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以某生产厂家的一种车削加工中心为研究对象，根据齐次坐标变换原理，推导了该机床刀具与工件之间相对位移的动态关系式。此式包括了该机床几何误差和热误差中主要影响机床精度的１４个误差因子。经基于此误差综合数学模型的实时补偿，工件之间的尺寸变化从原来大于４０μｍ降低到１２μｍ。
Taking a turning machining center of a manufacturer as the research object, the dynamic relation of the relative displacement between the tool and the workpiece of the machine tool is deduced according to the principle of homogeneous coordinate transformation. This equation includes 14 error factors that mainly affect the accuracy of the machine during geometric errors and thermal errors. Based on the real-time compensation based on this mathematical model of error, the dimensional changes between the workpieces are reduced from more than 40μm to 12μm.