螺旋锥齿轮在线检测的研究
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摘要
螺旋锥齿轮作为机械工业中传递相交轴或相错轴回转运动的重要基础元件,具有重迭系数大、承载能力高、运转平稳、噪音低等优点,因此广泛应用在各种高速、重载的机械传动中。由于其啮合原理比较复杂,导致了螺旋锥齿轮加工理论和检测技术也非常复杂。随着计算机技术、数字控制技术、数字测量技术的飞速发展,为实现螺旋锥齿轮集加工与测量于一体的闭环控制提供了可能。国外的齿轮测量中心虽然可以得到螺旋锥齿轮实际齿面上的几何信息,但价格昂贵,技术封锁。与国外相比,国内的研究起步晚,齿面测量技术相对落后,因此对螺旋锥齿轮的在线检测技术的研究显得尤为重要。
本文根据螺旋锥齿轮的啮合原理和切齿原理,建立了以机床加工调整参数为基础的螺旋锥齿轮的齿面方程,同时利用旋转投影法对理论齿面进行测量网格划分,通过编写MATLAB语言程序求解了各个测量节点的理论坐标值。并根据这些坐标值构造出齿面模型,为在线检测提供理论参照值及检测目标,是后续检测工作的基础；对螺旋锥齿轮的齿面数据采集方法进行了研究,包括测头的选择、坐标变换理论以及路径规划等方面,为保证测量的顺利进行,详细的分析了测头的路径规划方法及测头和测杆的避障方法,全方位对齿面数据采集过程加以分析。
最后构建了螺旋锥齿轮在线检测的实现方案,对组成在线检测系统的四个关键部分都做了详细说明,对系统的连接方案和测量过程进行了分析,为齿面在线检测的后续工作打下坚实基础,使螺旋锥齿轮的在线检测研究由理论上升到实际。
Spiral bevel gear, as the machinery industry in the intersecting or staggered axes rotary motion relative to the basis of the important components, with the advantages of overlap coefficient, high carrying capacity, smooth operation, low noise. Therefore it is widely used in various high-speed, heavy mechanical transmission areas. Because of its complex meshing theory, led to processing theory and measurement techniques is also very complex. With the rapid development of computer technology, digital control technology, digital measuring technology, making it is possible for the spiral bevel gear setting processing and measurement in one of the closed-loop control. While abroad, Gear Measuring Center can get tooth surface data but expensive, technology blockade. Compared with foreign, domestic researching started later, the tooth surface measurement technology is relatively backward, so the spiral bevel gear on-line measurement technique is very important.
In the thesis, based on the principle of spiral bevel gear, established a spiral bevel gear tooth surface equations which is based on adjusting the parameters of machine tool, using rotating projection method to divided the theoretical tooth surface into a certain size grid, then write MATLAB program to calculate each grid coordinates and establish tooth surface model based on these coordinates. Provide a theoretical reference value and target value for on-line measurement, they are the basis of follow-up work. The tooth surface data collection method is studied, including probe selection, coordinate transformation theory and path planning. To insure the measurement smoothly, the probe path planning, the probe and measurement rod of obstacle avoidance is analyzed in detail. The data collection method of tooth surface is analyzed comprehensively.
The on-line measurement implementation program has been designed. The four key parts of the program have done a detailed description. Connection scheme and measurement process of the system is analyzed. Lay a solid foundation for on-line measurement. Make the theory study rising to the actual.
本文根据螺旋锥齿轮的啮合原理和切齿原理,建立了以机床加工调整参数为基础的螺旋锥齿轮的齿面方程,同时利用旋转投影法对理论齿面进行测量网格划分,通过编写MATLAB语言程序求解了各个测量节点的理论坐标值。并根据这些坐标值构造出齿面模型,为在线检测提供理论参照值及检测目标,是后续检测工作的基础；对螺旋锥齿轮的齿面数据采集方法进行了研究,包括测头的选择、坐标变换理论以及路径规划等方面,为保证测量的顺利进行,详细的分析了测头的路径规划方法及测头和测杆的避障方法,全方位对齿面数据采集过程加以分析。
最后构建了螺旋锥齿轮在线检测的实现方案,对组成在线检测系统的四个关键部分都做了详细说明,对系统的连接方案和测量过程进行了分析,为齿面在线检测的后续工作打下坚实基础,使螺旋锥齿轮的在线检测研究由理论上升到实际。
Spiral bevel gear, as the machinery industry in the intersecting or staggered axes rotary motion relative to the basis of the important components, with the advantages of overlap coefficient, high carrying capacity, smooth operation, low noise. Therefore it is widely used in various high-speed, heavy mechanical transmission areas. Because of its complex meshing theory, led to processing theory and measurement techniques is also very complex. With the rapid development of computer technology, digital control technology, digital measuring technology, making it is possible for the spiral bevel gear setting processing and measurement in one of the closed-loop control. While abroad, Gear Measuring Center can get tooth surface data but expensive, technology blockade. Compared with foreign, domestic researching started later, the tooth surface measurement technology is relatively backward, so the spiral bevel gear on-line measurement technique is very important.
In the thesis, based on the principle of spiral bevel gear, established a spiral bevel gear tooth surface equations which is based on adjusting the parameters of machine tool, using rotating projection method to divided the theoretical tooth surface into a certain size grid, then write MATLAB program to calculate each grid coordinates and establish tooth surface model based on these coordinates. Provide a theoretical reference value and target value for on-line measurement, they are the basis of follow-up work. The tooth surface data collection method is studied, including probe selection, coordinate transformation theory and path planning. To insure the measurement smoothly, the probe path planning, the probe and measurement rod of obstacle avoidance is analyzed in detail. The data collection method of tooth surface is analyzed comprehensively.
The on-line measurement implementation program has been designed. The four key parts of the program have done a detailed description. Connection scheme and measurement process of the system is analyzed. Lay a solid foundation for on-line measurement. Make the theory study rising to the actual.
引文
[1]曾韬.螺旋锥齿轮设计与加工.哈尔滨：哈尔滨工业出版社,1989.
[2]刘雄伟.数控加工理论与编程技术.北京：机械工业出版社,1994.
[3]E. Wildhaber. Gear Tooth Curvature Treated Simply. American Machinist, 1945,8(18).
[4]E. Wildhaber. Basic Relationship of Hypoid Gears. American Machinist,1945,90(20).
[5]E. Wildhaber. Basic Relationship of Hypoid Gears-Ⅱ. American Machinist,1946,90(3).
[6]蒋文兵.螺旋锥齿轮五轴联动数控加工的研究.郑州：郑州大学,2003.
[7]E. Wildhaber. Basic Relationship of Hypoid Gears-Ⅲ. American Machinist,1946,90(5).
[8]M.L. Baxter. Basic Geometry and Tooth Contact of Hypoid Gear. Industrial Mathematics, 1961(2).
[9]M.L. Baxter. High Reduction Hypoid. Machine Design, 1961(27).
[10]董学朱.齿轮制造手册.北京：机械工业出版社,1999.
[11]吕罕聪.螺旋锥齿轮测量方法研究.西安：西安理工大学,2007.
[12]何超杰,高健,陈新.基于接触式测头的在线检测关键技术的研究.机床与液压,2008,36(2)：170-174.
[13]刘占强,赵军,于复生.用于加工中心的在线工件自动测量系统.工具技术,2000,34(9)：30-32.
[14]刘义午,刘丽冰.数控机床误差补偿研究技术.中国机械工程,1998,9(12)：48-52.
[15]魏华亮.我国CNC齿轮测量中心的发展现状.计量技术,2004,10：33-34.
[16]王军, 王小椿, 姜虹等.螺旋锥齿轮齿面的三坐标测量.机械工程学报,2003,39(6)：151-154.
[17]张兆龙,谢华锟,徐露.锥齿轮测量技术的发展及锥齿轮的局部互换性工具技术,2000,34(2)：40-43.
[18]王小椿,王军,姜虹等.螺旋锥齿轮的齿面测量及机床加工参数修正.机械工程学报,2003,39(8)：125-128.
[19]王志,谢华锟,王贵成.锥齿轮测量原理以及测量仪器最新进展.电测与仪表,2005,42：37-39.
[20]张康智,刘凌.加工中心在线检测技术的研究.控制与检测,2007,6(2)：56-59.
[21]王亚青.五轴数控机床在线检测技术研究.河北：河北工业大学,2003.
[22]谢华锟,王志,石照耀等.锥齿轮测量技术的最新进展.工具技术,2003,37(10)：48-51.
[23]张静,杨宏斌,邓效忠等.我国锥齿轮技术的现状和发展动向.河南科技大学学报(自然科学版),2003,24(1)：40-43.
[24]郑江,张保全,桂志国.现代齿轮技术的发展与我国齿轮制造面临的问题.华北工学院学报,1997,18(1)：50-54.
[25]北京齿轮厂.螺旋锥齿轮.第一版.北京：科学技术出版社,1974：1-71,339-371.
[26]蔡春源.机械设计手册.锥齿轮传动(第3卷).北京：机械工业出版社,1991.
[27]郑昌启.弧齿锥齿轮和准双曲面齿轮啮合原理、齿坯设计、加工调整和齿面分析计算原理.北京：机械工业出版社,1988：1-102,302-311.
[28]李特文.齿轮啮合原理.第二版.上海：上海科学技术出版社,1984：412-425.
[29]齿轮手册编委会.齿轮手册(下册).第二版.北京：机械工业出版社,2002,20：3-83.
[30]方宗德,杨宏斌,邓效忠.弧齿锥齿轮齿面优化修正及计算机仿真.航空动力学报,2002,17(1)： 140-144.
[31]Wang Jun, Wang Xiaochun, Jiang Hong, et al. Measurement and Compensation of Deviations of Real Tooth Surface of Spiral Bevel Gear. CHINESE JOURNAL OF AERONAUTICS, 2003,16(3):182-186.
[32]Faydor. L, Kieffer, et al. Identification and Minimization of Deviation of Real Gear Tooth Surface.Journal of Mechanical Design,ASME,1991,113(1):55-62.
[33]AGMA 2009-AXX,Bevel Gear Classification, Tolerances and Measuring Methods.USA, American Gear Manufacturers Association, 1996.
[34]Zhang Y, Litvin FL, Maruyama N, et al. Computer2ized Analysis of Meshing and Contact of Gear Real Tooth Surfaces. Journal of Mechanical Design,1994,116 (9):667-682.
[35]颜祯.基于CNC齿轮测量中心测量的螺旋锥齿轮齿形误差修正.长沙：中南大学,2008.
[36]孙祥,徐流美,吴清MATLAB7.0基础教程.北京：清华大学出版社,2005.
[37]史文彬.关于使用数控机床实现在线测量.太原：中北大学,2007.
[38]AOYONG PENG. Computerized design and stress analysis of spiral bevel gears with geodetic path of contact. Chicago:University of Illinois at Chicago,2000.
[39]QIMING LIAN. Computerized design, generation, simulation, and stress analysis of new types of spur gear drive. Chicago:University of Illinois at Chicago, 1996.
[40]李左章,王沉培,周云飞等.螺旋锥齿轮数控切齿机通用运动学变换.华中理工大学学报,2000,28(10)：10-12.
[41]李左章.螺旋锥齿轮NC加工的理论、方法及控制技术研究.武汉：华中科技大学,2001.
[42]Rexroth力士乐IndraMotinn MTX开放式控制系统.制造技术与机床,2004,6：99.
[43]Rexroth.力十乐CNC控制系统IndraMotion MTX.制造技术与机床,2005,11：130-131.
[44]Boseh Rexroth AG Eleetrie Drivesand Control. Rexroth IndraMotion MTX Programming Manual. Printed in Germany. R911316992.Edition 01.2006.
[45]Bosch Rexroth AG Electric Drives and Control. PLC Programming with Rexroth IndraLogic1.0 Operating and Programming Guide. Printed in Germany. R911305036, Edition 01,2003.
[46]Bosch Rexroth AG Electric Drives and Control. Rexroth IndraMotion MTX PLC Interface Project Planning Manual. Printed in Germany. R911316998,Edition 01,2006.
[2]刘雄伟.数控加工理论与编程技术.北京：机械工业出版社,1994.
[3]E. Wildhaber. Gear Tooth Curvature Treated Simply. American Machinist, 1945,8(18).
[4]E. Wildhaber. Basic Relationship of Hypoid Gears. American Machinist,1945,90(20).
[5]E. Wildhaber. Basic Relationship of Hypoid Gears-Ⅱ. American Machinist,1946,90(3).
[6]蒋文兵.螺旋锥齿轮五轴联动数控加工的研究.郑州：郑州大学,2003.
[7]E. Wildhaber. Basic Relationship of Hypoid Gears-Ⅲ. American Machinist,1946,90(5).
[8]M.L. Baxter. Basic Geometry and Tooth Contact of Hypoid Gear. Industrial Mathematics, 1961(2).
[9]M.L. Baxter. High Reduction Hypoid. Machine Design, 1961(27).
[10]董学朱.齿轮制造手册.北京：机械工业出版社,1999.
[11]吕罕聪.螺旋锥齿轮测量方法研究.西安：西安理工大学,2007.
[12]何超杰,高健,陈新.基于接触式测头的在线检测关键技术的研究.机床与液压,2008,36(2)：170-174.
[13]刘占强,赵军,于复生.用于加工中心的在线工件自动测量系统.工具技术,2000,34(9)：30-32.
[14]刘义午,刘丽冰.数控机床误差补偿研究技术.中国机械工程,1998,9(12)：48-52.
[15]魏华亮.我国CNC齿轮测量中心的发展现状.计量技术,2004,10：33-34.
[16]王军, 王小椿, 姜虹等.螺旋锥齿轮齿面的三坐标测量.机械工程学报,2003,39(6)：151-154.
[17]张兆龙,谢华锟,徐露.锥齿轮测量技术的发展及锥齿轮的局部互换性工具技术,2000,34(2)：40-43.
[18]王小椿,王军,姜虹等.螺旋锥齿轮的齿面测量及机床加工参数修正.机械工程学报,2003,39(8)：125-128.
[19]王志,谢华锟,王贵成.锥齿轮测量原理以及测量仪器最新进展.电测与仪表,2005,42：37-39.
[20]张康智,刘凌.加工中心在线检测技术的研究.控制与检测,2007,6(2)：56-59.
[21]王亚青.五轴数控机床在线检测技术研究.河北：河北工业大学,2003.
[22]谢华锟,王志,石照耀等.锥齿轮测量技术的最新进展.工具技术,2003,37(10)：48-51.
[23]张静,杨宏斌,邓效忠等.我国锥齿轮技术的现状和发展动向.河南科技大学学报(自然科学版),2003,24(1)：40-43.
[24]郑江,张保全,桂志国.现代齿轮技术的发展与我国齿轮制造面临的问题.华北工学院学报,1997,18(1)：50-54.
[25]北京齿轮厂.螺旋锥齿轮.第一版.北京：科学技术出版社,1974：1-71,339-371.
[26]蔡春源.机械设计手册.锥齿轮传动(第3卷).北京：机械工业出版社,1991.
[27]郑昌启.弧齿锥齿轮和准双曲面齿轮啮合原理、齿坯设计、加工调整和齿面分析计算原理.北京：机械工业出版社,1988：1-102,302-311.
[28]李特文.齿轮啮合原理.第二版.上海：上海科学技术出版社,1984：412-425.
[29]齿轮手册编委会.齿轮手册(下册).第二版.北京：机械工业出版社,2002,20：3-83.
[30]方宗德,杨宏斌,邓效忠.弧齿锥齿轮齿面优化修正及计算机仿真.航空动力学报,2002,17(1)： 140-144.
[31]Wang Jun, Wang Xiaochun, Jiang Hong, et al. Measurement and Compensation of Deviations of Real Tooth Surface of Spiral Bevel Gear. CHINESE JOURNAL OF AERONAUTICS, 2003,16(3):182-186.
[32]Faydor. L, Kieffer, et al. Identification and Minimization of Deviation of Real Gear Tooth Surface.Journal of Mechanical Design,ASME,1991,113(1):55-62.
[33]AGMA 2009-AXX,Bevel Gear Classification, Tolerances and Measuring Methods.USA, American Gear Manufacturers Association, 1996.
[34]Zhang Y, Litvin FL, Maruyama N, et al. Computer2ized Analysis of Meshing and Contact of Gear Real Tooth Surfaces. Journal of Mechanical Design,1994,116 (9):667-682.
[35]颜祯.基于CNC齿轮测量中心测量的螺旋锥齿轮齿形误差修正.长沙：中南大学,2008.
[36]孙祥,徐流美,吴清MATLAB7.0基础教程.北京：清华大学出版社,2005.
[37]史文彬.关于使用数控机床实现在线测量.太原：中北大学,2007.
[38]AOYONG PENG. Computerized design and stress analysis of spiral bevel gears with geodetic path of contact. Chicago:University of Illinois at Chicago,2000.
[39]QIMING LIAN. Computerized design, generation, simulation, and stress analysis of new types of spur gear drive. Chicago:University of Illinois at Chicago, 1996.
[40]李左章,王沉培,周云飞等.螺旋锥齿轮数控切齿机通用运动学变换.华中理工大学学报,2000,28(10)：10-12.
[41]李左章.螺旋锥齿轮NC加工的理论、方法及控制技术研究.武汉：华中科技大学,2001.
[42]Rexroth力士乐IndraMotinn MTX开放式控制系统.制造技术与机床,2004,6：99.
[43]Rexroth.力十乐CNC控制系统IndraMotion MTX.制造技术与机床,2005,11：130-131.
[44]Boseh Rexroth AG Eleetrie Drivesand Control. Rexroth IndraMotion MTX Programming Manual. Printed in Germany. R911316992.Edition 01.2006.
[45]Bosch Rexroth AG Electric Drives and Control. PLC Programming with Rexroth IndraLogic1.0 Operating and Programming Guide. Printed in Germany. R911305036, Edition 01,2003.
[46]Bosch Rexroth AG Electric Drives and Control. Rexroth IndraMotion MTX PLC Interface Project Planning Manual. Printed in Germany. R911316998,Edition 01,2006.