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<p>To address the gear interference problem in harmonic drive (HD) flexsplines (FS) during meshing transmission caused by tooth profile axial inclination after wave generator (WG) assembly under actual working conditions, this study focuses on composite cycloidal tooth profiles. Two methods, namely the linear modification(LM) method and the finite-element-method-based tooth profile modification (FEMM, defined as the construction of nonlinear axial modification along the tooth-width direction from the assembled finite-element displacement field), are employed, and MATLAB is used to simulate and analyze the pre- and post-modification motion trajectories. Finite element analyses were then conducted on HD models with linear method modification, finite element method modification, and unmodified profiles, comparing deformation and stress conditions during assembly and loaded operation. Due to the assembly-induced axial displacement being nonlinear along the tooth width and coupled with angular position (<i>θ</i>), linear approximation causes end-region mismatch, leading to secondary deformation and contact concentration. Accordingly, we adopt a FEMM that directly constructs nonlinear axial modification <i>t(z)</i> along the tooth width from the assembled 3D FE displacement field, thus eliminating the root causes of mismatch and contact concentration. Consequently, FEMM achieves lower peak stress and more uniform contact distribution under both assembly and loaded conditions. We also establish general criteria for operational stability and negligible secondary deformation, and propose a process-oriented FEMM workflow to provide transferable design guidelines across tooth profiles, tooth widths, and material parameters. For manufacturability, <i>t(z)</i> is parameterized as a three-station, low-degree spline with end weighting to ease machining and inspection. Compared with the linear method, FEMM only adds one assembled field extraction and one curve-fitting/verification step, resulting in limited additional computational cost.</p>

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Research on tooth profile modification of composite cycloidal harmonic drives

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Gao Ma,
  • Wei Wang,
  • Ronggang Yang,
  • Kai Song,
  • Zeyi Yao,
  • Haibing Li,
  • Jingyu Li

摘要

To address the gear interference problem in harmonic drive (HD) flexsplines (FS) during meshing transmission caused by tooth profile axial inclination after wave generator (WG) assembly under actual working conditions, this study focuses on composite cycloidal tooth profiles. Two methods, namely the linear modification(LM) method and the finite-element-method-based tooth profile modification (FEMM, defined as the construction of nonlinear axial modification along the tooth-width direction from the assembled finite-element displacement field), are employed, and MATLAB is used to simulate and analyze the pre- and post-modification motion trajectories. Finite element analyses were then conducted on HD models with linear method modification, finite element method modification, and unmodified profiles, comparing deformation and stress conditions during assembly and loaded operation. Due to the assembly-induced axial displacement being nonlinear along the tooth width and coupled with angular position (θ), linear approximation causes end-region mismatch, leading to secondary deformation and contact concentration. Accordingly, we adopt a FEMM that directly constructs nonlinear axial modification t(z) along the tooth width from the assembled 3D FE displacement field, thus eliminating the root causes of mismatch and contact concentration. Consequently, FEMM achieves lower peak stress and more uniform contact distribution under both assembly and loaded conditions. We also establish general criteria for operational stability and negligible secondary deformation, and propose a process-oriented FEMM workflow to provide transferable design guidelines across tooth profiles, tooth widths, and material parameters. For manufacturability, t(z) is parameterized as a three-station, low-degree spline with end weighting to ease machining and inspection. Compared with the linear method, FEMM only adds one assembled field extraction and one curve-fitting/verification step, resulting in limited additional computational cost.