Analytical methods for spur gear time-varying mesh stiffness:principles and comparative analysis
LI Ziyuan
ZHOU Jianxing
ZHANG Jingqi
YANG Yuliang
ZHENG Guolong
Abstract：[Objective]The time-varying mesh stiffness of gears is influenced by multiple coupled factors,including initial parameters,assembly errors,overlap ratio,wear,and thermo-mechanical coupling effects.To address the ambiguity in applicability boundaries caused by the diversity of existing numerical calculation methods,several typical numerical approaches were systematically elaborated and compared based on the fundamental calculation principles of gear mesh stiffness.[Methods]Firstly,a parametric model was established using cylindrical spur gear pairs as the research object.Secondly,a finite element model was constructed based on the parametric model.Thirdly,employing modular object-oriented programming approaches,the selected typical numerical calculation methods(ISO 6336-1:2019 standard,Ishikawa method,Weber method,and potential energy method)were programmatically implemented.Finally,the finite element model was solved and numerical calculations were performed for each method,followed by comprehensive comparative analysis from multiple perspectives including time-varying mesh stiffness variation patterns,single tooth stiffness,compliance components,average mesh stiffness,and average single tooth stiffness.[Results]The study reveals that the ISO 6336-1:2019 standard demonstrates strong engineering applicability but fails to construct a time-varying model.The analytical method and finite element method share similar mechanical principles,yet their relative error reaches 14%due to model simplification and theoretical discrepancies.The compliance calculated by the analytical method exhibits a nonlinear increasing trend from the tooth root to the tip,aligning with mesh deformation patterns and validating its modeling rationality.However,model modifications are required for complex gears or special operating conditions to enhance adaptability.The potential energy method,which accounts for coupled tooth-body deformation,achieves a computational efficiency significantly higher than the finite element method while maintaining an error margin within 1%.This comparative study clarifies the distinctions and commonalities among algorithms,providing guidance for method selection and the development of high-precision,high-efficiency gear stiffness calculation models.
Keywords：Time-varying mesh stiffnessAnalytic methodFinite element methodIshikawa methodPotential energy methodWeber method
Publication Date：2026-08-15
Online Publishing Date：2026-09-12(First online date of this platform, not the publication date of the document)
Pages：11( 169-178,191 )