Complete Shaking Force and Shaking Moment Balancing of Mechanisms Using a Moving Rigid Body

This paper addresses the mass balancing of mechanisms using a single rigid body („balancing body“). Firstly, the expressions of dynamic forces and moments acting on the machine frame, which are caused by arbitrary planar and spatial mechanisms are established. The general balancing conditions are then derived. By motion control of the balancing body, any resultant inertia forces and moments of several mechanisms can also be fully compensated. The desired motion of the balancing body is calculated in order that the sum of inertia forces and moments of the mechanisms and the balancing body is zero. Theoretically, the balancing body is possible to compensate the dynamic loads of the machine frame, even if several mechanisms with any structure are located in the machine frame. The balancing theory of planar mechanisms is presented in more detail. Finally, the proposed balancing method is illustrated by a numerical example, in which three components of dynamic loads caused by a planar mechanism in the steady state are given as the time-periodic functions. It can be shown that the proposed approach is an alternative to the conventional balancing methods and especially applicable in practice with piezoelectric actuators

Beitrag zur Diagnostik der Verzahnungen in Getrieben mittels Zeit-Frequenz-Analyse

Die vorliegende Arbeit befasst sich mit der Anwendung von Methoden der Zeit-Frequenz-Analyse zur Diagnostik der Verzahnungen in Getrieben anhand von Schwingungssignalen. Es werden neue Analysemethoden aus der Zeit-Frequenz-Analyse zur Verbesserung der Diagnosetechnik, wie die \u93Koeffizientenanalyse aus Zeit-Frequenz-Darstellungen\u93 oder die \u93Drehwinkel-Ordnungs-Darstellungen in Polarkoordinaten\u93 eingeführt. Basierend auf diesen Analyseverfahren wird eine geeignete Diagnosestrategie vorgestellt, mit der auch bei instationären Betriebszuständen Verzahnungsschäden sicher erkannt werden können. Zur praktischen Anwendung der Zeit-Frequenz-Analyse in der Verzahnungsdiagnose wird ein Rechenprogramm entwickelt, in dem eine Vielzahl von Signalanalyseprozeduren implementiert sind, um somit eine zuverlässige diagnostische Beurteilung von Verzahnungszuständen zu ermöglichen. In einem umfangreichen Versuchsprogramm werden die Anwendungsmöglichkeiten der beschriebenen Mittel und Verfahren auf verschiedenen Verzahnungsschäden in mehreren Abstufungen demonstriert, und die Eignung der Methoden wird beurteilt

Damping identification in multi-degree-of-freedom systems using the continuous wavelet transform

The identification of damping in multi-degree-of-freedom vibration systems is a well-known problem and appears to be of crucial interest. Compared to an estimation of the stiffness and mass, the damping coefficient or, alternatively, damping ratio is the most difficult quantity to determine. In this paper, the continuous wavelet transform based on the Morlet-wavelet function is used to identify the modal damping ratios of multi-degree-of-freedom vibration systems. A new wavelet-based method for the damping identification from measured free responses is presented. The proposed method was also tested by experiments on a steel beam

Modelling Parametric Vibration of Gear-Pair Systems as a Tool for Aiding Gear Fault Diagnosis

The main components in gear vibration spectra are the tooth-meshing frequency and its harmonics, together with sideband structures due to modulation effects. Sideband structures can be used as an important diagnostic symptom for gear fault detection. The main objective of the present paper is to unravel amplitude modulation effects which are responsible for generating such sidebands. The parametrically excited vibration of a gear-pair system in mesh was investigated. A comparison between the model result and actual experimental data from a test rig was also presented. Some analytical expressions are derived to provide a logical explanation for ob-served phenomena. The modelling result can be used to predict sideband amplitude in presence of the distributed gear faults such as non-uniform tooth wear, pittings. It may serve as a tool for aiding the gear fault diagnosis

Dynamic force analysis of a six-link planar mechanism under consideration of friction at the joints

The dynamic analysis of mechanisms with joints friction is complex since the frictional force depends nonlinearly on the resultant reactive force between the two mating surfaces of the joint. In this paper a non-iterative approximate method is used for determining the joint reaction forces and the driving torque of mechanisms is considered. By using the computing program MATLAB the dynamic forces of a six-link planar mechanism are calculated with this method

An efficient numerical procedure for calculating periodic vibrations of elastic mechanisms

This paper proposes a numerical procedure based on the well-known Newmark integration method to determine initial conditions for the periodic solution of a system of linear differential equations with time-periodic coefficients. Based on this, steady-state periodic vibrations of mechanisms with elastic elements governed by linearized differential equations with time-periodic coefficients can be conveniently calculated. The proposed procedure is demonstrated by a dynamic model of a planar four-bar mechanism with the flexible coupler

Complete shaking force and shaking moment balancing of spatial multibody systems with open kinematic chains

This paper deals with a solution for the problem of full shaking force and shaking moment balancing of spatial multi body systems with open kinematic chains. Firstly, the general conditions for complete dynamic balancing of spatial multibody systems are formulated. These include formulae for complete elimination of the resultant inertia force and inertia couple caused by all moving bodies. In the following example, the equations of complete shaking force and shaking moment balancing of a nine-bar direct drive manipulator are given

On the compression softening effect of prestressed beams

The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed, in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam. The forced transverse vibration of the beam with a moving external force has been considered. From this it follows compression softening effect of prestressed beams. A detailed comparison between the calculating results for the prestressed and the non-prestressed beam is also presented

Inverse kinematic and dynamic analysis of redundant measuring manipulator BKHN-MCX-04

This paper deals with the problem of inverse kinematics and dynamics of a measuring manipulator with kinematic redundancy which was designed and manufactured at Hanoi University of Technology for measuring the geometric tolerance of surfaces of machining components. A comparison between the calculation result and the experimental measurement is also presented