Algorithm For Form Error Evaluation Based On Chebyshev Approximation Theory

The modeling of form error associated with machinery and equipment is veryimportant for their performance and useful life. The mathematical model of the formerror is established, that satisfy definition and evaluating standards of form error.Moreover this dissertation research the algorithm overcomes the existing algorithmbug for form error evaluation base on Chebyshev approximation theory. Follow aremainly study contents in this paper.(1) This paper study and discuss the Chebyshev approximation theory and thistheory in form error estimation of the meaning and application, and improved that theapplication of the Chebyshev criterion is equivalent to the search for a minimum zone(MZ), which includes all measured data point. This paper design linear Chebyshevapproximation method and non-linear Chebyshev approximation method base onChebyshev approximation theory and the mathematical model of the form errorestimation.(2) This paper in turn set up the mathematic model of the form error，flatstraightness error, spatial straightness error, flatness error, circularity error, sphericityerror, cylindricity error and conicity error base on linear Chebyshev approximationmethod and non-linear Chebyshev approximation method, satisfying minimum zonecriterion. Then it discussed the calculating efficiency and performance of linearChebyshev approximation method and non-linear Chebyshev approximation method,and analyzes the applicable to the two algorithm’s best data collection points forbalance evaluation precision and algorithm efficiency.(3) Using Matlab, software of form error evaluating is developed. Modulestructure is adopted in this software and every element has one module. In order toimprove clear of the result, established the friendly visual interface, and design thefunction of data storage to meet users need.(4) Coordinate measuring machine is used to measure the coordinates of points atthe surface of the given workpieces, then the software of form error estimation is usedto evaluate the form error， i.e. flat straightness, spatial straightness, flatness,circularity, sphericity, cylindricity and conicity. The validity and accuracy of thealgorithms, the feasibility and practicability of software were proved trough theseexamples.