Multibody System Software Used for Research of Car Suspension System Dynamics

2014 ◽  
Vol 1036 ◽  
pp. 794-799 ◽  
Author(s):  
Łukasz Konieczny ◽  
Rafał Burdzik ◽  
Piotr Folęga
Keyword(s):  
System Dynamics ◽  
Modular Design ◽  
Differential Algebraic Equations ◽  
Suspension System ◽  
Motor Vehicles ◽  
Algebraic Equations ◽  
System Software ◽  
Lagrange Equations ◽  
Car Suspension ◽  
The Impact

The paper presents results of investigation of car suspension system dynamics. In this research the multibody (Multi Body System - MBS) system software MSC.Adams was used. ADAMS software (MSC.Software) is a commercial software to build a multibody structural models. Modular design allows for the usage of applications with different focuses, such as rail, aviation and motor vehicles. Models with a large number of freedom degrees of the components are built with mass concentrated on the assumption that the system is composed of a rigid (or deformable) bodies combined in a specific way (connection spherical, sliding, rotary), moving under the action of the forces and moments of different types (concentrated or distributed forces, the forces of contact). The complex multibody systems are automatically generated by the Lagrange equations of motion of the second kind in absolute coordinates. Integral procedures used to solve the differential-algebraic equations include multistep algorithms with variable row and a variable-and fixed-step and one-step algorithms. The Adams/Car module enables building and simulation-based examination of individual car subsystems such as, for instance, the suspension, steering or driving system as well as their combinations forming a complete car. The programme contains an extensive library of structural solutions applied in cars. The geometry and relationship data of individual components are stored in libraries, and software operation on a standard user level can be brought down to defining positions of constraints in space. The software is compatible with various CAD programmes, thus enabling import of elements created in other applications. The study was conducted for the vehicle model of Fiat Seicento. The examined system of the complete vehicle consists of 49 kinematic degrees of freedom. The article examined the impact of chosen parameters on vehicle vibration in an Adams Car Ride. Used in simulation Adams/Car /Ride module allows to test vehicle dynamics forcing the position of the plate of test stand . Virtual model of the vehicle is set on four servo-motors. They can control any excitation combination of individual actuators (dispalcement and amplitude, phase between extortion, etc.) and determine all kinds of vibration (vertical, lateral, angular). The study was conducted for selected parameters of the test rig.

Well-Posed Formulations for Nonholonomic Mechanical System Dynamics

2020 ◽  
Vol 15 (10) ◽  
Author(s):  
Edward J. Haug
Keyword(s):  
System Dynamics ◽  
Mechanical System ◽  
Lagrange Multiplier ◽  
Variational Formulation ◽  
Direct Consequence ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
First Order ◽  
Well Posed ◽  
Problem Data

Abstract Four formulations of nonholonomic mechanical system dynamics, with both holonomic and differential constraints, are presented and shown to be well posed; i.e., solutions exist, are unique, and depend continuously on problem data. They are (1) the d'Alembert variational formulation, (2) a broadly applicable manifold theoretic extension of Maggi's equations that is a system of first-order ordinary differential equations (ODE), (3) Lagrange multiplier-based index 3 differential-algebraic equations (index 3 DAE), and (4) Lagrange multiplier-based index 0 differential-algebraic equations (index 0 DAE). The ODE formulation is shown to be well posed, as a direct consequence of the theory of ODE. The variational formulation is shown to be equivalent to the ODE formulation, hence also well posed. Finally, the index 3 DAE and index 0 DAE formulations are shown to be equivalent to the variational and ODE formulations, hence also well posed. These results fill a void in the literature and provide a theoretical foundation for nonholonomic mechanical system dynamics that is comparable to the theory of ODE.

scholarly journals L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Bowen Li ◽  
Jieyu Ding ◽  
Yanan Li
Keyword(s):  
System Dynamics ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Multibody System Dynamics ◽  
Dynamics Simulation ◽  
Time Interval ◽  
Algebraic Equations ◽  
Stable Method ◽  
Long Term Conditions ◽  
Equidistant Nodes

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.

Two Friction’s Laws for Lagrange’s Equations of Multibody System with Dry Friction

2011 ◽  
Vol 328-330 ◽  
pp. 1697-1700
Author(s):  
Jian Feng Wang ◽  
Ying Jiu Liu ◽  
Shun Chuan Gao ◽  
Song Li ◽  
Feng Feng
Keyword(s):  
System Dynamics ◽  
Dry Friction ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Multibody System Dynamics ◽  
Algebraic Equations ◽  
Friction Forces ◽  
Friction Law ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

With the first kind of Lagrange’s equations, this paper presents the dynamical equations of multibody system with friction constraints. The generalized forces of friction forces are described in the form of matrix. Considering numerical method is widespread to analyze the characteristics of multibody system dynamics, this paper compares the two friction laws for solving the multibody system problem with dry friction constraints. Using Baumgarte’s and augmentation method, the differential-algebraic equations are given in the form of differential equations matrix to raise calculating efficiency. The friction force for Coulomb’s friction law and the continuous friction law is denoted, which converts subsection smooth systems to continuous smooth systems. An example is given to evaluate the validity of continuous law of friction. The numerical simulation shows that continuous law of friction is an effective method to process multibody system friction problem. The work in this paper also provides a new direction to research the non-smooth multibody system dynamics equation.

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