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Study on ultrasonic-assisted lapping of gears
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International Journal of Machine Tools & Manufacture 47 (2007) 2051–2056 www.elsevier.com/locate/ijmactool
Study on ultrasonic-assisted lapping of gears B.Y. Weia,b,, X.Z. Denga, Z.D. Fangb a
School of Mechanical & Electronic Engineering, Henan University of Science & Technology, 48 Xiyuan Road, Luoyang 471003, PR China b School of Mechanical & Electronic Engineering, Northwestern Polytechnical University, 127 West Youyi Road, Xi’an 710072, PR China Received 20 June 2005; received in revised form 24 October 2005; accepted 3 November 2005 Available online 18 May 2007
Abstract Ultrasonic-assisted lapping of gears is firstly proposed and compared with conventional lapping in material removal process and mechanism. The material removal mechanisms of the ultrasonic lapping include hammering, impacting and acoustic cavitation. The experiments showed that the material removal rate of ultrasonic lapping is nearly three times that of the conventional lapping in the same condition, and the ultrasonic lapping can produce a better tooth surface quality (Ra ¼ 0.2 mm and the section height c ¼ 1.2 mm) than the conventional lapping (Ra ¼ 0.33 mm and c ¼ 3.2 mm). Then a set of parametric experiments for the ultrasonic lapping was conducted with the Taguchi experimental design. The results of this set of experiments reveal that the optimum conditions for a high removal rate in the ultrasonic lapping experiments of spiral-bevel gears are of brake torque, 0.12 Nm; pinion rotational speed, 600 rpm; and slurry concentration with 20%. The contributions by percentage of torque, speed and concentration to the removal rate are 8.13, 19.26 and 68.11, respectively. r 2005 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic lapping; Material removal rate; Spiral bevel gears; Hypoid; Taguchi method
1. Introduction Ultrasonic machining (USM) is a non-conventional mechanical material removal process that has been widely used for machining both conductive and non-metallic materials, preferably those with low ductility and a hardness above 40 HRC, e.g. inorganic glasses, silicon nitride, nickel/titanium alloys [1]. Also, the rotary ultrasonic machining (RUM) and the ultrasonic-assisted conventional /non-conventional machining have been developed. They are used for machining metallic materials as well as non-metallic materials, such as ultrasonic assisted drilling, turning, grinding, polishing, lapping and honing. They are applied to metal materials and are claimed to be able to reduce machining time, work-piece residual stress and strain hardening, and to improve work-piece surface
Corresponding author. School of Mechanical & Electronic Engineering, Henan University of Science & Technology, 48 Xiyuan Road, Luoyang 471003, PRC. Tel.: +86 379 64271859; fax: +86 379 64229848. E-mail address: [email protected] (B.Y. Wei).
0890-6955/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.11.003
quality and tool life compared to conventional machining [1–5]. Ultrasonic-assisted hobbing, slotting and shaving of gears have also been studied and are thought to be able to reduce cutting power and cutter wear, and to improve the material machinability, the tooth surface quality and the cutting efficiency compared to the conventional machining of gears [6,7]. It is expected that the ultrasonic-assisted cutting will be used more extensively in machining high hardess tooth surface. At present, gears with a complex curve tooth, such as spiral bevel and hypoid gears, lack a good technique for the final finishing process. The present techniques are limited to grinding and lapping. Owing to the fact that the gear grinding is low in efficiency and high in product cost, and conventional lapping is poor in material removal rate and shows low precision in modifying tooth shape, ultrasonic-assisted lapping of gears (ULG) is proposed in this paper. Follow-up work is presented as follows: Firstly, rotary ultrasonic system is designed to perform the ULG; conventional lapping and ULG are compared in the material removal process and mechanism. Secondly, a
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set of parametric experiments are conducted. The results of this set of experiments reveal the influences of the controllable process parameters (i.e., the brake torque, rotational speed and slurry concentration) on the process outputs (i.e., MRR). Finally, the experimental results are presented and discussed, and conclusions are made.
2. Conventional lapping of gears Spiral bevel and hypoid gear sets are lapped to refine the tooth surface finish and to improve the tooth contact pattern. Errors arising in the preceding cutting and heat treatment operation can result in tooth shape errors, thus reducing tooth mating accuracy. The lapping operation may refine tooth contact surface finish and improve tooth mating. Fig. 1(a) shows the lapping movement manner of the pinion in relation to the gear member. It is necessary to displace the pinion in relation to the gear member in a manner that will move the tooth contact over the entire area of the tooth surface. The magnitude of displacement is controlled by three direction axes: (1) V-Axis (Offset) moves the gear making contact to the toe and heel; (2) H-Axis (pinion cone) moves the pinion making contact to the top and flank; (3) J-Axis (Gear cone) moves the pinion controlling backlash. The lapping operation is a cutting process where metal is removed and chips are formed. In the case of bevel and hypoid gears, the process may be referred to as equalizing lapping where both the work and the lap mutually improve their shape. Ideally, the tooth surfaces are separated by one layer of abrasive particles, which are suspended in the carrier medium called the vehicle, i.e. slurry. The vehicle also lubricates the work and prevents scoring. The film thickness of the vehicle is less than grain size of the abrasive particles under load (Fig. 2). The combination of relative sliding and normal and tangential forces (Fn and Fr in Fig. 2) between the mating tooth surfaces allow the abrasive particles to remove and microcut metal such that the surfaces are changed.
The process of the conventional lapping of gears has some limitations as follows: 1. Poor material removal rate (MRR)—due to the grain cutting movement and force relying only on the relative sliding and contact action between the two mating tooth surfaces. 2. Non-uniform lapping over tooth surface—due to the relative sliding rate being different for contact moving to the top and flank of tooth surfaces, respectively; especially for the spiral bevel, the pure rolling contact occurred at the pitch position of the tooth surface. 3. Poor correction of profile errors—due to the above two limitations in (1) and (2).
3. Ultrasonic-assisted lapping of gears ULG is similar to the RUM in configuration. The difference is that the ultrasonic vibration system fitted in the spindle in the RUM is to provide the ultrasonic vibration (about 20,000 Hz) for the tool tip [8], but the same vibration in ULG is to be provided for the pinion (see Fig. 1(b)). In ULG, besides the movement of the pinion relative to the gear member being the same as the abovedescribed lapping (see Fig. 1(a)), the pinion will oscillate
Fig. 2. Conventional lapping process.
Fig. 1. The method of lapping spiral-bevel or hypoid gears: (a) the lapping movements, (b) the ULG method.
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that cavitation contributes to 10% of ceramics and more than 50% of graphite [8]. As the pressure gradient of the solution inside a microcrack (or porosity) is higher than that outside, cavitation occurs easily. The more porous the work material the more material is removed by cavitation. For metal materials, it can be supposed that the cavitation does not directly remove material from surfaces and only takes the part of removing the adhesive chips in surfaces. Therefore, the cavitation will result in refining the tooth surface finish. From the material removal mechanisms of ULG, the following possible advantages can be seen:
Fig. 3. Schematic of the ULG process.
with the ultrasonic vibration. The ultrasonic vibration of the pinion will motivate the abrasive particles to cut the lapped tooth surfaces rapidly. As the tooth of the pinion is spiral, in Fig. 3, the ULG can be considered as a kind of oblique ultrasonic machining [2]. The tooth longitudinal vibration can be divided into the two partial ones in normal and tangential vibration (as two forces of Fn and Fr in Fig. 2). The dynamic motions of the two tooth surfaces and the abrasives are depicted in Fig. 3. At the beginning of the eroding period, the abrasives propelled by the mechanical motion of the pinion tooth of ultrasonic vibration pummel the surfaces of the tooth. The abrasives are hammered simultaneously into the two working surfaces because the tooth surface hardness of pinion and gear is similar. With the relative sliding of two tooth surfaces and the tangential vibration of the pinion tooth surface, the abrasives will simultaneously scrape the two working surfaces and form the chips, resulting in material removal from the two surfaces. With the increase in the gap of the two surfaces, dynamic bubbles occur and the slurry is accelerated. Then with the working gap compressed rapidly, an increased implosion occurs in the fluid, resulting in refinishing of the machined surface. As the working gap between the two tooth surfaces expands and contracts in 0.05 ms periodically, the eroding course occurs hundreds of times in a time contact of a pair of teeth, and a large amount of metal material is removed rapidly from the tooth surfaces such that the surfaces are modified. The cutting mechanisms of ULG are normally specified as hammering, impacting and acoustic cavitation. The hammering effect is caused by the pinion tooth surfaces hammering on the abrasives, making the abrasives penetrate the working surfaces. The impact mechanism utilizes the smaller abrasives bouncing and revolving in the working zone between the two tooth surfaces to polish the surfaces. The implosion of cavitation bubbles generated by ultrasonic energy accelerates the chips’ removal and the abrasives’ movement and destroys the weak surface configuration of microcracks or porosity. It is reported
(1) Higher MRR—due to the combination of hammering, tangential sliding and scraping. (2) Higher finish—due to impacting and cavitation. (3) Higher wear-resistance of tooth surfaces—with residual compressive stresses on tooth surfaces due to hammering and impacting producing a higher material density on the surface than the inner layer. 4. Experimental set-up The experimental set-up is schematically illustrated in Fig. 4. It consists of an ultrasonic spindle assembly, a measuring system, a load system and a slurry supply system. The ultrasonic spindle assembly consists of a transducer-horn set used to drive the pinion to perform the longitudinal ultrasonic vibration, which is controlled by an ultrasonic generator, and an electric motor used to drive the pinion to rotate, of which the rotational speed is controlled by a frequency converter. The measuring system consists of a torque–speed sensor and an amplifier-display unit that measures and shows the speed and torque of the pinion. The load system consists of a magnet brake used to load the driven gear, the brake torque which is controlled by a load controller. Parameters of gears to be lapped: modulus: 1.25 mm; tooth number: 17/43; materials: steel; tooth surface hardness: 50HRC to pinion; 48HRC to gear. Based on the experience from preliminary experiments and the limitations of the experimental set-up, the
Magnet brake
Load controller Frequency converter Transducer-horn Torquespeed sensor
Gear Pinion Slurry supply
Ultrasonic wave generator
Amplifierdisplay unit
Fig. 4. Schematic illustration of the experimental set-up.
Motor
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following three process parameters have been chosen to study their effects.
been lapped for three times, each lapping time lasting 2 min. The decrease in weight for each time have been measured by an electron-scale of 101 mg in accuracy, then the mean MRR is calculated and listed in Table 1. Finally, the tooth surface roughness (Ra) and the profile section height c for the bearing length ratio of profile Rmr(c) ¼ 100% (refer to ISO4287:1997) have been measured by the Hommel Tester T20. The value of profile section height c is an important index that estimates the wear resistance of a bearing component, thus it can be also introduced to rate the wear resistance of tooth surface. The less the value of c, the more the wear resistance of the surface of component. From the profile section height c and roughness Ra of tooth surface in Table 1, it can be seen that the ULG produces a better quality of tooth surface than the conventional lapping, thus the tooth surface machined by the ULG has a higher wear resistance. Also, the MRR of ULG is nearly three times that of the conventional lapping. Fig. 5 shows the scanning electron microscope (SEM) photographs of the lapped concave surface of the pinion tooth of the two samples, the ULG and the conventional lapping. From the photograph in Fig. 5(a), the even microgrooves and the ductile flow traces formed by the hammering and scraping of abrasive particles can be clearly seen, and the lapped surface is smooth akin to a polished surface. This result agrees with the above analysis of the material removal mechanisms of the ULG. But in Fig. 5(b), the microflaws formed by the metal material lacerated can be seen, the tooth surface showing roughness akin to a plane surface. From the SEM photographs of
(1) Torque: the brake load applied to the driven gear, determining the static compression on the lapped tooth surface. (2) Speed: the rotational speed of the pinion. (3) Slurry concentration: the abrasive concentration of the slurry by weight. The following machining conditions are kept constant throughout the experiments: Vibration frequency: f ¼ 19 kHz. As the dimension of lapped gear-set is small, the diameter of pinion is only f 20 mm, and a small vibration amplitude is applied in the lapping experiments. Vibration amplitude: A ¼ 9 mm, determined by the electric current reader of the ultrasonic generator, i.e. set a same reading at the beginning of each test. Vehicle: water. Abrasives: W40# silicon carbide. Slurry supply: 65.3 mL/s.
5. Comparison of ultrasonic with conventional lapping There are two samples of gear sets used in lapping experiments; no. 1 is lapped by the conventional method, another one, no. 2, lapped by the ULG. The experimental conditions are listed in Table 1. Both No. 1 and 2 have Table 1 Experimental comparison of the conventional lapping and ULG No.
1 2
Torque (Nm)
0.12 0.12
Speed (rpm)
600 600
Concentration (%)
25 25
Vibration f (kHz)
A (mm)
0 19
0 9
MRR. (mg/min)
Roughness Ra (mm)
Rmr(c) ¼ 100% c (mm)
29.210 87.257
0.33 0.20
3.2 1.2
Fig. 5. SEM Photograph of the lapped tooth surface: (a) the ultrasonic Lapping, (b) the conventional Lapping.
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Fig. 5, it can be seen that the ULG is superior to conventional lapping. 6. Taguchi experimental design According to the experimental design of Chang and Song [9], three levels of lapping parameters are selected, as shown in Table 2. In this study, an L9 orthogonal array with three columns and nine rows is used. Each lapping parameter is assigned to a column, making a total of nine lapping parameter combinations. The experimental layout for the three lapping parameters using the L9 orthogonal array is shown in Table 3 (three-level, three-variable, 9-test). In the follow-up experiments, there are nine samples of gear sets machined by the ultrasonic lapping, and the mean MRR has been calculated by measuring the decrease in the weight of the lapped pair of pinion and gear and listed in Table 3. 6.1. Analysis of signal-to-noise ratio The Taguchi method uses the signal-to-noise (S/N) ratio instead of the average values to interpret the trial data into values for the evaluation characteristic in the optimum setting analysis. If the S/N ratio Z is expressed in dB units, it can be defined by a logarithmic function based on the mean square deviation around the target: Z ¼ 10 logðMSDÞ,
(1)
Table 2 ULG parameters and their levels Symbol
A B C
Parameter
Unit
Torque Speed Concentration
Nm rpm %
where MSD is the mean-square deviation for the output characteristic. To obtain the optimal ULG performance, the-higherthe-better quality characteristic for removal rate should be used. The MSD for the-higher-the-better quality characteristic can be expressed as MSD ¼
n 1X 1 , n i¼1 T 2i
(2)
where n is the number of repeated experiments, and Ti is the value of the removal rate at the ith test. Table 3 shows the experimental MRR, and the corresponding S/N ratio calculated by means of Eqs (1) and (2). Fig. 6 shows the mean S/N response graph. A1B3C1 is the optimal combination of the ULG parameter levels for removal rate. 6.2. Analysis of variance (ANOVA) The purpose of the analysis of variance is to investigate the design parameters that significantly affect the quality characteristic. The ANOVA can be calculated by means of the Taguchi method as the Ref. [9]. The variance of the parameters tested of torque, speed and concentration is 3.83, 9.08 and 32.09, respectively, of which error is 2.12. The corresponding F-value is 1.81, 4.276 and 15.12, respectively. The contribution percentage of the torque, speed and concentration is 8.13, 19.26 and 68.11, respectively, of which error is 4.5%. As can be seen, the concentration is the most significant lapping parameter affecting the removal rate, followed by the speed. The change in the torque has no significant effect on the removal rate.
Level 1
2
3
6.3. Confirmation runs
0.12 200 20
1.0 400 25
2.0 600 30
Once the optimal level of the design parameters is determined, the final step is to predict and verify the quality
Table 3 Layout of L9 orthogonal array and ULG experimental results Test Parameters
1 2 3 4 5 6 7 8 9
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Experimental results
A Torque
B Speed
C Concentration
MRR (mg/ min)
S/N ratio (dB)
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
132.000 55.167 58.733 54.200 39.583 110.433 44.533 64.967 70.733
42.412 34.834 35.378 34.680 31.950 40.862 32.974 36.254 36.993
Fig. 6. The mean S/N graph for MRR.
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characteristic using the optimal level of the design parameters. The estimated S/N ratio Zopt using the optimal level of the design parameters can be calculated as Zopt ¼ Z^ þ
q X ð¯Zj Z^ Þ,
(3)
j¼1
where Z^ is the total mean S/N ratio, Z¯ j is the mean S/N ratio at the optimal level, and q is the number of the main design parameters that affect the quality characteristic. The comparison of the predicted with the actual removal rate using the optimal lapping parameters (A1B3C1) is done as follows: MRR. (mg/min) S/N ratio (dB)
Prediction 135.029 42.609
Experiment 132.030 42.281
The above result shows a good agreement between the predicted and actual removal rate. 7. Conclusions In the ultrasonic lapping of gears the material removal utilizes the ductile flow, the mechanisms of which are referred to as hammering and scraping, impacting and acoustic cavitation. The following conclusions can be drawn from the experimental results of this study: 1. In the same conditions, ultrasonic lapping produces a better tooth surface quality, Ra ¼ 0.2 mm and profile section height ¼ 1.2 mm than the conventional lapping, Ra ¼ 0.33 mm and c ¼ 3.2 mm, and the material removal rate of ultrasonic lapping is nearly three times that of the conventional lapping. 2. The optimum conditions for a high removal rate in experiments of the ultrasonic lapping spiral-bevel gear are of brake torque, 0.05 Nm; pinion rotational speed, 600 rpm; slurry concentration, 20%. 3. The contributions by percentage of torque, speed and concentration to the removal rate are 8.13, 19.26 and 68.11, respectively.
Finally, although the optimal combination of the parameter levels to the removal rate were obtained, it is worth mentioning that the removal rate decreases as the speed increases from 200 to 400 rpm, but increases as the speed increases from 400 to 600 rpm. Therefore, further investigation of the effect of the speed on removal rate has to be carried out.
Acknowledgements Financial assistance was provided by the National Natural Science Foundation of China (No. 50475060), the Nature Science Foundation of Henan province (No.0410052300).
References [1] T.B. Thoe, D.K. Aspinwall, M.L.H. Wise, Review on ultrasonic machining, International Journal of Machine Tools & Manufacture 38 (1998) 239–255. [2] J. Zhao, J.M. Zhan, R.C. Jin, An oblique ultrasonic polishing method by robot for free-form surfaces, International Journal of Machine Tools & Manufacture 40 (2000) 795–808. [3] T. Moriwaki, E. Shamoto, Ultra-precision diamond turning of stainless steel by applying ultrasonic vibration, Annals of CIRP 40 (2) (1991) 559–562. [4] H. Hocheng, K.L. Kuo, Fundamental study of ultrasonic polishing of mold steel, International Journal of Machine Tools & Manufacture 42 (2002) 7–13. [5] B. Zhao, Y.G. Zheng, Study on high efficiency characteristics of the ultrasonic vibration honing to precision surface of the difficultmachining-materials, China Mechanical Engineering 9 (8) (1998) 61–64 (in Chinese). [6] Y.L. Weibuchun (Author Japan), Y.K. Han, W.F. Xue, et al., (Translator), Precise Machining with Vibration Cutting, Press of Mechanical industry, Beijing, 1985 (in Chinese) [7] K.H. Luo, Study on Ultrasonic Vibration in Generating Cutting, in Chinese, Journal of Machine and Automation (9) (2001) 14–15. [8] H.M.S. Wang, Analysis of the effect of process parameters on material removal rate in ultrasonic machining, Ph.D. Thesis, Lehigh University, 1998. [9] K.Y. Chang, Y.H. Song, T.R. Lin, Analysis of lapping and polishing of a gauge block, International Journal of Advanced Manufacturing Technology 42 (2002) 7–13.
International Journal of Machine Tools & Manufacture 47 (2007) 2051–2056 www.elsevier.com/locate/ijmactool
Study on ultrasonic-assisted lapping of gears B.Y. Weia,b,, X.Z. Denga, Z.D. Fangb a
School of Mechanical & Electronic Engineering, Henan University of Science & Technology, 48 Xiyuan Road, Luoyang 471003, PR China b School of Mechanical & Electronic Engineering, Northwestern Polytechnical University, 127 West Youyi Road, Xi’an 710072, PR China Received 20 June 2005; received in revised form 24 October 2005; accepted 3 November 2005 Available online 18 May 2007
Abstract Ultrasonic-assisted lapping of gears is firstly proposed and compared with conventional lapping in material removal process and mechanism. The material removal mechanisms of the ultrasonic lapping include hammering, impacting and acoustic cavitation. The experiments showed that the material removal rate of ultrasonic lapping is nearly three times that of the conventional lapping in the same condition, and the ultrasonic lapping can produce a better tooth surface quality (Ra ¼ 0.2 mm and the section height c ¼ 1.2 mm) than the conventional lapping (Ra ¼ 0.33 mm and c ¼ 3.2 mm). Then a set of parametric experiments for the ultrasonic lapping was conducted with the Taguchi experimental design. The results of this set of experiments reveal that the optimum conditions for a high removal rate in the ultrasonic lapping experiments of spiral-bevel gears are of brake torque, 0.12 Nm; pinion rotational speed, 600 rpm; and slurry concentration with 20%. The contributions by percentage of torque, speed and concentration to the removal rate are 8.13, 19.26 and 68.11, respectively. r 2005 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic lapping; Material removal rate; Spiral bevel gears; Hypoid; Taguchi method
1. Introduction Ultrasonic machining (USM) is a non-conventional mechanical material removal process that has been widely used for machining both conductive and non-metallic materials, preferably those with low ductility and a hardness above 40 HRC, e.g. inorganic glasses, silicon nitride, nickel/titanium alloys [1]. Also, the rotary ultrasonic machining (RUM) and the ultrasonic-assisted conventional /non-conventional machining have been developed. They are used for machining metallic materials as well as non-metallic materials, such as ultrasonic assisted drilling, turning, grinding, polishing, lapping and honing. They are applied to metal materials and are claimed to be able to reduce machining time, work-piece residual stress and strain hardening, and to improve work-piece surface
Corresponding author. School of Mechanical & Electronic Engineering, Henan University of Science & Technology, 48 Xiyuan Road, Luoyang 471003, PRC. Tel.: +86 379 64271859; fax: +86 379 64229848. E-mail address: [email protected] (B.Y. Wei).
0890-6955/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.11.003
quality and tool life compared to conventional machining [1–5]. Ultrasonic-assisted hobbing, slotting and shaving of gears have also been studied and are thought to be able to reduce cutting power and cutter wear, and to improve the material machinability, the tooth surface quality and the cutting efficiency compared to the conventional machining of gears [6,7]. It is expected that the ultrasonic-assisted cutting will be used more extensively in machining high hardess tooth surface. At present, gears with a complex curve tooth, such as spiral bevel and hypoid gears, lack a good technique for the final finishing process. The present techniques are limited to grinding and lapping. Owing to the fact that the gear grinding is low in efficiency and high in product cost, and conventional lapping is poor in material removal rate and shows low precision in modifying tooth shape, ultrasonic-assisted lapping of gears (ULG) is proposed in this paper. Follow-up work is presented as follows: Firstly, rotary ultrasonic system is designed to perform the ULG; conventional lapping and ULG are compared in the material removal process and mechanism. Secondly, a
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set of parametric experiments are conducted. The results of this set of experiments reveal the influences of the controllable process parameters (i.e., the brake torque, rotational speed and slurry concentration) on the process outputs (i.e., MRR). Finally, the experimental results are presented and discussed, and conclusions are made.
2. Conventional lapping of gears Spiral bevel and hypoid gear sets are lapped to refine the tooth surface finish and to improve the tooth contact pattern. Errors arising in the preceding cutting and heat treatment operation can result in tooth shape errors, thus reducing tooth mating accuracy. The lapping operation may refine tooth contact surface finish and improve tooth mating. Fig. 1(a) shows the lapping movement manner of the pinion in relation to the gear member. It is necessary to displace the pinion in relation to the gear member in a manner that will move the tooth contact over the entire area of the tooth surface. The magnitude of displacement is controlled by three direction axes: (1) V-Axis (Offset) moves the gear making contact to the toe and heel; (2) H-Axis (pinion cone) moves the pinion making contact to the top and flank; (3) J-Axis (Gear cone) moves the pinion controlling backlash. The lapping operation is a cutting process where metal is removed and chips are formed. In the case of bevel and hypoid gears, the process may be referred to as equalizing lapping where both the work and the lap mutually improve their shape. Ideally, the tooth surfaces are separated by one layer of abrasive particles, which are suspended in the carrier medium called the vehicle, i.e. slurry. The vehicle also lubricates the work and prevents scoring. The film thickness of the vehicle is less than grain size of the abrasive particles under load (Fig. 2). The combination of relative sliding and normal and tangential forces (Fn and Fr in Fig. 2) between the mating tooth surfaces allow the abrasive particles to remove and microcut metal such that the surfaces are changed.
The process of the conventional lapping of gears has some limitations as follows: 1. Poor material removal rate (MRR)—due to the grain cutting movement and force relying only on the relative sliding and contact action between the two mating tooth surfaces. 2. Non-uniform lapping over tooth surface—due to the relative sliding rate being different for contact moving to the top and flank of tooth surfaces, respectively; especially for the spiral bevel, the pure rolling contact occurred at the pitch position of the tooth surface. 3. Poor correction of profile errors—due to the above two limitations in (1) and (2).
3. Ultrasonic-assisted lapping of gears ULG is similar to the RUM in configuration. The difference is that the ultrasonic vibration system fitted in the spindle in the RUM is to provide the ultrasonic vibration (about 20,000 Hz) for the tool tip [8], but the same vibration in ULG is to be provided for the pinion (see Fig. 1(b)). In ULG, besides the movement of the pinion relative to the gear member being the same as the abovedescribed lapping (see Fig. 1(a)), the pinion will oscillate
Fig. 2. Conventional lapping process.
Fig. 1. The method of lapping spiral-bevel or hypoid gears: (a) the lapping movements, (b) the ULG method.
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that cavitation contributes to 10% of ceramics and more than 50% of graphite [8]. As the pressure gradient of the solution inside a microcrack (or porosity) is higher than that outside, cavitation occurs easily. The more porous the work material the more material is removed by cavitation. For metal materials, it can be supposed that the cavitation does not directly remove material from surfaces and only takes the part of removing the adhesive chips in surfaces. Therefore, the cavitation will result in refining the tooth surface finish. From the material removal mechanisms of ULG, the following possible advantages can be seen:
Fig. 3. Schematic of the ULG process.
with the ultrasonic vibration. The ultrasonic vibration of the pinion will motivate the abrasive particles to cut the lapped tooth surfaces rapidly. As the tooth of the pinion is spiral, in Fig. 3, the ULG can be considered as a kind of oblique ultrasonic machining [2]. The tooth longitudinal vibration can be divided into the two partial ones in normal and tangential vibration (as two forces of Fn and Fr in Fig. 2). The dynamic motions of the two tooth surfaces and the abrasives are depicted in Fig. 3. At the beginning of the eroding period, the abrasives propelled by the mechanical motion of the pinion tooth of ultrasonic vibration pummel the surfaces of the tooth. The abrasives are hammered simultaneously into the two working surfaces because the tooth surface hardness of pinion and gear is similar. With the relative sliding of two tooth surfaces and the tangential vibration of the pinion tooth surface, the abrasives will simultaneously scrape the two working surfaces and form the chips, resulting in material removal from the two surfaces. With the increase in the gap of the two surfaces, dynamic bubbles occur and the slurry is accelerated. Then with the working gap compressed rapidly, an increased implosion occurs in the fluid, resulting in refinishing of the machined surface. As the working gap between the two tooth surfaces expands and contracts in 0.05 ms periodically, the eroding course occurs hundreds of times in a time contact of a pair of teeth, and a large amount of metal material is removed rapidly from the tooth surfaces such that the surfaces are modified. The cutting mechanisms of ULG are normally specified as hammering, impacting and acoustic cavitation. The hammering effect is caused by the pinion tooth surfaces hammering on the abrasives, making the abrasives penetrate the working surfaces. The impact mechanism utilizes the smaller abrasives bouncing and revolving in the working zone between the two tooth surfaces to polish the surfaces. The implosion of cavitation bubbles generated by ultrasonic energy accelerates the chips’ removal and the abrasives’ movement and destroys the weak surface configuration of microcracks or porosity. It is reported
(1) Higher MRR—due to the combination of hammering, tangential sliding and scraping. (2) Higher finish—due to impacting and cavitation. (3) Higher wear-resistance of tooth surfaces—with residual compressive stresses on tooth surfaces due to hammering and impacting producing a higher material density on the surface than the inner layer. 4. Experimental set-up The experimental set-up is schematically illustrated in Fig. 4. It consists of an ultrasonic spindle assembly, a measuring system, a load system and a slurry supply system. The ultrasonic spindle assembly consists of a transducer-horn set used to drive the pinion to perform the longitudinal ultrasonic vibration, which is controlled by an ultrasonic generator, and an electric motor used to drive the pinion to rotate, of which the rotational speed is controlled by a frequency converter. The measuring system consists of a torque–speed sensor and an amplifier-display unit that measures and shows the speed and torque of the pinion. The load system consists of a magnet brake used to load the driven gear, the brake torque which is controlled by a load controller. Parameters of gears to be lapped: modulus: 1.25 mm; tooth number: 17/43; materials: steel; tooth surface hardness: 50HRC to pinion; 48HRC to gear. Based on the experience from preliminary experiments and the limitations of the experimental set-up, the
Magnet brake
Load controller Frequency converter Transducer-horn Torquespeed sensor
Gear Pinion Slurry supply
Ultrasonic wave generator
Amplifierdisplay unit
Fig. 4. Schematic illustration of the experimental set-up.
Motor
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following three process parameters have been chosen to study their effects.
been lapped for three times, each lapping time lasting 2 min. The decrease in weight for each time have been measured by an electron-scale of 101 mg in accuracy, then the mean MRR is calculated and listed in Table 1. Finally, the tooth surface roughness (Ra) and the profile section height c for the bearing length ratio of profile Rmr(c) ¼ 100% (refer to ISO4287:1997) have been measured by the Hommel Tester T20. The value of profile section height c is an important index that estimates the wear resistance of a bearing component, thus it can be also introduced to rate the wear resistance of tooth surface. The less the value of c, the more the wear resistance of the surface of component. From the profile section height c and roughness Ra of tooth surface in Table 1, it can be seen that the ULG produces a better quality of tooth surface than the conventional lapping, thus the tooth surface machined by the ULG has a higher wear resistance. Also, the MRR of ULG is nearly three times that of the conventional lapping. Fig. 5 shows the scanning electron microscope (SEM) photographs of the lapped concave surface of the pinion tooth of the two samples, the ULG and the conventional lapping. From the photograph in Fig. 5(a), the even microgrooves and the ductile flow traces formed by the hammering and scraping of abrasive particles can be clearly seen, and the lapped surface is smooth akin to a polished surface. This result agrees with the above analysis of the material removal mechanisms of the ULG. But in Fig. 5(b), the microflaws formed by the metal material lacerated can be seen, the tooth surface showing roughness akin to a plane surface. From the SEM photographs of
(1) Torque: the brake load applied to the driven gear, determining the static compression on the lapped tooth surface. (2) Speed: the rotational speed of the pinion. (3) Slurry concentration: the abrasive concentration of the slurry by weight. The following machining conditions are kept constant throughout the experiments: Vibration frequency: f ¼ 19 kHz. As the dimension of lapped gear-set is small, the diameter of pinion is only f 20 mm, and a small vibration amplitude is applied in the lapping experiments. Vibration amplitude: A ¼ 9 mm, determined by the electric current reader of the ultrasonic generator, i.e. set a same reading at the beginning of each test. Vehicle: water. Abrasives: W40# silicon carbide. Slurry supply: 65.3 mL/s.
5. Comparison of ultrasonic with conventional lapping There are two samples of gear sets used in lapping experiments; no. 1 is lapped by the conventional method, another one, no. 2, lapped by the ULG. The experimental conditions are listed in Table 1. Both No. 1 and 2 have Table 1 Experimental comparison of the conventional lapping and ULG No.
1 2
Torque (Nm)
0.12 0.12
Speed (rpm)
600 600
Concentration (%)
25 25
Vibration f (kHz)
A (mm)
0 19
0 9
MRR. (mg/min)
Roughness Ra (mm)
Rmr(c) ¼ 100% c (mm)
29.210 87.257
0.33 0.20
3.2 1.2
Fig. 5. SEM Photograph of the lapped tooth surface: (a) the ultrasonic Lapping, (b) the conventional Lapping.
ARTICLE IN PRESS B.Y. Wei et al. / International Journal of Machine Tools & Manufacture 47 (2007) 2051–2056
Fig. 5, it can be seen that the ULG is superior to conventional lapping. 6. Taguchi experimental design According to the experimental design of Chang and Song [9], three levels of lapping parameters are selected, as shown in Table 2. In this study, an L9 orthogonal array with three columns and nine rows is used. Each lapping parameter is assigned to a column, making a total of nine lapping parameter combinations. The experimental layout for the three lapping parameters using the L9 orthogonal array is shown in Table 3 (three-level, three-variable, 9-test). In the follow-up experiments, there are nine samples of gear sets machined by the ultrasonic lapping, and the mean MRR has been calculated by measuring the decrease in the weight of the lapped pair of pinion and gear and listed in Table 3. 6.1. Analysis of signal-to-noise ratio The Taguchi method uses the signal-to-noise (S/N) ratio instead of the average values to interpret the trial data into values for the evaluation characteristic in the optimum setting analysis. If the S/N ratio Z is expressed in dB units, it can be defined by a logarithmic function based on the mean square deviation around the target: Z ¼ 10 logðMSDÞ,
(1)
Table 2 ULG parameters and their levels Symbol
A B C
Parameter
Unit
Torque Speed Concentration
Nm rpm %
where MSD is the mean-square deviation for the output characteristic. To obtain the optimal ULG performance, the-higherthe-better quality characteristic for removal rate should be used. The MSD for the-higher-the-better quality characteristic can be expressed as MSD ¼
n 1X 1 , n i¼1 T 2i
(2)
where n is the number of repeated experiments, and Ti is the value of the removal rate at the ith test. Table 3 shows the experimental MRR, and the corresponding S/N ratio calculated by means of Eqs (1) and (2). Fig. 6 shows the mean S/N response graph. A1B3C1 is the optimal combination of the ULG parameter levels for removal rate. 6.2. Analysis of variance (ANOVA) The purpose of the analysis of variance is to investigate the design parameters that significantly affect the quality characteristic. The ANOVA can be calculated by means of the Taguchi method as the Ref. [9]. The variance of the parameters tested of torque, speed and concentration is 3.83, 9.08 and 32.09, respectively, of which error is 2.12. The corresponding F-value is 1.81, 4.276 and 15.12, respectively. The contribution percentage of the torque, speed and concentration is 8.13, 19.26 and 68.11, respectively, of which error is 4.5%. As can be seen, the concentration is the most significant lapping parameter affecting the removal rate, followed by the speed. The change in the torque has no significant effect on the removal rate.
Level 1
2
3
6.3. Confirmation runs
0.12 200 20
1.0 400 25
2.0 600 30
Once the optimal level of the design parameters is determined, the final step is to predict and verify the quality
Table 3 Layout of L9 orthogonal array and ULG experimental results Test Parameters
1 2 3 4 5 6 7 8 9
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Experimental results
A Torque
B Speed
C Concentration
MRR (mg/ min)
S/N ratio (dB)
1 1 1 2 2 2 3 3 3
1 2 3 1 2 3 1 2 3
1 2 3 2 3 1 3 1 2
132.000 55.167 58.733 54.200 39.583 110.433 44.533 64.967 70.733
42.412 34.834 35.378 34.680 31.950 40.862 32.974 36.254 36.993
Fig. 6. The mean S/N graph for MRR.
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characteristic using the optimal level of the design parameters. The estimated S/N ratio Zopt using the optimal level of the design parameters can be calculated as Zopt ¼ Z^ þ
q X ð¯Zj Z^ Þ,
(3)
j¼1
where Z^ is the total mean S/N ratio, Z¯ j is the mean S/N ratio at the optimal level, and q is the number of the main design parameters that affect the quality characteristic. The comparison of the predicted with the actual removal rate using the optimal lapping parameters (A1B3C1) is done as follows: MRR. (mg/min) S/N ratio (dB)
Prediction 135.029 42.609
Experiment 132.030 42.281
The above result shows a good agreement between the predicted and actual removal rate. 7. Conclusions In the ultrasonic lapping of gears the material removal utilizes the ductile flow, the mechanisms of which are referred to as hammering and scraping, impacting and acoustic cavitation. The following conclusions can be drawn from the experimental results of this study: 1. In the same conditions, ultrasonic lapping produces a better tooth surface quality, Ra ¼ 0.2 mm and profile section height ¼ 1.2 mm than the conventional lapping, Ra ¼ 0.33 mm and c ¼ 3.2 mm, and the material removal rate of ultrasonic lapping is nearly three times that of the conventional lapping. 2. The optimum conditions for a high removal rate in experiments of the ultrasonic lapping spiral-bevel gear are of brake torque, 0.05 Nm; pinion rotational speed, 600 rpm; slurry concentration, 20%. 3. The contributions by percentage of torque, speed and concentration to the removal rate are 8.13, 19.26 and 68.11, respectively.
Finally, although the optimal combination of the parameter levels to the removal rate were obtained, it is worth mentioning that the removal rate decreases as the speed increases from 200 to 400 rpm, but increases as the speed increases from 400 to 600 rpm. Therefore, further investigation of the effect of the speed on removal rate has to be carried out.
Acknowledgements Financial assistance was provided by the National Natural Science Foundation of China (No. 50475060), the Nature Science Foundation of Henan province (No.0410052300).
References [1] T.B. Thoe, D.K. Aspinwall, M.L.H. Wise, Review on ultrasonic machining, International Journal of Machine Tools & Manufacture 38 (1998) 239–255. [2] J. Zhao, J.M. Zhan, R.C. Jin, An oblique ultrasonic polishing method by robot for free-form surfaces, International Journal of Machine Tools & Manufacture 40 (2000) 795–808. [3] T. Moriwaki, E. Shamoto, Ultra-precision diamond turning of stainless steel by applying ultrasonic vibration, Annals of CIRP 40 (2) (1991) 559–562. [4] H. Hocheng, K.L. Kuo, Fundamental study of ultrasonic polishing of mold steel, International Journal of Machine Tools & Manufacture 42 (2002) 7–13. [5] B. Zhao, Y.G. Zheng, Study on high efficiency characteristics of the ultrasonic vibration honing to precision surface of the difficultmachining-materials, China Mechanical Engineering 9 (8) (1998) 61–64 (in Chinese). [6] Y.L. Weibuchun (Author Japan), Y.K. Han, W.F. Xue, et al., (Translator), Precise Machining with Vibration Cutting, Press of Mechanical industry, Beijing, 1985 (in Chinese) [7] K.H. Luo, Study on Ultrasonic Vibration in Generating Cutting, in Chinese, Journal of Machine and Automation (9) (2001) 14–15. [8] H.M.S. Wang, Analysis of the effect of process parameters on material removal rate in ultrasonic machining, Ph.D. Thesis, Lehigh University, 1998. [9] K.Y. Chang, Y.H. Song, T.R. Lin, Analysis of lapping and polishing of a gauge block, International Journal of Advanced Manufacturing Technology 42 (2002) 7–13.