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1 Introduction
In the drilling process, the positional accuracy of the machined hole is affected by many factors, and the tooling error of the drill chuck is one of the influencing factors. In order to meet the positional accuracy requirements of the hole to be machined, the tool value error is generally calculated using the extreme value method. However, when the extreme value method is used, since the set limit state rarely occurs in actual machining of parts, the manufacturing precision and processing cost of the jig are improved. In addition, the extreme value method does not consider the influence of the assembly, so it is quite different from the actual situation. In this paper, after considering the influence of drill sleeve fitting and the actual distribution of component manufacturing deviations, a calculation method of tooling error is proposed, which is the real analysis method of tooling error of drilling fixture.
2 Influence of interference fit on the diameter of the cylindrical surface of the inner hole of the drill sleeve
The minimum theoretical shrinkage of the diameter of the cylindrical surface of the inner hole of the drill sleeve during the interference fit is caused by the radial interference of the outer cylindrical surface of the drill sleeve due to the specific interference fit between the drill sleeve and the clamp, so that the specific hole of the clamp is expanded, and the cylindrical surface of the drill sleeve is contracted. Let the theoretical radial pressure on the mating surface be P, and the theoretical shrinkage of the borehole diameter caused by P is e, according to the theory of elastic mechanics.
Where: p——the theoretical radial pressure on the concrete mating surface of the drill sleeve and the clamp (MN/m2)
D——unilateral interference (mm) for the specific fit of the drill sleeve and the clamp
Ei——Flexural modulus of drill sleeve material (MN/m2)
Ui - Poisson coefficient of drill sleeve material Ee - elastic modulus of clip material (MN/m2)
Ue - the specific material Poisson coefficient a - drill sleeve guide hole radius (mm)
B——the outer cylindrical surface radius of the drill sleeve (mm)
C——the specific equivalent radius (mm) of the clamp matched with the drill sleeve (C is equal to the minimum distance between the clamp and the center line of the drill sleeve mating hole to the outer edge of the clamp)
e——The theoretical shrinkage of the bore diameter of the drill sleeve caused by P during the interference fit. Substituting the formula (1) into the formula (2) (3)
make 
Then equation (3) can be simplified to
(4)
Actual shrinkage of the bore diameter of the drill sleeve during interference fit
During assembly, the peak of the microscopic unevenness of the mating surface of the drill sleeve will be flattened, so the actual interference after the drill fit is less than the theoretical interference, and the actual interference is calculated as follows: ds=d-h1 (R+Rze)=d-h2(R+R) (5)
d s = d - h 1 (R
In the formula, h1 and h2 are coefficients (when assembled by press-fit method, h1=1.2, h2=4.8; when assembled by temperature difference method, h1=h2=0).
According to formula (4) and formula (5), the formula for calculating the actual shrinkage of the inner diameter of the drill sleeve when the drill sleeve and the clip are specifically interference fit is
or
(6) 
Where: Rzi - surface roughness of the mating surface of the drill sleeve, microscopic unevenness, ten points height
Rze——the surface roughness of the specific mating surface of the clip is 10 o'clock height
Rai - the arithmetic mean deviation of the surface roughness profile of the mating face of the drill sleeve
Rae——the arithmetic mean deviation of the surface roughness profile of the specific mating surface of the clip
3 The calculation of the maximum probability of interference of the drill sleeve and the clamp in the actual state of the drill sleeve and the clamp are mostly single-piece small batch production, and the processing dimensional deviation is in accordance with the Rayleigh distribution, and the distribution density is
Where r is a random variable
S——parameter value According to the Rayleigh distribution formula, Dib=ESib-s axis=ESib-(1/3)Tib
D ib =ES ib - s axis =ES ib -(1/3)T ib (7)
Deb=EIeb+s hole=EIeb+(1/3)Teb
D eb =EI eb + s hole =EI eb +(1/3)T eb (8)
Where: Dib - the maximum probability deviation of the diameter of the outer diameter of the drill sleeve
Deb——the maximum probability deviation of the specific diameter of the hole
ESib - the upper and lower deviation of the outer diameter of the drill sleeve
EIeb - the upper and lower deviation of the hole diameter of the specific matching hole
Tib - diameter tolerance of the outer circumference of the drill sleeve
Teb——The diameter tolerance of the specific hole of the clamp is the maximum probability of unilateral interference when the drill sleeve and the clamp hole are matched. 
(9)
4 Calculation of the inner diameter of the drill sleeve under assembly
The diameter d of the inner hole of the drill sleeve is obtained by the maximum probability diameter of the inner hole of the drill sleeve minus the maximum probability of shrinkage of the bore diameter of the drill sleeve under the actual condition, and the comprehensive formula (8) and formula ( 9) The formula can be obtained as 
(10)
5 Real calculation of tool setting error of drilling machine fixture
Drill size maximum probability deviation
Since the production process of the drill bit is professional and mass production, the size distribution of the drill bit is normally distributed, and the maximum probability deviation is the intermediate deviation. The calculation formula is Dz=1â„2 (ESz+EIz).
D z =1â„2(ES z +EI z ) (11)
(11) where: Dz - the maximum probability deviation of the drill bit
ESz - the upper deviation of the drill bit
EIz - the lower deviation of the drill bit
The gap between the drill bit and the inner hole of the drill sleeve can be found by the formulas (10) and (11). The clearance between the drill bit and the inner hole of the drill sleeve is 
(12)
figure 1
Real calculation of tooling error of drilling machine fixture
As shown in Fig. 1, due to the existence of the gap D, the center line of the drill bit is skewed, thereby generating the machining hole position offset X (ie, the actual tool setting error), and the calculation formula is X=[(B+h+ H/2)/H]D (13)
Substituting equation (12) into equation (13) 
Where: B——Workpiece thickness (mm)
H——Drill sleeve height (mm)
H——the height of the chip removal space (mm)
6 Conclusion
Both theoretical analysis and processing practice show that the actual analysis method of the tooling error of the drilling fixture considers the influence of the interference fit of the drill sleeve, and also considers the actual distribution of the manufacturing deviation of the components that affect the tooling error. The extreme value method is more in line with the actual situation.
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