Determination of accelerated condition for brush wear of small brush-type DC motor in using Design of Experiment (DOE) based on the Taguchi method

Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-010-1230-6 Determination of accelerated condition for brush wear of small brush-type DC motor in using Design of Experiment (DOE) based on the Taguchi method Wae-Gyeong Shin 1,2,* and Soo-Hong Lee 2 1 Intelligent Vehicle Technology R&D Division, Korea Automotive Technology Institute, Chonan, 330-912, Korea 2 Department of Mechanical Engineering, Yonsei University, Seoul, 120-746, Korea (Manuscript Received August 16, 2010; Revised October 28, 2010; Accepted December 5, 2010) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract This research was conducted to understand friction and wear due to mechanical and electrical contact between a brush and a commutator, which play an important role in driving brush-type DC motors, and to predict the motor life through brush wear. To identify the influencing factors, the variables used in the experiments were the operating voltage, the current load, the rotational speed, and the environmental temperature. The design of experiment used for the analysis of brush wear was based on the Taguchi method. An independent condition was provided for each factor during the experiment. The results indicate the high contribution of current and temperature to the wear behavior. The operation voltage showed negligible influence on the wear behavior. Keywords: Design of experiment (DOE); Brush wear; Accelerated condition; Taguchi method; Electrical contact; Brush-type DC motor ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Design of experiment (DOE) refers to the experiment design method used for data analysis. It involves the process of finding the most economic and selective methodology for determining the factors influencing the characteristics of a product, arranging and performing experiments, and choosing a statistical method for analyzing data to obtain the highest amount of information with minimum effort and cost. Analysis of variance (ANOVA) is a frequently used method and uses the variance ratio, which is represented as the ratio of the distribution of the entire characteristic values and the sum of squares of factors, to find the factors with high influence compared with the error. The parameter design that converts the size of distribution into S/N (signal-to-noise ratio) to find the factor that reduces distribution is commonly used. Static characteristics have a fixed target value, and dynamic characteristics have intended values generated by adjusting the input, such as values generated by a control system. This study applied the Taguchi orthogonal array method for them to be applied to the reliability design. Reliability design requires an experiment plan that reflects the acceleration factors and noise factors, and the Taguchi method is used in most cases [1-3]. This study used the DOE This paper was recommended for publication in revised form by Editor Dae-Eun Kim * Corresponding author. Tel.: +82 41 559 3097, Fax.: +82 41 559 3069 E-mail address: wgshin@katech.re.kr KSME & Springer 2011 based on the Taguchi method to determine the major influences that accelerate the brush wear of the brush-type DC motor [4]. The DOE based on the Taguchi orthogonal array was applied in this study as a method to analyze the effect of each factor to evaluate accurately, objectively, and quantitatively the degree of influence of important factors on the data, which are usually difficult to measure due to noise factors such as environmental conditions and mechanical errors that cannot be controlled. 2. Determination of accelerated condition for the brush wear of a small brush-type DC motor 2.1 Setting the DOE based on orthogonal array This study used the DOE based on the Taguchi method to determine the major influences that accelerate the brush wear of the brush-type DC motor as shown in Fig. 1, determine the level of acceleration caused by each influence, and apply the levels to the design of the accelerated life test. As a method for analyzing the effect of each factor, this study applied the DOE based on the Taguchi orthogonal array to evaluate accurately, objectively, and quantitatively the degree of influences of important factors on the data, which are usually difficult to measure due to noise factors such as environmental conditions and mechanical errors that cannot be controlled. The signal factors in this study are the motor operating time, or in other words, the brush wearing time. The output or the characteristic value is defined by the brush wear length (mm);

318 W.-G. Shin and S.-H. Lee / Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 Table 1. Signal factor for the brush wear-out of the motor. Signal factor M1 M2 Operating time of motor (hr) 100 300 Table 2. Factors and levels of experiments for motor life. Control factor Level 1 Level 2 Level 3 A Operating Voltage (V) 13.5 14.8 16.2 B Current (A) 20 22 24 C Revolution (rpm) 3000 3500 4000 D Temperature (ºC) 25 50 60 Fig. 1. Schematic of the brush-type DC motor (1) Commutator bar; (2) Brush; (3) Brush holder; (4) Contact force spring; (5) Bearing; (6) Winding. therefore, the signal factor for the output is defined by the duration of the experiment as shown in Table 1. The second level is defined as 100 and 300 h. These operating times were selected to confirm the change in wear rates over a certain period. The elements that can accelerate brush wear in the motor operating environment include voltage, current, revolution (rpm), and air temperature. To examine and determine the importance of the elements that influence brush wear, four control factors were selected. A number of previous studies have indicated that these factors have significant influence on brush wear [5-8]. The combination of factors was also made by the level of experiment using the L9 (3 4 ) orthogonal array according to the DOE. Three levels were selected based on four control factors. The designed values for each level are represented in Table 2. The motor used in this study is a two-pole motor, enabling the analysis of two brushes, the positive and negative brushes, in one motor. The brush wear length varies with the direction of the current flow. The wear length of the positive brush is consistently higher than that of the negative brush at any sliding time. This factor is difficult to control. Therefore, the brush location is selected as a noise factor. The output for the signal factor is the wear length of the brush (mm), and the characteristic values for each control factor were maximized in the experiment. Fig. 2 shows the summary of the signal factors, control factors, and property values to be applied to the Taguchi method. This study analyzed the results of the Taguchi method with dynamic characteristics. The larger-the-better analysis with static characteristics was used as the DOE based on the Taguchi orthogonal array method for the analysis of the effect on motor acceleration factors such as current, voltage, rpm, and Fig. 2. P-diagram for the DOE using the Taguchi method. environmental temperature. KAISTAT_Taguchi Method v1.4 provided by the Korea Advanced Institute of Science and Technology was used for the analysis of the results [9]. 2.2 Analysis of Dynamic Characteristic The Taguchi method with dynamic characteristics analyzes the S/N ratio in Eq. (1) and the sensitivity in Eq. (2) to choose the optimum control factors. S/N represents the accuracy of the signal element for noise factors. The distribution of noise factors decreases when the S/N ratio increases. However, this study did not set the noise factors and pooled the S/N ratio instead. Sensitivity and inclination represent the accuracy of the system output in relation to the signal factors, and the sensitivity of output for the signal factors improves when the inclination increases. The target value in the analysis with dynamic characteristics changes continuously due to the value of the input signal expressed in functional relations. In most dynamic functions, the linear relationship between signal and output is desirable. For the parameters for the analysis with dynamic characteristics, the tester finds the design variable that influences the S/N ratio, increases its level, and uses the adjustment factors to adjust the inclination to the ideal value. Adjustment factors that do not have a significant effect on the S/N ratio but on the inclination are chosen. The loss has to be calculated considering the fact that the inclination will be adjusted. For the calculation of the S/N ratio in the analysis with dynamic characteristics, the arrangement of the inner side and outer side is the same as that in the analysis with static characteristics, but the signal factor is placed with the noise factor on the outside [10]. 1 ( Sβ Ve ) S/ N 10log r = (1) Ve 1 Sensitivity = 10log ( Sβ V e ) (2) r

W.-G. Shin and S.-H. Lee / Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 319 Table 3. Orthogonal array table for L9 (3 4 ) with 2 outer array. No Control Factor M1 (100h) M2 (300h) A B C D N1 N2 N1 N2 S/N ratio ANOVA performed after the pooling of A is shown in Table 7. The table shows that the factors with high inclination toward sensitivity are current, rpm, and temperature. Fig. 3 represents the plot for these factors. B1 and C3 were set to 20 A and 4000 rpm to increase the S/N ratio, and D3 was set to 60 C according to the typical dynamic characteristics analysis. However, there was a point in the experiment where a clear linear tendency crossing the origin between wear amount and time was observed, and there were other points where the linear relationship was not always considered as the ideal relationship. Therefore D (Temperature) is an adjustment factor among the control factors that does not have a significant effect on the S/N ratio but rather on the inclina- Sensitivity Test 1 1 1 1 1 0.35 0.42 0.94 1.06-26.2469-49.418 Test 2 1 2 2 2 0.7 1.08 2.24 2.64-29.0755-41.7307 Test 3 1 3 3 3 1.29 1.74 3.58 3.4-28.9537-38.4515 Test 4 2 1 2 3 0.67 0.58 1.89 1.55-28.2355-44.7684 Test 5 2 2 3 1 0.74 1.03 1.91 1.88-30.8912-43.6753 Test 6 2 3 1 2 1.01 1.6 2.42 2.07-36.2066-41.9846 Test 7 3 1 3 2 0.56 0.47 1.65 1.58-19.3864-45.4186 Test 8 3 2 1 3 0.9 1.49 2.30 2.25-34.3517-41.9753 Test 9 3 3 2 1 0.98 1.45 2.38 2.01-35.236-42.23 Table 4. ANOVA of the S/N ratio of dynamic characteristic analysis. Factor Φ S Ve CR F p- value A 2 20.5300 10.2650 9.4503 0.0000 0.0000 B 2 128.7586 64.3796 59.2695 0.0000 0.0000 C 2 56.0313 28.0156 25.7921 0.0000 0.0000 D 2 11.9225 5.9613 5.4881 0.0000 0.0000 total 8 217.2424 100.0000 Table 6. ANOVA of the sensitivity of dynamic characteristic analysis. A 2 0.1482 0.0741 0.1980 0.0000 0.0000 B 2 50.9527 25.4763 68.1046 0.0000 0.0000 C 2 6.3366 3.1683 8.4698 0.0000 0.0000 D 2 17.3778 8.6889 23.2276 0.0000 0.0000 Total 8 74.8153 100.0000 Table 7. ANOVA of the sensitivity of dynamic characteristic analysis after pooling A (voltage). B 2 50.9527 25.4763 67.9066 343.9218 0.0029 C 2 6.3366 3.1683 8.2717 42.7712 0.0228 D 2 17.3778 8.6889 23.0296 117.2972 0.0085 Error 2 0.1482 0.0741 0.7921 Total 8 74.8153 100.0000 Table 5. ANOVA of the S/N ratio of dynamic characteristic analysis after pooling A (voltage) and D (temperature). (a) B 2 128.7586 64.3796 51.8004 7.9352 0.0405 C 2 56.0313 28.0156 18.3228 3.4521 0.1345 Error 4 32.4526 8.1131 29.8768 Total 8 217.2425 100.0000 The experiment divided the control factors into voltage, current, temperature, and rpm using the Taguchi orthogonal array L9 (3 4 ); the nine samples were tested by varying each factor into three levels and measuring the brush wear amount (mm). The S/N ratio and sensitivity of dynamic characteristics were calculated by a zero point proportional calculation method using the data obtained from each experiment. Table 3 shows the arrangement of the test and the data analysis using the elements mentioned above. Table 4 shows the ANOVA for the S/N ratio. The contribution rate of A and D is low, and the ANOVA after pooling is represented in Table 5. The contribution rate of A and D is low, and thus it showed the effect of the factors (B and C) on the variance of the error value after pooling. These tables show that current and rpm are factors that influence the S/N ratio. Table 6 represents the ANOVA for sensitivity, and the (b) Fig. 3. S/N ratio and sensitivity of each factor and level for the main effect of brush wear (a) Effect plot of S/N ratio; (b) Effect plot of sensitivity.

320 W.-G. Shin and S.-H. Lee / Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 Table 8. Result of the S/N ratio of the larger-the-better characteristic at signal factor (M1: 100 h). No Control Factor M1 (100h) S/N A B C D N1 N2 ratio Test 1 1 1 1 1 0.35 0.42-8.3986 Test 2 1 2 2 2 0.7 1.08-1.6109 Test 3 1 3 3 3 1.29 1.74 3.2317 Test 4 2 1 2 3 0.67 0.58-4.15 Test 5 2 2 3 1 0.74 1.03-1.4125 Test 6 2 3 1 2 1.01 1.6 1.6402 Test 7 3 1 3 2 0.56 0.47-5.8635 Test 8 3 2 1 3 0.9 1.49 0.7443 Test 9 3 3 2 1 0.98 1.45 1.2009 Table 9. ANOVA of S/N ratio of the larger-the-better characteristic at signal factor (M1: 100 h). A 2 1.8145 0.9073 1.5362 0.0000 0.0000 B 2 103.2813 51.6406 87.4410 0.0000 0.0000 C 2 0.6956 0.3478 0.5889 0.0000 0.0000 D 2 12.3240 6.1620 10.4339 0.0000 0.0000 Total 8 118.1154 100.0000 Table 10. ANOVA of S/N ratio of the larger-the-better characteristic at signal factor (M1: 100 h) after pooling A (voltage) and C (revolution). B 2 103.2813 51.6406 86.3784 82.2916 0.0006 D 2 12.3240 6.1620 9.3713 9.8194 0.0286 Error 4 2.5101 0.6275 4.2503 Total 8 118.1154 100.0000 Table 11. Result of the S/N ratio of the larger-the-better characteristic at signal factor (M2: 300 h). No Control Factor M2 (300h) A B C D N1 N2 S/N ratio Test 1 1 1 1 1 0.94 1.06-8.3986 Test 2 1 2 2 2 2.24 2.64-1.6109 Test 3 1 3 3 3 3.58 3.4 3.2317 Test 4 2 1 2 3 1.89 1.55-4.15 Test 5 2 2 3 1 1.91 1.88-1.4125 Test 6 2 3 1 2 2.42 2.07 1.6402 Test 7 3 1 3 2 1.65 1.58-5.8635 Test 8 3 2 1 3 2.3 2.25 0.7443 Test 9 3 3 2 1 2.38 2.01 1.2009 Table 12. ANOVA of the S/N ratio of the larger-the-better characteristic at signal factor (M2: 300 h). A 2 0.3333 0.1666 0.4685 0.0000 0.0000 B 2 44.8993 22.4497 63.1165 0.0000 0.0000 C 2 7.7152 3.8576 10.8455 0.0000 0.0000 D 2 18.1894 9.0947 25.5695 0.0000 0.0000 Total 8 71.1372 100.0000 Table 13. ANOVA of the S/N ratio of the larger-the-better characteristic at signal factor (M2: 300 h) after pooling A (voltage). B 2 44.8993 22.4497 62.6481 134.7267 0.0074 C 2 7.7152 3.8576 10.3770 23.1505 0.0414 D 2 18.1894 9.0947 25.1010 54.5799 0.0180 Error 2 0.3333 0.1666 1.8739 Total 8 71.1372 100.0000 Fig. 4. Effect plot of the S/N ratio of signal factor (M1: 100 h) for the larger-the-better characteristic. tion. The analysis of static and larger-the-better characteristics was performed considering the appropriateness of the test data. 2.3 Analysis of Larger-the-Better Characteristics Fig. 5. Effect plot of the S/N ratio of signal factor (M2: 300 h) for larger-the-better characteristic. The conditions applied in the dynamic characteristics analysis were applied in the larger-the-better characteristics analysis. The larger-the-better characteristics analysis showed that the increase in the characteristic value, i.e., the S/N ratio, is significant. The S/N ratio of the larger-the-better characteristics in this study is represented as Eq. (3): 1 n 1 S/ N = 10log[ ]. (3) n 2 i= 1 yi In the equation above, n indicates the number of experiments performed, and y represents i th characteristic value. i

W.-G. Shin and S.-H. Lee / Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 321 Table 8 shows the S/N ratio obtained as a result of the largerthe-better characteristics analysis in the 100 h wear test chosen as the signal factor in the static characteristics analysis. Table 9 shows the ANOVA for the S/N ratio, and Table 10 shows the ANOVA for A and B after pooling based on the contribution rate of the sum of squares. B and D appeared to have a significant effect on the S/N ratio, and B3 and D3 increased the S/N ratio. As represented in Fig. 4, A and C did not have a significant influence on the S/N ratio. Table 11 shows the S/N ratio obtained as a result of the larger-the-better analysis based on a 300 h wear test selected as the signal factor among the static characteristics. Table 12 shows the ANOVA results for these S/N ratios, and Table 13 shows the ANOVA for A after pooling based on the contribution rate of the sum of squares. B, C, and D appeared to have a significant effect on the S/N ratio, and B3, C3, and D3 increased the S/N ratio. Fig. 5 shows the effect plot for these ratios. A did not have a significant effect, as represented in the picture. B (current) and D (temperature) were selected as acceleration factors based on the analysis results of M1 (100 h) and M2 (300 h); rpm was added to achieve better acceleration effects. According to the results of the dynamic characteristics analysis and larger-the-better characteristic analysis, the wear amount increased when the current, temperature, and rpm increased. However, the voltage did not appear to influence wearing independently because it acted as a composite element in connection with current, rpm, and temperature. Furthermore, significant effect was measured when the p-value was 0.05 or less, and the most influential factor was the current. In fact, the wearing was mostly current oriented, and the friction heat generated when the commutator and the brush came into contact with each other, as well as the arc caused by electric contract, degraded the brush material. Considering this, the Taguchi orthogonal array was applied for the brush wear test of the motor. The test showed that the current had the largest effect on the wearing of the brush. 3. Conclusions This paper introduced the DOE and performed a wear test on the four operating and environmental conditions such as input voltage, current influenced by resistance, rpm, and external temperature, while the motor is in the operating state. The following results are obtained. According to the analysis of the dynamic characteristics, the scale of sensitivity appeared in the order of current > revolution > temperature; therefore, the linear relationship was not always the ideal relationship because there was no point in the experiment where a clear linear tendency crossing the origin between wear amount and time could be observed. There were also points in the experiment that were difficult to understand. Current and external temperature were selected as acceleration factors according to the results of larger-the-better analysis; rpm could be added to achieve better acceleration effects. The wear acceleration factor that exhibited the largest effect when the motor operating condition and environmental condition were changed was the current influenced by the resistance applied in the motor operating environment. Nomenclature Φ : Free of degree S : Sum of squire Ve : Sum of average squire CR : Contribution ratio S/N : Signal-to-noise ratio References [1] P. Lim and G. E. Yang, Optimal cutting condition of tool life in the high speed machining by Taguchi design of experiments, Journal of the Korean Society of Manufacturing process engineers, 5 (4) (2006) 59-64. [2] M. Kim and B. J. Yum, Development of reliability design methodology using accelerated life testing and Taguchi method, Journal of Korean Institute of Industrial Engineers, 28 (4) (2002) 407-414. [3] Condra, L. W., Reliability improvement with design of experiments, Marcel Dekker, Inc., New York, USA (1993). [4] W. G. Shin and S. H. Lee, An analysis of the main factors on the wear of brushes for automotive small brush-type DC motor, Journal of Mechanical Science and Technology, 24 (2010) 37-41. [5] R.H.Savage, Carbon brush contact films, Gen.Elec.Rev., 48 (1945) 13-20. [6] J.M.Casstevens, H.G.Rylander, Z.Eliezer, Influence of high velocities and high current densities on the friction and wear behavior of copper-graphite brushes, Wear, 48 (1978) 121-130. [7] H. Zhao, G. Barberb, J. Liuc, Friction and wear in high speed sliding with and without electrical current, Wear, 249 (2001) 409-414. [8] A. Wilk, I. Moson, The wave character of commutator wear in electrical machines, Wear, 253 (2002) 935-945. [9] Design and analysis of Experiments ; Taguchi methods and orthogonal arrays, Textbook of an open lecture of the industry-university by KAIST (2007). [10] Y. G. Park and B. J. Yum, Development of performance measures for dynamic parameter design problems, International Journal of Manufacturing Technology and Management, 5 (1-2) (2003) 91-104.

322 W.-G. Shin and S.-H. Lee / Journal of Mechanical Science and Technology 25 (2) (2011) 317~322 Wae-Gyeong Shin is currently working as a senior researcher in Intelligent Vehicle Technology R&D Division of the Korea Automotive Technology Institute in Chonan, Korea. She received her bachelor s degree in Material Engineering in Gyeongsang National University in 1994 and her master s degree in Polymer Composite Material Engineering in Gyeongsang National University in 1996. She obtained her Ph..D. in Mechanical Engineering in Yonsei University, Seoul, Korea, in 2010. Her current research interests include materials properties analysis, electronic parts of automotives, electric vehicle, and reliability engineering. Soo-Hong Lee is currently working as a full-time professor at the Department of Mechanical Engineering in Yonsei University in Seoul, Korea. He received his bachelor s degree in Mechanical Engineering in Seoul National University in 1981 and his master s degree in Mechanical Engineering Design in Seoul National University in 1983. He obtained his Ph.D. from Stanford University, California, USA in 1991. His current research interests include Intelligent CAD, Knowledge-based Engineering Design, Concurrent Engineering, Product Design Management, Product Lifecycle Management, Artificial Intelligence in Design, and Design Automation.