Kinematic error modeling and analysis of the loading device based on multi-body theory and stream of variation theory
Because of some reasons such as machining error and assembly clearance, the loading device will produce kinematic error during movement. While kinematic error will have a great significance on the position accuracy of the loading device. For the above reasons, firstly, the topological structure of the loading device was described based on lower body arrays. The kinematic error matrices of adjacent parts in the loading device were obtained by multi-body system kinematic theory and homogeneous translation matrix (HTM). Then an improved error modeling method was put forward, which combined multi-body system theory with stream of variation theory. And the kinematic error model of the loading device was set up with this method. Numerical results could clearly display the error transformation and propagation among components. Finally, the effect of every kinematic error on final deviation was analyzed, and error sources of a greater effect on the final deviation were obtained. This method can provide a theoretical basis to improve the accuracy of the loading device.
Modeling and analysis of the volumetric errors of four-axis polishing platform
The volumetric error of a four-axis polishing platform with two aerostatic stages driven by linear motors and two rotational stages is modeled considering both position error and direction error by multi-body system theory.The individual geometric errors of the motion parts are measured by laser interferometer.The measuring results indicate that,for aerostatic stage,the position error shows neither linear increasing nor decreasing trend;the vertical straightness is larger than the position error and the vertical st4 aightness,which is obviously different from the errors of traditional ball screw driven platform.The position component and direction component of the volumetric error of the resultant motion of two linear axes are investigated theoretically and experimentally considering the comprehensive influence of the individual geometric errors of the aerostatic stages.It is found that the vertical component of the volumetric error of the aerostatic stage is obvious.The causes of the geometric errors of the aerostatic stages are revealed,which provides the theoretical basis for geometric error compensation of the polishing platform.
Assessing geometrical errors of multi-axis machines by three-dimensional length measurements
In this paper a method is presented for assessing geometrical errors of multi-axis machines based on volumetric three-dimensional length measurements. A universal machine error model is proposed since a large variety of machine configurations exists. Such models can be used for software error compensation techniques in order to improve the machine’s positioning behaviour as well as for diagnostic purposes. Length measurements are chosen for the measurement of the positioning errors of a multi-axis machine because these measurements can be executed in a short period of time in a relatively simple way combined with a high accuracy. In order to get comparable results for the geometrical errors as measured with conventional techniques, i.e., laser interferometry, the design of the measurement setup as well as the formulation of the machine error model (including parameter correlation effects) appeared to be of major importance and are subject of this paper.