外文翻譯--銑床主軸系統(tǒng)的振動響應分析 英文版

1、<p>　　Applied Mechanics and MaterialsOnline: 2015-03-16</p><p>　　ISSN: 1662-7482, Vol. 741, pp 435-440</p><p>　　doi:10.4028/www.scientific.net/AMM.741.435</p><p>　　© 2015

2、 Trans Tech Publications, Switzerland</p><p>　　Vibration Response Analysis on Spindle System of Milling Machine</p><p>　　Yao Tingqiang, Tan Yang, Huang Yayu</p><p>　　Faculty of Mech

3、anical and Electrical Engineering, Kunming University of Science and Technology,</p><p>　　Kunming, China</p><p>　　yaotingqiang@163.com, tanyang@163.com, huangyayu@163.com</p><p>　　K

4、ey words: stiffness; frequency response analysis; spindle system; milling machine</p><p>　　Abstract: The dynamic characteristics and dynamics parameters of rolling bearings is very important to dynamics and

5、vibration response of rotate machine such as rotor systems, gear systems and Spindle systems. The frequencies of rotate machine are affected by dynamics parameters of rolling bearings at different places. The purpose in

6、the work presented is to research a new approach and multibody model of Spindle systems with equivalent dynamics parameters of rolling bearings. The flexible Spindl</p><p>　　Introduction</p><p>

7、　　The performance of rotating mechanics has been affected by the dynamic characteristics of rolling bearings. The dynamic characteristics of the joint faces of rolling bearings are nonlinear and time-varying. The dynamic

8、s of rolling bearings and the dynamics parameters of Spindle system have been researched by many researchers. The research on single rolling bearing has been considered much more factors such as lubrication, cage, wavene

9、ss, roughness. The dynamics of multibody systems with rolling </p><p>　　The linear equivalent stiffness parameters and dynamics model of spindle system was constructed and the modal frequencies were calculat

10、ed by A.M.Sharan[2] , W.R.Wang and C.N.Chang[3], K.W.Wang and C.H.Chen[4].. The linear equivalent model of spindle-gear system was constructed and dynamics analysis by T.Q.Yao[5]. The modeling approach for interface stif

11、fness of spindle-tool holder has been discussed and the FEA of spindle systems been carried out by X.S.Gao[6]. The finite element modeling of hig</p><p>　　spindle-holder-tool joints and Effect of interfaces

12、on dynamic characteristics of a spindle system have been discussed by B.WANG[7,8]. The FEM model of three-layer structure spindle systems of</p><p>　　boring machine has been constructed and the linear stiffn

13、ess and damper parameters have been identified using parameter identification method by X.Han[9].</p><p>　　The method of equivalent dynamics model of spindle systems with different linear and nonlinear joint

14、 parameters has been discussed and verified in the presented work.</p><p>　　All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the wri

15、tten permission of Trans Tech Publications, www.ttp.net. (ID: 132.239.1.230, University of California, San Diego UCSD, La Jolla, USA-23/02/16,05:42:01)</p><p>　　order/frequency calculated experiment</p>

16、;<p>　　436Engineering Solutions for Manufacturing Processes V</p><p>　　The model of Spindle system</p><p>　　2.1 Flexible Spindle Model</p><p>　　In the Figure.1, The cutter i

17、s fixed on the N1 location, the double row roller bearing and is fixed on the N2 equivalent location, two angular ball bearings is fixed on the N3 equivalent location by face to face, the driven gear is assembled to N4 e

18、quivalent location by multiple spline. The FEM model of Spindle is constructed by modal synthesis method.</p><p><b>　　box</b></p><p>　　In this investigation, fixed interface componen

19、t mode method was used to model the flexible Spindle. This approach is based on the Rayleigh-Ritz method as developed by Craig and Bampton. In this approach a complex structure is divided into components whose modes are

20、subdivided into normal and constraint modes. The normal modes are obtained by solving the eigenvalues problem.</p><p>　　K ? ω2 M ? 0 (1) where K and M are stiffness and mass matrices. The boundaries of the s

21、tructure were fixed at the bearing locations represented by interface points. The number of normal modes of interest depends on the application and frequency band of interest.</p><p>　　The constraint modes a

22、re static deformation shapes obtained by applying a unit displacement to each boundary nodes while constraining the degrees of freedom of other boundary nodes. The number of constraint modes in flexible bodies depends on

23、 number of interface points. Each interface point is associated with six constraint modes.</p><p>　　The degrees of freedom of each component are reduced by using modal substitution l</p><p>　　wh

24、ere ul is displacement of nodes inside the component (internal nodes), uB is the displacement of nodes on the boundary of component (boundary nodes), uN are the natural modes, uC are the constraint modes, and qN are the

25、generalized co-ordinates of the natural modes. The behavior of the entire model is analyzed by assembling the response of each component.</p><p>　　Fig.2 The FEM of Spindle</p><p>　　Tab.1 The rel

26、ative error of the calculated and experiment results</p><p>　　relative error</p><p>　　11350.41345.80.34%</p><p>　　23486.13366.53.55%</p><p>　　a the first bend fre

27、quency, f1=1350.4Hz b the second bend frequency, f2=3486.1Hz Fig.3 The frequencies of Spindle</p><p>　　The relative errors of the calculated and experiment frequencies are showed in Tab.1. The vibration mode

28、s of the first and second frequencies are showed in Fig.3. The relative errors are small between the calculated and experiment frequencies.</p><p>　　2.2 Equivalent Dynamic Bearing Model</p><p>　

29、　A key aspect of modeling the bearing dynamics with the spring-damper element method is obtaining the total forces and moments acting on the whole rolling bearing. In the current model,</p><p>　　the linear a

30、nd nonlinear spring-damper element are considered as a part of the analysis respectively. In the reference[11], the linear and equivalent stiffness on the location N2 and N3 has been</p><p>　　calculated by t

31、he modal experiment and parameter identification method. The spring-damper element model is showed in the Fig.1c. In order to get the relatively accurate support stiffness parameters of rolling bearings, the relative err

32、ors between the calculated and experimented frequencies should be minimum by adjusting the linear and equivalent spring-damper parameters. However, this method can only achieved the first bend frequency, the error is too

33、 large for the other frequencies in the refer</p><p>　　2.3 Dynamic Spindle System Model</p><p>　　The shaft are modeled by the FEM and each rolling bearings are modeled by spring-damper elements.

34、 Interface points are established at points where the bearing supports on the Spindle. These interface points are made coincident with the bearing inner race center of gravity. Thus the dynamic response is passed from on

35、e model to other. Figure 1 depicts these interface point interactions as two headed arrows indicating that the exchange of dynamic response occurs from both the sides, namely, rolling</p><p>　　Eq.(3) is solv

36、ed by a linearization method for constrainted multibody sytems with Recurdyn. If the stiffness of rolling bearings has been given, the frequencies of Spindle system will be calculated. Details are discussed in the refere

37、nce[10]. Four models with flexible Spindle, rigid Spindle box, rigid bearing base and different spring-damper are discussed in the thesis. The four models are the linear and equal spring-damper model(①LESDM), the linear

38、and unequal spring-damper model(②LUSDM), the n</p><p>　　and nonlinear Unit is N/mm10/9 or N/mm3/2.</p><p>　　Results and Discussion</p><p>　　Experimental and Analytical Results Corro

39、boration.</p><p>　　The frequencies of Spindle and Spindle system predicted by the spring-damper Spindle model were corroborated with the results obtained from the Spindle system test rig showed in Fig.4 and

40、Fig.5.</p><p>　　438Engineering Solutions for Manufacturing Processes V</p><p>　　a the pulse excitation of Spindle b the experiment frequencies response results of Spindle Fig.4 The frequency re

41、sponse of Spindle by pulse excitation</p><p>　　The sine sweep vibration test of Spindle component has been applied to test the frequencies response and research the equivalent dynamics paramers. The Spindle

42、component is consisted of Spindle, Spindle box, rolling bearings and bearing base. To get accurate frequencies response, the sweep frequency range is 100Hz to 3000Hz and the sweep frequency increment has been selected as

43、 0.5Hz. The first three orders frequencies of the Spindle component are f1=317.4Hz, f2=1540.4Hz, f3=2244.0Hz.</p><p>　　a photograph of vibration test b frequency response results of 100-3000HZ Fig.5 Sine swe

44、ep vibration test of spindle systems</p><p>　　The equivalent stiffness parameters at N2 and N3 location of the Spindle component has been calculated by Eq.(4) and optimization analysis in Recurdyn software.

45、The calculated and experiment results and relative errors are showed in Tab.2.</p><p>　　Tab.2 The calculated and experiment frequencies and errors</p><p>　　The frequencies and vibration response

46、 of Spindle systems have been calculated by adjusting equivalent spring and damper elements to minimizing errors between the calculated and experiment frequencies. Then the equivalent stiffness parameters have been calcu

47、lated by the presented method.</p><p>　　Generally, the radial stiffness at the Spindle head N2 is greater than at the rear-end N3 to achieve the milling quality. In Tab.2, the errors of frequencies of ①LESDM

48、 and ②LUSDM are large except the first frequency. The ①LESDM and ②LUSDM are accurate for the first frequency, but inaccurate for high order frequencies. The ①LESDM and ②LUSDM are sometimes may be applied to calculate the

49、 equivalent stiffness parameters inaccurately. The errors of frequencies of ③NESDM and ④NUSDM are small, the resu</p><p>　　According to Hertz Contact Theory, the contact dynamics and vibration of rolling bea

50、rings are nonlinear. Therefore, the load-deformation factor of radial stiffness of roller bearings at the Spindle head N2 is showed as linear contact factor 10/9. The load-deformation factor for angular ball bearings at

51、the rear-end N3 is showed as point contact factor 3/2.</p><p>　　a first f1=317.1Hz b second f2=1501.2Hz c third f3=2246.8Hz Fig.6. Frequencies of Spindle component by the ④NUSDM</p><p>　　The fre

52、quencies of Spindle component supported by the ④NUSDM are showed in Fig.6. The first order frequency is 317.1Hz coupling rigid vibration of Spinlde, box and ④NUSDM. The second and third order frequencies are 1501.2Hz and

53、 2246.8Hz. They are coupling flexible bending vibration of Spinlde and ④NUSDM.The ④NUSDM is typically strong nonlinear model and gets nonlinear nonequivalent spring and damper elements. The ④NUSDM and the dynamics model

54、of Spindle have been verified by the calculated resul</p><p>　　Conclusions</p><p>　　The models of Spindle body and Spindle component have been constructed by FEM with equivalent spring damper el

55、ements. The simulations of vibration response have been carried out. The calculated frequencies are compared with the experiment results by the pulse excitation and the sine sweep vibration test. Therefore, the equivalen

56、t stiffness parameters have been calculated by minimizing errors between the calculated and experiment frequencies. It is believed that good agreements between the result</p><p>　　The presented method and th

57、e model are general and available to research the frequencies, vibration response and dynamics characteristics of Spindle systems.</p><p>　　Acknowledgements</p><p>　　The authors would thank the

58、funds provided by the Chinese Government through the Project NSFC-11002062, NSFC-11462008 and the Scientific Research Foundation for Introduced Talents in Kunming University of Science and Technology- KKSA201101018.</

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