This chapter contains sections titled:
Decomposition of the Transmission Error into its Constituent Components
Transformation of Locations on Tooth Contact Lines to Working‐Surface Coordinate System
Fourier‐Series Representation of Working‐Surface‐Deviation Transmission‐Error Contribution
Fourier‐Series Using Legendre Representation of Working‐Surface‐Deviations
Fourier‐Series Representation of Normalized Mesh Stiffness KM(s)/K̄M
Approximate Evaluation of Mesh‐Attenuation Functions
Accurate Evaluation of Fourier‐Series Coefficients of Normalized Reciprocal Mesh Stiffness K̄M/KM(s)
Fourier‐Series Representation of Working‐Surface‐Deviation Transmission‐Error Contributions Utilizing only Real (Not‐Complex) Quantities
Appendix 7.A. Integral Equation for and Interpretation of Local Tooth‐Pair Stiffness KTj(x, y) Per Unit Length of Line of Contact
Appendix 7.B. Transformation of Tooth‐Contact‐Line Coordinates to Cartesian Working‐Surface Coordinates
Appendix 7.C. Fourier Transform and Fourier Series
Appendix 7.D. Fourier Transform of Scanning Content of the Line Integral (Equation (7.24b,c)) fj(s)≜ secψb ∫yA(s)yB(s) fCj(y, βs + γy) dy
Appendix 7.E. Fractional Error in Truncated Infinite Geometric Series
Appendix 7.F. Evaluation of Discrete Convolution of Complex Quantities Using Real Quantities
References
Transmission‐Error Decomposition and Fourier Series Representation
Performance‐Based Gear Metrology ; 165-240
2012-11-23
76 pages
Article/Chapter (Book)
Electronic Resource
English
Legendre representation, locally‐stiffness‐weighted deviations , tooth‐contact‐line coordinate transformation, to Cartesian , transmission‐error decomposition, and Fourier series representation , single gear transmission error decomposition, from equispaced involute , mesh‐attenuation function, approximate evaluation , tooth deviation fluctuation, equaling gear rotation period , mathematical form of mesh‐attenuation function , tooth‐working‐surface lines of contact, and location transformation , mesh‐attenuation functions, generic form , transmission‐error prediction, in “time” and “frequency”
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