A New Unified Method of Calculating Form Error Based on Rigid-body Moving

摘要

Because the geometric shapes of minimum zone of various form errors are different, so the mathematic expressions for calculating form error are different, which is inconvenient for application in measurement of form errors. Finding a unified method of calculating form errors is necessary. To assort form errors according to their true features, aiming at one category that its true features have single geometric center, a new unified calculation method of form error called rigid-body moving was proposed, which accord with the criterion of minimum condition. According to this new method, firstly set the single geometric center of true feature on coordinate axis or coordinate plane or coordinates origin in 3D rectangular coordinates, and then build a unified mathematic model searching for the target location of minimum zone through translating and rotating the rigid-body composed by real features, thus realize calculation of form errors in a unified method. Because the form error objective functions have single valley character, it is proved that the results of form error monotonously converge to the accurate solution, and the effective moving steps depend on the deviation between the initial position and ideal position of rigid-body. And this calculation method and its conclusion were verified by actual examples, it has meaning of theory research and value of engineering application.