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.     

Spatial Dynamics of Multibody Tracked Vehicles Part I: Spatial Equations of Motion

In this paper, the nonlinear dynamic equations of motion of the three dimensional multibody tracked vehicle systems are developed, taking into consideration the degrees of freedom of the track chains. To avoid the solution of a system of differential and algebraic equations, the recursive kinematic equations of the vehicle are expressed in terms of the independent joint coordinates. In order to take advantage of sparse matrix algorithms, the independent differential equations of the three dimensional tracked vehicles are obtained using the velocity transformation method. The Newton-Euler equations of the vehicle components are defined and used to obtain a sparse matrix structure for the system dynamic equations which are represented in terms of a set of redundant coordinates and the joint forces. The acceleration solution obtained by solving this system of equations is used to define the independent joint accelerations. The use of the recursive equations eliminates the need of using the iterative Newton-Raphson algorithm currently used in the augmented multibody formulations. The numerical difficulties that result from the use of such augmented formulations in the dynamic simulations of complex tracked vehicles are demonstrated. In this investigation, the tracked vehicle system is assumed to consist of three kinematically decoupled subsystems. The first subsystem consists of the chassis, the rollers, the sprockets, and the idlers, while the second and third subsystems consist of the tracks which are modeled as closed kinematic chains that consist of rigid links connected by revolute joints. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach that defines the constraint forces at selected secondary joints of the tracks. The kinematic relationships of the rollers, idlers, and sprockets are expressed in terms of the coordinates of the chassis and the independent joint degrees of freedom, while the kinematic equations of the track links of a track chain are expressed in terms of the coordinates of a selected base link on the chain as well as the independent joint degrees of freedom. Singularities of the transformations of the base bodies are avoided by using Euler parameters. The nonlinear three dimensional contact forces that describe the interaction between the vehicle components as well as the results of the numerical simulations are presented in the second part of this paper.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

A Model Reduction Procedure for the Dynamic Analysis of Rail Vehicles Subjected to Linear Creep Forces

The set of differential equations governing the motion of an unrestrained coned wheelset travelling on a tangent section of track and acted upon by creep forces arising from the contact between wheel and rail are, in the terminology of numerical analysis, extremely "stiff". This stiffness can be attributed to the existence of two negative real eigenvalues in the solution of the eigenproblem associated with the linearized equations of motion. Compared with the two complex conjugate eigenvalues that complete this solution, the real eigenvalues have large magnitudes and necessitate that relatively. small timesteps be used in order to obtain an accurate numerical integration of the full set of equations of motion. However, by truncating the set of left and right eigenvectors to eliminate these real eigenvalues in a modal analysis of the wheelset, it was found that their contribution to the overall dynamic response is negligible. This same modal truncation approach was then applied to the sub-structured equations of motion for a simple rail vehicle system consisting of two wheelsets connected to a main body by linear springs and dampers. Essentially, the physical degrees of freedom for each wheelset substructure were replaced by a single complex coordinate obtained from the previous normal modes analysis. Using this model reduction procedure, accurate numerical results for the motion of the rail vehicle were generated several times faster than the results obtained by numerically integrating the full set of differential equations directly.     

Tractor-semitrailer model for vehicles carrying liquids

This article presents a model for solving solid-fluid interactions in vehicles carrying liquids. A tractor-semitrailer model is developed by incorporating suspension systems and tire dynamics. Owing to the solid-fluid interaction, equations of motion for the vehicle system are coupled. To simplify the complicated solution procedure, the coupled equations are solved separately using two different codes. Each code is analyzed separately; but as the parameters of the two codes depend on each other, the codes must be connected at the end of each time step. To determine the dynamic behavior of the system, different braking moments are applied. As the braking moments increase, braking time decreases. However, it turns out that increasing the braking moment to more than a certain level produces no significant results. It is also shown that vehicles carrying fluids need a greater amount of braking moments in comparison to vehicles carrying solids during braking. In addition, as the level of the fluid inside the tanker increases, from one-third to two-third of the tanker's volume, the sloshing forces applied to the tanker's walls increase. It was also concluded that the strategy used in this article to solve for the solid-fluid interaction by incorporating vehicle dynamic effects represents an effective method for determining the dynamic behavior of vehicles carrying fluids in other critical maneuvers.     

对冲击破碎机械工作机构撞击中心的分析

撞击中心对于机器的性能设计和节能研究至关重要。为了确定冲击、破碎机械工作机构撞击中心的位置，采用运动学和动力学的分析方法，分别以碰撞体和工作机构为研究对象，通过分析碰撞方程和运动方程，验证撞击中心的位置以及碰撞体应满足的几何条件，为冲击、破碎机械的设计提供了理论依据。     

Tractor–semitrailer model for vehicles carrying liquids

This article presents a model for solving solid–fluid interactions in vehicles carrying liquids. A tractor–semitrailer model is developed by incorporating suspension systems and tire dynamics. Owing to the solid–fluid interaction, equations of motion for the vehicle system are coupled. To simplify the complicated solution procedure, the coupled equations are solved separately using two different codes. Each code is analyzed separately; but as the parameters of the two codes depend on each other, the codes must be connected at the end of each time step. To determine the dynamic behavior of the system, different braking moments are applied. As the braking moments increase, braking time decreases. However, it turns out that increasing the braking moment to more than a certain level produces no significant results. It is also shown that vehicles carrying fluids need a greater amount of braking moments in comparison to vehicles carrying solids during braking. In addition, as the level of the fluid inside the tanker increases, from one-third to two-third of the tanker’s volume, the sloshing forces applied to the tanker’s walls increase. It was also concluded that the strategy used in this article to solve for the solid–fluid interaction by incorporating vehicle dynamic effects represents an effective method for determining the dynamic behavior of vehicles carrying fluids in other critical maneuvers.     

On the objective assessment and quantification of the transient-handling response of a vehicle

This article suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient-handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalized yaw impulse. This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front-tyre forces and the yaw moment due to the rear-tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, two-degree-of-freedom bicycle model, it is shown that the general form of the normalized yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected.     

On the objective assessment and quantification of the transient-handling response of a vehicle

This article suggests a new methodology for the objective assessment and quantification of the response of a vehicle subjected to transient-handling manoeuvres. For this purpose, a non-dimensional measure is defined, namely the normalized yaw impulse. This measure appears in two variations. In its general or dynamic form, it represents the difference between the yaw moment due to the front-tyre forces and the yaw moment due to the rear-tyre forces, divided by the sum of the aforementioned yaw moments. By employing a linear, two-degree-of-freedom bicycle model, it is shown that the general form of the normalized yaw impulse can be written as a function of the steer angle and the forward, lateral and yaw velocities of the vehicle. This form is referred to as the kinematic yaw impulse. It is demonstrated that the combined application of the dynamic and kinematic expressions of the yaw impulse not only facilitates the explicit assessment and quantification of the transient behaviour of a vehicle, but also reveals the influence of parameters such as the yaw moment of inertia, which traditionally leave the steady-state behaviour unaffected.     

Modelling and characteristic analysis of tri-axle trucks with hydraulically interconnected suspensions

In this paper, a new hydraulically interconnected suspension (HIS) system is proposed for the implementation of a resistance control for the pitch and bounce modes of tri-axle heavy trucks. A lumped-mass half-truck model is established using the free-body diagram method. The equations of motion of a mechanical and hydraulic coupled system are developed by incorporating the hydraulic strut forces into the mechanical subsystem as externally applied forces. The transfer matrix method (TMM) is used to evaluate the impedance matrix of the hydraulic subsystem consisting of models of fluid pipes, damper valves, accumulators, and three-way junctions. The TMM is further applied to find the quantitative relationships between the hydraulic strut forces and boundary flow of the mechanical–fluid interactive subsystem. The modal analysis method is employed to perform the vibration analysis between the trucks with the conventional suspension and the proposed HIS. Comparison analysis focuses on free vibration with identified eigenvalues and eigenvectors, isolation vibration capacity, and force vibration in terms of the power spectrum density responses. The obtained results show the effectiveness of the proposed HIS system in reducing the pitch motion of sprung mass and simultaneously maintaining the ride comfort. The pitch stiffness is increased while the bounce stiffness is slightly softened. The peak values of sprung mass and wheel hop motions are greatly reduced, and the vibration decay rate of sprung mass is also significantly increased.     

Dynamic tyre friction models for combined longitudinal and lateral vehicle motion

An extension to the LuGre dynamic friction model from longitudinal to longitudinal/lateral motion is developed in this paper. Application of this model to a tyre yields a pair of partial differential equations that model the tyre-road contact forces and aligning moment. A comparison of the steady-state behaviour of the dynamic model with existing static tyre friction models is presented. This comparison allows one to determine realistic values of the parameters for the new dynamic model. Via the introduction of a set of mean states we reduce the partial differential equations to a lumped model governed by a set of three ordinary differential equations. Such a lumped form describes the aggregate effect of the friction forces and moments and it can be useful for control design and online estimation. A method to incorporate wheel rim rotation is also proposed. The proposed model is evaluated by comparing both its steady-state as well as its dynamic characteristics via numerical simulations. The results of the simulations corroborate steady-state and dynamic/transient tyre characteristics found in the literature.     

Partial range scaling method based washout algorithm for a vehicle driving simulator and its evaluation

Unlike an actual vehicle, a vehicle driving simulator (VDS) has limited kinematics, workspace, and bounded dynamic characteristics making it very difficult to simulate dynamic motions of an actual vehicle. To solve these problems, a washout algorithm was developed. The developed algorithm restricts the workspace of the VDS to within the kinematic limit and makes the person driving the VDS perceive movement of an actual vehicle. However, the classic washout algorithm contains several problems, such as time delay and the generation of a wrong motion signal caused by characteristics of the filters. So the driver feels “simulator sickness,” such as fatigue, nausea, headache and so on because of differences between the sense of movement of the VDS and that of a real vehicle. In this paper, a partial range scaling method based washout algorithm, including a tilt coordination system, is developed to enhance the perception of motion and reduce simulator sickness. It is verified by a simulation, a survey, and a bio signal analysis using an electrocardiogram (ECG).     

惯性荷载和地震荷载作用下单桩横向非线性动力响应简化分析

根据已建立的地基土—单桩系统横向非线性动力响应简化分析模型和计算方法,讨论了动力荷载作用下单桩横向非线性惯性响应以及地震作用下单桩横向非线性运动响应,采用两个非线性运动响应因子表征地基土—单桩系统运动响应的非线性特性。计算结果表明:该模型不仅能够模拟在(准)静态单调循环荷载和简谐荷载作用下的单桩横向非线性惯性响应,而且可以反映地震过程中地基土—单桩系统横向非线性运动响应的基本特征。     

基于RTK五轮仪研制的汽车运动性能试验研究

利用GPS载波相位RTK技术研制成了汽车道路试验RTK五轮仪。应用该五轮仪进行了汽车的直线和曲线运动性能测试,结果表明可以更精确测取汽车运动性能参数,实现基于动态轨迹测量的汽车运动性能试验评价。     

Evaluation of the coupled dynamical response of a pantograph—catenary system: contact force and stresses

In this article, the static stresses in a catenary and its vibration modes are calculated by establishing the FEM model of the catenary with Euler-Bernoulli beam elements. The mode shapes of the catenary obtained are considered as the generalized variables which are used in the establishment of the motion equations of the catenary system. The physical model of the pantograph is simplified as a multi-body system with mass, stiffness, damping, and friction. On the basis of having derived the coupled motion equations of the pantograph-catenary system, its dynamic behavior is analyzed in detail and the contact force is calculated. Using the contact force as the external moving load of the FEM model of the catenary, the dynamic stress in the catenary is simulated. Through the detailed analysis and calculation, we not only obtain the dynamic stress response at any element of the catenary, but also its frequency responses. As the dynamic stress in the assistant wire is quite large, the influence of its structure on dynamic stress is analyzed and the way to reduce the dynamic stress is suggested. At last, the calculation method of dynamic stress is validated by a test.     

2缸发动机平衡机理研究及悬置系统优化设计

以2缸发动机为研究对象,分析发动机曲柄活塞机构的运动规律,推导发动机在实际工作时产生的不平衡激励力和力矩,研究2缸发动机的旋转惯性力和往复惯性力的平衡方法,对一台2缸发动机在不同平衡条件下产生的激励进行数值模拟。在此基础上,建立2缸发动机悬置系统优化模型,以悬置系统的固有频率、能量解耦率和悬置动反力为优化目标,用序列二次规划法进行多目标的优化,对一台2缸柴油机进行了悬置系统优化设计。分析结果表明该优化方法可以有效减少发动机传递给车身的激励。     

A semi-empirical dynamic tire model for combined-slip forces

This article presents a semi-empirical combined-slip tire model including transient behavior. It is assumed that the transient behavior is a result from the dynamic deformation of the tire carcass and that the interaction between the lateral and longitudinal slip, and forces can be explained by the deformation of the rubber treads. The deformation of the tire carcass makes the tread slip deviate from the wheel-rim motion in a way that may be described by differential equations. A method based on brush-model tire mechanics is used to construct the combined-slip forces as nonlinear scalings of corresponding pure-slip forces.     

Base Dynamic Parameter Estimation of a MacPherson Suspension Mechanism

Summary A MacPherson suspension mechanism is modeled as a two degrees of freedom spatial mechanism. Its dynamic response under two excitement forces is simulated with the motion equations in Euler Parameters with the off-the-center-of-mass body-fixed coordinates derived in this paper. Simulation results are sampled and input into a numerical estimation routine based on singular value decomposition (SVD). Accurate numerical estimation results are achieved. A set of base dynamic parameters in symbolic expressions is also derived from the numerical results utilizing the concepts of mass transfer and moments of inertia transfer. This makes it possible to apply the estimation results to any MacPherson suspension mechanism with the same joint configuration. The potential applications of the symbolic base dynamic parameters in suspension design are also considered.     

Base Dynamic Parameter Estimation of a MacPherson Suspension Mechanism

Summary A MacPherson suspension mechanism is modeled as a two degrees of freedom spatial mechanism. Its dynamic response under two excitement forces is simulated with the motion equations in Euler Parameters with the off-the-center-of-mass body-fixed coordinates derived in this paper. Simulation results are sampled and input into a numerical estimation routine based on singular value decomposition (SVD). Accurate numerical estimation results are achieved. A set of base dynamic parameters in symbolic expressions is also derived from the numerical results utilizing the concepts of mass transfer and moments of inertia transfer. This makes it possible to apply the estimation results to any MacPherson suspension mechanism with the same joint configuration. The potential applications of the symbolic base dynamic parameters in suspension design are also considered.