This kind of processing is approximate, because the arc string approximation is only the approximation of the curve in the two-dimensional sense, and the tool and the workpiece are three-dimensional bodies. The correct approximation error should be the maximum depth/undercut of the three-dimensional tool on the part surface. Said. The factors affecting its size are as follows: <2,3>: (1) the local geometry of the surface of the part; (2) the shape and size of the tool and the control mode of the tool axis; (3) the path of the tool on the surface; (4) ) The feed step size; (5) The structure and size of the rotating or swinging mechanism in the case of multiple axes. Three-coordinate general tool machining nonlinear error analysis and tooling step theory tool path <4> Three-axis machining theory tool path In the case of three-axis machining, the tool axis orientation is unchanged, and the tool motion is parallel to the z-axis. In the general tool motion description, the tool-surface meshing relationship is as shown. Let r(s) be any curve on the surface (s is the arc length parameter), and the m point on the tool axis is used as the reference point (tool point) for determining the tool motion, then the tool is cut along the r(s) The trajectory rm(s) is rm(s)=r(s)+R1n(s)+(R2+R1)nxy(s)/nxy(s) where n(s) is the surface unit normal vector at the cutting point Nxy(s) is the calculation expression of the component 2.2 nonlinear error on the xoy plane. As shown, let r0 and r1 be the two points on the curve r(s), where the arc length parameter r=0 at r0, r1 The arc length parameter is s1, and rm0 and rm1 are respectively corresponding tool point points, and the tool performs linear interpolation motion between the two points. In the linear interpolation process, for any meshing point rs (the arc length parameter is s, corresponding to the ideal tool position is rms), since the interpolation straight line deviates from the theoretical trajectory, considering the normal processing, the interpolation line has the largest rs on the interpolation line. The corresponding tool position rls cut or undercut can be determined by the following method. The rms point on the curve rm(s) is set and parallel to the plane passing the rs point and along the normal plane in the rs direction is the plane II, and rls is approximated by the intersection of the plane II and the line rl(t). Three-axis machining nonlinear shape error description The equation of the straight line rl(t) is rl(t)=rm0+t(rm1-rm0)0≤t≤1 The equation of plane II is (r-rms)rs=0Set rls The parameter is ts, then Substituting it into (1) gives ts=(rm0s+12rm0s2)rs(rm0s1+12rm0s21)rs(2) because rm=rs+R1n+(R2-R1)nxy/nxy so rm0=r0+R1n0+(R2-R1) (nxy/nxy)'rm0=r0+R1n0+(R2-R1)(nxy/nxy)" again rs=r0+sr0r0=r0=knn=-kn-gvn=-kn-gv-(k2n+2g)n( Nxy/nxy)'=(1-n2z)nxy+nznznxy(1-n2z)3/2=-kn(1-n2z)1/2xy-g(1-n2z)1/2vxy-(knz+gvz)nz (1-n2z)3/2nxy(nxy/nxy)"=(1-n2z)2nxy+2(1-n2z)nznznxy+(nznz-n3znz+n2z+2n2zn2z)nxy(1-n2z)5/2=2nz( Knz+gvz)kn(1-n2z)3/2xy+2nz(knz+gvz)g(1-n2z)3/2vxy+(n2z-1)(k2n+2g)+(2n2z+1)(knz+gvz) 2(1-n2z)5/2nxy where a(ax, ay, az), v(vx, vy, vz), n(nx, ny, nz) are the local coordinate system axy, vxy of the surface at r0, Nxy is the component kn on the xoy coordinate plane, respectively. g is the normal curvature and short-range torsion of the surface at point r0 along the a direction. Substituting the above into equation (2) and ignoring the high-order small quantity ts≈{1-R1 -(R2-R1)}s{1-R1-(R2-R1)}s1≈s/s1 is rls=rm0+(s/s1)(rm1-rm0)≈rm0+srm0+(1/2)ss1rm0(3 It can be seen that the position deviation of the actual position rls from the ideal position rms is rlsrms=(1+2), where 2 is parallel to the normal vector ns at rs, and its size produces a normal machining error in a ratio of 1:1; 1 parallel to rs The tangent plane is the error-insensitive direction, and the machining error caused by the high-order small amount is negligible. Therefore, the normal machining error of the tool at the rs point is ≈2=rlsrmsns(4) because rlsrms =rms-rls=0.5(s2-sls)rm0rm0=r0+R1n+(R2-R1)(nxy/nxy)"=-R1kna-R1gv+ Max is max=(s21/8){-kn+R1(k2n+2g)-(R2-R1) Conclusion The reasonable determination of the step size is a fundamental and important issue in surface machining. The nonlinear error expression of the three-coordinate machining obtained in this paper is a strict tool envelope forming error in the three-dimensional sense. Its size is defined in the surface normal direction, taking into account the local geometry of the part surface, the tool shape size and the tool axis control parameters. The influence of the feed direction of the cutter improves the approximate expression of the two-dimensional arc string approximation commonly used in CAD/CAM. It can be applied to many types of cutters and has good versatility. (Finish) Aluminum Casting Parts,Nonferrous Castings,Aluminum Casting Alloys,Hydraulics Part Prototypes Guangdong Fenghua Zhuoli Technology Co., Ltd , https://www.fhzl3d-print.com