双重螺旋法加工螺旋锥齿轮齿面的主动设计
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摘要
为解决双重螺旋法加工的螺旋锥齿轮接触区难调整的问题,根据螺旋锥齿轮加工的创成模型获得小轮共轭齿面,然后通过预置配对齿面的啮合性能,对小轮共轭齿面进行修形获得满足预置啮合性能的目标齿面;以小轮结果齿面与目标齿面偏差平方和最小为目标,将小轮加工参数调整量作为变量,考虑约束条件建立了优化模型,采用非线性约束优化求解的方法求解。最后以双重螺旋法加工的8×43的准双曲线齿轮副修型为例,通过数值计算和滚检试验来验证双重螺旋法加工齿面的主动设计方法有效性。
In order to solve the problem that the contact region of spiral bevel and hypoid gear which generated by duplex helical method was difficult to adjust,a pinion conjugate tooth surface was obtained by generating model for spiral bevel and hypoid gear,and then modified the pinion conjugate tooth surface according to the preset meshing performance of tooth surface to obtain a pinion target tooth surface. Considering the constraint condition,the optimal model was built by setting the least sum of square errors between the pinion resultant tooth surface and the pinion target on both sides as object and setting the adjustment amount of pinion machining parameters as variables. The model was solved by the method of nonlinearly constrained optimization. Taking a hypoid gear drive 8 × 43 that manufactured by duplex helical method,the proposed menthod were proven by numerical computation and rolling test.
In order to solve the problem that the contact region of spiral bevel and hypoid gear which generated by duplex helical method was difficult to adjust,a pinion conjugate tooth surface was obtained by generating model for spiral bevel and hypoid gear,and then modified the pinion conjugate tooth surface according to the preset meshing performance of tooth surface to obtain a pinion target tooth surface. Considering the constraint condition,the optimal model was built by setting the least sum of square errors between the pinion resultant tooth surface and the pinion target on both sides as object and setting the adjustment amount of pinion machining parameters as variables. The model was solved by the method of nonlinearly constrained optimization. Taking a hypoid gear drive 8 × 43 that manufactured by duplex helical method,the proposed menthod were proven by numerical computation and rolling test.
引文
[1]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,2015,51(21):15-23Zhang Y,Yan H Z,Zeng T.Cutting principle and tooth contact analysis of spiral bevel and hypoid gears generated by duplex helical method[J].Journal of Mechanical Engineering,2015,51(21):15-23(in Chinese)
[2]Litvin F L,Zhang Y.Local synthesis and tooth contact analysis of face-milled spiral bevel gears[R].NASA CR4342.Chicago,USA:NASA Lewis Research Center,1991
[3]Litvin F L,Fuentes A.Gear geometry and applied theory[M].Cambridge:Cambridge University Press,1994
[4]吴训成,毛世民,吴序堂.点啮合齿面主动设计理论和方法[J].机械科学与技术,2000,19(3):347-349Wu X C,Mao S M,Wu X T.On function-oriented design of point-contact tooth surfaces[J].Mechanical Science and Technology,2000,19(3):347-349(in Chinese)
[5]吴训成,金海松,罗素云.成形法大轮准双曲面齿轮传动点啮合齿面主动设计与理论检验[J].机床与液压,2009,37(12):31-35Wu X C,Jin H S,Luo S Y.Function-oriented design and theoretical verification of point-contact tooth surfaces of the hypoid gear drive with the formate gear[J].Machine Tool&Hydraulics,2009,37(12):31-35(in Chinese)
[6]周凯红,唐进元,严宏志.基于预定啮合特性的点啮合齿面设计方法[J].航空动力学报,2009,24(11):2612-2617Zhou K H,Tang J Y,Yan H Z.Research on meshing characteristics-based design of point-contact tooth surface[J].Journal of Aerospace Power,2009,24(11):2612-2617(in Chinese)
[7]周凯红,唐进元,曾韬.基于预定啮合特性的点啮合齿轮的CNC制造技术研究[J].机械工程学报,2009,45(9):173-182Zhou K H,Tang J Y,Zeng T.CNC manufacturing technology of point meshing gear based on predetermined meshing characteristics[J].Journal of Mechanical Engineering,2009,45(9):173-182(in Chinese)
[8]魏冰阳,邓效忠,仝昂鑫,等.曲面综合法弧齿锥齿轮加工参数计算[J].机械工程学报,2016,52(1):20-25Wei B Y,Deng X Z,Tong A X,et al.Surface synthesis method on generating parameters computation of spiral bevel-gears[J].Journal of Mechanical Engineering,2016,52(1):20-25(in Chinese)
[9]苏进展,贺朝霞.弧齿锥齿轮齿面的高精度修形方法[J].华南理工大学学报(自然科学版),2014,42(4):91-96,104Su J Z,He Z X.High-precision modification of tooth surface for spiral bevel gears[J].Journal of South China University of Technology(Natural Science Edition),2014,42(4):91-6,104(in Chinese)
[10]杜进辅,方宗德,张永振,等.摆线齿准双曲面齿轮齿面主动设计[J].国防科技大学学报,2015,37(6):167-174Du J F,Fang Z D,Zhang Y Z,et al.Active tooth surface design of cycloid hypoid gears[J].Journal of National University of Defense Technology,2015,37(6):167-174(in Chinese)
[11]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,1989Zeng T.Design and manufacture of spiral bevel and hypoid gears[M].Harbin:Harbin Institute of Technology Press,1989(in Chinese)
[12]聂少武.基于完全共轭的摆线锥齿轮齿面失配设计及修正理论研究[D].西安:西北工业大学,2015:37-39Nie S W.Study on tooth flank mismatch design and modification theory based on fully conjugated cycloid bevel gears[D].Xi'an:Northwestern Polytechnical University,2015:37-39(in Chinese)
[13]苏进展,张昆仑,刘永生.弧齿锥齿轮对称抛物线型传动误差设计[J].机械设计,2016,33(3):17-23Su J Z,Zhang K L,Liu Y S.Transmission error design of symmetric parabolic for spiral bevel gears[J].Journal of Machine Design,2016,33(3):17-23(in Chinese)
[14]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):195-200Cao X M,Deng X Z,Nie S W.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(in Chinese)
[15]吴会军,魏冰阳.接触迹对齿轮副啮合性能的影响[J].机械传动,2009,33(4):13-15Wu H J,Wei B Y.Influence of contact path on meshing behavior of gears[J].Journal of Mechanical Transmission,2009,33(4):13-15(in Chinese)
[2]Litvin F L,Zhang Y.Local synthesis and tooth contact analysis of face-milled spiral bevel gears[R].NASA CR4342.Chicago,USA:NASA Lewis Research Center,1991
[3]Litvin F L,Fuentes A.Gear geometry and applied theory[M].Cambridge:Cambridge University Press,1994
[4]吴训成,毛世民,吴序堂.点啮合齿面主动设计理论和方法[J].机械科学与技术,2000,19(3):347-349Wu X C,Mao S M,Wu X T.On function-oriented design of point-contact tooth surfaces[J].Mechanical Science and Technology,2000,19(3):347-349(in Chinese)
[5]吴训成,金海松,罗素云.成形法大轮准双曲面齿轮传动点啮合齿面主动设计与理论检验[J].机床与液压,2009,37(12):31-35Wu X C,Jin H S,Luo S Y.Function-oriented design and theoretical verification of point-contact tooth surfaces of the hypoid gear drive with the formate gear[J].Machine Tool&Hydraulics,2009,37(12):31-35(in Chinese)
[6]周凯红,唐进元,严宏志.基于预定啮合特性的点啮合齿面设计方法[J].航空动力学报,2009,24(11):2612-2617Zhou K H,Tang J Y,Yan H Z.Research on meshing characteristics-based design of point-contact tooth surface[J].Journal of Aerospace Power,2009,24(11):2612-2617(in Chinese)
[7]周凯红,唐进元,曾韬.基于预定啮合特性的点啮合齿轮的CNC制造技术研究[J].机械工程学报,2009,45(9):173-182Zhou K H,Tang J Y,Zeng T.CNC manufacturing technology of point meshing gear based on predetermined meshing characteristics[J].Journal of Mechanical Engineering,2009,45(9):173-182(in Chinese)
[8]魏冰阳,邓效忠,仝昂鑫,等.曲面综合法弧齿锥齿轮加工参数计算[J].机械工程学报,2016,52(1):20-25Wei B Y,Deng X Z,Tong A X,et al.Surface synthesis method on generating parameters computation of spiral bevel-gears[J].Journal of Mechanical Engineering,2016,52(1):20-25(in Chinese)
[9]苏进展,贺朝霞.弧齿锥齿轮齿面的高精度修形方法[J].华南理工大学学报(自然科学版),2014,42(4):91-96,104Su J Z,He Z X.High-precision modification of tooth surface for spiral bevel gears[J].Journal of South China University of Technology(Natural Science Edition),2014,42(4):91-6,104(in Chinese)
[10]杜进辅,方宗德,张永振,等.摆线齿准双曲面齿轮齿面主动设计[J].国防科技大学学报,2015,37(6):167-174Du J F,Fang Z D,Zhang Y Z,et al.Active tooth surface design of cycloid hypoid gears[J].Journal of National University of Defense Technology,2015,37(6):167-174(in Chinese)
[11]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,1989Zeng T.Design and manufacture of spiral bevel and hypoid gears[M].Harbin:Harbin Institute of Technology Press,1989(in Chinese)
[12]聂少武.基于完全共轭的摆线锥齿轮齿面失配设计及修正理论研究[D].西安:西北工业大学,2015:37-39Nie S W.Study on tooth flank mismatch design and modification theory based on fully conjugated cycloid bevel gears[D].Xi'an:Northwestern Polytechnical University,2015:37-39(in Chinese)
[13]苏进展,张昆仑,刘永生.弧齿锥齿轮对称抛物线型传动误差设计[J].机械设计,2016,33(3):17-23Su J Z,Zhang K L,Liu Y S.Transmission error design of symmetric parabolic for spiral bevel gears[J].Journal of Machine Design,2016,33(3):17-23(in Chinese)
[14]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):195-200Cao X M,Deng X Z,Nie S W.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(in Chinese)
[15]吴会军,魏冰阳.接触迹对齿轮副啮合性能的影响[J].机械传动,2009,33(4):13-15Wu H J,Wei B Y.Influence of contact path on meshing behavior of gears[J].Journal of Mechanical Transmission,2009,33(4):13-15(in Chinese)