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Theanalysis of dynamic characteristics of joints proposed inthis paper is also common for other types of joints, suchas cylinder joints, taper joints, etc. Therefore it is poss-ible to predict the dynamic behaviours of a wholemachine-tool structure at its design stage based on thedynamic fundamental characteristic parameters of jointsurfaces at unit area.5. Software development for predicting dynamicbehaviours of a whole machine-tool structureBased upon the proposed procedures, software forpredicting dynamic behaviours of a whole machine-toolstructure has been developed: NFAP (natural frequenciesanalysis program). The software consists of a pre-pro-cessing program, a post-processing program and a main-analysis program, which are written with FORTRANand C languages. The pre-processing program deals withmodeling for component equivalent and input-datumFig. 4. Software flow chart of predicting dynamic behaviours of awhole machine-tool structure. Fig. 5. ANC profile-machining centre with a moveable column.preparation. The post-processing program outputs natu-ral frequencies and plots the curve of frequency responseof receptance. The main-analysis program can calculatethe natural frequencies of a whole machine-tool struc-ture, including the dynamic analysis of joints that is sup-ported by the library of the dynamic fundamental charac-teristic parameters of joint surfaces at unit area. The flowchart of the main-analysis program is shown in Fig. 4.6. Case study for a whole machining centrestructureAs an example, dynamic behaviours of a CNC profile-machining centre with a moveable column were pre-dicted. Fig. 5 shows this machining centre structure, inwhich the tool-side structure (including the hind-bed, thesaddle, the column, the headstock, the milling head, theprofile arm, etc.) stands apart from the workpiece-sidestructure (including the work-table, the front-bed).. Thetable size is 3.2 × 1.2m and the table longitudinal travelFig. 6. Dynamic model of the tool-side structure.is 4m. Since the automatic tool changing system is pos-itioned on the foundation apart from the main structureof the machine tool, it is not depicted in Fig. 5. Thispaper mainly investigates the dynamic behaviours of thetool-side structure.According to the principle of modeling method pro-posed in this paper, the dynamic model of the tool-sidestructure is established with the distributed-mass beam,the lumped mass and the joint, as illustrated in Fig. 6 Inwhich the complex structures with multi-sections, suchas the bed, the column, the headstock and the profile-arm, are equivalent with several distributed-beamelements [8] which are synthesised by the rigidity com-bination constraints. The hind-bed under the movablecolumn is mounted on the foundation through bolts.These bolts are equivalent with complex springs. Thetwo guideways are equivalent with guideway joints. Theconcentrated-mass components such as motors, gears,the profile head, the balance mass, etc., are equivalentwith lumped-mass elements. Based on this model, thenatural frequencies of the tool-side structure are analysedwith the software NFAP. The curve of the frequencyresponse of receptance is illustrated in Fig. 7.In order to verify the validity of the proposed pro- Fig. 8. Experimental setup.cedures and the software NFAP, the dynamic behavioursof the tool-side structure were measured by exciting testthrough the HP35665A dynamic signal analyzer. Experi-mental apparatus is shown in Fig. 8. The exciting forceproduced by the impulse hammer was applied at the endof spindle in the direction of milling-head axis, and anaccelerometer was mounted at the end of spindle nearthe exciting point to pick up the response signal. Thecurves of power spectrum and coherence during the testare shown in Fig. 9. It can be seen from Fig. 9 that theresults of measuring are believable.In order to reduce the random error and improve sig-nal–to-noise ratio, the average results of five times theexciting test are adopted. The frequency response ofreceptance of the tool-side structure is measured throughexciting test as shown in Fig. 10.From Figs 7 and 10, the experimental and calculatedresults of natural frequencies of the tool-side structurecan be obtained and are all listed in Table 1.