Analytical methodology for the analysis of vibration for unconstrained discrete systems and applications to impedance control of redundant robots

This paper presents a general methodology for the analysis and synthesis of a positive semi-definite system described by mass, damping and stiffness matrices that is often encountered in impedance control in robotics research. This general methodology utilizes the fundamental kinematic concept of rigid-body and non-rigid-body motions of which all motions consist. The rigid-body mode results in no net change in the potential energy from the stiffness matrix of the multiple degree-of-freedom (DoF) discrete mechanical system. Example of an unconstrained discrete mechanical system is presented to illustrate the theoretical principle as applied in obtaining the free and forced vibration responses, as well as the dynamic characteristics of the system in natural frequency, $$\omega_n$$ ω n and damping ratio, $$\zeta$$ ζ . In addition, the methodology is applied to the impedance control of redundant robots. The rigid-body mode is equivalent to the motions of a redundant robot which result in no net change in potential energy, also called the zero-potential or ZP mode, of impedance control. Example of a redundant robot is used to demonstrate the application of the methodology in robotics. The dynamic characteristics of $$\omega _n$$ ω n and $$\zeta$$ ζ in the modal space are analyzed, which can be synthesized to modulate the damping of the system analytically.

ON THE ZEROS OF AN UNDAMPED THREE-DOF FLEXIBLE SYSTEM

This paper presents an investigation of zeros in the SISO dynamics of an undamped three-DoF LTI flexible system. Of particular interest are non-minimum phase zeros, which severely impact closed-loop performance. This study uses modal decomposition and zero loci to reveal all types of zeros — marginal minimum phase (MMP), real minimum phase (RMP), real non-minimum phase (RNMP), complex minimum phase (CMP) and complex non-minimum phase (CNMP) — that can exist in the system under various parametric conditions. It is shown that if CNMP zeros occur in the dynamics of an undamped LTI flexible system, they will always occur in a quartet of CMP-CNMP zeros. Consequently, the simplest undamped LTI flexible system that can exhibit CNMP zeros in its dynamics is a three-DoF system. Motivated by practical examples of flexible systems that exhibit CNMP zeros, the undamped three-DoF system considered in this paper comprises of one rigid-body mode and two flexible modes. For this system, the following conclusions are mathematically established: (1) This system exhibits all possible types of zeros. (2) The precise conditions on modal frequencies and modal residues associated with every possible zero provide a mathematical formulation of the necessary and sufficient conditions for the existence of each type of zero. (3) Alternating signs of modal residues is a necessary condition for the presence of CNMP zeros in the dynamics of this system. Conversely, avoiding alternating signs of modal residues is a sufficient condition to guarantee the absence of CNMP zeros in this system.

Calculation of Rigid-Body Motion of Integrated Raft Isolation System

Integrated raft isolation system (IRIS) has some advantages over raft system of much smaller scale, such as higher isolation efficiency, less use of elastic couplings, etc. But the calculation of IRIS’s dynamic characteristics is complex. Finite element method usually adopted by raft designers is inefficient due to the iterative nature of design process. In this paper a six-degree-of-freedom rigid-body motion model is presented to calculate the static，quasi-static and rigid-body mode behavior of IRIS. The model is especially suitable to compare different design schemes and select out feasible ones efficiently at the initial design stage of IRIS.

Five Pad Tilting Pad Bearing Design and Lateral Vibration Characteristics of Small Gas Turbine Supported by It and Roller Bearing

In tilting pad bearing design process, the selection of the proper configuration type of either a Load-Between-Pad (LBP) or Load-On-Pad (LOP) as well as preload and pivot offset conditions is to be carefully considered. Also the bearing needs to be designed in order to be suited for the rotor-bearing system and operating condition. In this paper, it is observed that the static and dynamic characteristics of a five pad tilting pad bearing for the LBP and LOP configurations are influenced by the variation of preload and pivot offset. In this context, rotor dynamic analysis of the 5 MW industrial gas turbine supported by the tilting pad bearing at the front and roller bearing at the rear is carried out based on the dynamic coefficients of the tilting pad bearing investigated. The result shows that two rigid body critical modes experience various changes according to the influence of the tilting pad bearing uniquely applied to one side of this machine. Mainly, the second critical speed, the rigid body mode of conical shape with high whirling in the tilting pad bearing, is significantly changed by preload and pivot offset regardless of the LBP and LOP configurations. And the first critical mode, the rigid body mode of conical shape with high whirling in the roller bearing, is sensitively affected by preload applied to the LOP configuration and by its asymmetric dynamic properties.

Suppression of vertical bending and rigid-body-mode vibration in railway vehicle car body by primary and secondary suspension control: Results of simulations and running tests using Shinkansen vehicle

To improve ride comfort in railway vehicles, the suppression of vertical bending vibration and rigid-body-mode vibration in the car body is essential. In this paper, a system is proposed that aims to reduce bending and rigid-body-mode vibration simultaneously by introducing damping control devices in the primary and secondary suspensions. The technique involves a control system of primary vertical dampers and air springs; the former are used to suppress the first bending mode vibration; the latter, to suppress the rigid-body-mode vibration. The results of both simulations and vehicle running tests on the Sanyo—Shinkansen line demonstrate that this system reduced vertical vibrations in the bogies and the car body using the sky-hook control theory. In the running tests in particular, the system reduced the vertical vibration acceleration PSD peak value in the first bending mode to almost 20 per cent and in the rigid body mode to almost 50 per cent compared with the case when the system was not used. As a result, the ride quality level LT (a widely used index of ride comfort in Japan) decreased by at least 3 dB, indicating greater ride comfort.