Error Modeling Of Run-out Based On Screw Theory And Influence Analysis Of Multi-Axis Machining

In multi-axis machining process,the phenomenon of cutter run-out caused by misalignment between the tool axis and the spindle axis is common and inevitable.It is liable to deteriorate the machining quality.Therefore,exploring the phenomenon of cutter run-out in multi-axis machining deeply has theoretical significance and practical value.The main work of this paper is as follows:1、Error modeling of cutting tool axis based on screw theory considering spindle motion error: Based on the five-axis CNC machine with dual rotary tables,the cutter run-out coupling principle of spindle axis is revealed,and the tool axis motion model is established based on screw theory.Finally,the cutter run-out error screw is defined which describes the position relationship between tool axis and spindle rotation axis.2、The position and orientation modeling of cutting tool axis based on cutter axis error: By increasing the instantaneous coordinates system(CST),the rotating coordinate system(CSR)and the transformational coordinate system(CSZ),the error screw is introduced to establish the machine kinematics model contains the spindle motion error.Then the error rule between the actual tool axis and ideal tool axis is analyzed.3、Modeling of cutter envelope based on cutter axis error: Taking a ball-end mill as an example,this paper deduces the equation of cutter envelope surface based on error screw by analyzing the envelope theory.In addition,the error rule of cutter envelope is solved via applying the distance function between actual envelope considering spindle motion error and ideal envelope.4、Cutting edge sweep surface modeling based on cutter axis error: Combined with the kinematics model of the machine tool,the rotating surface of the cutting edge of the ball cutter considering the spindle motion error is calculated.Then,the cross-sectional line of the cutting edge sweep surface on any layer is obtained by using the layered model.On the basis of upper work,precise geometric model of un-deformed chip is established.Meanwhile,the singlefactor method is used to analyze the influence of spindle motion error on the cutting edge trajectory section line and geometric model of un-deformed chip under different feed rates and layer heights.5、Experimental verification and example simulation: In order to obtain the parameters of the error screw model,parameter calibration process of the tool axis motion model considering the spindle motion error is introduced.Finally,the numerical examples are given to calculate the tool axis position error,tool movement envelope surface error,rotating surface error,cutting edge trajectory section line error and precise geometry error of the un-deformed chip between the two adjacent tool points.