| 2025 action plan of China emphasizes the high-precision machining strategy of sculptured surface.This paper aims to obtain and analyze the mathematical model of machining quality.Then comprehensively evaluate the quality of the processed surfaces by calculating the uncertainties of errors.The profile error,roughness error,waviness error and their uncertainties are calculated,which can provide the fundamental basis and improvement idea of evaluating the machining quality.The main work is shown as follows.For the profile error,the mathematical model is obtained.The sequential quadratic programming is adopted to calculate the nearest point and the optimal transformation matrix.Then the profile error is obtained.The formula of uncertainty is also obtained by the improved second-order GUM.For the roughness error,the Rz is calculated by Gaussian filtering and B-spline smoothing filtering respectively.Then the middle lines are simulated by the quadratic curves near the locations of crest and trough.The mathematical model of roughness Rz is obtained according to the expression of the middle lines.Finally,the uncertainty of roughness is calculated by GUM.For the waviness error,its mathematical model has some similarities with roughness error.The waviness error and its uncertainty are calculated according to the formula of roughness.Lastly,S-type specimen is adopted to calculate the profile error,waviness error and their uncertainties.For the roughness and uncertainty: when the surface is smooth,the roughness standard sample piece is used to evaluate the roughness and uncertainty according to the Gaussian filtering;when the surface is coarse,S-type specimen is used to evaluate the roughness and uncertainty according to the B-spline smoothing filtering.By improving the method of error evaluation,the precision of error evaluation is improved.The improved method provides a basis for high quality and high precision machining of sculptured surfaces. |
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