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AbstractA systematic procedure is proposed to predict the dynamic behaviours of a whole machine-tool structure. The prediction proceduremakes use of a receptance synthesis method, in which the dynamic model is composed of the elements such as the distributed-mass beam, the lumped mass and the joint. As an example, the dynamic characteristics of a guideway joint are analysed throughthe use of the dynamic fundamental characteristic parameters of joint surfaces at unit area obtained by experiments. The softwareto predict the dynamic behaviours of a whole machining tool structure is developed based upon the procedure. To demonstrate theutility of the proposed procedure and the developed software, the dynamic modeling of a whole machining centre structure hasbeen established and its natural frequencies are calculated by the software. The dynamic test for the whole machining centre showedthat the procedure and the software is valid to predict dynamic behaviours of a whole machine-tool structure at its design stage. 2003 Elsevier Science Ltd. All rights reserved.Keywords: Machine tools; Joint; Dynamic behaviours; Dynamic modeling; Computer-aided engineering; 49489
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Natural frequencies 1. IntroductionDue to fierce competition in the machine tools market,it is necessary to shorten the development cycle and toimprove the performance of products; that is to say, thesuccessful design of a new type of machine tool,especially of personalization-designed machine toolsmust be ensured. Therefore it is significant to developsoftware for predicting the dynamic behaviours of awhole machine-tool structure at its design stage. Theparts of the structure to be modified and the changes tobe made through the analysis and modification techniquecan be identified by computer-aided engineering (CAE).The first step in CAE is to predict the dynamic behav-iours of a whole machine-tool structure, which is mainlydiscussed in this paper. The prediction procedures andthe software have been developed. The investigations arecarried out for a machining centre structure to show thatthe software is effective to predict the dynamic behav- iours of a whole machine-tool structure and the predic-tion procedures proposed in this paper are valid.2. Dynamic model of a whole machine-toolstructureThe first step for predicting dynamic behaviours of awhole machine-tool structure is to establish a reasonabledynamic model. Three categories of dynamic structuralanalysis techniques are known at present. They are thedistributed-mass beam method [1], the lumped-constantbeam method [2], and the finite element method (FEM)[3]. Each of these methods is capable of estimating thedynamic behaviours of an elastic structure when its formis known. The calculating time of FEM is longer thanthe other two categories because of the complexity ofmodeling by FEM.Different from a single structure or a component, awhole machine-tool structure is composed of manycomponents connected with many joints. It is an inte-grated system. Since about 60% of the total dynamicstiffness and about 90% of the total damping in a wholemachine-tool structure originates in the joints [5,6], the dynamic characteristics of joints affect the dynamicbehaviours of a whole machine-tool structure consider-ably. Therefore the dynamic characteristics of jointsmust be taken into account during analysing dynamicbehaviours of a whole machine-tool structure [7].The dynamic characteristics of joints are affected bymany factors. Here the dynamic characteristics of jointsrefer to the dynamic stiffness and damping of joints.Experiments show that dynamic characteristics of jointsare intense non-linearity [4,10]. It is impossible to treatall of these factors by an analysing method in determin-ing the dynamic characteristics of joints. Joints cannotexist without the mechanical system.
The values of thedynamic stiffness and damping of joints obtaineddirectly by experiments are used in similar conditions inthe experiment [7]. Since there are so many valuesobtained by experiments and they are not general forvariable conditions, we cannot use them easily in pre-dicting dynamic behaviours of a new designed machinetool at its design stage. This paper solved this problemby use of the dynamic characteristic parameters of jointsurfaces at unit area, which are introduced in Section 4of this paper.For the intense non-linearity of dynamic character-istics of joints, the values of the dynamic stiffness anddamping of joints, which was based upon the dynamiccharacteristic parameters of joint surfaces at unit areaobtained by experiments, can be determined during theanalysis of the dynamic behaviours of a whole machine-tool structure. Therefore there would be many iterationsduring this analysis. Because the modelling of a wholemachine-tool structure by FEM is so complex that thecomputing time is very long, it is difficult to completethese iterations, and the computing time becomesunreasonable. How to establish a reasonable dynamicmodel of a whole machine-tool structure is a key topredicate the dynamic behaviours of a whole machine-tool structure.Because of the complexity of a whole machine-toolstructure, a reasonable dynamic model should not onlycalculate quickly for a whole machine-tool structure, butalso treat the non-linearity characteristics of joints easily.The dynamic model of a whole machine-tool structureproposed in this paper can meet these two requirements.Based on the former studies [1,2,7], three types ofelements, i.e. the distributed-mass beam, the lumpedmass and the joint, are included in the dynamic modelof a whole machine-tool structure proposed in this paper.The dynamic characteristics of joints are analysed basedon the dynamic fundamental characteristic parameters ofjoint surface at unit area obtained by experiments.In present modeling, the slender components in amachine-tool structure such as a column, a bed, an arm,a cross-rail, etc., are equivalent as the distributed-massbeam elements. Usually several equivalent beams areused to model a complex component with multi-sections[8]. The lumped-mass element is used to model theheavy concentrated mass such as a motor, a balance-mass, a gear, etc. The conjunction between two compo-nents can be equivalent as a joint element, such as aguideway joint, a bolt joint, a cylinder joint, etc. Theprocessing of modeling can be illustrated by a case studyof a machining centre structure in Section 6 of this paper.After appropriate elements are chosen depending upondifferent shapes of components in a machine-tool struc-ture, a reasonable dynamic model is established. Basedon the modeling we can analyse the dynamic behavioursof a whole machine-tool structure by the following pro-cedures.3. The analysis of dynamic behaviours of a wholemachine-tool structureIn this section, the dynamic equations of a wholemachine-tool structure are established based on thereceptance synthesis method. Using it, the natural fre-quencies of a whole machine-tool structure can be calcu-lated. The analysis is as follows.