Tool radius compensation based on tool radius compensation

In the precision CNC machining, when the CNC interpolation method is determined, one of the main factors that affect the machining accuracy is the rigidity of the processing system, and the rigidity is insufficient, causing the knife to be caused, thereby causing a machining error. Therefore, when programming in CNC, not only the radius compensation of the tool should be considered, but also the tool compensation due to the force of the tool should be considered. In this paper, a method of dynamically compensating the tool radius considering the tool radius compensation is given. It has been successfully applied to the surface machining of the vacuum pump rotor in a certain factory. 1 Tool radius compensation When machining the workpiece profile, the tool used always has a certain tool tip arc radius. This is a factor that must be taken into account in precision machining. Therefore, the tool trajectory at the center of the tool arc is not the actual profile of the workpiece. But it's the isometric line L2. Therefore, it is necessary to program according to the contour of the workpiece contour (Figure 1).

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Fig. 1 Tool nose arc radius and equidistance line

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Figure 2 Equidistance line

Let the profile line of the workpiece be l, and the radius of the tool arc is r. Let l move every point along the normal direction of this point by a distance r to get a new point. The trajectory of these new points is called l, etc. From the line, which is the trajectory of the center of the tool nose. As shown in Fig. 2, l is a known curve, p is an arbitrary point on it, its unit normal vector is n, and the point on the normal line whose length is equal to r is pe. When point p moves along the curve, normal The direction of the vector changes, and the line le of the point pe on each normal line is the equidistance line of l. Obviously, take a point in the negative direction of n, then the curve formed by this point is also the equidistance line of curve 1. When le is outside the curve l, it is called outer equidistance line (machined convex surface), le is called inner equidistance line (machined concave surface) when inside l. Let the equation of the curve l be s=[f(t),g(t)]. In the case of plot p, the tangential slope of the p point is tga= dy = dy/dt = g'(t) dx dx /dt f'(t) (1) Obtained by formula (1)

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Cosa= 1 = f' (1+tg2a)1⁄2 (f'2+g'2)1⁄2 sina= tga = g' (1+tg2a)1⁄2 (f'2+g'2)1⁄2 (2) It can be seen that the coordinate component of the normal unit vector n is {nx=-sina ny=cosa (3) According to the definition of the equidistance line, the trajectory of the center of the tool tip arc is {xe=x+rnx ye=y+rny (4 ) Substituting equations (2) and (3) into 1 Xe=x∓rg' (f'2+g'2)1⁄2 ye=y± rf' (f'2+g'2)1⁄2 (5) Equation (5) is the tool radius compensation formula. When machining a convex surface, Take the above symbol and take the following symbol when machining the concave surface. 2 The compensation of the knife quantity When the tool cuts the workpiece, due to the effect of the cutting force, there is a certain gap between the actual processing position and the theoretical position. We call this the difference between the cutting position and the theoretical position. During CNC programming, the tool amount should be compensated to improve the machining accuracy. As a special case, we first analyze the processing of the arc. As shown in Figure 3, the big circle represents the workpiece, and the three small circles represent the three different positions of the tool. Assume that the ABC arc is machined from A to C. The force of the tool at each point is as follows: A point { Fx = FB point { Fx = Fsina C point {Fx=0 Fy=0 Fy=Fcosa Fy=F Let ∆Xmax be the maximum amount of X-direction tool and ∆Ymax be the maximum amount of Y-direction tool, then let A, B, and C The quantity is A point {∆XA=-∆Xmax ∆YA=0 (6) B point{∆XB=-∆Xmaxsina ∆YB=∆Ymaxcosa (7) C point{∆XC=0 ∆YC=∆Ymax (8) ∆Xmax and ∆Ymax can be obtained by measuring special points (such as measuring the amount of A and C points). A positive value of ∆X means that the tool is positively oriented toward the X axis. Conversely, it means that the negative direction toward the X axis is that the tool: ∆Y is a positive value to indicate the positive direction to the Y axis, and vice versa means that the negative direction is set to the Y axis ( Same as below). Note that the positive and negative values ​​of ∆X and ∆Y are also related to a. From equation (2) we can see that the AC arc at any point makes the amount of cutters 1 ∆Xi=∆Xmaxsina=-∆Xmax g' (f'2+g'2)1⁄2 ∆Yi=∆Xmaxcosa=∆Ymax f' (f'2+g'2)1⁄2 (9) As a more general example As shown in Figure 4, point P0 is a point on the curve that facilitates measurement of the amount of tooling. In general, such a point can always be found. The knife quantity satisfies the following relationship: ∆X0=-∆Xmaxsina0 ∆Y0=∆Ymaxcosa0 (10) Pe is an arbitrary point on curve 1, and the amount of the knife at this point satisfies {∆Xe=-∆Xmaxsina ∆Ye= ∆Ymaxcosa (11) is available from equations (2), (10), and (11). The curve, the amount of the tool at any point is 1 ∆Xe= ∆X0g' = ∆X0· g' · (f'02+g'02)1⁄2 sina0(f'2+g'2)1⁄2 g'0 (f'2+g'2)1⁄2 ∆Ye= ∆Y0f' ∆Y0· f' · (f'02+g'02)1⁄2 cosa0(f'2+g'2)1⁄2 f'0 (f'2+g'2)1⁄2 (12)

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Figure 3 Stress conditions when machining arc ABC

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Fig. 4 Calculation of the average curve

It can be seen from equation (12) that as long as the coordinate value (X0, Y0) of the specific point P0 and the amount of the knife at this point are known, the amount of the knife can be obtained at any point. X0, Y0, ∆X0, ∆Y0 can be measured, so ∆Xe, ∆Ye can be found. 3 Conclusions The methods described in this paper have the following advantages in calculating the tool quantity: (1) Considering the influence of tool radius compensation: (2) Adopting a dynamic compensation method: (3) It is easy to understand and calculate. However, this method must measure the amount of knife at a specific point, and its accuracy is affected by the measurement error.

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