非正交航空弧齿锥齿轮磨削精度自适应加工参数驱动控制方法

孙甲尧; 郭紫贵; 王志伟; 丁撼; 李秀兰; 陈立

doi:10.13433/j.cnki.1003-8728.20200265

非正交航空弧齿锥齿轮磨削精度自适应加工参数驱动控制方法

doi: 10.13433/j.cnki.1003-8728.20200265

孙甲尧^{1, 2,},
郭紫贵²,
王志伟^1, ,,
丁撼¹,
李秀兰²,
陈立²

1.
中南大学高性能复杂制造国家重点实验室，长沙　410083
2.
张家界航空工业职业技术学院，湖南张家界　427000

基金项目: 湖南省自然科学基金项目（2021JJ60080，2019JJ70035）与湖南省教育厅科学研究项目（18C1779）

详细信息

作者简介:
孙甲尧（1981−），副教授，研究方向为齿轮加工工艺，4205220@qq.com

通讯作者:
王志伟，硕士，wangzw89@csu.edu.cn

中图分类号: TH122; V252.2
计量
- 文章访问数: 111
- HTML全文浏览量: 36
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2020-05-25
- 刊出日期: 2021-11-05

Adaptive Machine Settings Driven Grinding Accuracy Control Method for Non-orthogonal Aerospace Spiral Bevel Gears

SUN Jiayao^{1, 2
,},
GUO Zigui²,
WANG Zhiwei^{1
, ,},
DING Han¹,
LI Xiulan²,
CHEN Li²

1.
State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China
2.
Zhangjiajie Institute of Aeronautical Engineering, Zhangjiajie 427000, Hu′ nan, China

摘要

摘要: 非正交航空弧齿锥齿轮由于其高速重载服役特性，齿面磨削精度要求高，很难实现实际齿面与理论齿面的匹配。为了满足高效率高精度要求，本文提出了一种齿面精度自适应加工参数驱动控制方法。首先，基于先进的全工序法磨削仿真，进行加工参数驱动的齿面精确数学建模。然后，以磨削精度为控制目标，建立齿面误差测量、齿面设计，齿面误差反调集成的加工精度自适应控制模型。最后，通过齿面误差敏感性分析策略和改进Levenberg-Marquardt算法，实现预设目标齿面的自适应逼近，求解最终精确机床加工参数。本文提供的算例证明了该方法有效性。
- 非正交航空弧齿锥齿轮 /
- 全工序法磨削 /
- 加工参数 /
- 自适应控制 /
- Levenberg-Marquardt算法
Abstract: In consideration of high speed and heavy load operation characteristics of non-orthogonal aerospace spiral bevel gears and high tooth flank grinding accuracy, it is very difficult to achieve the matching of the actual tooth surface and the theoretical tooth surface. For satisfying the high accuracy and efficiency, an adaptive machine settings driven tooth flank accuracy control is proposed. Firstly, with simulation of advanced free-form grinding, machine settings driven tooth flank mathematical modeling is performed. Then, for tooth flank grinding accuracy control, adaptive grinding accuracy control model is established by correlating with the tooth flank form error measurement, tooth flank design and tooth flank form error modification. Finally, with applications of tooth flank form error sensitivity analysis strategy and the improved Levenberg-Marquardt algorithm, the adaptive approximation of the preset target tooth surface is achieved, and the final precise machine tool machining parameters are solved. Given numerical instance in this work can verify the validation of the proposed method.
- non-orthogonal aerospace spiral bevel gears /
- free-form grinding /
- machine settings /
- adaptive control /
- Levenberg-Marquardt algorithm.

HTML全文

图 1 非正交螺旋锥齿轮的双螺旋加工运动学仿真

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图 2 齿面加工精度测量

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图 3 加工精度控制模型

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图 4 非正交航空弧齿锥齿轮装配图

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图 5 小轮累计误差及初始误差统计图

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图 6 大轮凸面累计误差及初始误差统计

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图 7 小轮凹面残差图

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图 8 大轮凸面残差图

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表 1 31/38齿坯参数

参数	小轮	大轮
齿数	31	38
面宽/mm	32.00	32.00
压力角/(°)	20	20
轴交角/(°)	52	52
齿顶/mm	5.90	3.44
齿根高/mm	4.65	6.3
外锥距/mm	208.81	208.81
节锥角/(°)	23.16667	28.833333
面锥角/(°)	24.26667	29.600000
根锥角/(°)	22.4	27.73333
旋向	RH	LH

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表 2 31/38加工参数

参数名	小轮	大轮
刀盘直径D/mm	305.0400	304.80
刀顶距P_w/mm	2.1819	1.9050
外侧压力角AgO/mm	22.20	22.50
内侧压力角AgI/mm	22.60	22.50
外侧圆角半径RwI/mm	0.9800	1.0400
内侧圆角半径RwO/mm	1.0000	1.0400
外侧修形半径ρO/mm	260.0000	304.80
内侧修形半径ρI/mm	400.0000	1.9050
径向刀位S_r/mm	163.3098	163.52611
角向刀位q/(°)	50.4968	49.8142
刀倾角σ/(°)	3.44	0.5985
刀转角ξ/(°)	2.5969	14.88
垂直轮位E_M/mm	0.12558	0.0000
安装角γ_m/(°)	20.13	23.73
水平轮位X_B/mm	0.43873	0.00000
床位X_D/mm	−3.1264	−3.86914
滚比m	2.5258999	2.075437
螺旋修正系数Heli	6.68482	0.00000

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表 3 非正交航空弧齿锥齿轮反调结果

参数	小轮	大轮
径向刀	161.3222	161.653
角向刀位q/(°)	50.50201	49.8051
刀倾角σ/(°)	3.440614	0.6173
刀转角ξ/(°)	2.596959	14.88
垂直轮位E_M/mm	0.05488	0.0512
安装角γ_m/(°)	20.1016	23.754
水平轮位X_B/mm	0.438954	−1.3304
床位X_D/mm	−3.1439	−7.07774
滚比m	2.512648	2.080307
螺旋修正系数Heli	6.684794	0.00000

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参考文献(30)

[1]	曾韬. 螺旋锥齿轮设计与加工[M]. 哈尔滨: 哈尔滨工业大学出版社, 1989 ZENG T. Design and machining of spiral bevel gear[M]. Harbin: Harbin Institute of Technology Press, 1989 (in Chinese)
[2]	胡德金. 影响大型高硬球面磨削精度的因素及控制方法[J]. 上海交通大学学报, 2016, 50(7): 987-993 HU D J. Some factors influencing grinding accuracy of large sphere surface and control methods[J]. Journal of Shanghai Jiaotong University, 2016, 50(7): 987-993 (in Chinese)
[3]	刘春青, 王文汉. 基于人工神经网络-遗传算法的展成法球面精密磨削参数优化[J]. 工程设计学报, 2019, 26(4): 395-402 doi: 10.3785/j.issn.1006-754X.2019.04.004 LIU C Q, WANG W H. Parameter optimization of generating method spherical precision grinding based on ANN-GA[J]. Chinese Journal of Engineering Design, 2019, 26(4): 395-402 (in Chinese) doi: 10.3785/j.issn.1006-754X.2019.04.004
[4]	罗筱英, 唐进元. 结构参数对砂轮主轴系统动态性能的影响[J]. 机械工程学报, 2007, 43(3): 128-134 doi: 10.3321/j.issn:0577-6686.2007.03.022 LUO X Y, TANG J Y. Effect of structure parameters on dynamic properties of spindle system[J]. Chinese Journal of Mechanical Engineering, 2007, 43(3): 128-134 (in Chinese) doi: 10.3321/j.issn:0577-6686.2007.03.022
[5]	LITVIN F L, TSUNG W J, COY J J, et al. Generated spiral bevel gears: optimal machine-tool settings and tooth contact analysis[C]//Proceedings of 1985 SAE International Off-Highway and Powerplant Congress and Exposition. SAE International, 1985: 877-884
[6]	唐进元, 卢延峰, 周超. 有误差的螺旋锥齿轮传动接触分析[J]. 机械工程学报, 2008, 44(7): 16-23 doi: 10.3321/j.issn:0577-6686.2008.07.003 TANG J Y, LU Y F, ZHOU C. Error tooth contact analysis of spiral bevel gears transmission[J]. Chinese Journal of Mechanical Engineering, 2008, 44(7): 16-23 (in Chinese) doi: 10.3321/j.issn:0577-6686.2008.07.003
[7]	唐进元, 卢延峰, 周超. 调整参数误差对齿面接触质量的影响[J]. 航空动力学报, 2008, 23(9): 1718-1723 TANG J Y, LU Y F, ZHOU C. Effect of machine tool adjustment parameter errors on spiral bevel gears tooth contact quality[J]. Journal of Aerospace Power, 2008, 23(9): 1718-1723 (in Chinese)
[8]	GABICCINI M, BRACCI A, GUIGGIANI M. Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments[J]. Journal of Mechanical Design, 2009, 132(4): 041010
[9]	李丽霞, 李培军, 刘新状. 机床调整误差对弧齿锥齿轮大轮齿面形状影响规律的研究[J]. 机械传动, 2006, 30(4): 13-15 doi: 10.3969/j.issn.1004-2539.2006.04.005 LI L X, LI P J, LIU X Z. Research on the influence of the gear tooth surface shape of spiral bevel gear by adjustment error of machine tool[J]. Journal of Mechanical Transmission, 2006, 30(4): 13-15 (in Chinese) doi: 10.3969/j.issn.1004-2539.2006.04.005
[10]	唐进元, 聂金安, 王智泉. 螺旋锥齿轮HFT法加工的反调修正方法[J]. 中南大学学报, 2012, 43(6): 2142-2149 TANG J Y, NIE J A, WANG Z Q. Reverse correction of spiral bevel gear HFT method[J]. Journal of Central South University, 2012, 43(6): 2142-2149 (in Chinese)
[11]	唐进元, 邢彬. 基于三坐标测量机的螺旋锥齿轮加工参数反调修正[J]. 北京工业大学学报, 2010, 36(11): 1451-1456 TANG J Y, XING B. Machine-settings correction of spiral bevel gear based on coordinate measuring machine[J]. Journal of Beijing University of Technology, 2010, 36(11): 1451-1456 (in Chinese)
[12]	GLEASON. Generated hypoid gears duplex helical method[M]. Rochester: The Gleason Works, 1971: 56-70
[13]	LITVIN F L, KUAN C, WANG J C, et al. Minimization of deviations of gear real tooth surfaces determined by coordinate measurements[J]. Journal of Mechanical Design, 1993, 115(12): 995-1001
[14]	LIN C Y, TSAY C B, FONG Z H. Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface-deviation[J]. Mechanism and Machine Theory, 1998, 33(6): 785-803 doi: 10.1016/S0094-114X(97)00101-8
[15]	ARTONI A, GABICCINI M, GUIGGIANI M. Nonlinear identification of machine settings for flank form modifications in hypoid gears[J]. Journal of Mechanical Design, 2008, 130(11): 112602 doi: 10.1115/1.2976454
[16]	DING H, WAN G X, ZHOU Y S, et al. Nonlinearity analysis based algorithm for indentifying machine settings in the tooth flank topography correction for hypoid gears[J]. Mechanism and Machine Theory, 2017, 113: 1-21 doi: 10.1016/j.mechmachtheory.2017.02.007
[17]	DING H, TANG J Y, ZHONG J. Accurate nonlinear modeling and computing of grinding machine settings modification considering spatial geometric errors for hypoid gears[J]. Mechanism and Machine Theory, 2016, 99: 155-175 doi: 10.1016/j.mechmachtheory.2016.01.008
[18]	樊奇, 让·德福. 格里森专家制造系统(GEMS)开创弧齿锥齿轮及双曲面齿轮数字化制造新纪元[J]. 世界制造技术与装备市场, 2005(4): 87-93 doi: 10.3969/j.issn.1015-4809.2005.04.030 FAN Q, DAFOR R. Gleason expert manufacturing system (GEMS) opens a new era for digitized manufacturing of spiral bevel and hypoid gears[J]. World Manufacturing Engineering & Market, 2005(4): 87-93 (in Chinese) doi: 10.3969/j.issn.1015-4809.2005.04.030
[19]	FAN Q, DAFOE R S, SWANGER J W. Higher-order tooth flank form error correction for face-milled spiral bevel and hypoid gears[J]. Journal of Mechanical Design, 2008, 130(7): 072601 doi: 10.1115/1.2898878
[20]	DING H, TANG J Y, SHAO W, et al. Optimal modification of tooth flank form error considering measurement and compensation of cutter geometric errors for spiral bevel and hypoid gears[J]. Mechanism and Machine Theory, 2017, 118: 14-31 doi: 10.1016/j.mechmachtheory.2017.07.020
[21]	ARTONI A, BRACCI A, GABICCINI M, et al. Optimization of the loaded contact pattern in hypoid gears by automatic topography modification[J]. Journal of Mechanical Design, 2010, 131(1): 011008
[22]	ARTONI A, KOLIVAND A, KAHRAMAN M. An ease-off based optimization of the loaded transmission error of hypoid gears[J]. Journal of Mechanical Design, 2010, 132(1): 011010 doi: 10.1115/1.4000645
[23]	ARTONI A, GABICCINI M, GUIGGIANI M, et al. Multi-objective ease-off optimization of hypoid gears for their efficiency, noise, and durability performances[J]. Journal of Mechanical Design, 2011, 133(12): 121007 doi: 10.1115/1.4005234
[24]	陈书涵. 螺旋锥齿轮磨削误差产生机制及修正技术研究[D]. 长沙: 中南大学, 2009 CHEN S H. Research on generation mechanism and correction technique for spiral bevel gear's grinding errors[D]. Changsha: Central South University, 2009 (in Chinese)
[25]	唐进元, 李友元, 周超, 等. 螺旋锥齿轮数控磨齿机床空间误差与机机床调整参数的关系[J]. 机械工程学报, 2009, 45(4): 148-154 doi: 10.3901/JME.2009.04.148 TANG J Y, LI Y Y, ZHOU C, et al. Relation between CNC bevel gear generator spatial errors and machine setting errors[J]. Journal of Mechanical Engineering, 2009, 45(4): 148-154 (in Chinese) doi: 10.3901/JME.2009.04.148
[26]	SIMON V V. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors and misalignments[J]. Journal of Mechanical Design, 2008, 130(8): 082603 doi: 10.1115/1.2936903
[27]	DING H, TANG J Y, ZHONG J, et al. A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears[J]. Journal of Manufacturing Systems, 2016, 41: 228-238 doi: 10.1016/j.jmsy.2016.09.003
[28]	DING H, WAN Z G, ZHOU Y S, et al. A data-driven programming of the human-computer interactions for modeling a collaborative manufacturing system of hypoid gears by considering both geometric and physical performances[J]. Robotics and Computer-Integrated Manufacturing, 2018, 51: 121-138 doi: 10.1016/j.rcim.2017.10.003
[29]	DENG J, LI J B, DENG X Z. A network-based manufacturing model for spiral bevel gears[J]. Journal of Intelligent Manufacturing, 2018, 29(2): 353-367 doi: 10.1007/s10845-015-1111-z
[30]	范金燕, 袁亚湘. 非线性方程组数值方法[M]. 北京: 科学出版社, 2018 FAN J Y, YUAN Y X. Numerical methods for nonlinear equations[M]. Beijing: Science Press, 2018 (in Chinese)