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i=1 ∂y ∆xi ∂x0i (1) According to the limit principle of the differential concept, the smaller the |∆xi|, the higher the degree of approximation of ∆y. Since the process size L can be regarded as a function of several dimensions l1, l2,..., In on the workpiece and the positioning element, ie L=F(l1, l2,...,ln). According to the standard position concept of workpiece positioning, let l1=l01±1â„2∆l1,l2=l02±1â„2∆l2,...,ln=l0n±1â„2∆ln. Since the dimensional deviation ∆li is much smaller than the basic size (average size) l0i, the differential approximation formula (1) can be used to calculate the positioning error, ie ∆L=2 n
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i=1 ∂L ∆li = n
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i=1 ∂L ∆li ∂l0i 2 ∂l0i (2) The following describes the application of the localization error differential calculation method through a calculation example. Example 1: As shown in Figure 1, the circular surface of the disc-shaped workpiece rests on two cylindrical pins of the new V-shaped iron. The process dimension H is the center distance between the processed hole and the workpiece. Obviously, the workpiece center O is the process reference. The differential method is used to calculate the positioning error. The functional expression of process dimension H is H=h-OA=h-1â„2[(D+d)2-b2]1â„2 (3) where: d—two cylindrical pin diameters b—two cylindrical pin center distances h ——The distance from the axis of the machine tool to the center of the two pins is d, b, h are constant, D=D0±1â„2∆D is a variable, so the process dimension H is a function of the diameter D of the workpiece, according to formula (2) (3) Derivative derivative H=-1 D0+d ∆D=∆D=∆D 2 [(D0+d)2-b2] 1â„2 2{1-[b/(D0+d)]2]} 1â„2 2cosa0 (4) where d0=arcsin[b/(D0+d)] The negative sign after the first derivative in equation (4) indicates that the process dimension H decreases with increasing D. The final result of equation (4) shows that for a certain batch of workpieces, positioning errors can be calculated using a similar method when using the traditional V-shaped iron when positioning with the new V-shaped iron. In order to improve the positioning accuracy of the fixture, the value of a0 should be properly selected. 
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Differential calculation method for positioning error
When designing the fixture, the positioning error must be analyzed and calculated. When the process size is a linear relationship with the positioning reference, the positioning error is equal to the sum of the reference misalignment error and the reference displacement error, and the calculation is relatively simple. However, for the plane size system and the space size system, the calculation of the positioning error becomes more complicated due to the inconsistency of the size direction and the existence of an angle error. The application of positioning error differential calculus can make the above problems easier to solve. The positioning error differential calculation method is the application of the principle of differential approximation calculation of higher mathematics. Let the function y=F(x1,x2,...,xn), when the independent variables x1,x2,...,xn are in the variation of x01,x02,...,x0n |∆x1|,|∆x2|,..., When ∆xn| is small, the variation of y can be approximated as full differential ∆y= n