This paper compares selected optimization-based methods for the analysis of multibody systems with redundant constraints. The following numerical schemes are examined: direct integration method, Udwadia-Kalaba formulation, two types of least-squares block solution method and Udwadia-Phohomsiri formulation. In order to compare efficiency of the algorithms, a series of simulations is performed on two exemplary McPherson struts. In the first variant, the mechanism has no redundant constraints whereas the other is overconstrained. Three constraint stabilization schemes are also compared in terms of integration errors.

The goal of this research is to achieve close to real-time dynamics performance for allowing auto-pilot in-the-loop testing of unmanned ground vehicles (UGV) for urban as well as off-road scenarios. The overall vehicle dynamics performance is governed by the multibody dynamics model for the vehicle, the wheel/terrain interaction dynamics and the onboard control system. The topic of this paper is the development of computationally efficient and accurate dynamics model for ground vehicles with complex suspension dynamics. A challenge is that typical vehicle suspensions involve closed-chain loops which require expensive DAE integration techniques. In this paper, we illustrate the use the alternative constraint embedding technique to reduce the cost and improve the accuracy of the dynamics model for the vehicle.

This paper presents a methodology for contact detection between convex quadric surfaces using its implicit equations. With some small modifications in the equations, one can model superellipsoids, superhyperboloids of one or two sheets and supertoroids. This methodology is to be implemented on a multibody dynamics code, in order to simulate the interpenetration between mechanical systems, particularly, the simulation of collisions with motor vehicles and other road users, such as cars, motorcycles and pedestrians.

The contact detection of two bodies is formulated as a convex nonlinear constrained optimization problem that is solved using two methods, an Interior Point method (IP) and a Sequential Quadratic Programming method (SQP), coded in MATLAB and FORTRAN environment, respectively. The objective function to be minimized is the distance between both surfaces. The design constraints are the implicit superquadrics surfaces equations and operations between its normal vectors and the distance itself. The contact points or the points that minimize the distance between the surfaces are the design variables. Computational efficiency can be improved by using Bounding Volumes in contact detection pre-steps. First one approximate the geometry using spheres, and then Oriented Bounding Boxes (OBB).

Results show that the optimization technique suits for the accurate contact detection between objects modelled by implicit superquadric equations.

The paper describes the design and multibody dynamic analysis of a mechanically interconnected suspension, as applied to a small off-road vehicle. Interconnected suspensions use some sort of connection between the axles of a vehicle in order improve ride quality or vehicle handling. In principle, the connection may be hydraulic, pneumatic, or mechanical, but for installation in a typical passenger car, a mechanical connection would likely be impractical due to weight and complexity. In this paper, the vehicle in question is the University of Windsor SAE Baja off-road competition vehicle, and novel mechanical design is proposed. A multibody dynamic analysis is performed on the proposed design using the EoM open source multibody software developed by theUniversity ofWindsorVehicle Dynamics and Control research group in order to assess any potential performance improvements.

The present paper is dedicated to the analysis of deployable tensegrity columns. The main aim of this work is to present a technique, developed by combining the finite element (FE) analysis and the multibody dynamics (MBD) simulation, which enables precise and reliable simulations of deployable structures. While the finite element model of the column provides information on structural behavior in the deployed state, the dynamical modeling allows to analyze various deployment scenarios, choose active cables for the deployment and for the self-stress application, and to control distributions of internal forces during the assembly process. An example of a deployable column based on a popular tensegrity module – a 3-strut simplex – is presented. By analyzing the proposed column with the use of the developed method it is proven that the technique is suitable for complex simulations of deployable systems.

Parallel computers are becoming more available. The natural way to improve computational efficiency of multibody simulations seems to be parallel processing. Within this work we are trying to estimate the efficiency of parallel computations performed using one of the commercial multibody solver. First, the short theoretical outline is presented to give the overview of modeling issues in multibody dynamics. Next, the experimental part is demonstrated. The series of dynamics analyses are carried out. The test mechanisms with variable number of bodies are used to gather the performance results of the solver. The obtained data allow for estimating the number of bodies which are sufficient to gain benefits from parallel computing as well as their level. The parallel processing profits are taken into account in the case of contact forces present in the system. The performance benefits are indicated, when the multilink belt chain is simulated, in which contact forces are included in the model.

In the present work, a tire model is derived based on geometrically exact shells. The discretization is done with the help of isoparametric quadrilateral finite elements. The interpolation is performed with bilinear Lagrangian polynomials for the midsurface as well as for the director field. As time stepping method for the resulting differential algebraic equation a backward differentiation formula is chosen. A multilayer material model for geometrically exact shells is introduced, to describe the anisotropic behavior of the tire material. To handle the interaction with a rigid road surface, a unilateral frictional contact formulation is introduced. Therein a special surface to surface contact element is developed, which rebuilds the shape of the tire.

This paper presents the application of a co-simulation approach for the simulation of frictional contact in general-purpose multibody dynamics to a rotorcraft dynamics problem. The proposed approach is based on the co-simulation of a main problem, which is described and solved as a set of differential algebraic equations, with a subproblem that is characterized by nonsmooth dynamics events and solved using a timestepping technique. The implementation and validation of the formulation is presented. The method is applied to the analysis of the droop and anti-flap contacts of helicopter rotor blades. Simulations focusing on the problem of blade sailing are conducted to understand the behavior and assess the validity of the method. For this purpose, the results obtained using a contact model based on Hertzian reaction forces at the interface are compared with those of the proposed approach.

The dynamics of the turning process of a thin-walled cylinder in manufacturing is modeled using flexible multibody system theory. The obtained model is time varying due to workpiece rotation and tool feed and retarded, due to repeated cutting of the same surface. Instabilities can occur due to these consecutive cuts that must be avoided in practical application because of the detrimental effects on workpiece, tool and possibly the machine. Neglecting the small feed, the stability of the resulting periodic system with time-delay can be analyzed using the semi-discretization method. The use of an adaptronic tool holder comprising actuators and sensors to improve the dynamic stability is then investigated. Different control concepts, two collocated and two model-based, are implemented in simulation and tuned to increase the domain of stable cutting. Cutting of a moderately thin workpiece exhibits instabilities mainly due to tool vibration. In this case, the stability boundary can be significantly improved. When the instability is due to workpiece vibration, the collocated concepts fail completely. Model based concepts can still obtain some improvements, but are sensitive to modeling errors in the coupling of workpiece and tool.

There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections.

This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.

The beam elements, which are widely used in the absolute nodal coordinate formulation (ANCF) can be treated as isoparametric elements, and by analogy to the classical finite element analysis (FEA) are integrated with standard, spatial Gauss-Legendre quadratures. For this reason, the shape of the ANCF beam cross section is restricted only to the shape of rectangle. In this paper, a distinct method of integration of ANCF elements based on continuum mechanics approach is presented. This method allows for efficient analysis of the ANCF beam elements with circular cross section. The integration of element vectors and matrices is performed by separation of the quadrature into the part that integrate along beam axis and the part that integrate in the beam cross section. Then, an alternative quadrature is used to integrate in the circular shape of the cross section. Since the number of integration points in the alternative quadrature corresponds to the number of points in the standard Gaussian quadrature the change in the shape of the cross section does not affects negatively the element efficiency. The presented method was verified using selected numerical tests. They show good relatively agreement with the reference results. Apart from the analysis of the beams with the circular cross section, a possibility of further modifications in the methods of the element integration is also discussed. Due to the fact that locking influence on the convergence of the element is also observed, the methods of locking elimination in the proposed elements are also considered in the paper.

A formulation developed at the Laboratory of Mechanical Engineering allows robust and efficient simulation of large and complex multibody systems. Simulators of cars, excavators and other systems have been developed showing that real-time simulations are possible even when facing demanding manoeuvres. Hydraulic actuators are presented in many industrial applications of multibody systems, like in the case of the heavy machinery field. When simulating the dynamics of this kind of problems that combine multibody dynamics and hydraulics, two different approaches are common: to resort to kinematically guide the variable length of the actuator, thus avoiding the need to consider the dynamics of the hydraulic system; or to perform a multi-rate integration of both subsystems if a more detailed description of the problem is required, for example, when the objective of the study is to optimize the pump control. This work addresses the inclusion of hydraulic actuators dynamics in the above-mentioned self-developed multibody formulation, thus leading to a unified approach. An academic example serves to compare the efficiency, accuracy and ease of implementation of the simplified (kinematic guidance), multi-rate and unified approaches. Such a comparison is the main contribution of the paper, as it may serve to provide guidelines on which approach to select depending on the problem characteristics.

Despite the ever-increasing computational power of modern processors, the reduction of complex multibody dynamic models remains an important topic of investigation, particularly for design optimization, sensitivity analysis, parameter identification, and controller tuning tasks, which can require hundreds or thousands of simulations. In this work, we first develop a high-fidelity model of a production sports utility vehicle in Adams/Car. Single-link equivalent kinematic quarter-car (SLEKQ, pronounced “sleek”) models for the front and rear suspensions are then developed in MapleSim. To avoid the computational complexity associated with introducing bushings or kinematic loops, all suspension linkages are lumped into a single unsprung mass at each corner of the vehicle. The SLEKQ models are designed to replicate the kinematic behaviour of a full suspension model using lookup tables or polynomial functions, which are obtained from the high-fidelity Adams model in this work. The predictive capability of each SLEKQ model relies on the use of appropriate parameters for the nonlinear spring and damper, which include the stiffness and damping contributions of the bushings, and the unsprung mass. Homotopy optimization is used to identify the parameters that minimize the difference between the responses of the Adams and MapleSim models. Finally, the SLEKQ models are assembled to construct a reduced 10-degree-of-freedom model of the full vehicle, the dynamic performance of which is validated against that of the high-fidelity Adams model using four-post heave and pitch tests.

One of the applications of tether system is in the field of satellite technology, where the mother ship and satellite equipment are connected with a cable. In order to grasp the motion of this kind of tether system in detail, the tether can be effectively modeled as flexible body and dealt by multibody dynamic analysis. In the analysis and modeling of flexible body of tether, large deformation and large displacement must be considered. Multibody dynamic analysis such as Absolute Nodal Coordinate Formulation with an introduction of the effect of damping force formulation can be used to describe the motion behavior of a flexible body. In this study, a parameter identification technique via an experimental approach is proposed in order to verify the modeling method. An example of swing-up control using the genetic algorithm control approach is performed through simulation and experiment. The validity of the model and availability of motion control based on multibody dynamics analysis are shown by comparison between numerical simulation and experiment.