A method for synthesizing gear overall errors based on tooth profile waviness

Abstract

The present invention discloses a method for synthesizing gear overall errors based on tooth profile waviness. The method comprises the following steps: Step 1: establishing a tooth profile waviness measurement model using the normal polar coordinate method; Step 2: acquiring tooth profile waviness based on the gear measurement center; Step 3: synthesizing a gear overall error curve based on the tooth profile waviness; and Step 4: calculating the gear transmission error based on the gear overall error curve. The method uses an established precise measurement model to measure information such as tooth profile waviness and pitch deviation, thereby synthesizing an overall error curve. Finally, the gear transmission error curve is obtained through envelope calculation. This method can effectively improve the efficiency and reliability of gear precision measurement and provide more comprehensive and accurate error analysis results.

Description

Technical Field

[0001] The invention relates to a gear overall error synthesis method based on tooth profile waviness, and is aimed at involute cylindrical gears. Background Art

[0002] As a key basic transmission component, gears are widely used in various mechanical equipment to transmit motion and power due to their advantages such as 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. In the field of gear testing, the gear measuring center is currently the most widely used measuring instrument. This instrument can accurately measure individual gear errors such as tooth profile deviation, helix deviation, and pitch deviation, thereby evaluating gear accuracy. These measurement results can be used not only to analyze process errors in gear manufacturing, but also to predict gear performance. However, gear accuracy evaluation can only be analyzed from the perspective of a single tooth surface, and it is not possible to analyze the overall gear error.

[0003] Gear global error measurement is a new and efficient gear measurement technology. Leveraging computer technology, it uses a global gear error curve to construct a complete collection of individual and combined gear error information. It's well known that the measurement of gear dynamic performance primarily relies on single-flank gear meshing measuring instruments. Compared to conventional single-flank measurements, single-flank gear meshing measurements provide more global error information. Typical measuring instruments include the CZ150 and CZ450 for measuring cylindrical gear errors, manufactured by the Chengdu Tool Research Institute. However, these instruments are expensive and difficult to maintain, hindering the full realization of the advantages of the "global error measurement method" in practical applications.

[0004] To address these issues, a method for synthesizing overall error based on tooth profile waviness was proposed. This method uses tooth profile waviness as a measurement basis and uses computer technology to synthesize the tooth profile waviness into an overall gear error curve. This curve, derived through envelope calculation, then yields a gear transmission error curve. This overall gear error curve contains information on all parameters of the entire tooth surface under operating conditions. Because this method requires simple instrumentation, it facilitates the widespread and practical application of overall error analysis. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for synthesizing overall gear errors based on tooth profile waviness. Tooth surface waviness is the result of the combined influence of geometric characteristics 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 and helical waviness along the helix. By integrating the measurement results of tooth profile waviness, this method can efficiently and reliably synthesize the overall gear error curve. The gear transmission error curve can then be obtained through envelope calculation, providing a basis for gear accuracy assessment and quality control.

[0006] The present invention proposes a gear overall error synthesis method based on tooth profile waviness, which specifically includes the following steps:

[0007] Step 1: Establish a normal polar coordinate method tooth profile waviness measurement model

[0008] First, based on the measurement method of the involute tooth profile deviation, a suitable tooth profile waviness measurement method needs to be selected. For the present invention, a mathematical model for tooth profile waviness measurement is established using the polar coordinate method, and the tooth profile waviness is measured using the measurement center. The basic formula of this model is:

[0009]

[0010] Where φ is the angle of the gear rotation from the starting point to the measured point, x0 is the starting position of the probe, which is calculated from the starting point of the tooth profile detection range, and r b is the base circle radius.

[0011] According to the polar coordinate measurement principle for involute tooth profiles, the contact path between the stylus sphere and the involute tooth surface is the end face involute, which can be considered a plane curve. In the mathematical model of the generalized polar coordinate method, the stylus reading is affected by factors such as tooth profile deviation, measurement error introduced by offset variation, and control system errors. Therefore, these error factors must be comprehensively considered when establishing the model.

[0012] Step 2: Method for obtaining tooth profile waviness based on gear measurement center

[0013] During full-tooth measurement, the gear measuring center measures the tooth profile curve on the same normal plane. This measurement process adheres 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." The acquired coordinate data is one-dimensional and includes the total normal deviation values ​​for multiple tooth surface measurement points. This total normal deviation curve includes tooth profile waviness information, including shape error, waviness, and roughness.

[0014] During measurement, the wavelength observation of surface irregularities is limited due to data sampling rate limitations, resulting in a close relationship between measurement data density and data filtering. The number of data points within the measured length should be stated in the test report. For tooth profile waviness measurements, a minimum of 300 points or 5 points per millimeter (whichever is greater) should be included. These data points should be roughly equidistant along the length of the tooth profile to ensure measurement accuracy and data reliability.

[0015] Step 3: Synthesis of gear overall error curve based on tooth profile waviness

[0016] When measuring tooth profile waviness, 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 overall error, it is necessary to establish a corresponding calculation model to accurately calculate the rotation angle of each measuring point. The synthesis model is as follows: Figure 6 shown.

[0017] Specifically, the rotation angle calculation formula for each point is as follows:

[0018]

[0019] 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.

[0020] When synthesizing the overall error curve, the sum of the development angle, axial position, and rotational angle of each measurement point must be considered to ensure that the resulting error curve accurately reflects the overall deviation of the gear tooth profile. When all measurement points are arranged according to their rotational angle, a continuous closed measurement curve is formed, consisting of all measured tooth surfaces along the circumference. This method combines tooth profile waviness and pitch deviation to produce the overall gear error curve.

[0021] Step 4: Calculate the gear transmission error based on the gear overall error curve;

[0022] After synthesizing the gear overall error curve, the gear transmission error curve can be further calculated. The envelope of the overall error curve is calculated using the envelope method, and the gear transmission error curve is finally calculated. The specific calculation method is as follows:

[0023] S1. Define tooth profile waviness

[0024] The tooth profile waviness set of the kth tooth is defined as:

[0025] S k ={(x1,y1),(x2,y2),...,(x n ,y n )} (3)

[0026] Where x is the rotation angle, y is the tooth surface normal error, k is the kth tooth, the maximum value of k is the number of teeth, and n is the number of points measured on each tooth surface.

[0027] S2. Gear overall error curve synthesis

[0028] The overall gear error curve is represented by S:

[0029] S all ={S1,S2,...,S k} (4)

[0030] Where S k It represents the tooth surface error of the k-th tooth, k is the k-th tooth, and the maximum value of k is the number of teeth.

[0031] S3. Calculation of upper envelope of gear overall error

[0032] Rearrange the gear overall error curve in the order of rotation angle x from small to large to obtain a new set:

[0033] S new ={(x1,y1),(x2,y2),...,(x kn ,y kn )} (5)

[0034] S4. Calculate the gear transmission error curve

[0035] In the range of 360°, calculate S new The maximum value y corresponding to each rotation angle x max , each rotation angle x and its corresponding y max The gear transmission error curve is:

[0036] S total ={(x1,y1),(x2,y2),…,(x m ,y m )} (6)

[0037] Since the overall error curves calculated in step 3 overlap, m in the formula is not a fixed value and is calculated based on actual conditions.

[0038] Through the above steps, the gear transmission error curve can be accurately calculated within a 360° range. This curve reflects the maximum error at each measuring point on the gear tooth surface, providing an important basis for further gear accuracy analysis and optimization.

[0039] This paper proposes a method for calculating overall gear error based on tooth profile waviness. By establishing a precise measurement model, the tooth profile waviness and pitch deviation are measured, thereby synthesizing an overall error curve. Finally, the gear transmission error curve is obtained through envelope calculation. This method can effectively improve the efficiency and reliability of gear precision measurement and provide more comprehensive and accurate error analysis results. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Gear measuring center.

[0041] Figure 2 Schematic diagram of tooth profile waviness and pitch error measurement.

[0042] Figure 3 Schematic diagram of the tooth profile waviness measurement point spacing.

[0043] Figure 4 It is the tooth profile waviness information.

[0044] Figure 5 is the single tooth pitch deviation of the gear.

[0045] Figure 6 It is the synthetic model of gear overall error curve.

[0046] Figure 7 is the overall error curve of the gear.

[0047] Figure 8 To solve the gear transmission error curve using the envelope curve.

[0048] Figure 9 is the gear transmission error curve. DETAILED DESCRIPTION

[0049] 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.

[0050] The basic parameters of the selected characteristic gears are shown in Table 1.

[0051] Table 1 Parameters of the gears tested

[0052] parameter Number of teeth Modulus Pressure angle Helix angle Rotation Reshaping Tooth width Numerical 21 1.658mm 17.45° 23.2° right-handed Middle drum 20mm

[0053] Step 1: Establish a normal polar coordinate method tooth profile waviness measurement model

[0054] First, according to the measurement method of the involute tooth profile deviation, the polar coordinate method is selected to establish the tooth profile waviness measurement model. The polar coordinate method is the main measurement method of the gear measurement center, and its measurement principle is based on the polar coordinate system of the involute tooth profile. Based on this, according to the normal polar coordinate measurement principle of step 1, as shown in formula (1), the Klingelnberg P26 gear measurement center is selected as the measurement equipment, as shown in formula (1). Figure 1 The probe diameter is selected to be 1 mm to ensure that the tooth profile waviness and individual tooth pitch deviation can be measured.

[0055] Step 2: Method for obtaining tooth profile waviness based on gear measurement center

[0056] During the full gear measurement process, the gear measurement center is used to measure the tooth profile waviness and pitch deviation. The data collection, analysis, and evaluation process follow the gear precision standard GB10095.1-2022 "Tooth surface tolerance classification system for cylindrical gears Part 1: Definition and allowable values ​​of tooth surface deviation". The tooth profile waviness is measured at the middle of the tooth width, while the pitch is measured at the position of the measuring circle. The measurement position is as follows: Figure 2 The measurement points in the tooth profile direction are roughly equidistantly distributed along the developed length direction, as shown in 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 the meshing are calculated based on the meshing principle, thus determining the measurement starting position, evaluation position, final evaluation position, and final measurement position. During the involute tooth profile measurement, 480 measurement points were collected, which met the measurement requirements.

[0057] Table 2 Evaluation parameters of the tested gears

[0058] Measurement location Diameter of starting point Final measuring point diameter Starting point diameter Final evaluation point diameter Numerical 35.85mm 43.28mm 35.92mm 42.38mm

[0059] The waviness of the full tooth profile measured by the gear measuring center, such as Figure 4 The individual tooth pitch deviations measured at the gear measuring center are shown in Figure 5 shown.

[0060] Step 3: Synthesis of gear overall error curve based on tooth profile waviness

[0061] Based on the overall error curve synthesis method described in step 3, the synthesized model is as follows Figure 6 As shown, the rotation angle of each measuring point is calculated according to the following formula:

[0062]

[0063] 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 overall error curve after synthesis is as follows Figure 7 shown.

[0064] Step 4: Calculation of gear transmission error based on the gear overall error curve

[0065] By using the envelope method, Figure 7 The overall gear error curve is envelopingly calculated, and the transmission error curve is finally obtained. The specific calculation steps are as follows:

[0066] S1. Define tooth profile waviness information

[0067] The error set of the kth tooth is defined as:

[0068] S k ={(x1,y1),(x2,y2),…,(x 480 ,y 480 )}

[0069] At this time, the maximum value of k is 21, and the number of measurement points for each tooth profile is 480.

[0070] S2. Gear overall error curve synthesis

[0071] The overall gear error curve is represented by S:

[0072] S all ={S1,S2,…,S 21}

[0073] S3. Calculation of upper envelope of gear overall error

[0074] 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:

[0075] S new ={(x1,y1),(x2,y2),...,(x 21*480 ,y 21*480 )}

[0076] S4. Calculate the transmission error curve

[0077] 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 transmission error curve:

[0078] S total ={(x1,y1),(x2,y2),…,(x 9018 ,y 9018 )}

[0079] Figure 8 For the above calculation envelope process, the gear transmission error curve results are as follows: Figure 9 shown.

[0080] 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 overall error synthesis method based on tooth profile waviness, characterized in that: The following steps are involved: Step 1: Establish a tooth profile waviness measurement model using the normal polar coordinate method; First, according to the measurement method of involute tooth profile deviation, the tooth profile waviness measurement method needs to be selected; the mathematical model of tooth profile waviness measurement is established using the polar coordinate method, and the tooth profile waviness is measured using the measurement center; the tooth profile waviness measurement model formula of the normal polar coordinate method is: Where φ is the angle of the gear rotation from the starting point to the measured point, x0 is the starting position of the probe, which is calculated from the starting point of the tooth profile detection range, and r b is the base circle radius; According to the polar coordinate measurement principle of the involute tooth profile, the contact trajectory between the probe sphere and the involute tooth surface is the end face involute, which is regarded as a plane curve. In the mathematical model of the generalized polar coordinate method, the probe reading is affected by tooth profile deviation, measurement errors introduced by offset changes, and control system errors. These error factors must be comprehensively considered when establishing the model. Step 2: tooth profile waviness acquisition method based on gear measurement center; During full tooth measurement, the gear measurement center measures the normal total deviation tooth profile curve on the same normal plane of the gear. The measurement process follows gear accuracy standards, obtains coordinate data as one-dimensional data, and covers the normal total deviation values ​​of multiple tooth surface measurement points. The normal total deviation tooth profile curve contains tooth profile waviness information, namely the shape error, waviness, and roughness of the tooth profile. Step 3: Synthesis of gear overall error curve based on tooth profile waviness When measuring tooth profile waviness, 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 overall error, a corresponding calculation model is established to accurately calculate the rotation angle of each measuring point. Step 4: Calculate the gear transmission error based on the gear overall error curve; After synthesizing the gear overall error curve, the gear transmission error curve is calculated; the envelope of the overall error curve is calculated using the envelope method, and finally the gear transmission error curve is calculated.

2. The method for synthesizing gear overall errors based on tooth profile waviness according to claim 1, characterized in that: During the measurement process, due to the limitation of data sampling rate, the wavelength observation of surface irregularities is restricted, and there is a close relationship between the density of measurement data and data filtering. In the test report, the number of data points within the measuring length shall be indicated. For the measurement data points of tooth profile waviness, at least 300 points or 5 points per millimeter shall be included, whichever is larger.

3. The method for synthesizing gear overall errors based on tooth profile waviness according to claim 1, characterized in that: The measurement data points are distributed approximately equidistantly along the length direction of the tooth profile to ensure measurement accuracy and data reliability.

4. The method for synthesizing gear overall errors based on tooth profile waviness according to claim 1, characterized in that: The rotation angle calculation formula for each point is as follows: 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.

5. The method for synthesizing gear overall errors based on tooth profile waviness according to claim 1, characterized in that: When synthesizing the overall error curve, it is necessary to consider the sum of the development angle, axial position, and rotation angle of each measuring point to ensure that the final error curve can accurately reflect the overall deviation of the gear tooth profile; when all measuring points are arranged according to their rotation angles, a continuous closed measurement curve consisting of all measured tooth surfaces on the circumference is formed, and the tooth profile waviness and pitch deviation are combined to obtain the overall gear error curve.

6. The method for synthesizing gear overall errors based on tooth profile waviness according to claim 1, characterized in that: The specific calculation method for step 4 is as follows: S1. Define tooth profile waviness; The tooth profile waviness set of the kth tooth is defined as: S k ={(x1,y1),(x2,y2),...,(x n ,y n )}(3) Where x is the rotation angle, y is the normal error of the tooth surface, k is the kth tooth, the maximum value of k is the number of teeth, and n is the number of points measured on each tooth surface; S2. Synthesis of gear overall error curve; The overall gear error curve is represented by S: S all ={S1,S2,...,S k }(4) Where S k It represents the tooth surface error of the k-th tooth, k is the k-th tooth, and the maximum value of k is the number of teeth; S3. Calculation of the upper envelope of the gear overall error; Rearrange the gear overall error curve in the order of rotation angle 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 rotation angle x max , each rotation angle x and its corresponding y max The gear transmission error curve is: S total ={(x1,y1),(x2,y2),…,(x m ,y m )}(6) Through the above steps, the gear transmission error curve is accurately calculated within a 360° range. The gear transmission error curve reflects the maximum error at each measuring point on the gear tooth surface.

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