| This paper mainly introduces how to create the general geometric error model forthree axis CNC machine tool,the corresponding implementation in terms of softwareerror compensation method and do some simulations for validation by the matlabsoftware. First of all, on the basis of the existing research In the domestic andoverseas, this paper describes and summarizes the basic movement structure of CNCmachine tools by using the topological structure and the low-order body arrays ofmulti-body system theory. Based on this and combining the description method ofhow to build between two adjacent typical body applied in the multi-body systemtheory, this paper deduces and presents the mathematic expression of the displacement,velocity and acceleration describing the relative position and displacement when anytypical body of the multi-body system is in any position relating to a coordinatesystem.At the same time,the Denavit Hartenberg homogeneous transformation matrixis introduced in this paper, a matrix containing the location and orientationtransformation relationship between adjacent body. So far, the theory of multi-bodysystem kinematics suitable for mechanical system is described and summarized.According to the feature and movement principle achieved by analysing theCNC machine working procedure, the paper demonstrates CNC machine is a specialkind of open-loop multi-body system. Therefore, CNC machine tool having twobranches of multi-body system can be described and analysed as a multi-bodysystem,which we can see consists of workpiece-frame branch and machine-toolbranch.Then,based on the multi-body system theory,this paper presents a generalkinematic model in which the geometric errors are taken into consideration for thethree axis CNC machine.After that,considering the condition the CNC can producemore precise workpiece and its corresponding mathematics equations,this paperdemonstrates that how the geometric errors affect the defaults made by the CNCmachine while machining the workpiece.Then,taking the XD-40A three-axis CNC milling machine for example, themulti-body system theory is applied in the machining process.Combining the actualwork procedure of the target machine, the paper establishes machine tool geometricerror model.Based on the previous conclusion, the necessary condition for thefinishing line of the target machine tools, and ultimately derives the mathematicalrelationship among the ideal tool path, the corrected CNC instructions, and actual tool path.At last, the paper introduces the method of line9to the quick recognition andmeasurement of21items of geometric errors existing in the three-axis CNC millingmachine,and gives the analysis method of error compensation and calculation method,providing a theoretical basis for the implementation of software error compensation,according to the numerical control machine tool of three basic movements.At last,after reading the error data measured on the XD-40A machine and idealtool route,this paper presents the three corresponding results simulated byprogramming in the matlab software.Finally,by comparing the three results with eachother,the research route and corresponding method applied in this paper are properand effective. |
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