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Calculation of positioning error of V block

  Calculation of positioning error of V block

  There are two ways to calculate the positioning error of V block, which are synthesis method and limit position method. The author has used the function method to deduce the location error formula. The method is simple and practical. The limit position method and the function method have obvious advantages in calculating the combined positioning error.

  Here, the milling of keyway on cylindrical workpiece is taken as an example to illustrate the derivation of location error formula (only in vertical dimension requirements). See Figure 1, workpiece process drawing, keyway depth dimension can be marked in B1, B2, B3, three ways, the cylinder diameter is set to d0dd. Figure 2 shows the location of the workpiece on the V block, M as the reference and o as the center of the cylinder. The positioning errors dB1, dB2 and dB3 are calculated as follows:

  With the limit position method, the size of the B1 is A, and the positioning reference is M. Therefore, the error is the change of the AM size, while the error is the change of the dimension

  AM=OM-OA={d/[2sin (a/2) - (d/2)}

  So dB1=dd/2[1/sin (a/2) -1] (1)

  In the formula, the alpha is V block angle.

  The process standard for B2 size is O, and the positioning reference is M

  OM=d/[2sin (a/2)]

  DB2=dd/[2sin (a/2)] (2)

  The working standard of B3 size is C, and the positioning standard is M

  CM=OM+OC= (a/2) [1/sin (a/2) +1]

  Then dB3= (a/2), [1/sin (a/2), +1] (3)

  Function method

  The method is to establish a functional formula that requires the dimension to be guaranteed, and then to calculate the machining error by differentiation. Part of it is the location error.

  Use this method to determine when the first knife size, the traditional center of the workpiece positioning reference to knife block size as the knife size on the surface, as mentioned earlier, this method due to the influence of the position of a central line by the test error and uncertainty of mandrel diameter, the loss of precision, and is only two planes sure, so the impact on the D block size knife knife surface can be exempted from inspection accuracy of spindle. Then we can build the functions of B1, B2, and B3 as follows:

  B1=BM- (OM-OA) =h-{d/[2sin (a/2)]-d/2}

  B2=BM-OM=h-d/[2sin (a/2)]

  B3=OM+OC-BM={d/[2sin (a/2)]+d/2}-h

  The H is the size of the adjustment (tool), and these functions indicate that the depth dimension is a function of the tool size, the work diameter and the angle of the V block without considering the influence of other factors. We assume that the adjustment error is 0, and the V block angle absolute accuracy, then the keyway depth is only affected by the diameter of the workpiece. After differential, we can conveniently obtain (1), (2) and (3).