Dynamic simulation of crankshaft multibody systems

General multibody system approaches are often not sufficient for specific situations in applications to yield an efficient and accurate solution. We concentrate on the simulation of the crankshaft dynamics which is characterized by flexible bodies and force laws describing the interaction between the bodies. The use of the floating frame of reference approach in our model leads to an index-2 DAE system. The algebraic constraints originate from the reference conditions and the normalization equation for the quaternions. For the time integration of this system, two aspects have to be taken into account: firstly, for efficiency exploiting the structure of the system and using parallelization. Secondly, consistent initial values also with respect to a related index-3 system have to be computed in order to compute missing initial velocities and to reduce transient phenomena. The work of C.B. Drab, J.R. Haslinger, and R.U. Pfau is supported by the “Bundesministerium für Wirtschaft und Arbeit” and by the government of Upper Austria within the framework “Industrielle Kompetenzzentren und Netzwerke”.     

Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction

This paper presents a methodology for treating energy consistency when considering simultaneous impacts and contacts with friction in the simulation of systems of interconnected bodies. Hard impact and contact is considered where deformation of the impacting surfaces is negligible. The proposed approach uses a discrete algebraic model of impact in conjunction with moment and tangential coefficients of restitution (CORs) to develop a general impact law for determining post-impact velocities. This process depends on impulse–momentum theory, the complementarity conditions, a principle of maximum dissipation, and the determination of contact forces and post-impact accelerations. The proposed methodology also uses an energy-modifying COR to directly control the system’s energy profile over time. The key result is that different energy profiles yield different results and thus energy consistency should be considered carefully in the development of dynamic simulations. The approach is illustrated on a double pendulum, considered to be a benchmark case, and a bicycle structure.     

Equilibrium analysis of multibody dynamic systems using genetic algorithm in comparison with constrained and unconstrained optimization techniques

The present paper describes a set of procedures for the solution of nonlinear equilibrium problems in complex multibody systems. To find the equilibrium position of the system, six different optimization algorithms are used to minimize the total potential energy (TPE) of the system and compared with respect to accuracy and efficiency. A computer program is developed to evaluate the equality constraints and objective function of a general multibody dynamic system to find the equilibrium condition. It is seen that the indirect methods have better results and converge faster. Also it is shown that the genetic algorithm (GA) results in a global optimum while the other methods converge to a local optimum.     

基于Simscape的塑料-钢螺旋蜗轮蜗杆稳态热分析

为了获得塑料-钢材料的螺旋齿蜗轮蜗杆啮合过程中的热量分布,根据热网络分布原理,利用Simscape仿真软件建立了热网络模型,分析了其啮合时的功率损失,得出其热阻计算模型和系统的稳态温度分布及热流量分布。仿真结果表明,蜗杆的温度远远高于其他节点温度,齿轮主要以蜗杆热传导的方式散热,通过选择热传导系数更大的蜗杆材料或采用减小蜗杆长度的设计可以改善蜗杆端传导散热。     

On the effect of linear algebra implementations in real-time multibody system dynamics

This paper compares the efficiency of multibody system (MBS) dynamic simulation codes that rely on different implementations of linear algebra operations. The dynamics of an N-loop four-bar mechanism has been solved with an index-3 augmented Lagrangian formulation combined with the trapezoidal rule as numerical integrator. Different implementations for this method, both dense and sparse, have been developed, using a number of linear algebra software libraries (including sparse linear equation solvers) and optimized sparse matrix computation strategies. Numerical experiments have been performed in order to measure their performance, as a function of problem size and matrix filling. Results show that optimal implementations can increase the simulation efficiency in a factor of 2–3, compared with our starting classical implementations, and in some topics they disagree with widespread beliefs in MBS dynamics. Finally, advices are provided to select the implementation which delivers the best performance for a certain MBS dynamic simulation.     

Multibody approach for tolerance analysis and optimization of mechanical systems

A multibody approach is suitable for tolerance analysis of mechanical systems since multibody formulation can directly consider part-level tolerance variables. In this study, procedures for performing tolerance analysis and corresponding sensitivity analysis for spatial multibody systems are proposed. First, statistical formulation for performing multibody system tolerance analysis is developed to obtain system level tolerance for given part-level tolerances. One very useful aspect of the proposed formulation is that in the process of computing system tolerance, the sensitivity of system tolerance with respect to part-level tolerances can be additionally obtained. The kinematics of spatial multibody systems has been redefined in terms of both generalized coordinates and part-level tolerance variables. Tolerances in geometry of a body are specified in terms of the variations in relative locations of joint definition points and relative distance between them. Tolerances in the joint kinematics are defined through variations in vector closure equations and orthogonality equations that are two fundamental constraint equations for most kinematic joints. To demonstrate the validity and effectiveness of the proposed tolerance analysis procedure, tolerance analysis of a spatial 4-bar mechanism and tolerance optimization are performed.     

车下设备悬挂参数与车体结构之间的匹配关系研究

本文通过建立等效欧拉梁车体与设备垂向耦合振动模型,研究了车下设备刚性悬挂与弹性悬挂对车体振动的影响。研究结果表明,车下设备采用弹性悬挂的设计方式能够有效抑制车体的弹性振动。为了研究车下设备弹性悬挂参数与车体结构之间的匹配关系,本文基于模态叠加法原理法建立了考虑车体弹性振动和车下设备的高速动车组刚柔耦合动力学模型。通过该三维模型分析了车下设备质量偏心和弹性悬挂参数对车体振动响应的影响规律。仿真结果表明,车下设备横向偏心主要影响车体的横向振动特性,而车下设备纵向偏心主要影响车体的垂向振动特性;当车下设备的悬挂频率接近车体的垂向弯曲频率时能够降低车体的整体振动水平,而当车下设备的悬挂频率低于车体的垂向弯曲频率时,提高车下设备弹性悬挂系统的阻尼能够一定程度上抑制车体的弹性振动。     

基于Simscape和RecurDyn的履带车辆动力学仿真技术研究

基于Matlab/Simscape建立履带车辆发动机和传动系统的物理模型.基于多体动力学软件RecurDyn建立履带车辆行动部分虚拟样机.通过Simulink和RecurDyn的接口技术,建立了发动机-传动装置-行动装置的履带车辆联合仿真模型.对履带车辆在硬路面进行直驶仿真,得到了换挡时的车速及驱动轮扭矩变化曲线;对履带车辆在硬路面进行无级转向仿真,得到了转向时驱动轮转速曲线和扭矩曲线、车速曲线和履带车辆运动轨迹.仿真结果表明,论文建立的履带车辆联合仿真模型有效可行,为履带车辆动力学仿真分析提供了新的思路.     

A new solution for mechanisms including Coulomb friction

This paper presents a new solution method for the analysis of multibody systems with Coulomb friction. Complete equations of motion and reaction forces are derived by using Lagrangian formulation and the traditional friction circle concepts for the analysis of Coulomb friction. The numerical solutions by the new method, as well as the conventional method for comparision, are illustrated. The new method saves considerably the computer execution time to solve equations of motion and reaction forces compared with the conventional method for same accuracy. The higher the coefficient of friction is, the more the computation time of the conventional method is needed but the computation time of the new method is nearly independent on the coefficient of friction.     

弹性支承体与旋转叶片耦合系统的固有频率分析

应用多体系统动力学理论建立弹性支承体与旋转叶片耦合系统的动力学方程 ,在系统稳定运动状态下 ,对耦合系统的动力学方程进行线性化处理 ,然后计算其系统固有频率 ;分析弹性支承体变形对系统固有频率的影响