Harmonic reducer transmission error evaluation method

Abstract

The invention relates to the field of harmonic reducers, and discloses a harmonic reducer transmission error evaluation method which comprises a transmission error test method, evaluation indexes, a transmission error mechanism model and index connotation. The method can be used for effectively testing, evaluating, feeding back and optimizing the transmission precision of the harmonic reducer. The method has important technical guidance significance for performance grade evaluation and optimization improvement of the harmonic reducer.

Description

Technical Field

[0001] This invention relates to the field of harmonic reducers, and more specifically to a method for evaluating the transmission error of a harmonic reducer. Background Technology

[0002] Existing methods for measuring transmission errors in harmonic reducers involve driving the test piece at the input end, with the output end either unloaded or under a specified load. After the speed and load stabilize, the real-time rotation angle values ​​at the input and output ends are recorded within one revolution at the output end, with the output speed required to be no greater than 5 r / min. This indicates that the testing conditions are not standardized, which reduces the comparability of test results.

[0003] Furthermore, existing evaluation methods for harmonic reducer transmission errors use a single evaluation index—the difference between the extreme values ​​of measured values—which reflects incomplete information. Moreover, current testing and evaluation methods treat the reducer as a "black box" for performance level evaluation, failing to provide feedback and optimization of reducer design, manufacturing, and assembly processes based on test results. Summary of the Invention

[0004] The present invention aims to provide a method for evaluating the transmission error of harmonic reducers, thereby optimizing the evaluation method for the transmission error of harmonic reducers and revealing its error transmission mechanism to achieve accurate tracing of the source of error.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a method for evaluating the transmission error of a harmonic reducer, including a method for testing the transmission error of the reducer, a method for determining the error evaluation index, and a method for judging the error formation mechanism; The test method for reducer transmission error includes: testing under no-load and rated load conditions, with the input shaft speed at ±5 rpm and the output shaft rotating at least one revolution. The unidirectional test time is set to (2+N / 5) min, where N is the reducer transmission ratio. The test process includes: A. First, speed up loading and ensure stable operation; B. Then, the transmission error measurement period begins, during which the reducer runs stably for N / 5 minutes. C. Then maintain stable operation and uninstall at a reduced speed; D. Then change the rotation direction to accelerate loading and stabilize operation; E. Repeat step B; F. Repeat step C.

[0006] Preferably, as an improvement, the indicators determined in the error evaluation index determination method include the difference between two extreme values ​​in the time domain and the amplitudes of the components with frequencies of 1 / Nωb, ωb, and 2ωb.

[0007] Preferably, as an improvement, the error formation mechanism judgment method includes positive evaluation and reverse feedback of transmission error guided by wave generator misalignment and gear tooth machining error.

[0008] Preferably, as an improvement, the influence of gear tooth machining error on transmission error is analyzed using tangential comprehensive error analysis.

[0009] This invention combines the transmission characteristics of harmonic reducers (rigid-flexible combination, multi-tooth meshing transmission, and machining and assembly errors) to analyze the physical meaning of transmission errors, and considers the influence of measurement position and test conditions to improve the transmission error evaluation method of reducers. By comprehensively considering wave generator misalignment (eccentricity and skewness errors) and gear tooth errors, a transmission error calculation formula is derived, revealing the error transmission mechanism of internal components of the harmonic reducer, enabling tracing the source of transmission errors from harmonic reducer to component and assembly errors.

[0010] The key technical points of this invention include: First, linear interpolation is performed on the transmission error to obtain transmission error data distributed at equal intervals according to the input shaft rotation angle. Then, the data is detrended to ensure that the mean of the processed data is zero. Finally, a Fast Fourier Transform is performed on the data to obtain the frequency components of the error signal based on the input shaft rotation speed. Based on this, a time-frequency domain multivariate evaluation index for the reducer transmission error is constructed.

[0011] Second: Mathematical modeling of wave generator misalignment and gear tooth error is performed. Based on the planar motion model of the reducer, the motion effect of the flexible wheel cup is considered to construct a transmission error calculation model.

[0012] The technical effects of this invention include: First: It includes four evaluation indicators in the time and frequency domains, which more completely reflects the transmission error characteristics of the reducer under the condition of processing and assembly defects.

[0013] Second: Constructing a transmission error model reveals the formation mechanism of the reducer motion difference, enabling positive evaluation and reverse feedback of transmission errors. Attached Figure Description

[0014] Figure 1 This is a process diagram of the transmission error testing method according to an embodiment of the present invention.

[0015] Figure 2 This is a time-domain diagram of an embodiment of the present invention.

[0016] Figure 3 This is a frequency domain diagram of an embodiment of the present invention.

[0017] Figure 4 This is a mathematical model diagram of the misalignment of the wave generator in an embodiment of the invention.

[0018] Figure 5This is a mathematical model diagram of gear tooth error in an embodiment of the present invention.

[0019] Figure 6 This is a diagram of the speed reducer transmission error model in an embodiment of the present invention. Detailed Implementation

[0020] The following detailed description illustrates the specific implementation method: Example: Method for evaluating transmission error of harmonic reducer, such as... Figure 1 As shown, the tests were conducted under no-load (geometric transmission error, mainly affected by the geometric error of the contact surface) and rated load (static transmission error, which reflects not only the geometric error of the contact surface but also the effect of elastic deformation caused by loading), with an input shaft speed of ±5 rpm. To fully test the transmission error of the reducer, the output shaft was required to rotate at least one revolution during the test. Considering fluctuations after loading or acceleration, the unidirectional test time was set to (2+N / 5) min (where N is the reducer transmission ratio) to improve testing efficiency. Segment a represents accelerating and loading within 1 minute to achieve stable operation; segment b is the transmission error measurement period, during which the reducer runs stably for N / 5 min (the time for one revolution of the output shaft); segment c represents the period after the transmission error test is completed, maintaining stable operation for a certain time before decelerating and unloading, then changing the direction of rotation to enter time segments d, e, and f (similar to time segments a, b, and c, where the acceleration in the two test directions is the same). After completing the above steps under no-load and rated load conditions, the transmission error test of the reducer is complete.

[0021] A typical transmission error curve of a harmonic reducer is stable with beat frequency characteristics in the time domain and exhibits a frequency of 2ω in the frequency domain. b The component is the main component of the error (ω). b (This refers to the rotational frequency of the wave generator). However, when the reducer has manufacturing or assembly quality defects, such as... Figure 2 As shown, the main component of transmission error is not only the frequency of 2ω. b The component, with a frequency of 1 / Nω b or ω b The proportion of the error component is also large. Existing transmission error indices are the difference between two extreme values ​​in the time domain. When the reducer has no quality defects, these indices can effectively reflect the reducer's performance status; however, they cannot reflect the reducer's defects when defects exist. To comprehensively reflect the reducer's performance and quality status, this invention proposes three frequency domain indices based on existing time domain indices, such as... Figure 3 As shown, these are frequencies of 1 / Nω. b ω b and 2ω b The amplitude of the component.

[0022] To clarify the meaning of the evaluation indicators, this invention patent considers the misalignment of the wave generator and the gear tooth machining error to reveal the formation mechanism of the reducer's motion error, which is used to guide the positive evaluation and reverse feedback of transmission errors. For example... Figure 4 This is a schematic diagram of the eccentricity and skewness errors of the wave generator, where axis O... C Z1 and O F Z3 represents the axis of the rigid wheel and the wave generator, OZ2 is the input axis, and point O... F It is the geometric center of the wave generator. Coordinate system O F The Y3 axis of -X3Y3Z3 coincides with the major axis of the wave generator, and the plane X3O F Y3 and X1O C Y1 coincides with the mid-plane of the wave generator. Points O and O F Located in plane X1O C In Y1 and X2OY2, axes Y2 and Y3 are parallel to plane Y1O. C Z1 and plane Y2OZ2. Axis O C There are two angular deviations between Z1 and axis OZ2, namely Y1O C Angle β2 on plane Z1, and X1O C Angle β3 lies in the Z1 plane. Similarly, angles α2 and α3 are axes OZ2 and OZ2, respectively. F The angular deviation between Z3. The eccentricity error is determined by the lengths e1 and e2 and the angles β1 and α1, while the skew error is determined by the four angular deviations β2, β3, α2, and α3. Among them, e1, β1, β2, and β3 mainly come from the assembly defects of the wave generator into the flexspline, while e2, α1, α2, and α3 are mainly caused by the processing defects of the wave generator.

[0023] This patent analyzes the impact of gear tooth machining errors on motion errors using a comprehensive error index (tangential comprehensive error). For example... Figure 5 The experimental curve of the tangential synthesis error can be divided into two parts using Fourier transform: long-wavelength and short-wavelength components. In practice, the single-tooth tangential synthesis deviation is usually considered to be the same as the short-wavelength component of the tangential synthesis error, which is difficult to identify and model using a mathematical model. Figure 5 As shown, it is characterized by small amplitude and high frequency. Therefore, its influence on motion error is not considered in this patent. The long-wavelength component of the tangential composite error can usually be represented by a sine function.

[0024] In the formula, a, ω and φ represent the magnitude, frequency and initial phase angle of the gear tooth error, respectively.

[0025] like Figure 6As shown, points B and C are two points fixed on the pitch curves of the flexible and rigid wheels, respectively. Initially, points B and C coincide, but after the wave generator is rotated clockwise by a certain angle... Ideally, when the wave generator is considered a stationary component, such as... Figure 6 As shown, points B and C eventually move to points B' and C', respectively, with the arc lengths traversed by points B and C being equal. In reality, due to manufacturing and assembly errors, point C ultimately lies at point C''. According to the kinematic model of the flexible wheel cup, this can be achieved by making the arc lengths on the closed end and the deformed end of the flexible wheel equal (see...). Figure 6 l C'C” =l DE To derive the non-uniform motion component θ of the error. me .set up Figure 6 Mid-arc length l AD To represent the equivalent arc length of the torsional flexibility and clearance at the closed end of the flexure, the transmission error can be expressed as: Among them l FS It is the total length of the flexible pitch curve.

[0026] Based on the above discussion, and according to the motion error model, the transmission error of the harmonic reducer caused by the combination of gear tooth error and wave generator misalignment can be obtained as follows: Wherein, τ1 and τ2 are the equivalent displacements of the meshing point along the pitch circle direction of the deformed flexible gear in the two meshing zones 1 and 2 of the harmonic reducer caused by gear tooth error and misalignment with the wave generator, respectively, and k e The error averaging coefficient can be expressed as follows: Among them, Z mp The number of meshing tooth pairs in a meshing region, with coefficient k B The value range is 0.8 to 1.0.

[0027] This invention reveals the mapping relationship between reducer transmission error and its design parameters, machining and assembly quality, and the rigid-flexible multi-tooth transmission characteristics of the reducer. Based on this, machining and assembly defects in the reducer can be revealed using transmission error test data, thereby improving transmission performance. For example, common transmission error anomalies can be explained using this model as follows: (Frequency ω) b The error component amplitude is relatively large. This is attributed to the fact that when misalignment E1 (misalignment between the input shaft and the geometric axis of the rigid wheel) exists, misalignment E2 (misalignment between the input shaft and the geometric axis of the wave generator) is also large. In other words, the hole for assembling the input shaft on the wave generator is not machined properly. The frequency is ω. b The error component of / N has a relatively large amplitude. This is due to two reasons: firstly, the errors in the rigid or flexible gear teeth are large, resulting in a transmission error component (ω) caused by the combined effect of these gear tooth errors.b The error is due to two main reasons. First, the assembly error of the flexible gear cup (the deviation of the cup's rotation axis from its geometric axis) is too large. The beat frequency phenomenon of the transmission error curve is a unique characteristic caused by the gear tooth error of the reducer and its transmission principle. It cannot be eliminated, only reduced.

[0028] The above descriptions are merely embodiments of the present invention, and common knowledge such as specific technical solutions and / or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for evaluating the transmission error of a harmonic reducer, characterized in that: This includes methods for testing transmission errors in speed reducers, methods for determining error evaluation indicators, and methods for judging error formation mechanisms. The test method for reducer transmission error includes: testing under no-load and rated load conditions, with the input shaft speed at ±5 rpm and the output shaft rotating at least one revolution. The unidirectional test time is set to (2+N / 5) min, where N is the reducer transmission ratio. The test process includes: A. First, speed up loading and ensure stable operation; B. Then, the transmission error measurement period begins, during which the reducer runs stably for N / 5 minutes. C. Then maintain stable operation and uninstall at a reduced speed; D. Then change the rotation direction to accelerate loading and stabilize operation; E. Repeat step B; F. Repeat step C.

2. The method for evaluating the transmission error of a harmonic reducer according to claim 1, characterized in that: The error evaluation index determination method defines the indexes including the difference between two extreme values ​​in the time domain and the amplitudes of the components with frequencies of 1 / Nωb, ωb, and 2ωb.

3. The method for evaluating the transmission error of a harmonic reducer according to claim 2, characterized in that: The error formation mechanism judgment method includes positive evaluation and reverse feedback of transmission error guided by wave generator misalignment and gear tooth machining error.

4. The method for evaluating the transmission error of a harmonic reducer according to claim 3, characterized in that: The influence of gear tooth machining error on transmission error is analyzed using tangential comprehensive error analysis.

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