Linearization and Model Reduction of Contact Dynamics Simulation

Author(s):  
Jianxun Liang ◽  
Ou Ma ◽  
Caishan Liu

Finite element methods are widely used for simulations of contact dynamics of flexible multibody systems. Such a simulation is computationally very inefficient because the system’s dimension is usually very large and the simulation time step has to be very small in order to ensure numerical stability. A potential solution to the problem is to apply a model reduction method in the simulation. Although many model reduction techniques have been developed, most of them cannot be readily applied due to the high nonlinearity of the involved contact dynamics model. This paper presents a solution to the problem. The approach is based on a modified Lyapunov balanced truncation method. A numerical example is presented to demonstrate that, by applying the proposed model reduction method, the simulation process can be significantly speeded up while the resulting error caused by the model reduction is still within an acceptable level.

Author(s):  
Jianxun Liang ◽  
Ou Ma

Finite element models can accurately simulate impact-contact dynamics response of a multibody dynamical system. However, such a simulation remains very inefficient because very small integration time step must be used when solving the involved differential equations. Although many model reduction techniques can be used to improve the efficiency of finite element based simulations, most of these techniques cannot be readily applied to contact dynamics simulations due to the high nonlinearity of the contact dynamics model. This paper presents a model reduction approach for finite-element based multibody contact dynamics simulation, based on a modified Lyapunov balanced truncation method. An example is presented to demonstrate that, by applying the model reduction the simulation process is significantly speeded up and the resulting error is bounded within an acceptable level. The performance of the method with respect to some influential factors such as element size, shape and contact stiffness is also investigated.


Electronics ◽  
2021 ◽  
Vol 10 (16) ◽  
pp. 1994
Author(s):  
Shirin Noei ◽  
Mohammadreza Parvizimosaed ◽  
Mohammadreza Noei

The Society of Automotive Engineers (SAE) defines six levels of driving automation, ranging from Level 0 to Level 5. Automated driving systems perform entire dynamic driving tasks for Levels 3–5 automated vehicles. Delegating dynamic driving tasks from driver to automated driving systems can eliminate crashes attributed to driver errors. Sharing status, sharing intent, seeking agreement, or sharing prescriptive information between road users and vehicles dedicated to automated driving systems can further enhance dynamic driving task performance, safety, and traffic operations. Extensive simulation is required to reduce operating costs and achieve an acceptable risk level before testing cooperative automated driving systems in laboratory environments, test tracks, or public roads. Cooperative automated driving systems can be simulated using a vehicle dynamics simulation tool (e.g., CarMaker and CarSim) or a traffic microsimulation tool (e.g., Vissim and Aimsun). Vehicle dynamics simulation tools are mainly used for verification and validation purposes on a small scale, while traffic microsimulation tools are mainly used for verification purposes on a large scale. Vehicle dynamics simulation tools can simulate longitudinal, lateral, and vertical dynamics for only a few vehicles in each scenario (e.g., up to ten vehicles in CarMaker and up to twenty vehicles in CarSim). Conventional traffic microsimulation tools can simulate vehicle-following, lane-changing, and gap-acceptance behaviors for many vehicles in each scenario without simulating vehicle powertrain. Vehicle dynamics simulation tools are more compute-intensive but more accurate than traffic microsimulation tools. Due to software architecture or computing power limitations, simplifying assumptions underlying convectional traffic microsimulation tools may have been a necessary compromise long ago. There is, therefore, a need for a simulation tool to optimize computational complexity and accuracy to simulate many vehicles in each scenario with reasonable accuracy. This research proposes a traffic microsimulation tool that employs a simplified vehicle powertrain model and a model-based fault detection method to simulate many vehicles with reasonable accuracy at each simulation time step under noise and unknown inputs. Our traffic microsimulation tool considers driver characteristics, vehicle model, grade, pavement conditions, operating mode, vehicle-to-vehicle communication vulnerabilities, and traffic conditions to estimate longitudinal control variables with reasonable accuracy at each simulation time step for many conventional vehicles, vehicles dedicated to automated driving systems, and vehicles equipped with cooperative automated driving systems. Proposed vehicle-following model and longitudinal control functions are verified for fourteen vehicle models, operating in manual, automated, and cooperative automated modes over two driving schedules under three malicious fault magnitudes on transmitted accelerations.


Author(s):  
Andreas Müller

Redundant constraints in multibody system (MBS) models, reflected by a singular constraint Jacobian, impair the efficient dynamics simulation. In particular, kinematic loop constraints are often found to be permanently redundant. This problem is commonly attacked numerically by decomposing the constraint Jacobian either at every simulation time step or beforehand in an admissible assembly (assuming that the redundancy is permanent). This paper presents a method for the elimination of permanently redundant loop closure constraints, which, instead of numerically decomposing the constraints, relies on the geometric characterization of kinematic loops comprising lower kinematic pairs. In particular, the invariant vector space of velocities of a kinematic loop is taken into account, which can be determined as the sum of Lie (screw) algebras of two subchains of a kinematic loop. The actual reduction is achieved by restricting the constraints to this space. The presented method does not interfere with the actual generation of constraints but can be considered as a preprocessing step of MBS models. It is numerically robust and only uses a geometrically exact model. The method is able to completely eliminate redundant loop constraints for “nonparadoxical” single-loop mechanisms and applies conservatively to multiloop MBS. The presented method only requires information (vectors, matrices) that is readily available in any MBS simulation package. The only numerical operations involved are cross products and a singular value decomposition of a low dimensional matrix.


Author(s):  
Klaus Po¨hland ◽  
Jan Berssenbru¨gge ◽  
Holger Krumm ◽  
Peter Ebbesmeyer

This work describes the conception and prototypic implementation of a program to simulate the dynamics within a rail-based undercarriage in real time. A software library for real time simulation of multibody systems (MBS) and a library to create Virtual Reality (VR) applications, function as a basis for this work. The main emphasis lies on the integration of the multibody-simulation into an interactive 3D environment to enable the user to interact with the model and its dynamics simulation in real time. The basic idea of this paper is to simulate a simplified dynamics model of a virtual prototype only as precise as necessary to obtain a better understanding of the prototype’s dynamics. The level-of-detail technique, frequently being used when CAD data is prepared for the use in VR, is utilized here on the simplified dynamics model of a virtual prototype.


2012 ◽  
Vol 562-564 ◽  
pp. 842-846 ◽  
Author(s):  
Zhen Xu ◽  
Hua Deng ◽  
Qi Wang

In the present paper, a multiteeth meshing gear contact dynamics model is proposed by introducing a modified robotic contact model. The inertial property, backlash of gear teeth and coincidence degree of gear meshing are considered into the model. In addition, the proposed model is used to simulate discontinuous meshing gear contact. Simultaneously, the gear meshing contact dynamical finite element model is also simulated using the Ansys/LS-DYNA software to demonstrate the rationality of the proposed model.


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