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Article
Publication date: 1 March 1986

Ronald L. Huston

This paper presents algorithms for computing the angular velocities of the bodies of a multibody system. A multibody system is any collection of connected bodies. The…

Abstract

This paper presents algorithms for computing the angular velocities of the bodies of a multibody system. A multibody system is any collection of connected bodies. The focus is upon multibody systems consisting of spherically pinned rigid bodies which do not form closed loops. Simple formulae are presented for computing the angular velocities. It is shown that once the angular velocities are known the entire kinematical description and hence, the dynamics of the system, may be developed routinely and in automated fashion. Extension to more general multibody systems follows without conceptual change in the procedures.

Details

Engineering Computations, vol. 3 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 1992

KJELL MAGNE MATHISEN and PÅL G. BERGAN

This paper discusses algorithms for large displacement analysis of interconnected flexible and rigid multibody systems. Hydrostatic and hydrodynamic loads for systems

Abstract

This paper discusses algorithms for large displacement analysis of interconnected flexible and rigid multibody systems. Hydrostatic and hydrodynamic loads for systems being submerged in water are also considered. The systems may consist of cables and beams and may combine very flexible parts with rigid parts. Various ways of introducing structural joints are discussed. A special implementation of the Hilber‐Hughes‐Taylor time integration scheme for constrained non‐linear systems is outlined. The formulation is general and allows for displacements and rotational motion of unlimited size. Aspects concerning efficient solution of constrained dynamic problems are discussed. These capabilities have been implemented in a general purpose non‐linear finite element program. Applications involving static and dynamic analysis of a bi‐articulated tower and a floating tripod platform kept in place by three anchor lines are discussed.

Details

Engineering Computations, vol. 9 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 5 October 2012

Denis Anders, Stefan Uhlar, Melanie Krüger, Michael Groß and Kerstin Weinberg

Wind turbines are of growing importance for the production of renewable energy. The kinetic energy of the blowing air induces a rotary motion and is thus converted into…

Abstract

Purpose

Wind turbines are of growing importance for the production of renewable energy. The kinetic energy of the blowing air induces a rotary motion and is thus converted into electricity. From the mechanical point of view the complex dynamics of wind turbines become a matter of interest for structural optimization and optimal control in order to improve stability and energy efficiency. The purpose of this paper therefore is to present a mechanical model of a three‐blade wind turbine with a momentum and energy conserving time integration of the system.

Design/methodology/approach

The authors present a mechanical model based upon a rotationless formulation of rigid body dynamics coupled with flexible components. The resulting set of differential‐algebraic equations will be solved by using energy‐consistent time‐stepping schemes. Rigid and orthotropic‐elastic body models of a wind turbine show the robustness and accuracy of these schemes for the relevant problem.

Findings

Numerical studies prove that physically consistent time‐stepping schemes provide reliable results, especially for hybrid wind turbine models.

Originality/value

The application of energy‐consistent methods for time discretization is intended to provide computational robustness and to reduce the computational costs of the dynamical wind turbine systems. The model is aimed to give a first access into the investigation of fluid‐structure interaction for wind turbines.

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Article
Publication date: 12 June 2017

Fan Shen, Siyuan Rong, Naigang Cui and Xianren Kong

The purpose of this paper is to provide a method with convenient modelling as well as precise computation to the research of complex multi-body system, such as robot arms…

Abstract

Purpose

The purpose of this paper is to provide a method with convenient modelling as well as precise computation to the research of complex multi-body system, such as robot arms and solar power satellite. Classical modelling method does not always fit these two requirements.

Design/methodology/approach

In this paper, tensor coordinates (TC) and homogeneous tensor coordinates (HTC) method with gradient components are developed, which also have a convenient interface with classical theory.

Findings

The HTC proved its precision and effectiveness by two examples. In HTC model, equations have a more convenient form as matrix and the results coincide well with classical one.

Research limitations/implications

There is no plenty detailed operations supported in mathematics yet, which may be developed in further research.

Practical implications

With TC/HTC method, the research work can be separated more thoroughly: a simpler modelling work is left to scientists, when more computing work is handed to the computers. It may ease scientists’ brains in multibody modelling.

Originality/value

The HTC method has the advantages of absolute nodal coordinate formulations, tensor and homogeneous coordinate (HC) and it may be used in multibody mechanics, or other related engineerings.

Details

Engineering Computations, vol. 34 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 June 2014

Zheng Feng Bai, Yang Zhao and Jun Chen

The existence of clearance in joints of positioning mechanism is inevitable and the movements of the real mechanism are deflected from the ideal mechanism due to the…

Abstract

Purpose

The existence of clearance in joints of positioning mechanism is inevitable and the movements of the real mechanism are deflected from the ideal mechanism due to the clearances. The purpose of this paper is to investigate the effects of clearance on the dynamic characteristics of dual-axis positioning mechanism of a satellite antenna.

Design/methodology/approach

The dynamics analysis of dual-axis positioning mechanism with clearance are investigated using a computational approach based on virtual prototyping technology. The contact model in joint clearance is established by using a hybrid nonlinear continuous contact force model and the friction effect is considered by using a modified Coulomb friction model. Then the numerical simulation of dual-axis positioning mechanism with joint clearance is carried out and four case studies are implemented for different clearance sizes.

Findings

Clearance leads to degradation of the dynamic performance of the system. The existence of clearance causes impact dynamic loads, and influences the motion accuracy and stability of the dual-axis positioning mechanism. Larger clearance induces higher frequency shakes and larger shake amplitudes, which will deteriorate positioning accuracy.

Practical implications

Providing an effective and practical method to analyze dynamic characteristics of dual-axis positioning mechanism of satellite antenna with joint clearance and describing the dynamic characteristics of the dual-axis positioning system more realistically, which improves the engineering application.

Originality/value

The paper is the basis of mechanism design, precision analysis and robust control system design of dual-axis positioning mechanism of satellite antenna.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 7 August 2017

Esmaeil Salahshoor and Saeed Ebrahimi

The purpose of this paper is to investigate the effect of joint clearance on the behavior of a needle driver mechanism (a slider-crank linkage) of a typical sewing machine…

Abstract

Purpose

The purpose of this paper is to investigate the effect of joint clearance on the behavior of a needle driver mechanism (a slider-crank linkage) of a typical sewing machine with an imperfect joint between the coupler and the slider (including needle).

Design/methodology/approach

In order to model the clearance, the momentum exchange approach is used. The Lankarani and Nikravesh’s continuous contact force model is used to model the contact force, and the modified Coulomb’s friction law represents the friction between sliding members. The penetration force applied on the needle by fabric is chosen based on an experimental data in the literature. The dynamic response is validated for the existing properties in the literature without considering the penetration force.

Findings

It is shown that the clearance joint made considerable effect on the dynamic response of the system. The rough changes of the needle acceleration and jerk are obvious. The base reaction force changed roughly and did not vary as smooth as that of the mechanism with ideal joint. So, clearance joint in the mechanism could lead to an undesirable vibration in the system. Furthermore, the crank driver must provide a non-smooth moment on the crank to keep the crank rotational velocity constant. Moreover, reducing the clearance size sufficiently could make the dynamic response closer to that of the mechanism with ideal joint. In addition, smoother crank moment could be required if the clearance size is reduced sufficiently. Furthermore, the rough change of the base reaction force which can represent the vibration caused by the mechanism on the fixed frame could be reduced if the clearance size is small enough.

Originality/value

Lockstitch sewing machine is one of the most common apparel industrial machines. The needle driver mechanism of a sewing machine could have an important role for proper stitch forming. On the other hand, clearances are inevitable in assemblage of mechanisms to allow the relative motion between the members. This clearance is due to machining tolerances, wear, material deformations, and imperfections, and it can worsen mechanism performance such as precision, dynamic behavior and vibration. Unfortunately, despite the importance of the dynamic behavior of the needle driver mechanism from practical point of view, very little publications have focused especially on the investigation of the effect of clearance joint on the dynamic behavior of the sewing machine which could lead to undesired vibration of the system and shorter lifetime as a result. In this paper, the dynamic behavior of the system including, needle velocity and acceleration, crank moment and base reaction force was compared with that of the ideal mechanism. Finally, the effect of clearance size on the dynamic behavior of the system was investigated.

Details

International Journal of Clothing Science and Technology, vol. 29 no. 4
Type: Research Article
ISSN: 0955-6222

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Article
Publication date: 11 November 2020

Duncai Lei, Xiannian Kong, Siyu Chen, Jinyuan Tang and Zehua Hu

The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and…

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Abstract

Purpose

The purpose of this paper is to investigate the dynamic responses of a spur gear pair with unloaded static transmission error (STE) excitation numerically and experimentally and the influences of the system factors including mesh stiffness, error excitation and torque on the dynamic transmission error (DTE).

Design/methodology/approach

A simple lumped parameters dynamic model of a gear pair considering time-varying mesh stiffness, backlash and unloaded STE excitation is developed. The STE is calculated from the measured tooth profile deviation under the unloaded condition. A four-square gear test rig is designed to measure and analyze the DTE and vibration responses of the gear pair. The dynamic responses of the gear transmission are studied numerically and experimentally.

Findings

The predicted numerical DTE matches well with the experimental results. When the real unloaded STE excitation without any approximation is used, the dynamic response is dominated by the mesh frequency and its high order harmonic components, which may not be result caused by the assembling error. The sub-harmonic and super-harmonic resonant behaviors are excited because of the high order harmonic components of STE. It will not certainly prevent the separations of mesh teeth when the gear pair is under the condition of high speed and heavy load.

Originality/value

This study helps to improve the modeling method of the dynamic analysis of spur gear transmission and provide some reference for the understanding of the influence of mesh stiffness, STE excitation and system torque on the vibration behaviors.

Details

Engineering Computations, vol. 38 no. 6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 20 December 2017

Haidong Yu, Chunzhang Zhao, Bin Zheng and Hao Wang

Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines…

Abstract

Purpose

Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines the performances, reliability and service life of the products. To achieve the automatic assembly of large-scale thin-walled structures, the sizing force of the structures with deviations should be calculated, and its assembling ability should be studied before assembly process. The purpose of this study is to establish a precise model to describe the deviations of structures and to study the variation propagation during assembly process.

Design/methodology/approach

Curved thin-walled structures are modeled by using the shell element via the absolute nodal coordinate formulation. Two typical deviation modes of the structure are defined. The generalized elastic force of shell elements with anisotropic materials is deduced based on a continuum mechanics approach to account for the geometric non-linearity. The quasi-static method is introduced to describe the assembly process. The effects of the deviation forms, geometrical parameters of the thin-walled structures and material properties on assembly quality are investigated numerically.

Findings

The geometric non-linearity of structure and anisotropy of materials strongly affect the variation propagation and the assembly quality. The transformation and accumulation effects of the deviations are apparent in the multiple assembly process. The constraints on the structures during assembly can reduce assembly deviation.

Originality/value

The plate element via the absolute nodal coordinate formulation is first introduced to the variation propagation analysis. Two typical shape deviation modes are defined. The elastic force of structures with anisotropic materials is deduced. The variation propagation during the assembly of structures with various geometrical and material parameters is investigated.

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Article
Publication date: 1 June 1997

M. Botz and P. Hagedorn

A number of computer codes are available for the automatic generation of the equations of motion of multibody systems formed by rigid bodies. Systems containing deformable…

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Abstract

A number of computer codes are available for the automatic generation of the equations of motion of multibody systems formed by rigid bodies. Systems containing deformable components generally cannot be treated readily by these programs. Demonstrates how multibody systems containing both rigid and deformable components can be handled with the aid of Autolev, a symbol manipulator for dynamics, when such components are discretized by a Rayleigh‐Ritz procedure. A computer code called Ritz was written to perform this task interactively with Autolev, and a Fortran program is generated automatically for the numerical simulation of motions of the system under consideration. The numerical results are then converted to Matlab format, so that plotting routines and other facilities available in Matlab can be used to process the results further.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 April 2008

S. Ebrahimi and P. Eberhard

This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of…

Abstract

This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in [7]. Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.

Details

Multidiscipline Modeling in Materials and Structures, vol. 4 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

1 – 10 of 225