Joint coordinate method for analysis and design of multibody systems: Part 2. System topology

In Part 1 of this paper, the method of joint coordinate formulation for multibody dynamics was reviewed. The application of this method to forward and inverse dynamics, static equilibrium, and design sensitivity analyses was studied. In Part 2 of the paper, systematic procedures for constructing the necessary matrices for the joint coordinate formulation are discussed in detail. These matrices are; the primary and the secondary path matrices describing the topology of the system, the velocity transformation matrix, and the generalized inertia matrix. The procedures for constructing these matrices and other necessary elements for the joint coordinate formulation can easily be implemented in a computer program for analysis and design process.     

On configurations of symbolic equations of motion for rigid multibody systems

An algorithmic procedure for generating symbolic equations of motion for rigid multibody systems based on a Matrix-Vector approach is presented in this paper. The ease of computation and power inherent in this approach are demonstrated through a series of illustrative examples. Various techniques such as simultaneous generation of second order differential equations of motion and conversion to first order differential equations of motion in Hamiltonian variables, generalized coordinates transformation, order reduction using holonomic and nonholonomic constraint equations and block construction of equations of motion for the compound system from the equations of motion of the sub-systems are described.     

Thermal analysis of viscoelastic multibody systems

Thermal analysis of the transient motion of a multibody system, consisting of interconnected rigid, elastic, and viscoelastic components is presented. The configuration of each elastic or viscoelastic body is identified using three sets of modes, rigid-body, reference and normal modes. Rigid-body modes describe translations and large rotations of the body reference. The finite element method is employed to describe body deformations, and reference conditions are imposed in order to define a unique displacement field. Accordingly, normal modes of vibrations of flexible components can be used to reduce the number of elastic coordinates, thus eliminating high-frequency modes of vibration. The system equations of motion are formulated using Lagrange's equation, and nonlinear algebraic equations, describing constraints between adjacent bodies, are coupled to the equations of motion using a Lagrange multiplier technique.     

多刚体系统运动学分析的自然坐标法及在悬架运动学分析中的应用

本文介绍了一种适用于计算机分析的多刚体系统运动学分析的自然坐标法。利用自然坐标描述多刚体系统时,只需要一些点和一些单位向量,刚体的约束方程和运动副的约束方程组成了多刚体系统的运动学约束方程。约束方程均为线性或二次方程,因此求解方便。文中利用该方法分析了Maepherson悬架的轮胎横向滑移量、主倾内倾角等与车轮上、下跳动距离的关系。     

A study on numerical solution method for efficient dynamic analysis of constrained multibody systems

A new and efficient computational method for constrained multibody systems is proposed. In the proposed method, local parametrization method is employed to apply the same solution method for position, velocity, and acceleration analyses since the coefficient matrices for each analysis have an identical matrix pattern. The skyline solution method is used to overcome numerical inefficiency when solving large scaled equations. Also, subsystem mpartitioning method is derived systematically to perform parallel processing for real time simulation. To show the numerical accuracy and efficiency of the proposed method, three numerical problems are solved.     

Sensitivity analysis for estimation of inertial parameters of multibody mechanical systems

As an important issue, we first address in this paper the problem of a regression matrix with non-homogeneous physical units in the parameter estimation of multibody systems. This matrix contains the most important information about the motion of the system. Attention must be paid to this before implementing any parameter estimation algorithm due to the unit inconsistency in matrix multiplication required in such algorithms. A procedure to treat this problem in a proper way will be proposed. An experiment on a six degrees of freedom (DOF) robotic device, whose reference link follows a desired trajectory, is performed. The data collected from the experiment are then used for sensitivity analysis of inertial parameters based on the unit-homogenized regression matrix of the system. In this way, we characterize the influence of each selected inertial parameter on the dynamics of the system using unit-consistent mathematical manipulations.     

Application of modified local parametrization method for the constrained multibody dynamic systems

This paper presents a corrector method for analyzing the dynamic behaviour of constrained multibody systems. For correcting the state variables this method uses Lagrange-Newton method, which is a nonlinear programming technique. The Lagrange-Newton method uses the Lagrangian function that is a combined form of state variables with constraints, and the iteration formulation for convergence can be derived by the Newton-Raphson method. This algorithm does not update the Lagrange multipliers in the iteration formulation, for correcting the state variables, and is to project the state variables on the constraint manifold, in contrast to the previous local parametrization method. The validity of the algorithm and numerical solutions is verified through the convergence theorem denoting the convergence order of numerical solutions and the dynamic analysis of the full vehicle 3D model. The numerical solutions are compared with the ADAMS solutions     

A continuous force model for the impact analysis of flexible multibody systems

A new continuous impact model applicable to multibody systems consisting of interconnected rigid and flexible bodies is presented. The continuous impulsive force that acts during the short-lived interval of impact is written in terms of the relative displacement and velocity of the impacting bodies. In the method developed in this paper, the material compliance and damping coefficients are determined from energy balance relations. In order to account for the kinematic constraints between the two impacting bodies and other bodies in the system, an effective mass compensation is proposed. Flexible bodies in the system are discretized using the finite element methods. The generalized impulsive forces associated with the system generalized coordinates are then derived using the virtual work and are written in terms of a coupled set of reference and modal elastic coordinates. Numerical examples are presented in order to demonstrate the feasibility of the mathematical model developed in this paper.     

Modal analysis of constrained multibody systems undergoing constant accelerated motions

The modal characteristics of constrained multibody systems undergoing constant accelerated motions are investigated in this paper. Relative coordinates are employed to derive the equations of motion, which are generally nonlinear in terms of the coordinates. The dynamic equilibrium position of a constrained multibody system needs to be obtained from the nonlinear equations of motion, which are then linearized at the dynamic equilibrium position. The mass and the stiffness matrices for the modal analysis can be obtained from the linearized equations of motion. To verify the effectiveness and the accuracy of the proposed method, two numerical examples are solved and the results obtained by using the proposed method are compared with those obtained by analytical and other numerical methods. The proposed method is found to be accurate as well as effective in predicting the modal characteristics of constrained multibody systems undergoing constant accelerated motions.     

The boundary fitted coordinate method to improve the numerical analysis of electron optical systems

This paper illustrates some of the advantages of using the boundary fitted coordinate technique in the numerical simulation of electron-optical systems. The boundary fitted coordinate technique can be used as an automatic mesh generator for the finite-element solution of field distributions, while at the same time allowing for the possibility of high order inter-polation on the mesh, typically required for the accurate plotting of electron trajectory paths. For the finite difference method of solving field distributions, the boundary fitted coordinate method can generate regular meshes, which fit curved shaped boundaries.     

Research of design and analysis integrated information modeling framework for multibody mechanical system: with its application in the LHD design

Many complex mechanical products can be considered as multibody systems; 3D computer-aided design (CAD), multibody dynamics, finite element-based strength and fatigue analyses, optimization, and other CAE tools, are often used to develop this kind of product. But design is difficult and challenging because of information inconsistence among different engineering domains, and isolated information model islands exist. Lots of research are attracted to design and analysis information integration, but attentions are mainly focused on integration of CAD–finite element analysis (FEA), supporting the bottom-up design principle, while multibody dynamics analysis for analyzing global performance of a mechanical system is rarely considered, which follows the top-down design principle. In this paper, a novel multilevel system representation modeling framework for supporting both bottom-up and top-down or mixed design methods is proposed. It can integrate the product design CAD models with multibody dynamics, finite element-based strength and fatigue analyses, realizing a CAD–dynamic–FEA–fatigue analysis integration. It can also support data exchange and transfer in multidomain analyses. The framework is illustrated with a case study of a load haul dump (LHD) design using currently available software tools. Furthermore, a design case study of the working unit of the LHD is given to highlight the applicability of the modeling framework for multibody mechanical systems. It has been demonstrated that the framework can describe information exchanging and integration among CAD, FEA-based strength and fatigue analyses, and multibody dynamics analysis during a multibody mechanical product design process.     

Effect of damping parameters on dynamic behavior of program controllable drives of coordinate systems with belt drive: Part 1

The results of a study on how damping affects the parameters of oscillations that appear in belt drives of coordinate systems when used in the process equipment for diamond disk cutting of plates from semiconducting materials (silicon, sapphire, etc.). Oscillation often impair workmanship. Methods of reducing the amplitude of oscillations by controlling the damping parameters are shown.     

Capacitive measuring system for two-phase flow monitoring. Part 1: Hardware design and evaluation

Two-phase flows are commonly found in many industrial applications, such as oil and gas production. The monitoring of such flows is performed either in field applications or in pilot plant studies. In both cases, simple and robust measuring techniques are required. Capacitive probes have been applied for void fraction measurement in pipes in research and industry. However, capacitive measuring systems applied so far are tailored for specific applications and may not be easily adaptable. In addition, more and more soft-computing methods are applied for advanced data processing and parameter extraction which requires more computational power of sensor systems for online data processing. We develop a capacitive system provided with a microcontroller in which necessary routines for data processing may be embedded. System design is detailed explained and system's performance is evaluated, showing appropriate accuracy and time response for the investigation of two-phase flows.     

Determination and mapping of measurement and design coordinate systems using computational geometric techniques

Automotive industry is one of the most prospective manufacturing industries in the present world. In order to keep up with the challenges of competitors, the automobile industries are taking necessary steps to satisfy the customers by supplying products of good quality at lower cost. The machine vision inspection systems play an important role in quality control with their accurate dimensional measurement capability. The data obtained from these systems have to be analyzed using appropriate algorithms. In the present work, algorithms based on computational geometric techniques have been developed, to set up the coordinate system for the data obtained from the laser vision system for subframe and lower arm assembly of automobile front chassis module. The concept of a convex hull and a modified Voronoi diagram are utilized for establishing the coordinate system for measurement data. The design coordinate system is determined using the Voronoi diagrams. The measurement and design coordinate systems are mapped using 3D transformations. The results obtained for the sample data are also presented in this paper.     

On the improvement of a fully recursive formulation for the dynamic analysis of multibody systems

Virtual work in multibody systems is frequently expressed as the inner product of the virtual displacement and the resultant force at the centroid. But provided that the resultant force is converted into the equipollent forces there is no restriction on where the analysis reference point is placed. There are basically three candidate points : the centroid, joint point and the instant global origin. The traditional fully recursive formulation uses the centroid, but the present work verifies that the instant global origin always shows better efficiency (e.g. 86% CPU time of the centroid for quarter car model) and joint point shows the efficiency between that of the centroid and the instant global origin. A discussion on how important it is to define the analysis reference point properly in a fully recursive formulation is also presented.     

齿轮系统非线性动力学微分方程的渐进法

利用渐进法研究了一类考虑时变啮合刚度和间隙的齿轮系统的非线性动力学微分方程,建立了这类模型的解的统一形式。通过计算表明,渐进法具有良好的通用性,尤其适用于求解大型非线性微分方程组。最后给出了渐进法的计算结果,并且验证能与数值计算结果很好地吻合。     

Seven-bar mechanical press with hybrid-driven mechanism for deep drawing; Part 1: kinematics analysis and optimum design

Modeling and dynamic analysis of the electromechanical coupling system of a hybrid-driven mechanical press were undertaken. A dynamic model of a two-degrees-of-freedom seven-bar linkage was developed using Lagrange’s equation. According to the equivalent circuit of a DC motor and a brushless servomotor, a dynamic model and negative feed-back model were separately developed. The fourth-order Runge-Kutta method, an explicit method, was employed as the integration technique in a computer simulation, and the time history of the hybrid-driven press was obtained.     

A novel parallel-kinematics mechanisms for integrated, multi-axis nanopositioning: Part 1. Kinematics and design for fabrication

Multi-axis micro and nanopositioning systems are increasingly used in much of the metrology and process equipment related to the field of nanotechnology. This, the first of a two-part series of papers on a novel piezo-driven, parallel-kinematics XYZ nanopositioning (PKXYZNP) stage, concentrates on the development of a viable scheme to achieve pure spatial translation. First, the mechanism is shown to admit closed-form solutions to both; the forward and reverse kinematic problems. The Jacobian and the dynamics of the system indicate that the mechanical structure produces a relatively large work volume, and is capable of high bandwidth and uniform performance across it. The fabrication of the system is described along with some basic testing of its Jacobian and its modal frequencies. Using capacitive gages, the stage is capable of about 85 μm of motion along each axis with a resolution of about 2–4 nm. The controls, testing and performance are discussed in detail in the companion paper [Dong J, Yao Q, Ferreira PM. A novel parallel-kinematics mechanism for integrated, multi-axis nanopositioning. Part 2. Dynamics, control and performance analysis. Precis Eng].     

Noise and vibration in brake systems of vehicles. Part 1: Experimental procedures

The paper describes the vibroacoustic phenomena generated during frictional interaction of solid bodies. A classification is given for brake-induced noise. Modern experimental methods for studying vibroacoustic phenomena in metal-polymer friction contacts are analyzed. The main approaches to reducing noise and vibration in vehicle brakes are considered.     

现代设计理论方法在机械系统设计中的应用

阐述了传统机械系统设计方法和机械系统的现设计理论方法的特征;在传统机械系统设计的基础上提出了机械系统动态设计的概念、方法、目的等;并介绍了机械系统的建模方法及动态设计方法;提出对机械系统进行动态优化设计的方法。