Tooth profile waviness-based gear overall error synthesis method

Abstract

The invention discloses a gear overall error synthesis method based on tooth profile waviness. The method comprises the steps that 1, a normal polar coordinate method tooth profile waviness measurement model is established; step 2, a tooth profile waviness acquisition method based on a gear measurement center; 3, synthesizing a gear overall error curve based on the tooth profile waviness; 4, gear transmission error calculation based on the gear overall error curve; according to the method, information such as the tooth profile waviness and the tooth pitch deviation is measured through the established accurate measurement model, so that the overall error curve is synthesized, and the gear transmission error curve is finally obtained through envelope calculation. According to the method, the efficiency and reliability of gear precision measurement can be effectively improved, and a more comprehensive and accurate error analysis result is provided.

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 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. In the field of gear testing, the gear measuring center is currently the most widely used measuring instrument. The instrument can accurately measure single gear errors such as gear profile deviation, helix deviation, and pitch deviation, thereby evaluating the gear accuracy. These measurement results can not only be used to analyze process errors in gear processing, but also to predict the performance of gears. However, the gear accuracy evaluation can only be analyzed from the perspective of a single tooth surface, and the overall gear error cannot be analyzed.

[0003] Gear overall error measurement is a new and efficient gear measurement technology. With the help of computer technology, it uses the gear overall error curve to form a complete collection of individual and comprehensive error information of the gear. As we all know, the measurement of gear dynamic performance mainly relies on the single-sided gear meshing measuring instrument. Compared with general single-item measurement, the single-sided gear meshing measurement can provide more overall error information. Typical measuring instruments include CZ150 and CZ450 produced by Chengdu Tool Research Institute for measuring cylindrical gear errors, but these instruments are expensive and difficult to maintain, so the advantages of the "overall error measurement method" have not yet been fully reflected in practical applications.

[0004] In order to solve these problems, a method of overall error synthesis based on tooth profile waviness is proposed. This method uses tooth profile waviness as the measurement basis, synthesizes the tooth profile waviness into a gear overall error curve using computer technology, and obtains the gear transmission error curve through envelope calculation. This gear overall error curve contains information on all parameters of the entire tooth surface of the gear under working conditions. Since the instrument required for this method is simple, it is helpful to promote the promotion and application of overall error in practice. Summary of the invention

[0005] The purpose of the present invention is to provide a method for synthesizing the overall gear error based on tooth profile 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. By integrating the measurement results of tooth profile waviness, this method can efficiently and reliably synthesize the overall gear error curve, and obtain the gear transmission error curve through envelope calculation, thereby providing a basis for gear accuracy evaluation and quality control.

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

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

[0008] First, according to the measurement method of the involute tooth profile deviation, a suitable tooth profile waviness measurement method needs to be selected. According to the present invention, 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 basic formula of the model is:

[0009]

[0010] Where φ is the angle of the gear from the starting point to the measured point, x 0 is the starting position of the probe, calculated from the starting point of the tooth profile detection range, r b is the base circle radius.

[0011] 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 can be regarded as a plane curve. In the mathematical model of the generalized polar coordinate method, the probe reading will be affected by factors such as tooth profile deviation, measurement error introduced by offset change, and control system error. Therefore, these error factors need to be comprehensively considered when establishing the model.

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

[0013] During the full tooth measurement process, the gear profile curve of the same normal plane of the gear is measured through the gear measurement center. The measurement process follows the gear accuracy standard GB10095.1-2022 "Cylindrical Gear Tooth Surface Tolerance Grading System Part 1: Definition and Allowable Values ​​of Tooth Surface Deviation". The acquired coordinate data is one-dimensional data and covers the normal total deviation values ​​of multiple tooth surface measurement points. This normal total deviation curve contains the tooth profile waviness information, that is, the shape error, waviness, and roughness of the tooth profile.

[0014] During the measurement process, due to the limitation of data sampling rate, the wavelength observation of surface irregular morphology is limited, so there is a close connection between the density of measured data and data filtering. In the test report, the number of data points within the measured length should be indicated. For the measurement data points of tooth profile waviness, at least 300 points or 5 points per millimeter (the larger value of the two) are included. These measurement data points are roughly equidistantly distributed 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 the waviness of the tooth profile, each measuring point corresponds to a development angle, which indicates the specific position of the gear in 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, D 0 is the pitch circle diameter, ξ is the development angle, and τ is the pitch angle.

[0020] 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. In this way, the tooth profile waviness and pitch deviation can be combined to obtain the overall gear error curve.

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

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

[0023] S1. Definition of tooth profile waviness

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

[0025] S k ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(x n ,y n )} (3)

[0026] 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.

[0027] S2. Synthesis of gear overall error curve

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

[0029] S all ={S 1 ,S 2 ,...,S k} (4)

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

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

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

[0033] S new ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(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 ={(x 1 ,y 1 ),(x 2 ,y 2 ),…,(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] The present invention proposes a method for calculating the overall gear error based on tooth profile waviness. By establishing an accurate measurement model, the tooth profile waviness and pitch deviation information are measured to synthesize the overall error curve, and the gear transmission error curve is finally 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 Measuring center of gear.

[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 pitch deviation of the gear.

[0045] Figure 6 It is the synthesis 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] Fig. 9 is the gear transmission error curve. DETAILED DESCRIPTION

[0049] 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.

[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 Numeric 21 1.658mm 17.45° 23.2° Right 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 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 gear full tooth 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 accuracy standard GB10095.1-2022 "Cylindrical Gear Tooth Surface Tolerance Grading System Part 1: Definition and Allowable Value of Tooth Surface Deviation". The tooth profile waviness measurement position is located in the middle of the tooth width, while the pitch measurement position is located 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. 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 trimming. 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 involute tooth profile measurement, 480 measurement points were collected, and the number of measurement points 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 Numeric 35.85mm 43.28mm 35.92mm 42.38mm

[0059] The full tooth profile waviness measured by the gear measuring center, such as Figure 4 The individual 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 synthetic 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, D 0is 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: Gear transmission error calculation 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 calculated. 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 ={(x 1 ,y 1 ),(x 2 ,y 2 ),…,(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. Synthesis of gear overall error curve

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

[0072] S all ={S 1 ,S 2 ,…,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 ={(x 1 ,y 1 ),(x 2 ,y 2 ),...,(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 ymax The value of is the transmission error curve:

[0078] S total ={(x 1 ,y 1 ),(x 2 ,y 2 ),…,(x 9018 ,y 9018 )}

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

[0080] 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 overall error synthesis method based on tooth profile waviness, characterized in that: The following steps are involved: Step 1: Establish a normal polar coordinate method tooth profile waviness measurement model; 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 from the starting point to the measured point, x0 is the starting position of the probe, calculated from the starting point of the tooth profile detection range, r b is the base circle radius; According to the polar coordinate measurement principle of 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 will be affected by the tooth profile deviation, the measurement error introduced by the offset change, and the control system error factor. These error factors need to be comprehensively considered when establishing the model; Step 2: tooth profile waviness acquisition method based on gear measurement center; During the full tooth measurement process, the normal total deviation tooth profile curve of the same normal plane of the gear is measured by the gear measurement center; the measurement process follows the gear accuracy standard, the coordinate data obtained is 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, that is, 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 the waviness of the tooth profile, each measuring point corresponds to a development angle, which indicates the specific position of the gear in 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: Calculation of gear transmission error based on the gear overall error curve; After synthesizing the overall gear error curve, the gear transmission error curve is calculated; the envelope curve of the overall error curve is calculated using the envelope curve 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 irregular morphology is limited, and there is a close connection 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 composed 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 of step 4 is as follows: S1. Define the 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 kth tooth, k is the kth tooth, and the maximum value of k is the number of teeth; S3. Calculation of upper envelope of gear overall error; The gear overall error curve is rearranged in 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 range of 360°, and the gear transmission error curve reflects the maximum error at each measuring point on the gear tooth surface.

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