Radial Modification Design of Triple Arc Tooth Profile of Flexspline on Uniformly Distributed Spatial Backlash based on Harmonic Gear

Zhongfu Cheng; Jingzhong Xing; Liteng Shi; Xiaoxia Chen

doi:10.16578/j.issn.1004.2539.2021.12.008

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Radial Modification Design of Triple Arc Tooth Profile of Flexspline on Uniformly Distributed Spatial Backlash based on Harmonic Gear

Design· Calculation | 更新时间：2022-09-15

- Radial Modification Design of Triple Arc Tooth Profile of Flexspline on Uniformly Distributed Spatial Backlash based on Harmonic Gear
- Journal of Mechanical Transmission Vol. 45, Issue 12, Pages: 48-55(2021)
- 作者机构：
  
  1.广东省高性能伺服系统企业重点实验室珠海格力电器股份有限公司，广东珠海 579070
  2.天津工业大学机械工程学院，天津 300387
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2021.12.008
  CLC：
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程中甫,邢静忠,石立腾等.基于谐波齿轮空间侧隙均匀化的三圆弧齿廓柔轮的径向修形设计[J].机械传动,2021,45(12):48-55.

Cheng Zhongfu,Xing Jingzhong,Shi Liteng,et al.Radial Modification Design of Triple Arc Tooth Profile of Flexspline on Uniformly Distributed Spatial Backlash based on Harmonic Gear[J].Journal of Mechanical Transmission,2021,45(12):48-55.
程中甫,邢静忠,石立腾等.基于谐波齿轮空间侧隙均匀化的三圆弧齿廓柔轮的径向修形设计[J].机械传动,2021,45(12):48-55. DOI： 10.16578/j.issn.1004.2539.2021.12.008.

Cheng Zhongfu,Xing Jingzhong,Shi Liteng,et al.Radial Modification Design of Triple Arc Tooth Profile of Flexspline on Uniformly Distributed Spatial Backlash based on Harmonic Gear[J].Journal of Mechanical Transmission,2021,45(12):48-55. DOI： 10.16578/j.issn.1004.2539.2021.12.008.

摘要

为改善径向变位加工的柔轮空间齿廓与平面齿廓刚轮的啮合状态，建立柔轮齿廓径向修形设计方法。利用柔轮装配变形的精确算法确定椭圆凸轮波发生器作用下的轮齿位置，再利用圆弧齿廓间的周向侧隙算法获得侧隙。按照直母线假定确定出轴向多个截面内的轮齿定位，进而获得侧隙，以揭示柔轮锥度变形后的空间侧隙分布。未修形的侧隙显示：按照共轭啮合理论设计的刚轮齿廓只在设计截面实现了小而均匀的侧隙分布，前端和后端出现严重干涉。利用前端和后端向内的刀具变位可消除干涉。经迭代设计的径向修形可实现所有截面侧隙趋于零的最佳状态，获得从前到后的线啮合状态。啮合轨迹线仿真表明：合理的径向修形可实现更好地齿面啮合状态。

Abstract

For better meshing status between spatial tooth profile of flexspline machined by radial modification of the tool and the planar tooth profile of circular spline，a design method for radial modification of flexspline tooth profile is proposed. The radial and circumferential positions of flexspline teeth under the action of elliptic wave generator are obtained by using the exact algorithm of flexspline assembly deformation，then backlash is obtained by the backlash algorithm between circular arc tooth profiles. According to the assumption of the straight-line generator，the positioning of the teeth profiles and backlashes in several cross sections are determined，then the backlash is obtained to reveal the spatial backlashes distribution in the cross-sections along the axial direction of flexspline with tapered deformation. The backlash distribution without radial modification shows that the backlash of the conjugated tooth profile of circular spline designed with conjugated meshing theory is very small and uniform in the design cross section，and serious interferences occur in the front and back sections. Inward modification of the cutting tool in the front and back sections can eliminate the interference. Reasonable radial modification designed iteratively achieves the optimal backlashes approaching zero in all cross sections，and realize a line meshing state from the front to the back sections. The simulation of meshing trajectory shows that the reasonable radial modification can achieve a better meshing state between tooth profiles.

关键词

三圆弧齿廓锥度变形空间啮合侧隙侧隙算法啮合运动仿真

Keywords

Triple arc tooth profileTapered deformationSpatial backlashBacklash algorithmMeshing motion simulation

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