Gear meshing noise evaluation method based on gear transmission error curve

Abstract

The invention discloses a gear meshing noise evaluation method based on a gear transmission error curve. The gear meshing noise evaluation method specifically comprises the following steps of 1, obtaining tooth surface waviness based on a gear measurement center; step 2, synthesizing a whole tooth surface waviness curve of the gear; 3, gear transmission error calculation based on an envelope line; 4, carrying out Fourier analysis on the gear transmission error curve based on sine fitting; step 5, calculating an order spectrum; step 6, abnormal order analysis; a gear transmission error curve can be decomposed into harmonic components with different frequencies through sine fitting Fourier analysis, and each harmonic corresponds to a specific order in a gear error. The abnormal order can excite vibration of a specific frequency, and when the gear noise problem is analyzed, the step of recognizing and eliminating the abnormal order is a key step.

Description

Technical Field

[0001] The invention relates to a gear meshing noise evaluation method based on a gear transmission error curve, and is aimed at involute cylindrical gears. Background Art

[0002] As a key basic transmission element, gears are widely used in various mechanical equipment to transmit motion and power due to their large load-bearing capacity, high transmission accuracy, and stable transmission power. Therefore, ensuring the quality of gears is crucial to promoting gear manufacturing and application. As electric vehicles have higher requirements for gear processing, the requirements for gear measurement have also increased, and gear error analysis has become an important link to ensure the reliability of measurement results. The requirements for geometry, tolerance, and surface accuracy of electric vehicle powertrain components are constantly increasing, and gear transmission devices are therefore facing more stringent performance requirements. Gear noise, in particular, has become an important quality control link and is one of the important indicators alongside strength, fatigue life, and transmission efficiency.

[0003] Traditional gear measurement center analysis methods can perform quality inspections on the production process and finished products to ensure that the size, shape and performance of the gears meet standards and requirements. Although these methods are very effective in maintaining gear quality, they are difficult to provide in-depth and easy-to-interpret data for noise analysis. In applications with high requirements for gear noise, such as electric vehicles, although the accuracy of all gears meets the tolerance requirements, some reducers still fail to meet the standards in the final offline testing stage, which may be caused by periodic errors on the tooth surface.

[0004] To address these issues, a gear meshing noise evaluation method based on the gear transmission error curve is proposed to analyze the periodic components in the gear transmission error curve. By comparing the order values ​​of the production gears with the verified reference gears, the quality of the production gears can be better controlled. This analysis is combined with traditional gear inspection data, and no additional testing time is required, only increased analysis time, thus saving a lot of time. Significant cost savings can be achieved by identifying gears with higher order values ​​before assembly. Summary of the invention

[0005] The present invention proposes a method for defining gear waviness. Tooth surface waviness is the result of the combined influence of geometric features such as tooth surface shape error, surface waviness and surface roughness. Tooth surface waviness can be divided into two types: tooth profile waviness along the tooth profile direction and helix line waviness along the helix line direction. The full tooth surface waviness of the gear is the comprehensive result of superimposing the pitch error on the tooth surface waviness along the generation line direction of the involute on the basis of the gear meshing principle and according to the generation principle of the involute, referred to as gear waviness. The purpose of the present invention is to utilize the measured tooth profile waviness, helix line waviness and single pitch deviation measured by the gear measurement center, synthesize the gear waviness based on the gear meshing principle, calculate the gear transmission error through the envelope, perform Fourier analysis on the gear transmission error curve, calculate the frequency spectrum, and efficiently and reliably analyze the influence of periodic errors in tooth surface processing on gear meshing noise.

[0006] The present invention proposes a gear meshing noise evaluation method based on gear waviness, which specifically includes the following method steps:

[0007] Step 1: Acquire the tooth surface waviness based on the gear measurement center;

[0008] In gear measurement, the tooth surface waviness includes information such as tooth surface shape error, waviness and roughness. In order to perform Fourier analysis, you first need to select the measurement data points for analysis. The specific steps are as follows:

[0009] S1. Data measurement requirements:

[0010] According to the gear precision standard GB10095.1-2022 "Cylindrical Gear Tooth Surface Tolerance Grading System Part 1: Definition and Allowable Value of Tooth Surface Deviation", the gear measurement center is measured on the spiral line under the same gear diameter or the tooth profile curve on the same normal plane to obtain one-dimensional coordinate data. The collected data should cover the total normal deviation value of multiple tooth surface measurement points.

[0011] S2. Data point filtering:

[0012] To ensure the accuracy and reliability of the measured data, a balance must be maintained between the density of data points and filtering processing. Based on the limitation of the data sampling rate, an appropriate filter cutoff frequency is selected to avoid introducing gross errors. The tooth surface waviness data should contain at least 300 points or 5 points per millimeter (the larger of the two).

[0013] S3. Data point description:

[0014] The number of data points within the measurement range should be clearly marked in the test report, and the filtering method and related parameters used should be recorded in detail to ensure the traceability and consistency of the measurement results.

[0015] Through the above steps, data suitable for Fourier analysis can be systematically selected. These screened and processed data will be used to perform Fourier analysis on the gear transmission error curve, thereby supporting error assessment during gear precision manufacturing and quality control.

[0016] Step 2: Synthesis of the gear full tooth surface waviness curve;

[0017] When measuring gear tooth profile deviation or helix deviation, each measuring point corresponds to a development angle, which represents the specific position of the gear in the development motion. In order to realize the waviness synthesis of the entire gear tooth surface, it is necessary to establish a corresponding calculation model, accurately calculate the rotation angle of each measuring point, and complete the calculation through formula (1) and formula (2).

[0018]

[0019]

[0020] In the formula is the rotation angle, Δz is the axial distance between the two ends of the gear, β is the helix angle, D0 is the pitch circle diameter, ξ is the development angle, and τ is the pitch angle.

[0021] When synthesizing the waviness of the entire gear tooth surface, it is necessary to consider the sum of the development angle, axial position and rotation angle of each measuring point to ensure that an accurate waviness curve is finally generated. When all measuring points are arranged according to their rotation angles, a continuous closed measuring curve consisting of all measuring teeth on the circumference is formed.

[0022] Step 3: Calculation of gear transmission error based on envelope curve;

[0023] After synthesizing the gear waviness, it is necessary to further calculate the gear transmission error. The gear transmission error curve is calculated using the envelope method. The calculation method is as follows:

[0024] S1. Define the tooth surface waviness, which can be the tooth profile waviness or the helical waviness

[0025] The error set of the kth tooth is defined as:

[0026] S k ={(x1,y1),(x2,y2),...,(x n ,y n )}(3)

[0027] Where k is the kth tooth, k is the maximum number of teeth, and n is the number of points measured on each tooth surface.

[0028] S2. indicates gear waviness

[0029] The tooth surface waviness is represented by S:

[0030] S all ={S1,S2,...,S k}(4)

[0031] Where S k It represents the tooth surface waviness of the kth tooth, where k is at most the number of teeth.

[0032] S3. Envelope calculation

[0033] Rearrange the tooth surface waviness in the order of x from small to large to obtain a new set:

[0034] S new ={(x1,y1),(x2,y2),...,(x kn ,y kn )}(5)

[0035] S4. Calculate the gear transmission error curve

[0036] In the range of 360°, calculate S new The maximum value y corresponding to each x in max , each x and its corresponding y max The gear transmission error curve is:

[0037] S total ={(x1,y1),(x2,y2),...,(x m ,y m )}(6)

[0038] Step 4: Fourier analysis of gear transmission error curve based on sine fitting

[0039] To evaluate the gear transmission error curve, an independent evaluation strategy was chosen. A sinusoidal function was fitted to the gear transmission error curve according to the least squares method:

[0040]

[0041] Where λ k is the wavelength, A k The wavelength is λ k The corresponding amplitude is The wavelength is λ k The initial phase at x j is the horizontal coordinate of the tooth profile point, y j It is the error value of measuring tooth profile point.

[0042] Absolute rotation angle x j Can be arbitrary and does not need to be equidistantly distributed.

[0043] Step 5: Calculate the order spectrum;

[0044] The most critical step in the Fourier analysis of tooth surface is to calculate the amplitude of the fitted sine wave function within the selected frequency range. max The fitted sine function is considered as the first main order. Then, this main sine wave function is removed from the gear transmission error curve, and the remaining gear transmission error curve is reanalyzed. The compensating sine wave with the second largest amplitude is considered as the second main order. All spectrum results are calculated in sequence. The steps are as follows:

[0045] S1. Determine the wavelength of the fitted sine function

[0046] Calculate the data of the first m orders, and the wavelength of the corresponding sine function:

[0047] λ={λ1,λ1,…,λ m}(8)

[0048] S2. Solve for the amplitude

[0049] Calculate the corresponding amplitudes at this time:

[0050] A={A1,A2,…,A m}(9)

[0051] S3. Solving the initial phase

[0052] The corresponding initial phase is:

[0053]

[0054] S4. Solving the spectrum

[0055] The spectrum results are:

[0056] Q={(1,A1),(1,A2),...,(m,A m )} (11)

[0057] Step 6: Abnormal order analysis;

[0058] The gear transmission error curve can be decomposed into harmonic components of different frequencies through sine fitting Fourier analysis, and each harmonic corresponds to a specific order in the gear error. When certain abnormal orders appear, it usually indicates that there are problems in the gear manufacturing or assembly process, such as eccentricity, tooth surface periodic error or pitch error.

[0059] Abnormal orders will excite vibrations of specific frequencies that happen to fall within the resonant frequency range of the reducer structure or other mechanical systems, thereby amplifying the noise. In addition, high-frequency periodic errors tend to generate high-frequency noise, while low-frequency periodic errors tend to induce low-frequency vibrations and low-frequency noise. Therefore, identifying and eliminating abnormal orders is a key step in analyzing gear noise problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Measuring center of gear.

[0061] Figure 2 It is the waviness of the tooth profile and the helix line on the left and right tooth surfaces of the gear.

[0062] Figure 3 It is the single pitch deviation of the left and right tooth surfaces of the gear.

[0063] Figure 4 It is the synthetic model of the gear tooth surface waviness.

[0064] Figure 5 is the waviness of the entire gear tooth surface.

[0065] Figure 6 To obtain the gear transmission error curve using the envelope.

[0066] Figure 7 It is the first-order sinusoidal fitting of the gear transmission error curve.

[0067] Figure 8 It is the second-order sinusoidal fitting of the gear transmission error curve.

[0068] Fig. 9 It is the first-order sinusoidal fitting of the gear full tooth surface waviness and gear transmission error curve.

[0069] Fig.10 It is the second-order sinusoidal fitting of the gear full tooth surface waviness and gear transmission error curve.

[0070] Fig.11 This is the Fourier analysis result of the gear transmission error curve. DETAILED DESCRIPTION

[0071] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0072] The basic parameters of the selected characteristic gears are shown in Table 1.

[0073] Table 1 Parameters of the gears tested

[0074]

[0075] Step 1: Acquisition of tooth profile waviness information data

[0076] Klingelnberg P26 is selected as the measuring device, such as Figure 1As shown. The probe diameter is selected to be 1mm to ensure that the full gear tooth surface waviness can be measured. The data collection, analysis, and evaluation process follows the gear accuracy standard GB10095.1-2022 "Cylindrical Gear Tooth Surface Tolerance Grading System Part 1: Definition and Allowable Value of Tooth Surface Deviation". During the gear full tooth measurement process, the gear measurement center is used to measure the tooth profile waviness, helix line waviness, and single pitch deviation. The tooth profile waviness and helix line waviness of the left and right tooth surfaces of the gear are shown in the figure. Figure 2 The single pitch deviation is shown in Figure 3 As shown. The probe should cover the entire tooth profile length, with the starting point below the tooth profile control circle. The measurement process continuously passes through the tooth surface and passes through the actual starting point of the top repair. The starting and ending points of the meshing are calculated based on the meshing principle to determine the starting position, starting evaluation position, final evaluation position, and final measurement position of the measurement. In the measurement of involute tooth profile waviness and helical waviness, 480 measurement points were collected, and the number of measurement points met the measurement requirements.

[0077] Table 2 Evaluation parameters of the tested gears

[0078] Measurement location Starting point diameter Final measuring point diameter Starting point diameter Final evaluation point diameter Numeric 49.459mm 60.237mm 49.794mm 58.154mm

[0079] Step 2: Synthesis of the gear tooth surface waviness curve

[0080] According to the gear full tooth surface waviness curve synthesis method described in step 3, the synthesis model is as follows Figure 4 As shown, the rotation angle of each measuring point is calculated according to the following formula:

[0081]

[0082]

[0083] In the formula is the rotation angle, Δz is the axial distance between the two ends of the gear, β is the helix angle, D0 is the pitch diameter, ξ is the development angle, and τ is the pitch angle. The synthesized gear waviness curve is as follows: Figure 5 shown.

[0084] Step 4: Gear transmission error calculation based on envelope curve

[0085] By using the envelope method, Figure 5 The envelope of the gear tooth surface waviness is calculated, and the gear transmission error curve is finally generated. The specific calculation steps are as follows:

[0086] S1. Define the tooth profile error set

[0087] The error set of the kth tooth is defined as:

[0088] S k ={(x1,y1),(x2,y2),...,(x480 ,y 480 )}

[0089] At this time, the maximum value of k is 21, and the number of measurement points for each tooth profile is 480.

[0090] S2. indicates the whole tooth surface waviness information

[0091] The gear full tooth surface waviness information is represented by S:

[0092] S all ={S1,S2,...,S 21}

[0093] S3. Rearrange error data

[0094] The waviness information of the entire tooth surface is rearranged in the order of rotation angle x from small to large to obtain a new set:

[0095] S new ={(x1,y1),(x2,y2),...,(x 21*480 ,y 21*480 )}

[0096] S4. Calculate the gear transmission error curve

[0097] In the range of 360°, calculate S new The maximum error y corresponding to each rotation angle x max , each rotation angle x and its corresponding error y max The value of is the gear transmission error curve:

[0098] S total ={(x1,y1),(x2,y2),...,(x 8806 ,y 8806 )}

[0099] Step 5: Fourier analysis of gear transmission error curve based on sine fitting

[0100] To evaluate the gear transmission error curve, an independent evaluation strategy was chosen. A sinusoidal function was fitted to the gear transmission error curve according to the least squares method:

[0101]

[0102] Where λ k is the wavelength, A k The wavelength is λ k The corresponding amplitude is The wavelength is λ k The initial phase at x j is the horizontal coordinate of the tooth profile point, yj It is the error value of measuring tooth profile point.

[0103] Step 5: Calculate the order spectrum

[0104] Maximum amplitude A max The fitted sine function is considered as the first main order. Then, this main sine wave function is removed from the gear transmission error curve, and the remaining gear transmission error curve is reanalyzed. The compensating sine wave with the second largest amplitude is considered as the second main order. All spectrum results are calculated in sequence. The steps are as follows:

[0105] S1. Determine the wavelength of the fitted sine function

[0106] Calculate the data of the first m orders, and the wavelength of the corresponding sine function:

[0107] λ={λ1,λ1,…,λ m}

[0108] S2. Solve for the amplitude

[0109] Calculate the corresponding amplitudes at this time:

[0110] A={A1,A2,…,A m}

[0111] S3. Solving the initial phase

[0112] The corresponding initial phase is:

[0113]

[0114] S4. Solving the spectrum

[0115] The spectrum results are:

[0116] Q={(1,A1),(1,A2),…,(m,A m )}

[0117] Maximum amplitude A max The compensated sine wave is regarded as the first main frequency, such as Figure 7 This main sine wave function is then removed from the deviation curve and the remaining deviation is reanalyzed. The compensating sine wave with the second largest amplitude is considered the second main frequency, as shown in Figure 8 As shown. The first main order sine function fitting and the gear waviness curve are fitted according to the phase relationship as shown Fig. 9 As shown in Figure 1, this main sine wave function is removed from the deviation curve, and then a compensating sine wave with the second largest amplitude is fitted. The result is as follows: Fig.10 As shown. Plot all the spectrum results in turn, such as Fig.11 shown.

[0118] Step 6: Abnormal Order Analysis

[0119] When abnormal orders appear in the spectrum results, it usually indicates problems in the gear manufacturing or assembly process, such as eccentricity, periodic error of tooth profile, or pitch error. Abnormal orders will excite vibrations of specific frequencies that happen to fall within the resonant frequency range of the accelerator structure or other mechanical systems, thereby amplifying the noise.

[0120] analyze Fig.11 The Fourier analysis results of the gear transmission error curve show that the first order is mainly caused by the deviation of the single tooth pitch. The abnormal problems of the tooth number order and the tooth number multiple order are mainly caused by the middle drum in the design.

[0121] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A gear meshing noise evaluation method based on gear transmission error curve, characterized in that: The gear waviness, spiral waviness and single pitch deviation measured by the gear measurement center are used to synthesize the gear waviness based on the gear meshing principle. The gear transmission error is calculated through the envelope curve. The gear transmission error curve is subjected to Fourier analysis to calculate the frequency spectrum. The influence of periodic errors in tooth surface processing on gear meshing noise is analyzed efficiently and reliably. The specific steps are as follows: Step 1: Acquire the tooth surface waviness based on the gear measurement center; In gear measurement, tooth surface waviness includes tooth surface shape error, waviness and roughness; in order to perform Fourier analysis, the measurement data points for analysis are selected; Step 2: Synthesis of the gear full tooth surface waviness curve; When measuring gear tooth profile deviation or helix deviation, each measuring point corresponds to a development angle, which represents the specific position of the gear in the development motion. In order to realize the waviness synthesis of the entire gear tooth surface, it is necessary to establish a corresponding calculation model, accurately calculate the rotation angle of each measuring point, and complete the calculation through formula (1) and formula (2). In the formula is the rotation angle, Δz is the axial distance between the two ends of the gear, β is the helix angle, D0 is the pitch circle diameter, ξ is the development angle, and τ is the pitch angle; When synthesizing the waviness of the entire gear tooth surface, it is necessary to consider the sum of the development angle, axial position and rotation angle of each measuring point to ensure that an accurate waviness curve is finally generated; when all measuring points are arranged according to their rotation angles, a continuous closed measuring curve consisting of all measuring teeth on the circumference is formed; Step 3: Calculation of gear transmission error based on envelope curve; After synthesizing the gear waviness, it is necessary to further calculate the gear transmission error; the gear transmission error curve is calculated by the envelope method; Step 4: Fourier analysis of gear transmission error curve based on sine fitting; To evaluate the gear transmission error curve, an independent evaluation strategy was chosen; a sinusoidal function was fitted to the gear transmission error curve according to the least squares method: Where λ k is the wavelength, A k The wavelength is λ k The corresponding amplitude is The wavelength is λ k The initial phase at x j is the horizontal coordinate of the tooth profile point, y j is the error value of the measured tooth profile point; Step 5: Calculate the order spectrum; The most critical step in the Fourier analysis of tooth surfaces is to calculate the amplitude of the fitted sine wave function within the selected frequency range; Maximum amplitude A max The fitted sine function is regarded as the first main order; then, this main sine wave function is removed from the gear transmission error curve, and the remaining gear transmission error curve is re-analyzed; the compensation sine wave with the second largest amplitude is regarded as the second main order; all spectrum results are calculated in sequence; Step 6: Abnormal order analysis; The gear transmission error curve is decomposed into harmonic components of different frequencies through sine fitting Fourier analysis. Each harmonic corresponds to a specific order in the gear error. When certain abnormal orders appear, it indicates that there are problems in the gear manufacturing or assembly process, including eccentricity, tooth surface periodic error or pitch error.

2. The gear meshing noise evaluation method based on the gear transmission error curve according to claim 1, characterized in that: In step 1, the specific steps are as follows: S1. Data measurement requirements: According to the gear accuracy standard, the gear measurement center is used to measure the spiral line under the same gear diameter or the tooth profile curve on the same normal plane to obtain one-dimensional coordinate data; the collected data covers the total normal deviation values ​​of multiple tooth surface measurement points; S2. Data point filtering: To ensure the accuracy and reliability of the measured data, a balance must be maintained between the density of data points and filtering processing; based on the limitation of the data sampling rate, an appropriate filter cutoff frequency should be selected to avoid the introduction of gross errors; the tooth surface waviness data should contain at least 300 points or 5 points per millimeter; S3. Data point description: Clearly mark the number of data points within the measurement range and record the filtering method and related parameters used to ensure the traceability and consistency of the measurement results; Through the above steps, data suitable for Fourier analysis are selected; these screened and processed data are used to perform Fourier analysis on the gear transmission error curve, thereby supporting error assessment in the process of gear precision manufacturing and quality control.

3. The gear meshing noise evaluation method based on the gear transmission error curve according to claim 1 is characterized in that: The calculation method for step 3 is as follows: S1. Define the tooth surface waviness, which is the tooth profile waviness or helical line waviness The error set of the kth tooth is defined as: S k ={(x1,y1),(x2,y2),...,(x n ,y n )}(3) Where k is the kth tooth, k is the maximum number of teeth, and n is the number of points measured on each tooth surface; S2. indicates gear waviness The tooth surface waviness is represented by S: S all ={S1,S2,...,S k }(4) Where S k It represents the tooth surface waviness of the kth tooth, where k is the maximum number of teeth; S3. Envelope calculation Rearrange the tooth surface waviness in the order of x from small to large to obtain a new set: S new ={(x1,y1),(x2,y2),...,(x kn ,y kn )}(5) S4. Calculate the gear transmission error curve In the range of 360°, calculate S new The maximum value y corresponding to each x in max , each x and its corresponding y max The gear transmission error curve is: S total ={(x1,y1),(x2,y2),...,(x m ,y m )}(6)。 4. The gear meshing noise evaluation method based on the gear transmission error curve according to claim 1 is characterized in that: The steps in step 5 are as follows: S1. Determine the wavelength of the fitted sine function Calculate the data of the first m orders, and the wavelength of the corresponding sine function: λ={λ1,λ1,...,λ m }(8) S2. Solve for the amplitude Calculate the corresponding amplitudes at this time: <h2 style=";text-align:left;direction:ltr">A = {A1,A2,...,A<h2 style=";text-align:left;direction:ltr"> m <h2 style=";text-align:left;direction:ltr"> (9) S3. Solving the initial phase The corresponding initial phase is: S4. Solving the spectrum The spectrum results are: Q={(1,A1),(1,A2),...,(m,A m )} (11)。 5. The gear meshing noise evaluation method based on gear transmission error curve according to claim 1, characterized in that: In step 6, abnormal orders will excite vibrations of specific frequencies, which happen to fall within the resonant frequency range of the reducer structure or other mechanical systems, thereby amplifying the noise; high-frequency periodic errors tend to produce high-frequency noise, while low-frequency periodic errors tend to cause low-frequency vibrations and low-frequency noise; when analyzing gear noise, identify and eliminate abnormal orders.

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