A gear meshing noise evaluation method based on gear transmission error curve

Abstract

The present invention discloses a gear meshing noise evaluation method based on a gear transmission error curve, specifically comprising the following steps: Step 1: Acquisition of tooth surface waviness based on the gear measurement center; Step 2: Synthesis of the gear full tooth surface waviness curve; Step 3: Calculation of gear transmission error based on the envelope; Step 4: Fourier analysis of the gear transmission error curve based on sine fitting; Step 5: Calculation of the order spectrum; Step 6: Analysis of abnormal orders. The gear transmission error curve can be decomposed into harmonic components of different frequencies through sine fitting Fourier analysis, with each harmonic corresponding to a specific order in the gear error. Abnormal orders can excite vibrations of specific frequencies. Identifying and eliminating abnormal orders is a key step in analyzing gear noise problems.

Description

Technical Field

[0001] The present 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, fundamental transmission component, gears are widely used in various mechanical devices to transmit motion and power due to their high load-bearing capacity, high transmission accuracy, and stable transmission power. Therefore, ensuring gear quality is crucial to promoting gear manufacturing and application. As electric vehicles increase their requirements for gear processing, so too do the requirements for gear measurement. Gear error analysis has become a crucial step in ensuring the reliability of measurement results. Electric vehicle powertrain components are increasingly demanding geometric shapes, tolerances, and surface finishes, placing even more stringent performance requirements on gear transmissions. Gear noise, in particular, has become a crucial quality control factor, a key indicator alongside strength, fatigue life, and transmission efficiency.

[0003] Traditional gear measurement center analysis methods provide quality inspections during production and on finished products to ensure that gear dimensions, shape, and performance meet standards and requirements. While these methods are effective in maintaining gear quality, they struggle to provide insightful, easily interpretable data for noise analysis. In applications with high gear noise requirements, such as electric vehicles, some reducers fail to meet the standards during final offline testing, even though all gears meet tolerance requirements. This may be due to periodic errors in the tooth surfaces.

[0004] To address these issues, a gear mesh noise evaluation method based on the gear transmission error curve was proposed to analyze the periodic components in the gear transmission error curve. By comparing the order values ​​of production gears with verified reference gears, the quality of the produced gears can be better controlled. This analysis, combined with traditional gear inspection data, eliminates the need for additional testing time, only increasing analysis time, resulting in significant time savings. By identifying gears with high order noise before assembly, significant cost savings can be achieved. 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 helical line waviness along the helix direction. The full tooth surface waviness of a gear is the comprehensive result of superimposing the pitch error along the generation line direction of the involute on the tooth surface waviness based on the gear meshing principle and 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, helical line waviness and single tooth 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 line, 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, tooth surface waviness includes information such as tooth surface shape error, waviness, and roughness. In order to perform Fourier analysis, it is first necessary to select the measurement data points for analysis. The specific steps are as follows:

[0009] S1. Data measurement requirements:

[0010] According to the gear accuracy standard GB10095.1-2022, "Tooth Surface Tolerance Grading System for Cylindrical Gears Part 1: Definition and Permissible Values ​​of Tooth Surface Deviation," one-dimensional coordinate data is acquired by measuring the tooth profile curve on a helix or normal plane at the same gear diameter using the gear measurement center. The collected data should cover the total normal deviation values ​​of multiple tooth surface measurement points.

[0011] S2. Data point filtering:

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

[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. This filtered 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 tooth surface waviness curve;

[0017] When measuring gear tooth profile deviation or helix deviation, each measurement point corresponds to a development angle, which represents the specific position of the gear during the development motion. In order to achieve full gear tooth surface waviness synthesis, it is necessary to establish a corresponding calculation model to accurately calculate the rotation angle of each measurement point and complete the calculation using formulas (1) and (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 a gear tooth surface, the sum of the development angle, axial position, and rotational angle of each measurement point must be considered to ensure an accurate waviness curve is generated. When all measurement points are arranged according to their rotational angles, a continuous closed measurement curve is formed, consisting of all the measured teeth on the circumference.

[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 time x j is the horizontal coordinate of the tooth profile point, y j is the error value of the measured 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 the first main order. This main sine wave function is then 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 the second main order. All spectrum results are calculated sequentially. 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 the amplitude

[0049] Calculate the corresponding amplitudes at this time:

[0050] A={A1,A2,…,A m}(9)

[0051] S3. Solve the initial phase

[0052] The corresponding initial phase is:

[0053]

[0054] S4. Calculate the spectrum

[0055] The spectrum results are:

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

[0057] Step 6: Abnormal order analysis;

[0058] Gear transmission error curves can be decomposed into harmonic components of varying frequencies through sine fitting and Fourier analysis. Each harmonic corresponds to a specific order in the gear error. The presence of abnormal orders typically indicates problems in the gear manufacturing or assembly process, such as eccentricity, periodic tooth surface error, or pitch error.

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

[0060] Figure 1 Gear measuring center.

[0061] Figure 2 It is the tooth profile waviness and helix waviness of 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 use the envelope curve to obtain the gear transmission error curve.

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

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

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

[0071] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments. All technologies implemented based on the present invention fall within 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 as 1mm to ensure that the full tooth surface waviness of the gear can be measured. The data collection, analysis and evaluation process complies with the wheel precision standard GB10095.1-2022 "Cylindrical Gear Tooth Surface Tolerance Grading System Part 1: Definition and Permissible Value of Tooth Surface Deviation". During the full tooth measurement of the gear, the gear measuring center is used to measure the tooth profile waviness, helical line waviness and single pitch deviation. The tooth profile waviness and helical line waviness of the left and right tooth surfaces of the gear are as follows Figure 2 As shown. The single pitch deviation is as follows Figure 3 As shown in the figure, the probe should cover the entire tooth profile length, starting below the tooth profile control circle. The measurement process should continuously pass through the tooth surface and pass through the actual starting point of the top trimming. The starting and ending points of meshing are calculated based on the meshing principle, thus determining the measurement starting position, evaluation starting position, final evaluation position, and final measurement position. In both the involute tooth profile waviness and helical waviness measurements, 480 measurement points were collected, which meets the measurement requirements.

[0077] Table 2 Evaluation parameters of the tested gears

[0078] Measurement location Diameter of starting point Final measuring point diameter Starting point diameter Final evaluation point diameter Numerical 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: Calculation of gear transmission error 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 waviness information of the entire tooth surface

[0091] The gear 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 time x j is the horizontal coordinate of the tooth profile point, yj is the error value of the measured tooth profile point.

[0103] Step 5: Calculate the order spectrum

[0104] Maximum amplitude A max The fitted sine function is considered the first main order. This main sine wave function is then 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 the second main order. All spectrum results are calculated sequentially. 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 the amplitude

[0109] Calculate the corresponding amplitudes at this time:

[0110] A={A1,A2,…,A m}

[0111] S3. Solve the initial phase

[0112] The corresponding initial phase is:

[0113]

[0114] S4. Calculate 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. Fit the first main order sine function and the gear waviness curve according to the phase relationship as shown Figure 9 As shown in Figure 2, this main sinusoidal wave function is removed from the deviation curve, and then the compensating sinusoidal wave with the second largest amplitude is fitted. The result is as follows: Figure 10 As shown. Plot all spectrum results in turn, such as Figure 11 shown.

[0118] Step 6: Abnormal Order Analysis

[0119] Abnormal orders in the spectral results often indicate problems in the gear manufacturing or assembly process, such as eccentricity, periodic tooth profile errors, or pitch errors. Abnormal orders can excite vibrations at specific frequencies that fall within the resonant frequency range of the accelerator structure or other mechanical systems, thereby amplifying the noise.

[0120] analyze Figure 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 drum in the design.

[0121] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily 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 is not limited to the embodiments shown herein but is intended to conform 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 tooth profile waviness, helix waviness, and individual 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 using the envelope curve. Fourier analysis is performed on the gear transmission error curve to calculate the frequency spectrum. This allows for efficient and reliable analysis of the impact of periodic errors in tooth surface machining on gear meshing noise. 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 form error, waviness, and roughness. In order to perform Fourier analysis, the measurement data points for analysis are selected. Step 2: Synthesis of the gear 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 during the development motion. In order to achieve the synthesis of the waviness of the entire gear tooth surface, it is necessary to establish a corresponding calculation model to accurately calculate the rotation angle of each measuring point and complete the calculation using formulas (1) and (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 ultimately generated. When all measuring points are arranged according to their rotation angles, a continuous closed measurement curve consisting of all the 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 using 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 time 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 value 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 limitations of the data sampling rate, an appropriate filter cutoff frequency should be selected to avoid introducing 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 during gear precision manufacturing and quality control.

3. The gear meshing noise evaluation method based on the gear transmission error curve according to claim 1, characterized in that: The calculation method for step 3 is as follows: S1. Define the tooth surface waviness as tooth profile waviness or helical 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, 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 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. Solve the initial phase The corresponding initial phase is: S4. Calculate the spectrum The spectrum results are: Q={(1,A1),(1,A2),...,(m,A m )} (11)。 5. The gear meshing noise evaluation method based on the 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 generate 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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