TH6340B臥式加工中心鼠牙盤式分度工作臺機械設(shè)計

TH6340B臥式加工中心鼠牙盤式分度工作臺機械設(shè)計,TH6340B臥式加工中心鼠牙盤式分度工作臺機械設(shè)計,th6340b,臥式,加工,中心,鼠牙盤式,分度,工作臺,機械設(shè)計 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2, pp. 177-182 APRIL 2011 / 177 DOI: 10.1007/s12541-011-0025-8 1. Introduction With the recent rapid development of industry, the need has increased for precision cutting of various kinds of machine parts. In particular, in the cutting industry, it is important to enhance cutting efficiency and precision simultaneously. 1,2 In the field of metal cutting, machining error in milling, drilling and external lathe turning has been studied much more than internal boring. Boring means enlarging a hole that was already cut by drilling, or casting to the designed dimension. Therefore, control of dimensional tolerance and surface roughness is important. 3 Boring is similar to external lathe turning, in the sense of using a single point cutting tool. However, the shape of the boring tool has to be restricted by the workpiece hole diameter and depth. This is the difference between boring and external lathe turning. Generally, the overhang of the boring bar has to be short to guarantee machining stability. Thomas et al. 4 emphasize that because of the reduced damping ratio, the short overhang of the boring tool is good for tool stiffness but poor for vibration. Chun and Ko 5 point out that the change in dynamic stiffness of the boring tool is decided by overhang and dynamic stiffness is increased nonlinearly with overhang length. The sources of machining error are tool deflection and wear, thermal effects, and machine tool errors. Tool deflection caused by cutting forces is a dominant factor in machining errors. 6 The cutting force is separated into main, thrust, and feed cutting forces. Among these, the main and thrust cutting forces induce tool deflection, whereas machining leads to machining error. 7 With recent enhancements in technology, the shapes of cutting tools and workpieces have become more complicated. Therefore, it is difficult to predict the cutting force and tool deflection precisely, and the experience of field operators is inevitable. The purpose of this paper was to identify the effect of overhang and cutting conditions on machining error quantitatively, during internal lathe boring of AISI4140, which is generally used for machine elements. To this end, the response surface method (RSM) 8,9 was applied to establish an estimation model. Similar to the study of Chun and Ko 5 overhang, feed per revolution and cutting depth were chosen as factors for the model. The cutting speed, which is the main factor of built-up edge (BUE) and tool life, was kept constant at 200 m/min. A central composite design was used for the purpose of minimizing the number of experiments. Fitness was verified by analysis of variance (ANOVA), residual analysis, and coefficient of determination after building the first and second regression model, respectively. 2. The Response Surface Method RSM is a collection of mathematical and statistical techniques Study on the Response Surface Model of Machining Error in Internal Lathe Boring Se-Ho Chun 1 and Tae Jo Ko 2,# 1 Graduate School of Mechanical Engineering, Yeungnam University, 214-1, Dae-dong, Gyeonsan, Gyeongbuk, South Korea, 712-749 2 School of Mechanical Engineering, Yeungnam University, 214-1, Dae-dong, Gyeonsan, Gyeongbuk, South Korea, 712-749 # Corresponding Author / E-mail: tjkoyu.ac.kr, TEL: +82-53-810-3836, FAX: +82-53-810-4627 KEYWORDS: Boring Bar, Machining Error, Response Surface Method, Central Composite Design, ANOVA, Residual Analysis To achieve high quality and precision of machining products, the machining error must be examined. The machining error, defined as the difference between designed surface and the actual tool, is generally caused by tool deflection and wear, thermal effects and machine tool errors. Among these error sources, tool deflection is usually known as the most significant factor. The tool deflection problem is analyzed using the instantaneous cutting forces on the cutting edge. This study presents a model of the machining error caused by tool deflection in the internal boring process. The machining error prediction model was described by the surface response method using overhang, feed per revolution and depth of cut as the factors for the analysis. The least square method revealed that overhang and depth of cut were significant factors within 90% confidence intervals. Analysis of variance (ANOVA) and residual analysis show that the second-order model is adequate. Manuscript received: November 23, 2009 / Accepted: November 24, 2010 KSPE and Springer 2011 178 / APRIL 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2 useful for modeling and analyzing problems in which a response of interest is influenced by several variables, and the objective is to optimize this response. A response surface is a functional relation between response variable and factors. RSM assumes a statistical model with respect to the response surface. Then, the response surface model is estimated with regression analysis of test data generated by several conditions composed from the design factors. Generally, it is difficult to know the response surface formula, and therefore the approximated model is assumed first. After that, this model is verified by lack of fit. In RSM, the first and second order regression models are normally used. The third order regression model can be, but is seldom, used. 8 Central composite design is a representative experimental design of RSM. To estimate the experimental surface with the minimum number of experiments, central and axial points are added in the 2 k experiments, where k means the number of factors. Therefore, sequential experiments are possible here. If the 2 k factor experiments are lack of fit with the first-order regression model, the second-order regression model do not need new experiments but need to adding new data points on the center and axes of the 2 k experiments. To analyze the first and second order regression models simultaneously, in this study the experimental design, including experimental points (2 k ), axial points (2k) and central points (n c ), was selected. Therefore, the total number of experiments was 2 k +2k+n c . 8-11 3. Machining Error Mechanism The cutting force induces deflection in the cutting tool and workpiece. The cutting force is a dominant factor in analyzing machining error from the deflection of cutting tool and workpiece. The cutting tool deflection is analyzed as a response to the instantaneous cutting force. 12 In the case of the boring tool, the cutting force model for analyzing a cutting tool deflection is simplified as the cantilever beam (see Fig. 1). The expression for the cutting tool deflection(x) at position x from the free end point is as follows. 3 () () 3 FLx x EI = (1) where F is the cutting force, L is tool overhang, E and I are the elasticity modulus and moment of inertia of the tool. The deflection of the boring tool is determined by the tool material, diameter and overhang. Obviously, overhang changes according to the clamping position, as shown in Fig. 2. In this case, the tool deflection is composed of deflections m by the main cutting force and t by the thrust cutting force. Deflection by the main cutting force moves the cutting edge under the tool center line. Therefore, the radial rake angle becomes negative, and consequently, the relief angle decreases, which induces large flank wear. 7 In this paper, the difference between tool diameter before machining (designed surface, D ) and workpiece diameter (machined surface, M ) is defined as machining error. Fig. 3 shows the simulation analysis of cutting force variation in Fig. 1 Tool deflection model DM Error = Fig. 2 Deflection of the boring tool Fig. 3 Cutting force analysis by AdvantEdge INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2 APRIL 2011 / 179 the internal boring using the commercial cutting analysis software of AdvantEdge (ThirdWave Co.). The simulation was conducted with the cutting condition of 0.25 mm/rev, depth of cut of 1 mm, and cutting velocity of 200 m/min. The main (y direction) cutting force is the largest while the thrust (x direction) cutting force is ranked second. The feed (z direction) force is the smallest and it acts on the axial direction of the boring bar. The axial stiffness of the boring bar is sufficient, i.e., the influence of the feed force is negligible. 4. Experiment 4.1 Experimental Design The boring bar and insert were S16R SCLCR 09 and CCMT 09T308 MT TT3500 from TaeguTec, respectively. The boring bar was clamped into the tool holder with a sleeve on the tool post. Overhang was defined as the distance from the end of the insert to the front of the sleeve. The workpiece outer and inner diameter were 80 and 40 mm, respectively, and the inner hole depth was 50 mm. The mechanical properties of the workpiece material AISI4140 are specified in Table 1. Consistency of the experiment was kept by brand new tools and changing new specimen at each time. The horizontal lathe was a DC-2 model (DMC Co.) machine, and the power on the main spindle was 5.5 kW. The deflection of boring bar is affected by the cutting force. The cutting force is dependent on tool-workpiece contact area (chip area) which is composed of feed per revolution and depth of cut. In this experiment, overhang, feed per revolution, and depth of cut were selected as the design factors in the sense of the tool deflection. Cutting velocity was set as constant. A central composite design was selected to construct the response model with respect to characteristic values. Uncoded variables were notated as 1 (Overhang), 2 (Feed), and 3 (Cutting depth). The experimental range was assumed to be 1L , 1H , 2L , 2H , and 3L , 3H , and the relations between real and coded variables were determined by Eqs. (2), (3), and (4), as follows. The inverted data is shown in Table 2. 9 11 1 11 2.4( ) HL X = (2) 22 2 22 2.4( ) HL X = (3) 33 3 33 2.4( ) HL X = (4) where 11 1 , 2 LH + = 22 2 2 L H + = and 33 3 . 2 L H + = For all the cutting conditions, the machining power was limited below 70% of the main spindle power. To avoid the ploughing force 13,16 that is mainly influenced by the size effect, the minimum feed per revolution was set higher than 0.03 mm/rev considering the size of the honing dimension at the insert edge. Because the distance from the central to the axial point in experiment design was 1.2, all the cutting conditions were in the allowable range. As shown in Fig. 4, the total number of experiments was 18 based on experiment points (18), axial points (614) and central points (1518). 4.2 Experimental Results Table 3 shows the experimental results according to the designed cutting conditions. As defined in Fig. 2, machining error Table 1 Mechanical properties of AISI4140 Specification Value Yield strength (kg f /mm 2 ) 85 Tensile strength (kg f /mm 2 ) 100 Elongation (%) 12 Reduction of area (%) 45 Charpy impact value (kg f m/cm 2 ) 6 Hardness (HB) 285352 Table 2 Levels of the variables in the experiment Coding 1.2 1 0 1 1.2 Overhang (mm) 30.4 32 40 48 49.6 Feed (mm/rev) 0.03 0.05 0.15 0.25 0.27 Depth of cut (mm) 0.12 0.2 0.6 1 1.08 Fig. 4 Central composite design for experiment 14 Table 3 Design of experiment and results X 1 2 X 3 Error 1 1 1 1 0.105 2 1 1 1 0.281 3 1 1 1 0.144 4 1 1 1 0.289 5 1 1 1 0.162 6 1 1 1 0.275 7 1 1 1 0.153 8 1 1 1 0.304 9 1.2 0 0 0.192 10 1.2 0 0 0.336 11 0 1.2 0 0.190 12 0 1.2 0 0.189 13 0 0 1.2 0.133 14 0 0 1.2 0.287 15 0 0 0 0.184 16 0 0 0 0.180 17 0 0 0 0.191 18 0 0 0 0.187 180 / APRIL 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2 was defined as the difference between the virtual diameter generated by the air cutting state and the measured internal workpiece diameter after machining. The measurement position for the internal diameter was 10 mm engaging distance from the start of machining, which was selected as the representative data for analysis. If the aspect ratio, defined as diameter to length (L/D) in the lathe process, is less than 4, the machining accuracy is almost the same in all the machined areas, because the workpiece is strong enough. 15 In this experiment, the aspect ratio was smaller than 2, so the variation in measurement data is negligible along with the other measuring places. 5. Analysis of Results and Prediction Model 5.1 First-Order Regression Model Equation (5) shows the first-order regression model that is composed of newly defined independent variables by Eqs. (2), (3), and (4). The coefficients estimated by the least squares method are shown in Table 4. 0112233 12 1 2 13 1 3 23 2 3 YXXX XX XX XX =+ + + + (5) Considering the coefficients within 90% significance level, 2 , 12 , 13 , 23 are factors that decrease the models accuracy. The effects of feed per revolution and its interaction terms are insignificant. To improve the model, estimation has to be done without insignificant factors. Expression (6) shows the re-estimated model after removing the insignificant factors, such as X 2 and its interaction effects. 13 0.210111 0.069651 0.023879YXX=+ + (6) Table 5 shows the ANOVA for the estimated model, and the coefficient of determination is 0.77 for the first-order regression. To verify the regression model, we performed residual analysis. The normal probability plot and residual histogram from this analysis are depicted in Figs. 5 and 6, respectively. As shown in Fig. 5, the departures are scattered. It indicates the abnormalities in the residual distribution. Alternatively, the residual histogram shows that frequency of the residual is not satisfied with the normal distribution and the frequency of residual is highest between -0.01 and -0.03. This means that the first-order regression model is weak in explaining the machining errors. 5.2 Second-Order Regression Model The second-order regression model is expressed as Eq. (7), and the estimated coefficients by the least squares method are shown in Table 6. 222 011223311 22 33 12 1 2 13 1 3 23 2 3 YXXXXXX XX XX XX =+ + + + + + + (7) Here, the influence of overhang is larger than the other factors to the machining errors. Since its squared term is also significant, the response surface will be curved with respect to the change in the factor level. Similarly, with the first order regression model, the terms of feed per revolution and its interaction are insignificant within the 90% significance level. Therefore, those factors are pulled down to error terms, and finally, a new estimation model, shown in Eq. (8), was taken. The coefficient of determination estimated from Eq. (8) was 0.852, which was an improvement over the first-order regression model. 2 131 0.18979 0.06965 0.02388 0.03362YXXX=+ + + (8) Table 7 shows the ANOVA result of the second-order regression model, and on the other hand, Figs. 7 and 8 show the results of Table 4 First-order regression coefficient Coef. Coef. SE T P 0 0.210111 0.009199 22.840 0.000 1 0.069651 0.011832 5.887 0.000 2 0.006048 0.011832 0.511 0.619 3 0.023879 0.011832 2.018 0.069 12 0.000875 0.013799 0.063 0.951 13 0.007215 0.013799 0.516 0.616 23 0.003375 0.013799 0.245 0.811 Notes) Coef. SE: Standard error of a coefficient, T: T-test, P: Probability of type I error Table 5 ANOVA of first regression model DF Seq SS Adj. MS F P Regression 2 0.0589 0.02949 25.05 0.000 Linear 2 0.0589 0.02949 25.05 0.000 Residual Error 15 0.0176 0.00117 Pure Error 9 0.0013 0.00014 Sum 17 0.0766 Notes) DF: Degree of freedom, Seq. SS: Sequential sum of squares, Adj. MS: Adjusted mean squares, F: Fisher statistic(F-test) Fig. 5 Normal probability plot of the residuals Fig. 6 Histogram of the residuals INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2 APRIL 2011 / 181 normal probability and histogram of the residuals, respectively. As shown in Fig. 7, the result is enhanced more than the first-order regression model. Also, the frequency of the residual was satisfied with the normal distribution as shown in Fig. 8, and the second- order regression model was suitable for explaining the machining errors. 5.3 Contour Plot and Surface Plot A contour plot expresses the response surface in the second- dimensional plane. On the other hand, a surface plot expresses the response surface in the third-dimensional space to explain the response values. Figures 9 and 10, respectively, show the contour and surface plots of the second-order regression model. All points on the contour plot were experimental points, and the factor X 2 was fixed to zero as a median. The contours of X 1 direction are denser than X 3 direction. Alternatively, in Fig. 10, the machining error rises sharply with increase of X 1 . 6. Conclusions The purpose of this study was to build an estimation model for machining errors during internal boring of SCM440 materials. The experiment was performed according to a central composite design with three factors that were believed to be parameters in machining errors. RSM was adopted to estimate machining errors. Alternatively, through ANOVA and residual analysis, the significance of factors and the fitness of the designed model were verified. From the experimental results and model analysis, the following conclusions were drawn. 1. The second-order regression model is more suitable than the first-order regression model for describing the internal boring process, from the view point of ANOVA and residual analysis. In this case, the second regression models coefficient of determination was 0.852. 2. Overhang and depth of cut were relatively more significant than feed per revolution in terms of machining errors. Table 6 Second-order regression coefficient Coef. Coef. SE T P 0 0.196336 0.01475 13.308 0.000 1 0.069651 0.01038 6.712 0.000 2 0.006048 0.01038 0.583 0.576 3 0.023879 0.01038 2.301 0.050 11 0.037342 0.01532 2.437 0.041 22 0.014394 0.01532 0.939 0.375 33 0.000158 0.01532 0.010 0.992 12 0.000875 0.01210 0.072 0.944 13 0.007125 0.01210 0.589 0.572 23 0.003375 0.01210 0.279 0.787 Table 7 ANOVA of second regression model DF Seq SS Adj MS F P Regression 3 0.0652 0.02176 26.82 0.000 Linear 2 0.0589 0.02949 36.35 0.000 Square 1 0.0062 0.00629 7.76 0.015 Residual Error 14 0.0113 0.00081 Pure Error 9 0.0013 0.00014 Sum 17 0.0766 Fig. 7 Normal probability plot of the residuals Fig. 8 Histogram of the residuals Fig. 9 Contour plot of machining error Fig. 10 Surface plot of machining error 182 / APRIL 2011 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 12, No. 2 3. It is recommended that the control of cutting depth is more effective method for minimizing the machining error in internal lathe boring. Also, short overhang is preferable. This study can be referenced when designing the hole depth and tolerance of products. ACKNOWLEDGEMENT This research was supported by the Yeungnam University research grants in 2008. REFERENCES 1. Onwubolu, C. G., “A Note on Surface Roughness Prediction Model in Machining of Carbon Steel by PVD Coated Cutting Tools,” American Journal of Applied Sciences, Vol. 2, No. 6, pp. 1109-1112, 2005. 2. Sharma, S. V., Dhiman, S., Sehgal, R. and Sharma, S. K., “Assessment and Optimization of Cutting Parameters while Turning AISI 52100 Steel,” Int. J. Precis. Eng. Manuf., Vol. 9, No. 2, pp. 54-62, 2008. 3. Beauchamp, Y., Thomas, M., Youssef, Y. A. and Masounave, J., “Investigation of Cutting Parameter Effects on Surface Roughness in Lathe Boring Operation by Use of a Full Factorial Design,” 18 th International Conference on Computers and Industrial Engineering, Vol. 31, No. 3-4, pp. 645-651, 1996. 4. Thomas, M. and Beauchamp, Y., “Statistical Investigation of Modal Parameters of Cutting Tools in Dry Turning,” International Journal of Machine Tools and Manufacture, Vol. 43, No. 11, pp. 1093-1106, 2003. 5. Chun, S. H. and Ko, T. J., “Study on the Dynamic Stiffness Variation of Boring Bar by Taguc