Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems

Abstract

In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements.

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

“…Thus, the journal would no longer rotate around clearance circle. Moghadasi et al [464] performed a topology optimization of a planar slider-crank mechanism with a rigid crank and a flexible connecting rod. An efficient modified approach based on the classic Hertzian contact law was presented to model the revolute joint connected to the sliding mass and the crank.…”

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

“…1 The first stage deployment of a spinning solar sail [6] Topology optimization of an FMBS has called considerable attention in recent years to reduce the moving weight, improve the energy efficiency and enhance the dynamic performance. Since the pioneering work by Bendsøe and Kikuchi [13], several approaches [14] have been studied for the topology optimization of fluids, acoustics, electromagnetics and optics, as well as FMBS [15][16][17][18][19], but not yet for any FMBS with variable-length subject to both large overall motion and large deformation. This is probably due to the fact that the variable-length gives rise to three challenges for the topology optimization.…”

“…Consequently, the topology optimization can be performed using the method of the equivalent static loads (ESL) or directly from the dynamic simulation of an FMBS. The former is named the ESL method [15,18,[27][28][29][30][31], while the latter is called the integrated optimization method [16,32]. For an FMBS with variable-length bodies, the design domain varies over time.…”

“…Held et al [17] studied the effect of the model reduction of FFRF on the topology optimization results of an FMBS by using the solid isotropic material with penalization (SIMP) approach. Moghadasi et al [18] involved an accurate revolute joints and bearing domains model into the topology optimization of an FMBS via SIMP approach. Tromme et al [16] employed an LSM to optimize the flexible bodies of an FMBS and used elliptical holes to generate new topologies.…”

Rotation-joint stiffness modeling for industrial robots considering contacts

“…Recent studies use the finite element method (FEM) to analyze the stiffness matrix of the revolute joint connection between two adjacent links, where the preload, external wrenches, and friction can be considered as the contact constraints. [16][17][18] However, FEM is suitable to model the joint stiffness for the redundant legs and parallel kinematic machines (PKMs), which has the simple joint structures limited. As mentioned previously, the industrial robotic joint system is a complex structure composed of several components including the motor, synchronous belt, and reducer, as shown in Figure 1.…”