Real analysis method of tool clamping error in drilling machine

1 Introduction In the drilling process, the accuracy of the position of the machined hole is affected by many factors. One of the influencing factors is the tool setting error of the drilling fixture. In order to meet the position accuracy requirements of the machined hole, the extreme value method is generally used to calculate the tool setting error. However, when calculated by the extreme value method, the set limit state rarely occurs during the actual machining of parts, resulting in an increase in the manufacturing precision and processing cost of the jig. In addition, the extremum method does not take into account the impact of assembly, so it is quite different from the actual situation. In this paper, after considering the impact of drilling sleeve fitment and the actual distribution of manufacturing deviations of various components, a calculation method for tooling error is proposed, which is a real-state analysis method for tool setting errors in drilling fixtures. 2 Influence of interference fit on the diameter dimension of the cylindrical surface of drill sleeve inner hole When the interference fit, the minimum theoretical shrinkage of the diameter of the cylindrical surface of the drill sleeve is caused by the interference fit between the drill sleeve and the clamp. The expansion of the specific hole of the clamp, the cylinder surface of the drilling sleeve hole shrinks. Let the theoretical radial pressure on the mating surface be P, and the theoretical shrinkage of the inner diameter of the drill sleeve caused by P should be e. According to the theory of elastic mechanics, we can see that

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(1)

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(2) In the formula: p——theoretical radial pressure (MN/m2) on the specific mating surface of the drill sleeve and clamp d—the unilateral interference amount (mm) of the drill sleeve and the clamp specific fit Ei—the drill sleeve Material Elastic Modulus (MN/m2) ui——Bosborne Coefficient of drill collar material Ee——Clamp concrete material elastic modulus (MN/m2) ue——Clamp concrete material Poisson coefficient a——Drill collar radius ( Mm) b—Diameter of outer cylindrical surface of drill sleeve (mm) c——specific equivalent radius (mm) of the clamp matched with the drill sleeve (C is equal to the minimum distance between the centerline of the clamp fitting hole and the outer diameter of the fitting hole of the drill sleeve) e——Theoretical shrinkage of drill hole diameter caused by P during interference fit. Substituting equation (1) into equation (2). (3)
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Then formula (3) can be simplified as (4) The actual shrinkage of the inner diameter of drill sleeve during interference fit. During assembly, the peak of the microscopic roughness of the mating surface of the drill sleeve will be flattened, so the actual amount of interference after assembly of the drill sleeve is smaller than theoretical interference. The amount of actual interference is calculated as follows: ds=d-h1(R<sub>+Rze)=d-h2(R<sub>+R<sub>) (5)
In the formula, h1 and h2 are coefficients (when assembling by press fitting, h1=1.2, h2=4.8; when assembled by temperature difference method, h1=h2=0). According to equations (4) and (5), the formula for the actual shrinkage of the diameter of the inner diameter of the drilling sleeve when the drilling sleeve and the clamp is specifically in interference fit is
or (6) In the formula: Rzi——Roughness of the surface of the drill sleeve mating surface is 10 points high Rze—The surface roughness of the mating surface of the mating surface is slightly uneven. The height of ten points Rai—The surface of the mating surface of the drill sleeve is rough. Degree of Arithmetic Arithmetic Mean Deviation Rae - Arithmetic Mean Deviation of the Surface Roughness Contour of the Specific Matching Surface 3 The Calculation of the Maximum Probability of the Actual Drilling Sleeve and Clip The calculation of the interference amount The drill bushes and clamps are mostly single-piece and small batch production. , The processing size deviation is in accordance with the Rayleigh distribution, and the distribution density is

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Where r - random variable s - parameter value according to the Rayleigh distribution formula has Dib = ESib-s axis = ESib-(1/3) Tib (7) Deb = EIeb + s hole = EIeb + (1/3) Teb (8) Where: Dib——the maximum probability deviation of the outer diameter of the drill collar Deb——the maximum probability deviation of the specific fitting hole diameter ESib——the upper and lower deviation of the outer diameter of the drill sleeve EIeb——clamp specific The upper and lower deviations of the matching hole diameter Tib—the diameter tolerance of the drill sleeve outer circle Teb—the maximum probability of unilateral interference when the drilling sleeve and the clamp hole are mated with the diameter tolerance of the specific hole

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(9) 4 Calculation of the diameter of the inner drilling hole of the assembly under actual conditions The diameter d of the inner diameter of the drilling sleeve in the assembly state is calculated by subtracting the maximum probability diameter of the inner drilling hole of the drilling bush from the actual state. The maximum probability of shrinkage is obtained. The formulas (8) and (9) can be obtained as

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(10) 5 Actual calculation of drill tool clamping tool error The maximum probability deviation of drill bit size Since the drill bit production process is professional and mass production, the size distribution of the drill bit is a normal distribution, and the maximum probability deviation is the middle deviation. Its calculation formula is Dz=1⁄2(ESz+EIz) (11) (11) Where: Dz——the maximum probability deviation of 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 drilling hole is Equations (10), (11) can be used to find the gap between the drill bit and drill collar in the real state

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(12)

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figure 1

As shown in Fig. 1, the actual calculation of the tool clamping tool offset error is due to the existence of the gap D, which causes the centerline of the drill bit to be skewed. This results in the displacement of the machining hole position X (that is, the real tool offset error). For X=[(B+h+H/2)/H]D (13) Substituting Equation (12) into Equation (13) is available

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In the formula: B - workpiece thickness (mm) H - drill sleeve height (mm) h - height of the chip removal space (mm) 6 Conclusion Theoretical analysis and processing practices have shown that: due to drill tool clamp tool error real The analysis method considers the influence of the interference fit of the drill sleeve, and also takes into account the actual distribution of the manufacturing deviations of various components that affect the tool offset error, and therefore is more in line with the actual situation than the traditional extreme value method.

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