CN105300691B - Bevel Gear Transmission error measurement method based on best locating distance - Google Patents
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Abstract
Bevel Gear Transmission error measurement method based on best locating distance, including step：(1) bevel gear pair is subjected to gear single-flank testing mounted on the front end of measuring system live spindle to design locating distance, changes steamboat locating distance, is measured in multiple points, obtain the best locating distance of bevel gear pair；(2) after obtaining the best locating distance of bevel gear pair, gear single-flank testing is carried out on the position and draws driving error curve；(3) four basic deviations are extracted by calculating on driving error curve, and carries out the evaluation of accuracy class according to accuracy standard；(4) calculating such as Fast Fourier Transform (FFT), inverse fast fourier transform are carried out to driving error, obtains other several aberration curves, the transmission quality of gear pair is further analyzed.The present invention calculates driving error curve, analyzes, and obtains multinomial individual event deviation and curve, can more accurately evaluate the transmission quality of bevel gear pair.
Description
Technical Field
The invention relates to the field of precision testing technology and instruments, in particular to a bevel gear transmission error measuring method based on an optimal mounting distance.
Background
Bevel gear drives are widely used in the automotive, helicopter, machine tool and power tool manufacturing industries. The bevel gear pair is a basic element for realizing the transmission of the motion of the intersecting axes, and the manufacturing precision and the quality of the bevel gear pair directly influence the efficiency, the noise, the motion precision and the service life of machine equipment.
The transmission error is the difference of the actual displacement of the output end of the transmission system relative to the theoretical displacement. The manufacturing error of the gear in the processing process, the assembly error in the installation process, the temperature deformation and the stress elastic deformation in the transmission process all generate transmission errors, so the transmission quality of the gear can be evaluated and the error source can be diagnosed by measuring the transmission errors. The single-side meshing measurement movement is close to the use state of the gear, so that the transmission quality of the gear can be detected more efficiently and more accurately.
When the traditional single-face meshing method is adopted for measuring the transmission error, a standard gear is meshed with a gear to be measured, or a pair of bevel gear pairs is meshed. When a single bevel gear is measured in mesh with a standard gear or when a pair of bevel gear pairs is measured, the measurement according to the conventional method is not accurate enough. And the transmission stability of the bevel gear pair has a close relation with the mounting distance, and the most accurate measurement result can be obtained only by measuring the bevel gear pair at the position with the optimal mounting distance.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a bevel gear transmission error measuring method based on an optimal mounting distance.
The invention is realized by adopting the following technical means:
the bevel gear transmission error measurement method based on the optimal mounting distance is characterized by comprising the following steps of: the method comprises the following steps:
1) the bevel gear pair is arranged at the front end of a rotating main shaft of the measuring system according to the designed installation distance, and the installation distance offset and the searching times of the small wheel are set in the parameter setting of the installation distance searching. Then, single-side meshing measurement is carried out on each set point to obtain a transmission error curve of the bevel gear pair, FFT is carried out on the transmission error curve to obtain the first third harmonic amplitude of each point of the transmission error curve, and then the optimal mounting distance of the bevel gear pair is obtained through calculation of the harmonic amplitudes;
2) after the optimal mounting distance of the bevel gear pair is obtained, adjusting the positions of the two gears to enable the gear pair to be meshed at the optimal mounting distance, then carrying out single-side meshing measurement, measuring the rotation angle value of the two gears through a circular grating which is arranged on a rotating main shaft and is close to the bevel gear, and obtaining a transmission error curve of the bevel gear pair through calculation;
3) calculating a transmission error curve, extracting four single deviations which are respectively tangential comprehensive total deviation of the gear pair, tangential comprehensive deviation of one tooth of the gear pair, accumulated total deviation of tooth pitch and accumulated deviation of single tooth pitch, and evaluating the precision grade;
4) and further calculating and analyzing the transmission error curve to obtain other deviation curves which are respectively as follows: a rotating harmonic curve, a pitch cumulative deviation curve, an average tooth profile error curve, a long wave component curve, a short wave component curve, an angular velocity amplitude spectrum, an angular velocity average error curve, an angular acceleration amplitude spectrum and an angular acceleration average error curve.
Said step 1), the measurement of the transmission error is carried out at the optimum mounting distance position determined in 1).
Due to the adoption of the technical scheme, the invention has the beneficial effects that:
the bevel gear pair is measured at the optimal mounting distance position, and effective guarantee is provided for the accuracy of the measuring result. The method can be used for extracting the single error and analyzing the frequency domain aiming at the transmission error of the bevel gear pair, and can be used for evaluating the transmission quality of the bevel gear pair more accurately.
Drawings
FIG. 1 is a flow chart of a bevel gear transmission error measurement method.
FIG. 2 is a block diagram of a transmission error measurement system.
FIG. 3 shows the transmission error curve and the representation of the individual errors on the curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the present invention is further described below with reference to the accompanying drawings and embodiments. The description of the figures serves to explain the method and embodiments of the invention.
The flow of the bevel gear transmission error measuring method based on the optimal mounting distance is shown in figure 1, and the specific implementation steps of the method are as follows:
first, a measurement system structure employed for the transmission error measurement of the present invention is explained with reference to fig. 2. The measuring system comprises a pair of meshed bevel gear pairs, two circular grating measuring systems, a data acquisition card, a driving device and a controller. The circular grating measuring system is formed by connecting a reading head, a DSI interface and a subdivider; the driving device is formed by connecting a spindle motor and a driver; in the pair of meshed bevel gear pairs, the small wheel is driven by the spindle motor to drive the large wheel meshed with the small wheel to rotate. The two circular gratings respectively measure the rotation angle value of the coaxial gear, the measured angle value enters a data acquisition card through a reading head, a DSI interface and a subdivider, and the numerical value of the transmission error is obtained through calculation.
Firstly, the optimal installation distance is searched before formal transmission error measurement is carried out. Setting a middle point, a step pitch and a searching point number of the mounting distance search, sequentially carrying out single-side meshing measurement at the set point positions, carrying out FFT (fast Fourier transform) on transmission error data of each point to obtain a first third-order tooth frequency harmonic amplitude of a transmission error amplitude frequency spectrum of each point, multiplying each subharmonic amplitude by a corresponding Q factor after dividing each subharmonic amplitude by the harmonic tolerance value, then adding to obtain a transmission quality factor F of the gear pair at the position, comparing F values of the points, and taking the point with the minimum F value as the optimal mounting distance;
and secondly, adjusting the position of the bevel gear pair to enable the large wheel and the small wheel to be meshed at the optimal mounting distance found in the first step, and measuring the transmission error. The transmission error is measured in two ways, namely a way based on the number of revolutions of the large wheel and a way based on the whole meshing period. The transmission error is measured based on the number of revolutions of the large wheel, i.e. according to the number of revolutions of the large wheel set in the parameter setting. Based on the mode of meshing the whole period, the big wheel and the small wheel are all required to complete the meshing of the whole rotation, namely the rotation number is an integer, and the calculation formula of the whole meshing period is as follows:
wherein: n is2For large number of revolutions, Z1X is the greatest common divisor of the numbers of teeth of the larger and smaller gears.
And thirdly, after the transmission error of the gear pair is measured, firstly, extracting and calculating a single error to respectively obtain the tangential comprehensive total deviation of the gear pair, the one-tooth tangential comprehensive deviation of the gear pair, the accumulated total deviation of the tooth pitch and the single tooth pitch deviation. The representation of the four single-term errors on the transmission error curve is shown in fig. 2, and the extraction algorithm of the single-term errors is as follows:
tangential comprehensive total deviation F of gear pairi’：F′i＝Max(φ[i])-Min(φ[i]),i＝1,…,N,(μm)
Where N is the number of sample points, i is the ith sample point,is the transmission error value at the ith sampling point;
one tooth tangential comprehensive deviation of gear pair
Wherein,is to beDivided into Z sections with the same number of measured gear teeth,for variations in circumferential displacement in the k-th pitch angle, where
Cumulative total deviation of tooth pitch
Wherein,is an array formed by the midpoint error values of each pitch angle;
cumulative deviation of individual tooth pitch
Wherein,is to beAnd (4) forming an array by the difference values of the adjacent points.
Fourthly, establishing a tolerance database, inquiring the tolerance database in measurement software, sequentially searching all the deviations calculated in the third step in the tolerance database according to the reference circle diameter and the modulus of the gear, and evaluating the precision grades of all the deviations;
fifthly, further processing the transmission error signal such as spectrum analysis, filtering analysis and the like to obtain the following curves: the system comprises a transmission error amplitude frequency spectrum, a rotation harmonic curve, a tooth pitch accumulated deviation curve, an average tooth profile error curve, a long wave component curve, a short wave component curve, an angular velocity amplitude spectrum, an angular velocity average error curve, an angular acceleration amplitude spectrum and an angular acceleration average error curve. Wherein the rotation harmonic curve and the pitch cumulative deviation curve can be obtained only in a measurement mode based on the whole period of meshing of the gear pair. The curves were obtained as follows:
transmission error amplitude spectrum: carrying out FFT (fast Fourier transform) on the measured transmission error data, solving a relation curve of the amplitude and the frequency of the transmission error data, and quantizing the frequency into a multiple of the tooth frequency;
rotating harmonic curve: when the gear pair is engaged in the whole period, a curve in the range of 0.8 times of the front gear frequency of the transmission error amplitude frequency spectrum is amplified and displayed to obtain a rotating harmonic curve;
pitch cumulative deviation curve: the pitch cumulative deviation curve can be obtained by performing inverse Fourier transform on the corresponding points of each subharmonic of the rotational harmonic, and two curves can be obtained by performing Fourier transform on each subharmonic of the big wheel and the small wheel respectively during the inverse Fourier transform. In the two curves, the longer period is the accumulated error of the tooth pitch of the large wheel, and the shorter period is the accumulated deviation of the tooth pitch of the small wheel;
mean tooth profile deviation curve: and (4) carrying out inverse Fourier transform on points corresponding to each harmonic in the transmission error amplitude frequency spectrum to obtain an average tooth profile deviation curve.
Long wave component curve: removing high frequency component in transmission error by low pass filter, and cutting off frequency lambda of signalcSet to the tooth frequency lambdaz0.2 times, i.e. the coefficient q in the following equation is equal to 0.2;
λc＝q·λz(q<1)
short-wave component curve: subtracting the long wave component from the transmission error to obtain a short wave component curve;
angular velocity amplitude spectrum: the transmission error amplitude spectrum is obtained by first differentiating the time;
angular velocity mean error curve: carrying out inverse Fourier transform on each harmonic of the angular velocity amplitude spectrum to obtain the harmonic;
angular acceleration amplitude spectrum: the angular velocity amplitude spectrum is obtained by first differentiating the time;
angular acceleration mean deviation difference curve: and carrying out inverse Fourier transform on each harmonic of the angular acceleration frequency spectrum to obtain the angular acceleration frequency spectrum.
According to the analysis result of the example, the method provided by the invention can be used for measuring and analyzing the transmission error under the optimal installation distance, the determination of the optimal installation distance ensures the measurement accuracy, a more accurate and detailed analysis method is provided for the transmission error of the gear pair, and the transmission quality of the gear pair can be more comprehensively analyzed and evaluated. The above description of typical examples is not intended to limit the invention, which may be modified and improved without departing from the scope of the invention, as defined in the claims and the equivalents thereof.
Claims (2)
1. The bevel gear transmission error measurement method based on the optimal mounting distance is characterized by comprising the following steps of: firstly, finding the optimal installation distance of a bevel gear pair, then installing the bevel gear pair at the optimal installation distance and carrying out single-side meshing measurement to obtain a transmission error signal of the gear pair and carrying out calculation and analysis;
the method comprises the following concrete implementation steps of,
1) mounting a bevel gear pair at the front end of a rotating main shaft of a measuring system at a designed mounting distance, and setting the mounting distance offset and the searching times of a small wheel in the parameter setting of mounting distance searching; then, single-side meshing measurement is carried out on each set point to obtain a transmission error curve of the bevel gear pair, FFT is carried out on the transmission error curve to obtain the first third tooth frequency harmonic amplitude of each point of the transmission error curve, and then the optimal installation distance of the bevel gear pair is obtained through calculation of the harmonic amplitudes;
2) after the optimal mounting distance of the bevel gear pair is obtained, adjusting the positions of the two gears to enable the gear pair to be meshed at the optimal mounting distance, then carrying out single-side meshing measurement, measuring the rotation angle value of the two gears through a circular grating which is arranged on a rotating main shaft and is close to the bevel gear, and obtaining a transmission error curve of the bevel gear pair through calculation;
3) calculating a transmission error curve, extracting four single deviations which are respectively tangential comprehensive total deviation of the gear pair, tangential comprehensive deviation of one tooth of the gear pair, accumulated total deviation of tooth pitch and accumulated deviation of single tooth pitch, and evaluating the precision grade;
4) and further calculating and analyzing the transmission error curve to obtain other deviation curves which are respectively as follows: a rotating harmonic curve, a pitch cumulative deviation curve, an average tooth profile error curve, a long wave component curve, a short wave component curve, an angular velocity amplitude spectrum, an angular velocity average error curve, an angular acceleration amplitude spectrum and an angular acceleration average error curve;
said step 1), the measurement of the transmission error is carried out at each set point determined in 1);
the measuring system comprises a pair of meshed bevel gear pairs, two circular grating measuring systems, a data acquisition card, a driving device and a controller; the circular grating measuring system is formed by connecting a reading head, a DSI interface and a subdivider; the driving device consists of a spindle motor and a driver; in the pair of meshed bevel gear pairs, the small wheel is driven by the spindle motor to drive the large wheel meshed with the small wheel to rotate; the two circular grating measuring systems respectively measure the rotation angle value of the coaxial gear, the measured angle value enters a data acquisition card through a reading head, a DSI interface and a subdivider, and the numerical value of the transmission error is obtained through calculation;
the specific implementation steps of the steps 1) to 4) are as follows,
the step 1) specifically comprises the steps of searching the optimal mounting distance before formal transmission error measurement is carried out; setting a middle point searched by a mounting distance, a small wheel mounting distance offset and searching times, sequentially carrying out single-side meshing measurement at set point positions, carrying out FFT (fast Fourier transform) on transmission error data of each point to obtain a first third-order tooth frequency harmonic amplitude of each point transmission error amplitude frequency spectrum, multiplying each second-order tooth frequency harmonic amplitude by a corresponding influence factor Q after dividing each second-order tooth frequency harmonic amplitude by the harmonic tolerance value, then adding to obtain a transmission quality factor F of a gear pair at the position, comparing F values of the points, and taking the point with the minimum F value as the optimal mounting distance;
the step 2) specifically comprises the steps of adjusting the position of a bevel gear pair to enable a large wheel and a small wheel to be meshed at the optimal mounting distance position found in the step 1) to measure the transmission error; the transmission error is measured in two modes, namely a mode based on the revolution of a large wheel and a mode based on the whole meshing period; measuring the transmission error according to the rotation number of the large wheel set in the parameter setting on the basis of the rotation number of the large wheel; based on the mode of meshing whole period, the large wheel and the small wheel are meshed for whole rotation, namely the rotation number is an integer, and the meshing whole period is the rotation number n of the large wheel2Is calculated as follows:
wherein: n is2For large number of revolutions, Z1Is the number of teeth of the small gear, and X is the greatest common divisor of the number of teeth of the large gear and the small gear;
the step 3) specifically comprises the steps of firstly extracting and calculating the single deviation after measuring the transmission error of the meshing of the optimal mounting distance position of the gear pair, and respectively obtaining the tangential comprehensive total deviation of the gear pair, the one-tooth tangential comprehensive deviation of the gear pair, the accumulated total deviation of the tooth pitch and the accumulated deviation of the single tooth pitch; the extraction algorithm of the individual deviations is as follows:
tangential comprehensive total deviation F of gear pairi’：FiUnit of' is μm; where N is the number of sample points, i is the ith sample point,is the transmission error value at the ith sampling point;
one-tooth tangential comprehensive deviation f of gear pairi’：i＝1,…,N，fiUnit of' is μm; wherein,is to beDivided into Z intervals having the same number of teeth as the large gear,for variations in circumferential displacement in the k-th pitch angle, where Unit of (d) is μm;
cumulative total pitch deviation Fp：m＝1,…,Z，FpUnit of (d) is μm; wherein,is an array formed by the midpoint error values of each pitch angle;
cumulative deviation f of individual tooth pitchpt：n＝1,…,Z-1,fptUnit of (d) is μm; wherein,is to beThe difference values of adjacent points in the array form an array;
establishing a tolerance database, inquiring the tolerance database in measurement software, sequentially searching each calculated deviation in the tolerance database according to the reference circle diameter and the modulus of the gear, and evaluating the precision grade of each deviation;
the step 4) specifically comprises the following steps of carrying out further spectrum analysis and filtering analysis processing on the transmission error curve measured by single-sided meshing to obtain the following curves: a transmission error amplitude frequency spectrum, a rotation harmonic curve, a tooth pitch accumulated deviation curve, an average tooth profile error curve, a long wave component curve, a short wave component curve, an angular velocity amplitude spectrum, an angular velocity average error curve, an angular acceleration amplitude spectrum and an angular acceleration average error curve; wherein the rotational harmonic curve and the pitch cumulative deviation curve are obtained only in a manner based on the whole period of meshing.
2. The bevel gear transmission error measurement method based on the optimal mounting distance according to claim 1, characterized in that: step 4) the curves are obtained in the following manner,
transmission error amplitude spectrum: carrying out FFT (fast Fourier transform) on the measured transmission error data, solving a relation curve of the amplitude and the frequency of the transmission error data, and quantizing the frequency into a multiple of the tooth frequency;
rotating harmonic curve: when the gear pair is engaged in the whole period, the curve in the range of 0.8 times of the tooth frequency of the front transmission error amplitude frequency spectrum is amplified and displayed to obtain a rotating harmonic curve;
pitch cumulative deviation curve: the pitch accumulated deviation curve can be obtained by performing inverse Fourier transform on the corresponding points of each subharmonic of the rotating harmonic, and when the inverse Fourier transform is performed, the inverse Fourier transform is performed on each subharmonic of the large wheel and each subharmonic of the small wheel respectively, so that two curves can be obtained; the longer cycle of the two curves is a pitch accumulated deviation curve of a large wheel, and the shorter cycle is a pitch accumulated deviation curve of a small wheel;
mean tooth profile error curve: carrying out inverse Fourier transform on points corresponding to each harmonic in the transmission error amplitude frequency spectrum to obtain an average tooth profile error curve;
long wave component curve: removing high frequency component in transmission error by low pass filter, and cutting off frequency lambda of signalcSet to the tooth frequency lambdaz0.2 times, i.e. the coefficient q in the following equation is equal to 0.2;
λc＝q·λz，q<1
short-wave component curve: subtracting the long wave component from the transmission error to obtain a short wave component curve;
angular velocity amplitude spectrum: carrying out primary differentiation on the transmission error amplitude spectrum to obtain the transmission error amplitude spectrum;
angular velocity mean error curve: carrying out inverse Fourier transform on each harmonic of the angular velocity amplitude spectrum to obtain the harmonic;
angular acceleration amplitude spectrum: the angular velocity amplitude spectrum is obtained by carrying out primary differentiation on time;
angular acceleration mean error curve: and carrying out inverse Fourier transform on each harmonic of the angular acceleration amplitude spectrum to obtain the angular acceleration amplitude spectrum.
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| CN111999053A (en) * | 2020-07-20 | 2020-11-27 | 湖南中大创远数控装备有限公司 | Spiral bevel gear single-face meshing detection device and method |
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