Research On Uncertainty Of Measurement Result Of Form Error And Its Application

Form errors of machinery parts and other industry products are caused by the inexactness of manufacturing. They have great influence to the product performance and assemble quality,and must be inspected and controlled. The measurement uncertainty must be included in the measurement result of form error. But until now,unfortunately,the method for estimating the uncertainty of measurement result of form error has not been researched and developed systematically. Research on the method for estimating the uncertainty of measurement results of form error is one important subject in the field of metrology and measuring error theory.Relative problems about the uncertainty of the measurement result of form error are researched to some extent in this paper. First,the research status of home and abroad on this subject are surveyed and analyzed. Some methods and theories,such as normal distribution,non-normal distribution theories,least-square theory,maximum entropy method(MEM),Monte Carlo method,order statistics,bootstrap method and so on,are used to analyze the factors that influence the measurement result of form error,and to search ways or methods to estimate the uncertainty of the measurement result of form error validly and reasonably.The main results of research and creative achievements are as follows:(1) The measurement methods of form error are summed and sorted. The uncertainty estimations of the direct measurement result of measurement point for different items of form error are analyzed and studied in detail,and corresponding uncertainty estimation formula are presented. By means of the method of multi-variance linear least-square theory,the covariance between the direct measurement result of measurement points of straightness and flatness are calculated. Probability distributions of uncertainty of the direct measurement result of measurement point and other measurement data are discussed with MEM. It's reasonable that the uncertainty distribution of instrument reading data at measurement point is regarded as uniform distribution,and the uncertainty distribution of direct measurement result of measurement point is regarded as normal distribution.(2) The problems of uncertainty estimation are analyzed in detail when measurement results of form errors are evaluated with the methods of least-square and minimum zone. A series of uncertainty propagation formulas of form error items are deducted under the condition of linear evolution model. When the evolution model is non-linear,an estimation method -Monte Carlo method is proposed to simulate the data and calculate the uncertainty of the measurement result of form error. An uncertainty estimation theory-bootstrap is introduced and analyzed.(3) According to the evaluation models of form error,the probability distribution types of form error are researched,and the uncertainty of measurement result of form error is estimated with them. By inspecting the total distribution of form deviation,the reasons are analyzed. The conclusions are different between the uncertainty distributions gained by use of order statistics and evolution model method of form errors. The application conditions are presented.(4) The influences of quantities and the distribution strategy of measurement points to the uncertainty of form error measurement results are also studied. According to frequency spectrum analysis of form errors,a general principal of deciding quantities of measurement acquisition points is confirmed. The relationship between the number of measurement points and measurement results are analyzed. Some estimation methods are proposed to estimate the uncertainty caused by different number of measurement points. And the reasons are also analyzed that different distribution strategies cause different measurement results.(5) Some problems associated with the combined uncertainty and expanded uncertainty are researched. When the measurement result is effected by the number of measurement points that causes the differential between actual value and meas...