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The measurement of the diameter of the addendum circle and the root circle [1][2] first counts the number of gear teeth z, then measure da and df with a precision vernier caliper or micrometer, and measure several sets of data in different radial directions, and take the average.
Measuring the number of teeth, the diameter of the tip circle, the diameter of the root circle, the length of the common normal line, the calculation of the normal circular pitch, the table to determine the normal modulus and the pressure angle, the evaluation of the helix angle, the hobbing machine, the correction of the helix angle, the correction of the β after the difference The hanging wheel test z, da, dfWk, Wk-1Pb=Wk-Wk-1Mn/DP, aβ0=arccos[mnz/(da-2mn)]a, bβ=arctg(btgβ0±a)/b when the gear is being tested When the number of teeth is an odd number, the diameter of the tip circle cannot be directly measured. The value of Da in the first measurement can be measured, and the diameter da of the tip circle can be calculated by the formula (1) or (2).
Da=2secaDθ(1) where: arctan2abDθ=approximate algorithm: 90secadDz°=(2) Similarly, the approximation algorithm of the root circle is 90secfdDz°=(3) Measurement and calculation of the tip circle diameter For odd gears, d can be determined by the diameter d of the inner bore and the distance H1 from the inner bore wall to the crest and the df can be determined by measuring the diameter d of the inner bore and the distance H2 from the inner bore to the root. See, for example: Da=d 2H1(4)df=d 2H2(5) Measurement of the common height of the tooth height with a precision vernier caliper and determination of the base section According to the principle of the involute gear, the following formula for calculating the length of the common normal line: Wk=(k- 1) In Pb+Sb(6) where: Pb is the base circular pitch; Sb is the base circular tooth thickness; k is the cross-counting number.
When measuring the length of the common normal line, the common normal micrometer is generally used, and the appropriate number of teeth should be selected. If the number of teeth is too large, the claws are in contact with the top of the teeth, and vice versa, the contact with the roots of the teeth may cause inaccuracy. The selection of the number of teeth is calculated in many literatures, and often involves the coefficient of displacement and the height of the crown. However, in practice, it is only necessary to make the claws in contact with the middle of the teeth. The appropriate number of teeth across without having to calculate.
The measurement of the helix angle of the helix angle β includes the magnitude and direction of the helix angle, and the measurement of the size is divided into a coarse measurement and an accurate measurement.
The traditional method of coarse measurement of the helix angle of the helix angle β is the rubbing method. For the sake of convenience, the author recommends the calculation of the tip circle: according to the measured diameter of the tip circle, regardless of whether the gear is displaced or not. According to the formula, the calculation of the helix angle β0:β0=arccos[mnz/(da-2mn)] helix angle β is accurate. For gear processing, a hobbing machine is generally required. Therefore, the differential mechanism of the hobbing machine can be used to accurately measure the spiral. angle. The steps of measuring the helix angle of the gear hobbing machine are as follows: (1) Calculate the differential hanging wheel according to the spiral angle obtained by the rough measurement; (2) clamp the measured gear on the gear hobbing machine and align it; adjust the gear hobbing machine: hang the differential Hanging the wheel, at the same time, disengage the split tooth movement, so that the workbench only has additional motion, and ensure that the hob shaft can't rotate (otherwise it is not accurate), the hob holder can make vertical movement; fix the lever bar dial indicator in the roll On the tool holder, the probe is perpendicular to the middle position of the measured tooth surface, and the contact measurement is maintained throughout the measurement process.
Start the machine, move the tool holder vertically, record the fluctuation and change direction of the dial gauge reading, correct the helix angle, and then re-match the differential hanging wheel according to the corrected β value until the reading of the dial gauge is basically maintained. constant. The principle of the correction is as follows: The schematic diagram of the table rotation direction correction is based on the trigonometric function relationship: tgβ=(btgβ0±a)/b=tgβ0±a/b where: a is the reading variation, mm; b is The measured axial length, mm; β0 is the helix angle of the differential hanging wheel.
Conclusion The tip circle, the root circle diameter and the common normal length can be accurately measured, and the calculation method is simple. The hobbing machine can carry out the precise hanging wheel according to the helix angle. Therefore, the tooth profile measured by the above method is more accurate. Since the only parameters required in the process are selected from the manufacturing point of view, repeated derivation and calculation of other parameters are avoided, which saves a lot of time. This method is not only applicable to the mapping of a single helical gear of unknown standard, but also to other situations.
In addition, because of the equipment and measuring tools that must be used in gear machining, it is very practical for manufacturers with gear processing capabilities. The gears measured by this method, especially the gears in imported construction machinery, have good interchangeability and can replace imported parts and have achieved satisfactory results.