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【JX15-14】100MD60Y4磨削用电主轴的设计（CAD+论文）
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【JX15-14】100MD60Y4磨削用电主轴的设计CAD+论文
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【JX15-14】100MD60Y4磨削用电主轴的设计（CAD+论文）,JX15-14,【JX15-14】100MD60Y4磨削用电主轴的设计CAD+论文
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An application of Taguchi method on the high-speed motorized spindle system design Chi-Wei Lin Department of Industrial Engineering and Systems Management, Feng Chia University, Taichung, Taiwan Abstract As spindle speeds increase, the variations caused by high-speedeff ects become more signifi cant. Therefore, in the initial design stage, it is necessary for machine tool design engineers to con- struct a robust high-speed machine tool that possesses high fi rst-mode natural frequencies and is insensitive to highoperatingspeeds. In this paper,Taguchi methodis used to identifythe optimal values of design variables for a robust high-speed spindle system with respect to the signal-to- noise ratio of system fi rst-mode natural frequency. The L18orthogonal array covers seven main design variables at three levels each, one main design variable at two levels, and the noise fac- tor spindle speeds at six levels. The results show that the new optimal design has improved the signal-to-noise ratio of the fi rst-mode natural frequencyby 2.06 dB from the original design; this implies that the quality loss has been reduced to 62 percent of its original value. The optimal design has been verifi ed by a confi rmation numerical experiment. Keywords: Taguchi method; Robust design; High-speed motorized spindle system design; System dynamics; FEM model 1. Introduction High-speed machining (HSM) is an emerging material removal processing technology. Al- thoughtheoriesofhigh-speedmetalcuttingcanbetracedbackto the1930s,commercialmachine tools capable of achieving these cutting speeds did not exist until the late 1980s 1, 2. Only re- cently, industries have started experimentingwith the use of high-speedmachinetools in produc- tion. The aircraft industry was fi rst; automobile fi rms and mold-and-die makers have followed. To furtherenhanceproductivity,manymachinetool buildersandacademicresearchershave been endeavoring to produce machine tools with improved spindles that can rotate faster than earlier spindle systems. Spindle system design has become one of the most important components of high-speed machine tool development. The design process for a motorized spindle system usually begins with identifi cation of the bearing types, confi gurations, preloading methods, and spindle motor systems that would be Tel: +886-4-24517250 Ext. 3636; Fax: +886-4-24510240. Email address: cwlin.tw. (Chi-Wei Lin) Preprint submitted to JMESOctober 4, 2011 本論文收錄於： Pr o c e e d i n g s o f t h e I n s t i t u t i o n o f M e c h a n i c a l En g i n e e r s , Pa r t C: Jo u r n a l o f M e c h a n i c a l En g i n e e r i n g S c i e n c e S e p t e m b e r 2 0 11 v o l . 2 2 5 n o . 9 2 19 8 - 2 2 0 5 appropriate for the desired machining application 3. Once a spindle concept has been clari- fi ed, detailed design specifi cations, such as static and dynamic stiff ness levels, maximum oper- ating speeds, power requirements, etc. are used to defi ne the values of design variables of the spindle system. However, in the initial stage of the high-speed spindle design, the most im- portant consideration is that the fi rst-mode natural frequency (FMNF) is much higher than the maximum spindle speed; if FMNF is not high enough, forced resonance may occur 4. It is also worth noting that as spindle speed increases, high-speed eff ects on the fi rst-mode natural frequency of a spindle system may become more signifi cant. To understand the complicated thermo-mechanical-dynamic behaviors of motorized spindles during high-speed rotations, Lin et al. 5 proposed a comprehensive, integrated fi nite element method (FEM) model of motor- ized spindle systems, in which changes in bearing preload and shaft rigidity cannot be ignored. This model has been verifi ed on a high-speed machining testbed equipped with a custom-built, high-performance motorized spindle 6. The results showed that the natural frequencies of the spindle system decreased as spindle speed increased and split into backward and forward modes due to the high-speed eff ects caused by centrifugal forces and gyroscopic moments respectively. This implies that the fi rst-mode natural frequency of a high-speed spindle system may vary in its life cycle, because in practice, spindle speeds usually need to be adjusted to fi t applications and machining conditions. Therefore, it is necessary for machine tool design engineers to construct a robust, high-speedmachine tool that not only possesses high fi rst-mode natural frequencies but also is insensitive to operating speeds, particularly when high-speed eff ects exist. Since there are two objectives that seek to be optimized and, usually, the equation for fi nding the fi rst-mode natural frequency is revealed as nonlinear, the problem discussed in this paper can be catego- rized as a nonlinear multiobjective optimization program, which may not be solved eff ectively by traditional gradient-based methods. The methods originated by Dr. Genichi Taguchi, especially the technique of parameter de- sign, have been proved to be very effi cient means to achieve robustness. Taguchi method has been applied successfully in thousands of companies worldwide for the past 40 years, with ex- cellent results 7. For static problems, such as the one investigated in this paper, the Taguchi approach divides the factors that aff ect product quality characteristics into two categories: the control factors (CFs) and the noise factors (NFs). Design teams can easily specify the levels of CFs, but cannot control NFs. Taguchis parameter design methodology reveals that we can simultaneously robustize the high-speed spindle system design against noise factors, i.e. spindle speeds, and maximize the system fi rst-mode natural frequency by specifying the levels of the control factors, i.e. the nominal values of design variables. In order to fi nd the optimal levels of the control factors, fractional factorial designs using tables of orthogonal arrays are utilized in Taguchi method to avoid ineffi ciently testing all possible combinations 8. This quality engi- neering method has also been utilized successfully in many academic researches to fi nd optimal parameter levels 9, 10, 11, 12, 13? ? ? . In this paper, to attain robustness for high-speed spindle systems at the detailed design stage, we use the parameter design technique of Taguchi method to determine the levels of design vari- ables that simultaneously maximize the fi rst-mode natural frequency and minimize the variation caused in it by high-speed eff ects. First, the parameter design methodology is introduced. Then, a comprehensivedynamicmodelof the motorizedhigh-speedspindle system, as shown in Fig. 1, is briefl y discussed and the primary design variables and their levels are determined accordingly. By applyingTaguchi method,the optimal levels of these design variables are obtained and a con- fi rmatory test is conducted to verify the results, and accordingly, statistically signifi cant design variables are identifi ed throughanalysis of variance(ANOVA). Finally, a conclusion is presented 2 60mm BORE x 95 mm O.D. x 18mm WIDE ANGULAR CONTACT HYBRID CERAMIC CLASS 7/9 45mm BORE x 75 mm O.D. x 18mm WIDE ANGULAR CONTACT HYBRID CERAMIC CLASS 7/9 #1#2 #3#4 Figure 1. The high-speed spindle bearing system to summarize the results of this paper. 2. Parameter Design Technique in Taguchi Method Inthis research,theTaguchiparameterdesigntechniqueis usedtodecidethelevelsofcontrol factors for the most robust design. A signal-to-noise ratio (SNR) is derived from a quality loss function to measure the system quality characteristics. The SNR has diff erent forms for diff erent types of quality loss functions. For the-larger-the-better cases such as the one studied in this paper, the SNR () can be written as 8 = 10log Pn i=11/y 2 i n (1) where yiis the observed data of the quality characteristics concerned, and n is the sample size. Taguchi designed orthogonal arrays to study the eff ects of control factors and to decide their optimal levels with a small numberof experiments; this approachis moreeffi cient than a full fac- torial experimental design. An orthogonal array provides a balanced set of experimentation runs such that conclusionscan be drawnin a balancedfashion7. To select an appropriateorthogonal array, one must fi rst determine how many degrees of freedom (DOF) exist; the number of DOF depends on the numbers of control factors and their levels. In Taguchi method, the orthogonal arrays are represented as Latin squares La, where a shows the total number of experimentation runs needed. Taguchi method provides a well-developed approach for parameter design problems; the implementation of the present research is summarized as the following steps: 8, 9, 7 : 1. Identifythe appropriatequality characteristics and determine an ideal functionof the qual- ity characteristics. 2. Identifyallthe controlandnoisefactorsthatinfl uencethequalitycharacteristicsanddefi ne their levels. 3. Select an orthogonal array that is appropriate to the sizes and levels of the control and noise factors; form the inner and outer arrays. 3 Figure 2. The mechanism of spindle integrated dynamic FEM model 4. Conduct experiments based on the arrangement of the orthogonal arrays. 5. Analyze the data to calculate the eff ects of the control factors on the quality characteristics (i.e. SNR) and determine the optimal levels of all control factors. 6. Identify signifi cant control factors which aff ect SNR through ANOVA. 7. Verify the optimal design with a confi rmation numerical experiment. Ashasbeenmentioned,thequalitycharacteristicofthehigh-speedspindlesystemconsidered in this paper is the fi rst-mode natural frequency; this research seeks to maximize this variable. Before the second step is described, the dynamic model of the high-speed spindle system is introduced concisely to identify the main design variables and to demonstrate infl uences of the noise factor (spindle speed) on the systems fi rst-mode natural frequency. 3. The Integrated FEM Model of the High-Speed Spindle System The dynamics of high-speed motorized spindles are highly complicated because there are several non-linear and closed-loop phenomena that interact thermally and mechanically with each other. For design purposes, the rectangular blocks in Fig. 2 show the essential physical models required to describe the dynamic properties of spindle systems, including an integrated dynamicFEMmodelofthespindle,anFEMmodelofthespindleshaft,abearingstiff nessmodel, a thermal preload model, a thermal expansion model, and a heat transfer model. In this paper, the integrated FEM model developed and experimentally improved by Lin et al. 5 is applied to optimize the motorized spindle system shown in Fig. 1 with respect to high-speed eff ects; the front bearing pairs are rigidly preloaded with spacers of specifi c sizes and the preload is 891 N. If the spindle shaft element is modeled as a Timoshenkobeam and the displacements of each node are assigned with four degrees of freedom (two for the lateral and two for the angular), the integrated dynamic FEM model for the motorized spindle can be expressed as 4 (MT + MR) q G q + (K 2(MT MR)q = Q(t)(2) 4 where q is the global node displacement of the spindle bearing system in rotational frame coordinates; is the spindle speed; MT is the transitional mass matrix; MR is the rotational mass matrix; G is the gyroscopic matrix of the spindle shaft; K is the system stiff ness matrix constituted by spindle shaft and radial bearing stiff ness; and Q(t) is the load vector. This model does not consider any structural damping or axial forces. From Eq. (2) it can be seen that the matrices MT, MR, G, and K are all determined from the size and material of the spindle shaft; K is also a function of the locations of the bearings and the preloads performed on them. Fig. 2 shows major independent variables in the dynamic model. The independent variables are divided into two categories, denoted as design variables (DVs) and operation variables (OVs). The DVs, such as the dimensions of the spindle shaft and bearings, are decided in the design stage and are rarely modifi ed after the spindle has been delivered to the user, while the OVs, such as spindle speed, are set on the shop fl oor; DVs and OVs comprise the control factors and noise factors respectively. The eight important DVs identifi ed by Lin and Tu 4, described in Table 1, include material of spindle, diameters and total length of the spindle shaft, bearing initial preload, spacings be- tween the bearings of the front or rear bearing set, spacing between the middle line of the front and rear bearing sets, and spacing of the middle line of the front and rear bearing sets to the end of the cutting tool. These eight design variables are the control factors of this research. Table 1 also shows the levels as well as the DOFs for these factors. The column “Level 2” indicates the nominal values of the original design (Fig. 1) for each control factor. Note that since the cross section of the spindle shaft used in this research is not uniform, the symbol Doriin the row of CF “B” represents the original design value of each cross sections diameter, and since the CFs E, F, G, and H are related to the length of the spindle shaft, which varies across the experiment runs, the level values of these CFs in the table are represented as percentages of the total length of the spindle shaft (CF “C”). Finally, the noise factor, spindle speed, is considered at six levels from 0 rpm to 25,000 rpm with a 5,000 rpm increment. Table 1. The control factors and their levels SymbolDesign VariableUnitLevel 1Level 2Level 3DOF AMaterial of the spindle shaftMPa1.9 10112.1 10111 B*Diameters of the spindle shaftmm0.8*DoriDori1.2*Dori2 CTotal length of the spindle shaftmm657.5692.1726.72 DRear bearing initial preloadN3003403702 E* Spacing between the bearings of front bear- ing set mm8.00%10.00%12.00%2 F* Spacing between the bearings of rear bearing set mm4.20%6.20%8.20%2 G* Spacing between the middle lines of front and rear bearing sets mm51.50%54.50%57.50%2 H* Spacing between the middle line of front and rear bearing sets and the free end of cutter mm58.15%59.65%61.15%2 Total DOF15 * Dori= the diameters of each cross section of the spindle shaft for the original design. *The percentages are with respect to the length of the spindle shaft (CF “C”). As shown in Fig. 3, the original spindle shaft is represented by a 23-element fi nite element model. From Fig. 3, it can be seen that the front bearings are located on nodes 8 and 11, and the rear bearings are located on nodes 20 and 21 of the spindle shaft. A program has been 5 Figure 3. Elements of the spindle system written in MATLAB to convert the above system data into a set of equations of motion; the fi rst- modenatural frequencycan be obtainedaccordingly. Detailed derivationsand validationof these equations and information on the dimensions of the elements and bearings can be found in 5. 4. To-be-optimized Design Variables For Taguchi Method In this section, the appropriate orthogonal array is determined from the DOFs of the control factors; experiments are conducted according to the arrangement of the orthogonal array. From an analysis of the SNR data from the experimental results, the optimal levels of control factors are identifi ed. ANOVA of SNR data shows the relative signifi cance levels of control factors. To avoid errors, only the diff erences made by signifi cant control factors are considered in prediction of the optimum FMNF; the predicted optimum is confi rmed experimentally (FEM). 4.1. Orthogonal Array Experiment To determine an appropriate orthogonal array for the control factors, the total DOF must be obtained fi rst. As shown in Table 1, there are 15 DOF in total; therefore, the orthogonal array L18 , one of the arrays that Taguchi most recommended for its ability to smear the eff ects of interactions among several main eff ects 14, is selected as the inner array to arrange the combinations of the eight control factors. The arrangement is shown in columns 2 to 9 of Table 2. In these columns, control factors A to H are in the top row, and the eighteen rows below them, containing the numbers 1, 2, and 3, indicate the levels of the correspondingcontrol factors that are adjusted in each experimental run. The next 11 columns describe six speeds; all non- zero speeds must be described twice, once for backward mode (BWM) and once for forward mode (FWM). Centrifugal forces and gyroscopic eff ects cause the system FMNF to vary with the spindle speed; they split FMNF into two diff erent modes (BWM and FWM) at non-zero spindle speeds. These 11 columns are the outer array for the noise factor; the spindle speeds are on the top, ranging from 0 rpm to 25,000 rpm with a 5,000 rpm increment. An additional row indicates the backward mode and forward mode for each speed except 0 rpm. The experimental plan requires 18 runs. In each run, the control factors are set to the levels shown in Table 2. For example, in run 1, level 1 is assigned to control factors “A” to “H” in the MATLAB FEM program, and the program is executed at spindle speeds from 0 to 25,000 rpm with a 5,000 rpm increment; this produces 11 diff erent outcomes, as shown in the row for run 1 in Table 2. The SNR for each experimentalrun can be calculated by using Eq. (1); the results are presented in the SNR column of Table 2. 6 Table 2. Experimental results for FMNF (Hz) and SNR 0 rpm5,000 rpm10,000 rpm15,000 rpm20,000 rpm25,000 rpmSNR RunABCDEFGHBWMFWMBWMFWMBWMFWMBWMFWMBWMFWM(dB) 111111111842.2836.4841.3823.0832.9801.6816.5771.9792.0733.9759.558.09 211222222784.3779.3782.5766.3772.8744.8754.6714.8727.9676.4693.057.41 311333333727.1722.2724.9708.7714.1686.1694.2654.3665.1613.5626.956.67 41
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