A Shannon sampling approach to form error estimation

2002 ◽  
Vol 216 (2) ◽  
pp. 225-233 ◽  
Author(s):  
T-H Yang ◽  
J Jackman
Keyword(s):  
Error Estimation ◽  
Form Error ◽  
Sampling Approach

Co-Kriging Method for Form Error Estimation Incorporating Condition Variable Measurements

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Shichang Du ◽  
Lan Fei
Keyword(s):  
Spatial Correlation ◽  
Spatial Statistics ◽  
Error Estimation ◽  
Surface Form ◽  
Form Error ◽  
Machining Processes ◽  
Machining Conditions ◽  
Machining Errors ◽  
Part Surface ◽  
Cross Variogram

The form error estimation under various machining conditions is an essential step in the assessment of product surface quality generated in machining processes. Coordinate measuring machines (CMMs) are widely used to measure complicated surface form error. However, considering measurement cost, only a few measurement points are collected offline by a CMM for a part surface. Therefore, spatial statistics is adopted to interpolate more points for more accurate form error estimation. It is of great significance to decrease the deviation between the interpolated height value and the real one. Compared to univariate spatial statistics, only concerning spatial correlation of height value, this paper presents a method based on multivariate spatial statistics, co-Kriging (CK), to estimate surface form error not only concerning spatial correlation but also concerning the influence of machining conditions. This method can reconstruct a more accurate part surface and make the estimation deviation smaller. It characterizes the spatial correlation of machining errors by variogram and cross-variogram, and it is implemented on one of the common features: flatness error. Simulated datasets as well as actual CMM data are applied to demonstrate the improvement achieved by the proposed multivariate spatial statistics method over the univariate method and other interpolation methods.

Sampling strategy and error estimation for evaluation of quadratic form error using Cartesian coordinate data

2017 ◽  
Vol 11 (7) ◽  
pp. 839-846 ◽  
Author(s):  
Liu Fei ◽  
Liu Dan ◽  
Liang Lin ◽  
Xu Guanghua ◽  
Zhang Qing ◽  
...  
Keyword(s):  
Quadratic Form ◽  
Error Estimation ◽  
Sampling Strategy ◽  
Form Error ◽  
Cartesian Coordinate ◽  
Coordinate Data

scholarly journals A Probabilistic View of Problems in Form Error Estimation

1997 ◽  
Vol 119 (3) ◽  
pp. 375-382 ◽  
Author(s):  
Tai-Hung Yang ◽  
J. Jackman
Keyword(s):  
Error Estimation ◽  
Surface Characteristics ◽  
Sampling Techniques ◽  
Discrete Point ◽  
Form Error ◽  
Estimation Errors ◽  
Form Errors ◽  
Form Tolerance ◽  
Surface Profiles ◽  
Selection For

Form error estimation techniques based on discrete point measurements can lead to significant errors in form tolerance evaluation. By modeling surface profiles as random variables, we show how sample size and fitting techniques affect form error estimation. Depending on the surface characteristics, typical sampling techniques can result in estimation errors of as much as 50 percent. Another issue raised in the fitting approach is the metric p selection for the fitting objective. We show that for p = 2 and p = ∞, the selection does not appear to significantly affect the estimation of form errors.

scholarly journals Form Error Estimation Using Spatial Statistics

1999 ◽  
Vol 122 (1) ◽  
pp. 262-272 ◽  
Author(s):  
Tai-Hung Yang ◽  
John Jackman
Keyword(s):  
Error Estimates ◽  
Statistical Methods ◽  
Spatial Statistics ◽  
Error Estimation ◽  
Manufacturing Processes ◽  
Form Error ◽  
Essential Step ◽  
Large Sets ◽  
Uniform Sample ◽  
Estimate Form

Form error estimation is an essential step in the assessment of product geometry created through one or more manufacturing processes. We present a new method using spatial statistics to estimate form error. Using large sets of uniform sample points measured from five common machined surfaces, we compare the form error estimates using individual points and fitted surfaces obtained through spatial statistical methods. The results show that spatial statistics can provide more accurate estimates of form error under certain conditions. [S1087-1357(00)01701-9]

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