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With the rapid development of science and technology, there is an increasing demand for the measurement of gears. Now, the cylindrical gears with 1 to 3 levels of measurement accuracy have been manufactured by Changchun Institute of Optics and Fine Mechanics. However, at present, the gear measuring instruments at home and abroad can only measure cylindrical gears of 2~5 grades.
In 1970, China first researched the "gear single-sided meshing overall error measurement technology. 1. Its advantage is that the measured gear is meshed with the measuring gear (or measuring worm) on one side, the measurement process is closer to the use process, and the measurement result can be continuous. It reflects the error of all the meshing points of the whole gear (including tangential error and radial error), which can more fully reflect the transmission quality of the gear. It can also measure the tooth profile error when using the inter-tooth measurement method. The measurement technology can only measure the tooth profile error of the 5-stage accuracy cylindrical gear. For this reason, we propose a three-point method gear full harmonic error separation technology based on the research of gear single-sided meshing overall error measurement technology. The technology is implemented on a single-sided meshing integral error measuring instrument with a grating gear. It is picked up by three static grating reading heads installed at the instrument moving grating and a static grating reading head installed at the measuring worm moving grating. The signal is compared with the phase, and the error is separated by the three-point method in the rotation of the measured gear, and the system error of the instrument shaft measurement chain and the measured gear can be separated.
2 Measurement principle 2.1 Gear single-sided meshing overall error measurement technology Received: 200 Bu 08-01 Northwestern Polytechnical University, professor, male, 70 years old, 70007 is the involute profile of the gear in polar coordinates. From the geometric relationship, the radius of the base circle, Mm;: "involute expansion angle, rad;" - the involute pair represents the single-bit error curve of the gear in polar coordinates.
Equation (3) is expanded into a Fourier series, that is, a Fourier coefficient. Equation (4) can be used for harmonic analysis.
(or the tangential comprehensive error curve of the base circle) is shown in the single-bit error curve in Cartesian coordinates: AF. All-direction comprehensive error, Mm; today's one-to-one tangential integrated error, Mm; a gear pressure angle.
In order to be able to measure the full tooth profile error of each tooth of the gear, the inter-tooth measurement method of the gear single-sided meshing overall error measurement technique can be utilized. In the interdental measurement method, a multi-head (double or triple) measuring worm is used as the measuring element. This measuring worm leaves only one head for the working tooth surface, and the tooth surface of the other head is worn low and does not participate in the meshing. Therefore, the measuring worm and the measured gear are actually inter-toothed. In this way, the degree of coincidence is less than one, so that the overall error curve can be meshed at the full tooth height, and the full tooth profile error curve (including the top edge meshing error curve of the measuring component and the gear) is measured.
In addition, in addition to reading (tangential integrated error) f (one tooth tangential integrated error), it is also possible to read APp (tooth pitch cumulative error) and Pt (tooth pitch deviation) today > (tooth shape error) and The error value of the error item such as Pb (base deviation).
However, the gear single-sided meshing overall error measuring instrument used today cannot meet the requirements of precision gear measurement due to the existence of instrument shaft measuring chain error (including measuring worm error, grating sensor error, bearing rotation error, etc.). For example, the domestically produced CD320G-C type grating gear single-sided meshing integral error measuring instrument and CZ450 gear overall error measuring instrument can only measure the tooth profile error of the 5-level accuracy cylindrical gear; the German-made 891E type is gradually opened. The line inspection instrument and the SP60 type involute inspection instrument made in Switzerland can only measure the tooth profile error of the 2-stage accuracy cylindrical gear. To this end, we have studied the three-point method gear full harmonic error separation technology to meet the requirements of precision gear measurement based on the research of gear single-sided meshing overall error measurement technology.
2.2 Three-point method gear full harmonic error separation technology 2.2.1 Measurement principle See the three-point measurement principle of the complete harmonic error of a gear on a single-sided meshing integral error measuring instrument. In the middle, O is the intersection of the axes of the three static grating reading heads (A, B and C) at the gear moving grating, with O as the pole, and the axis of the static grating reading head A is the polar axis OX to establish a polar coordinate system.
The angle between the static grating reading heads A and B is 5A and the angle between C is 7, OP is the radial direction, 0 is the polar angle, and Y is the base circle radius. Let g(0) be the total harmonic error of the measured gear, and s(0) be the systematic error of the instrument shaft measurement chain.
During the measurement, the instrument table rotates clockwise. The three-point measurement principle diagrams A, B, and C three static grating read heads are respectively compared with a static grating read head installed at the measuring worm moving grating through three phase meters. The composite error output by each phase meter is the A/D conversion of the combined error of the three phase meter outputs. The discretization of equations (5), (6) and (7) is (S2n)s; qq /s is an irreducible true fraction, and after the influence of q=)sin(2:n/t), the translational characteristic of the Fourier transform can be used to make the discrete Fourier transform on both sides of the equation (1). Y1. When W(k) ping 0 and p/s and q/s are irreducible, the inverse harmonic Fourier transform can obtain the full harmonic error of the measured gear to substitute g(n) ( 8), the systematic error of the instrument shaft measurement chain is the discrete Fourier inverse transform