1. Key Laboratory of Road Construction Technology and Equipment, Ministry of Education, Chang’an University, Xi’an 710064, China 2. Shantui Construction Machinery Limited Company, Jining 272073, China 3. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China
A completing process method for spiral bevel gears directly facing the Free-form machine tool was proposed in order to use the flexibility and freedom of the Free-form machine tool, and the sensitivity of the pinion tooth surface to the motion error of the machine tool was analyzed. Firstly, given the wheel tooth surface, the active design of the microgeometry of the pinion tooth surface was conducted. Secondly, the pinion cutting model by the completing process method was established directly based on a four-axis linkage Free-form machine tool. Then, according to the target parameters of the pinion tooth surface, the relative motion between the cutter and the machined pinion was solved, and the fifth-degree motion polynomial of each axis of the machine tool and the remaining undetermined profile parameters of the pinion cutter were obtained. Finally, the influence of the motion error of each axis of the machine tool on the topological shape of the pinion tooth surface was analyzed. Numerical results show that the parameters of each discrete point of the contact path of the drive tooth surface of the pinion and the parameters of the reference point of the coast tooth surface of the pinion can be ensured by this method. In addition, the motion error of each axis of the machine tool can cause the spiral angle error, the diagonal error and the pressure angle error of the pinion tooth surface, and the Y-axis has the least influence on the pinion tooth surface.
Fig.1Controlled parameters on modified tooth surface of pinion
Fig.2Machine tool, cutter, and schematic diagram for machining pinion based on Free-form machine tool
Fig.3Calculation flow chart of pinion cutting parameters by completing process method based on Free-form machine tool
项
z
${\mathit{\Sigma}}$/(°)
$ a $/mm
旋向
${\;\beta _{\text{m} } }$/(°)
$ {d_{\text{e}}} $/mm
$ \delta $/(°)
$ {\delta _{\text{a}}} $/(°)
$ {\delta _{\text{f}}} $/(°)
小轮
15
90
0
左旋
31
93.333
18.435
22.086
16.915
大轮
45
90
0
右旋
31
280.000
71.565
73.085
67.914
Tab.1Gear blank parameters of spiral bevel gear pair
坐标轴
0次项 系数
1次项 系数
2次项 系数
3次项 系数
4次项 系数
5次项 系数
X
?84.931 926
24.121 703
4.239 980
?0.248 903
?0.263 390
?0.156 503
Y
?0.188 649
?0.094 379
?0.010 120
?0.321 459
?0.825 279
?0.734 557
Z
?75.172 414
?25.245 899
2.797 448
0.748 208
0.108 400
0.109 390
A
17
0
0
0
0
0
Tab.2Polynomial coefficients of each axis motion of machining pinion
Fig.4Tooth contact analysis of drive side and virtual measurement of pinion concave tooth surface
Fig.5Tooth contact analysis of coast side and virtual measurement of pinion convex tooth surface
Fig.6Motion curve and first derivative of each axis for machining pinion on four-axis linkage Free-form machine tool
Fig.7Normal deviation of pinion tooth surface caused by change of 0-order and 1-order coefficients of each axis polynomial for machining pinion by four-axis linkage Free-form machine tool
[1]
KLINGELNBERG J. Bevel Gear [M]. Hückeswagen: Springer, 2016.
[2]
曾韬, 王志永, 曾亦愚, 等 论中国锥齿轮技术的转型升级[J]. 机械传动, 2014, 38 (10): 81- 89 ZENG Tao, WANG Zhi-yong, ZENG Yi-yu, et al Transformation and upgrading of bevel gear technology in China[J]. Journal of Mechanical Transmission, 2014, 38 (10): 81- 89
The Gleason Works. Generated spiral bevel gears duplex helical method including grinding (SGDH) [Z]. Rochester, New York: The Gleason Works, 1985.
[5]
The Gleason Works. Electronic computer program Aoo212 [Z]. 1978.
[6]
PISULA J, PLOCICA M. Numerical model of bevel gears cutting by duplex helical method [J]. Key Engineering Materials, 2011, 490: 237-246.
[7]
GONZALEZ-PEREZ I, FUENTES A, HAYASAKA K. Computerized design and tooth contact analysis of spiral bevel gears generated by the duplex helical method [C]// ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Washington, DC: ASME, 2011: 149-158.
[8]
刘东方. 弧齿锥齿轮双重双面法TCA分析与加工实验[D]. 洛阳: 河南科技大学, 2014. LIU Dong-fang. Spiral bevel gear TCA analysis and machining experiment with duplex spread-blade method [D]. Luoyang: Henan University of Science and Technology, 2014.
[9]
翁承. 弧齿锥齿轮双重双面螺旋法研究及齿面接触分析[D]. 西安: 西安交通大学, 2014. WENG Cheng. Research on the spiral bevel gears generated by the duplex helical method and its tooth contact analysis [D]. Xi’an: Xi’an Jiaotong University, 2014.
[10]
吴训成. 基于功能需求的弧齿面主动设计与先进制造技术研究[D]. 西安: 西安交通大学, 2000. WU Xun-cheng. Research on the function-oriented active tooth surface design and advanced manufacturing technology for the curved tooth bevel gears [D]. Xi’an: Xi’an Jiaotong University, 2000.
[11]
KAWASAKI K, TAMURA H Method for cutting hypoid gears (duplex spread-blade method)[J]. JSME International Journal, 1997, 40 (4): 768- 775
doi: 10.1299/jsmec.40.768
[12]
KAWASAKI K, TAMURA H Duplex spread blade method for cutting hypoid gears with modified tooth surface[J]. Journal of Mechanical Design, 1998, 120 (3): 441- 447
doi: 10.1115/1.2829171
[13]
ZHANG Y, YAN H Z New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method[J]. Mechanism and Machine Theory, 2016, 100: 283- 295
doi: 10.1016/j.mechmachtheory.2016.02.015
[14]
ZHANG Y, YAN H Z, ZENG T Computerised design and simulation of meshing and contact of formate hypoid gears generated with a duplex helical method[J]. Strojniški Vestnik: Journal of Mechanical Engineering, 2015, 61 (9): 523- 532
doi: 10.5545/sv-jme.2015.2627
[15]
张宇, 严宏志, 曾韬 弧齿锥齿轮双重螺旋法切齿原理及齿面接触分析研究[J]. 机械工程学报, 2015, 52 (21): 15- 23 ZHANG Yu, YAN Hong-zhi, ZENG Tao Cutting principle and tooth contact analysis of spiral bevel and hypoid gears generated by duplex helical method[J]. Journal of Mechanical Engineering, 2015, 52 (21): 15- 23
[16]
严宏志, 胡志安, 肖蒙, 等 双重螺旋法加工螺旋锥齿轮齿面的主动设计[J]. 机械科学与技术, 2017, 36 (11): 1646- 1652 YAN Hong-zhi, HU Zhi-an, XIAO Meng, et al Active design for tooth surface of spiral bevel and hypoid gears generated by duplex helical method[J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36 (11): 1646- 1652
[17]
马朋朋. 螺旋锥齿轮全工序切齿方法研究[D]. 重庆: 重庆理工大学, 2018. MA Peng-peng. Study on completed cutting method of spiral bevel gear [D]. Chongqing: Chongqing University, 2018.
[18]
严宏志, 艾伍轶, 周腾飞, 等 相对位置误差对双重螺旋法加工齿轮副接触性能的影响[J]. 机械科学与技术, 2018, 37 (3): 364- 371 YAN Hong-zhi, AI Wu-yi, ZHOU Teng-fei, et al Influence of contact performance of spiral bevel gears generated by duplex helical method with relative position errors[J]. Mechanical Science and Technology for Aerospace Engineering, 2018, 37 (3): 364- 371
[19]
陈义忠, 吴顺兴, 朱楚, 等 双重螺旋法加工齿轮副安装位置对其正反驱啮合性能的影响[J]. 机械科学与技术, 2020, 39 (12): 1813- 1821 CHEN Yi-zhong, WU Shun-yi, ZHU Chu, et al Influence of installation position of gear pair machined with duplex helical method on meshing performance with advancing or retreating conditions[J]. Mechanical Science and Technology for Aerospace Engineering, 2020, 39 (12): 1813- 1821
[20]
严宏志, 艾伍轶, 吴聪, 等 双重螺旋法圆弧刀廓加工齿轮副的齿面啮合特性分析[J]. 中南大学学报:自然科学版, 2018, 49 (10): 2438- 2446 YAN Hong-zhi, AI Wu-yi, WU Cong, et al Meshing characteristics analysis for spiral bevel gears generated by duplex helical method with arc blade profile[J]. Journal of Central South University: Science and Technology, 2018, 49 (10): 2438- 2446
[21]
ZHANG Y, YAN H Z, ZENG T, et al Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade[J]. Journal of Central South University, 2016, 23 (3): 544- 554
doi: 10.1007/s11771-016-3101-5
[22]
严宏志, 邓辰, 胡志安, 等 双重螺旋法切齿参数对螺旋锥齿轮啮合特性的影响[J]. 现代制造工程, 2019, 461 (2): 76- 83 YAN Hong-zhi, DENG Chen, HU Zhi-an, et al Effect of duplex helical method cutting parameters on spiral bevel gears meshing characteristic[J]. Modern Manufacturing Engineering, 2019, 461 (2): 76- 83
[23]
PISULA J An analysis of the effect of the application of helical motion and assembly errors on the meshing of a spiral bevel gear using duplex helical method[J]. Advances in Manufacturing Science and Technology, 2016, 40 (1): 19- 31
[24]
严宏志, 吴顺兴, 肖蒙 双重螺旋法齿面分区修形对降低安装误差敏感性的影响[J]. 中南大学学报:自然科学版, 2019, (2): 286- 294 YAN Hong-zhi, WU Shun-xing, XIAO Meng Effect of tooth surface zoning modification by duplex helical method on reducing sensitivity of installation error[J]. Journal of Central South University: Science and Technology, 2019, (2): 286- 294
[25]
耿龙龙, 邓静, 聂少武, 等 弧齿锥齿轮双重螺旋法加工数学模型及齿面偏差修正研究[J]. 机械传动, 2020, (9): 7- 13 GENG Long-long, DENG Jing, NIE Shao-wu, et al Research on mathematical model and flank deviation correction of spiral bevel gear by duplex helical method[J]. Journal of Mechanical Transmission, 2020, (9): 7- 13
[26]
曹雪梅, 邓效忠, 聂少武 基于共轭齿面修正的航空弧齿锥齿轮高阶传动误差齿面拓扑结构设计[J]. 航空动力学报, 2015, 30 (1): 195- 200 CAO Xue-mei, DENG Xiao-zhong, NIE Shao-wu Ease-off flank topography design for aviation spiral bevel gears with higher-order transmission errors by modification of conjugate flank[J]. Journal of Aerospace Power, 2015, 30 (1): 195- 200
