Modelling and calculation of properties of sliding guideways

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Abstract

Properties of a machine tool significantly depend on the stiffness of its constructional system, which consists of the stiffness of all parts of the system. Special importance is attributed to the stiffness of the movable and fixed joints existing in the machine load carrying system. The paper describes a method of calculation of the static properties of guideway joints using finite element analysis. In its computational models, the presented method considers phenomena occurring in the contact layer of these joints.

Introduction

Utility value of a production machine is determined, to a significant degree, by accuracy of the machined workpieces. The most important factors affecting that accuracy are the static and dynamic stiffness of the machine, usually determined by relative displacements between a workpiece and a tool. The stiffness of the whole machine consists of the stiffness of all its units under load, but the most important is the stiffness of the joints in the load carrying system. It has been estimated that, in the relative displacement of a workpiece and a tool, the part of the displacement occurring in the joints can reach 30–90% 1, 2, 3, 4. The joints, as material discontinuities, are also the places where constructional damping occurs due to dissipation of the energy of mechanical vibration and thus reduction of its amplitude. Component elements of the joints, especially surfaces of movable joints, are subject to intensive wear, which should also be monitored and forecast.

The objective of the research was development and implementation of some methods enabling analysis of the properties of a machine tool constructional system (MTCS), taking into account the elastic properties of the joints 1, 5, 6. Application of commercial software systems for finite element analysis (FEA) was assumed. In previously published papers 1, 4, 7, 8, some attempts were made to solve the above-mentioned problems using FEA, but the results were not always satisfactory because of the accepted simplifications or time-consuming non-automatic modifications of the computational model.

Section snippets

Properties of the contact layer in a joint and its model

Properties of a joint depend on the applied loads and on properties of the materials in contact—both their geometric shape and surface properties in the contact area.

Results of research of the phenomenon of two contacting surfaces 9, 10show that the real contact area between two elements does not exceed several per cent of their nominal surface because of errors in their machining (Fig. 1).

Experiments [3]prove the elastic–plastic nature of normal deformations during the first load of the

Application of finite element analysis in modelling of guideway systems

For the purpose of analysis of joints using FEA it is possible to apply a concept of isolating from a joint of two elements their contact layer as a so-called “third body” [19](Fig. 4). In that case, modelling of the contact pair consists of attributing the contact layer properties different from those of the contacting elements, resulting from the contact phenomena.

In order to build a model for the FEA analysis, the nominal contact surface is divided into substitute elements of a size

Verification of the computational method

The method of calculation developed was tested for several selected systems containing joints, from the simplest models of contact pairs to a real system examined experimentally.

Application of the presented method

Calculation of a machine tool guideway system was performed using selected CAD and FEA systems (AutoCAD and Cosmos/M), integrated and supplemented with procedures for iterative computation.

The displacements in a machine tool model, calculated using the described method, are shown in Fig. 13. In Fig. 14(a), the calculated pressure distribution on the working surfaces of the guideways is given, from which the maximum values of normal pressure can be read. Visualization of the normal pressure

Conclusions

The developed modelling methodology and the software system for design calculations are intended for design of production machines utilizing sliding guideway joints.

The method and the applied algorithms enable:

  • modelling of normal and tangential contact deformations in joints;

  • giving consideration to non-linear characteristics of the contact layer;

  • iteratively solving non-linear problems in automatic cycles of FEA model modifications;

  • integration of the process of modelling geometry in a CAD system

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