wishbone suspension, the various types, each with differing characteristics, are distinguished. Regions are defined within which suspension systems will have certain properties, and the boundaries of these regions are determined. By a suitable choice of defining parameters, the Macpherson strut suspension is shown to be equivalent to a double wishbone suspension, and therefore the analysis of the double wishbone suspension is applicable to the Macpherson strut. By comparison with the double wishbone suspensions the remaining suspensions considered have only limited ability to vary their suspension characteristics. The effects of suspension design on the steady state roll angle, suspension jacking, and load transfer are investigated. A single end suspension is first considered, and the dependence of the roll angle and suspension jacking on the suspension derivatives is demonstrated. This dependence enables the significance of the various regions derived earlier to be stated. For the complete vehicle, the suspension derivatives again determine the roll angle, and in this case the wheel load transfers are also dependent, via the body transferred rolling moment, on the suspension derivatives. The suspension derivatives are required in handling studies and the method of analysis is capable of giving considerable insight into the general behaviour of suspension systems.