A double circular arc harmonic reducer transmission error modeling method considering fault factors

Abstract

The present application belongs to the technical field of gear transmission error modeling, aiming to solve the problem that the current research on the influence of faults on transmission error is not thorough, and there is no transmission error model of harmonic reducer containing faults. A double-arc harmonic reducer transmission error modeling method considering fault factors is provided, including the following steps: analyzing the error sources of the harmonic reducer to obtain the eccentric vector angular displacement error related to the rigid wheel, the flexible wheel and the wave generator; regarding different types of error sources as satisfying normal distribution relationship, considering the error homogenization effect, obtaining the comprehensive transmission error of the harmonic reducer; based on the change of the transmission error component amplitude of each error source in the comprehensive transmission error when the harmonic reducer fails, obtaining the transmission error model of the harmonic reducer affected by the fault. This method can analyze the transmission error change of each error source according to the fault influence, and provide a more accurate error model under fault.

Description

Technical Field

[0001] This invention belongs to the field of gear transmission error modeling technology, specifically relating to a method for modeling gear transmission errors in a dual circular arc harmonic reducer. Background Technology

[0002] Harmonic reducers consist of a wave generator, flexible bearings, a flexspline, and a rigid wheel, transmitting motion and force through the deformation of the flexspline. Harmonic reducers offer advantages such as compact structure, small size, light weight, high transmission ratio and load capacity, and high transmission accuracy. Transmission error is a crucial indicator of a harmonic reducer's transmission performance, representing the angular difference between the ideal and actual positions of the output gear. The transmission error signal is obtained by acquiring and calculating the input and output angles using encoders mounted on the input and output shafts. Compared to commonly used fault diagnosis signals such as vibration and temperature signals, the transmission error signal contains richer operational status information. Furthermore, due to the higher accuracy of the encoder and the simpler, more direct transmission path, the transmission error signal is less susceptible to external environmental interference, making it more suitable for fault diagnosis.

[0003] However, the impact of faults on transmission errors is not yet thoroughly studied, and there is no transmission error model for harmonic reducers with faults. Summary of the Invention

[0004] In order to solve at least one of the above-mentioned technical problems in the prior art, the present invention provides a method for modeling transmission errors of a dual circular arc harmonic reducer that takes into account fault factors.

[0005] This invention is achieved using the following technical solution: a method for modeling transmission errors of a dual-circular-arc harmonic reducer considering fault factors, comprising the following steps:

[0006] Based on the transmission principle and structural composition of the double circular arc harmonic reducer, the error sources affecting the transmission error of the harmonic reducer are identified; the structure of the harmonic reducer includes a rigid wheel, a flexible wheel, and a wave generator.

[0007] Analyzing the error sources of the harmonic reducer, we obtain the angular displacement errors of each eccentric vector related to the rigid wheel, flexible wheel, and wave generator;

[0008] Based on the error frequency of the angular displacement error of each eccentric vector, different types of error sources are classified.

[0009] By treating different types of error sources as satisfying a normal distribution relationship and considering the error averaging effect, the comprehensive transmission error of the harmonic reducer is obtained.

[0010] Based on the changes in the amplitude of the transmission error components of each error source in the comprehensive transmission error when a harmonic reducer fails, a transmission error model of the harmonic reducer affected by the fault is obtained. The transmission error model reflects the degree to which the eccentric vector of each error source is affected by the fault.

[0011] Preferably, the error sources of the harmonic reducer include manufacturing errors and assembly errors. The manufacturing errors include the combined eccentricity vector of the rigid wheel, the combined eccentricity vector of the flexible wheel, and the combined tangential error of one tooth. The assembly errors include the rigid wheel assembly error, the eccentricity vector that does not rotate with the flexible wheel, the eccentricity vector that rotates with the flexible wheel, the eccentricity vector that rotates with the wave generator, and the eccentricity vector that does not rotate with the wave generator.

[0012] Preferably, in the manufacturing error, the angular displacement error caused by the combined eccentricity vector of the rigid wheel is expressed as:

[0013]

[0014] Where, r bCS r is the base circle radius of the rigid wheel; CS r is the pitch circle radius of the rigid wheel; bCS =r CS cosα n ;α n ω is the engagement angle; ω is the rotational speed of the wave generator; t is time; ΔF p1 For the cumulative pitch error of the rigid wheel; φ 11 For ΔF p1 The initial phase angle; e 11n The component of the combined eccentricity vector of the rigid wheel along the meshing line;

[0015] The angular displacement error caused by the combined eccentricity vector of the flexible wheel is expressed as:

[0016]

[0017] Where, ΔF p2 For the cumulative pitch error of the flexible wheel; ΔF p2 The initial phase angle is φ 12 ;e 21n For the eccentric vector of the flexible wheel; z CS z is the number of teeth on the rigid wheel; FS This refers to the number of teeth on the flexible gear.

[0018] The angular displacement error caused by the combined tangential error of one tooth of the rigid wheel and the flexible wheel is expressed as:

[0019]

[0020] Where, Δf f1 and Δf f2These represent the combined tangential error of one tooth of the rigid wheel and the flexible wheel, respectively; N is the number of teeth meshing simultaneously.

[0021] Preferably, in the assembly error, the angular displacement error caused by the assembly error of the rigid wheel is expressed as:

[0022]

[0023] Where, ΔE 21 e represents the assembly error of the rigid wheel. 21 =ΔE 21 / 2;φ 21 For ΔE 21 The initial phase angle;

[0024] The angular displacement error caused by the eccentric vector that does not rotate with the flexible wheel is expressed as:

[0025]

[0026] Where, ΔE 22 φ represents the eccentric vector that does not rotate with the flexure; 22 Indicates ΔE 22 The initial phase angle;

[0027] The angular displacement error caused by the eccentric vector as the flexure rotates is expressed as:

[0028]

[0029] Where, ΔE 23 φ represents the eccentric vector that rotates with the flexure. 23 Indicates ΔE 23 The initial phase angle;

[0030] The angular displacement error caused by the eccentric vector rotating with the wave generator is expressed as:

[0031]

[0032] Where, ΔE 31 It is the eccentric vector that rotates with the wave generator; θ1 represents the eccentric vector ΔE. 31 The angle between the wave generator and its major axis;

[0033] The angular displacement error caused by the eccentric vector that does not rotate with the wave generator is expressed as:

[0034]

[0035] Where, ΔE 32 It is an eccentric vector that does not rotate with the wave generator; φ 32 It is ΔE 32 The initial phase angle.

[0036] Preferably, based on the different error frequencies, the error sources are divided into five categories:

[0037] The first type is the transmission error caused by the eccentric vector that rotates with the wave, and the output error frequency is a constant value;

[0038] The second type is the transmission error caused by an eccentric vector that does not rotate with the flexspline; the output error frequency is the same as the input frequency of the wave generator. times;

[0039] The third type is the transmission error caused by the combined eccentric vector of the rigid wheel, the assembly error of the rigid wheel, and the eccentric vector that does not rotate with the wave generator. The output error frequency is twice the input frequency of the wave generator.

[0040] The fourth type is the transmission error caused by the combined eccentric vector of the flex wheel and the eccentric vector that rotates with the flex wheel. The output error frequency is equal to the input frequency of the wave generator. times;

[0041] The fifth type is the transmission error caused by the combined error of a single tooth tangential direction, with the output frequency being equal to the input frequency. times.

[0042] Preferably, the formula for calculating the overall transmission error is:

[0043]

[0044] Among them, K b Δ is the operating condition coefficient; N is the total number of meshing teeth; Δ ij ξ represents the transmission error caused by each error source; ξ is the conversion coefficient from linear to angular; and d is the pitch circle diameter of the flexure.

[0045] Preferably, when a harmonic reducer fails, the change in the amplitude of the transmission error components of each error source in the overall transmission error can be expressed as:

[0046] Where, Δ′F pj j = 1, 2 represents the cumulative error of the cycle under fault conditions; k pj This represents the cumulative error increment during fault conditions; Δ′E xy x = 2, 3; y = 1, 2, 3 represent assembly errors under fault conditions; k xy Δ′f represents the assembly error increment under fault conditions. fi , i = 1, 2 represent the tangential adjacent combined error under fault conditions; k fi denoted as the tangential adjacent comprehensive error increment under fault conditions; p represents the gear meshing process; P represents the meshing process of the faulty gear tooth.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] This invention presents a modeling method for transmission errors in a dual-circular-arc harmonic reducer that considers fault factors. The method first analyzes the manufacturing and assembly errors of the wave generator, rigid wheel, and flexible wheel, and calculates the resulting angular displacement errors. Then, based on the distribution of different error terms, the overall transmission error of the assembled harmonic reducer is considered as the sum of the transmission errors caused by various eccentricity vectors of assembly and manufacturing errors. In the event of a fault, this method can analyze the changes in transmission errors from each error source based on the fault's impact, providing a more accurate fault-based error model and offering a theoretical basis for improving the transmission accuracy and lifespan prediction accuracy of harmonic reducers. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 This is a schematic diagram of the gear meshing in the harmonic reducer of the present invention;

[0052] Figure 3 This is a schematic diagram of the harmonic reducer gear meshing in the coordinate axis in this invention;

[0053] Figure 4 This is a schematic diagram of the integrated eccentric vector in this invention;

[0054] Figure 5 This is a schematic diagram of assembly errors in this invention;

[0055] Figure 6 This is a schematic diagram of the wave generator error in this invention;

[0056] Figure 7 This is a transmission error signal diagram when the harmonic reducer fails in this invention. Detailed Implementation

[0057] The technical solutions of the embodiments of the present invention will be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should fall within the scope of the technical content disclosed in the present invention. It should be noted that in this specification, relational terms such as "first" and "second" are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0059] This invention provides an embodiment:

[0060] like Figure 1 As shown, a method for modeling transmission errors of a dual-circular-arc harmonic reducer considering fault factors includes the following steps:

[0061] Based on the transmission principle and structural composition of the double circular arc harmonic reducer, the error sources affecting the transmission error of the harmonic reducer are obtained. The structure of the harmonic reducer includes a rigid wheel, a flexible wheel, and a wave generator. Analyzing the error sources of the harmonic reducer, the angular displacement errors of each eccentric vector related to the rigid wheel, flexible wheel, and wave generator are obtained. Based on the error frequency of each eccentric vector angular displacement error, different types of error sources are classified. Treating different types of error sources as satisfying a normal distribution relationship and considering the error averaging effect, the comprehensive transmission error of the harmonic reducer is obtained. Based on the changes in the amplitude of the transmission error components of each error source in the comprehensive transmission error when the harmonic reducer fails, combined with the harmonic transmission principle and the causes of its errors, a transmission error model of the harmonic reducer affected by the fault is obtained. This transmission error model reflects the degree to which the eccentric vector of each error source is affected by the fault.

[0062] In this embodiment, the error sources of the harmonic reducer include manufacturing errors and assembly errors. Manufacturing errors include the combined eccentricity vector of the rigid wheel, the combined eccentricity vector of the flexible wheel, and the combined tangential error of one tooth. Assembly errors include the rigid wheel assembly error, eccentricity vectors that do not rotate with the flexible wheel, eccentricity vectors that rotate with the flexible wheel, eccentricity vectors that rotate with the wave generator, and eccentricity vectors that do not rotate with the wave generator. Under normal circumstances, manufacturing and assembly errors of various key components of the harmonic reducer will cause the actual meshing point to deviate from the theoretical meshing point, thus generating transmission errors. For ease of calculation, each error is converted into a corresponding eccentricity vector.

[0063] like Figure 2As shown, for dual-wave drives, the harmonic reducer has two meshing zones simultaneously. Without considering manufacturing and assembly errors, the meshing in the two zones should be completely identical. However, in reality, due to manufacturing and assembly errors, the meshing zones are not perfectly symmetrical; the meshing depth increases on one side, while the meshing on the other side weakens. Therefore, the influence of the dominant zone is mainly analyzed. This also illustrates that the transmission error caused by the manufacturing error of the rigid-flexible wheel has a cycle of half a revolution of the wave generator.

[0064] Figure 3 The gear meshing situation is illustrated, where K is the theoretical meshing point. The combined eccentricity vector e at the theoretical meshing point K can be decomposed into e along the meshing line direction. n and e perpendicular to the line of engagement t .

[0065] like Figure 4 As shown, in manufacturing errors, for the combined eccentricity vector e of the rigid wheel 11 Its component along the line of engagement is denoted as e. 11n Its frequency of change is twice the rotational frequency of the wave generator, which can be expressed as:

[0066]

[0067] Among them, e 11 It is the combined eccentricity vector of the rigid wheel, e 11 =ΔF p1 / 2cosα n θ is the angle between the major axis of the ellipse and the Y-axis, θ = 2ωt;

[0068] The angular displacement error caused by the combined eccentricity vector of the rigid wheel is expressed as:

[0069]

[0070] Where, r bCS r is the base circle radius of the rigid wheel; CS r is the pitch circle radius of the rigid wheel; bCS =r CS cosα n ;α n ω is the engagement angle; ω is the rotational speed of the wave generator; t is time; ΔF p1 For the cumulative pitch error of the rigid wheel; φ 11 For ΔF p1 The initial phase angle; e 11n This represents the component of the rigid wheel's composite eccentricity vector along the meshing line.

[0071] For the composite eccentricity vector e of the flexible wheel 21n Similar to a rigid wheel, the angular displacement error caused by the combined eccentricity vector of a flexible wheel can be derived as follows:

[0072]

[0073] Where, ΔF p2 For the cumulative pitch error of the flexible wheel; ΔF p2 The initial phase angle is φ 12 ;e 21n For the eccentric vector of the flexible wheel; z CS z is the number of teeth on the rigid wheel; FS This refers to the number of teeth on the flexible gear.

[0074] The combined tangential error of a single tooth is determined by the tooth profile errors of the meshing teeth of the rigid and flexible gears. Each meshing of the rigid and flexible gears results in one tooth profile error affecting the harmonic transmission, thus influencing harmonic transmission within each meshing cycle. During the operation of the harmonic reducer, multiple pairs of teeth mesh simultaneously. Considering their similar effects on the harmonic transmission, their effects are treated as identical to simplify the model. The angular displacement error caused by the combined tangential error of a single tooth of the rigid and flexible gears is expressed as:

[0075]

[0076] Where, Δf f1 and Δf f2 These represent the combined tangential error of one tooth of the rigid wheel and the flexible wheel, respectively; N is the number of teeth meshing simultaneously.

[0077] like Figure 5 As shown, in the assembly error, after the double circular arc harmonic reducer is installed, the assembly error of the rigid wheel remains constant. Therefore, the angular displacement error caused by the rigid wheel assembly error is expressed as:

[0078]

[0079] Where, ΔE 21 e represents the assembly error of the rigid wheel. 21 =ΔE 21 / 2;φ 21 For ΔE 21 The initial phase angle;

[0080] Assembly errors of flex wheels are divided into two categories: assembly errors caused by eccentric vectors that do not rotate with the flex wheel and assembly errors caused by eccentric vectors that rotate with the flex wheel.

[0081] The first type of assembly error remains constant. As the flex wheel rotates slowly, it affects the meshing between the flex wheel and the rigid wheel at different positions, leading to transmission errors. That is, this type of assembly error will produce a periodic change during one revolution of the flex wheel. The angular displacement error caused by the eccentric vector that does not rotate with the flex wheel is expressed as:

[0082]

[0083] Where, ΔE 22 φ represents the eccentric vector that does not rotate with the flexure; 22 Indicates ΔE 22 The initial phase angle;

[0084] The second type of assembly error is affected by the position of the meshing zone, and its variation frequency corresponds to the rotation frequency of the flexure relative to the wave generator. The angular displacement error caused by the eccentric vector of the flexure rotation is expressed as:

[0085]

[0086] Where, ΔE 23 φ represents the eccentric vector that rotates with the flexure. 23 Indicates ΔE 23 The initial phase angle;

[0087] The errors of wave generators mainly come from machining errors and assembly errors. Based on their influence on the meshing of rigid and flexible wheels, they can be divided into two categories: the first category is the eccentric vector that rotates with the wave generator; the second category is the eccentric vector that does not rotate with the wave generator.

[0088] like Figure 6 As shown, the first type of eccentric vector has a fixed effect on the meshing of the rigid wheel and the flexible wheel, resulting in a constant angular displacement error. The angular displacement error caused by the eccentric vector rotating with the wave generator is expressed as:

[0089]

[0090] Where, ΔE 31 It is the eccentric vector that rotates with the wave generator; θ1 represents the eccentric vector ΔE. 31 The angle between the wave generator and its major axis;

[0091] Once the wave generator is assembled, the second type of eccentric vector remains constant. It can be equivalent to the opposite eccentric vector acting on the rigid wheel. The angular displacement error caused by this eccentric vector, which does not rotate with the wave generator, is expressed as:

[0092]

[0093] Where, ΔE 32 It is an eccentric vector that does not rotate with the wave generator; φ 32 It is ΔE 32 The initial phase angle.

[0094] In summary, the angular displacement errors of harmonic reducers under normal conditions can be categorized into the following types, as shown in the table. Therefore, the comprehensive transmission error is the sum of each angular displacement error, which can be expressed as:

[0095] Δ=∑Δ ij

[0096]

[0097] Based on their error frequencies, error sources are categorized into five types: The first type is transmission error caused by an eccentric vector that rotates with the wave, with an output error frequency that is constant; the second type is transmission error caused by an eccentric vector that does not rotate with the flexspline, with an output error frequency that is equal to the input frequency of the wave generator. The third category is the transmission error caused by the combined eccentric vector of the rigid wheel, the assembly error of the rigid wheel, and the eccentric vector that does not rotate with the wave generator; the output error frequency is twice the input frequency of the wave generator. The fourth category is the transmission error caused by the combined eccentric vector of the flexible wheel and the eccentric vector that rotates with the flexible wheel; the output error frequency is twice the input frequency of the wave generator. The fifth type is the transmission error caused by the combined error of a single tooth tangential direction, with the output frequency being a multiple of the input frequency. times.

[0098] Different types of error sources satisfy different probability distribution forms. If we consider them all to satisfy a normal distribution relationship, the comprehensive transmission error can be expressed as the sum of the transmission errors caused by the various eccentric vectors of assembly error and machining error. Considering the error averaging effect, the formula for calculating the comprehensive transmission error is:

[0099]

[0100] Among them, K b The operating condition factor is typically between 0.8 and 1.0; here, we take 1.0. N is the total number of meshing teeth; Δ ij ξ represents the transmission error caused by each error source; ξ is the conversion coefficient from linear to angular; and d is the pitch circle diameter of the flexure.

[0101] Since the transmission error caused by the combined tangential error of one tooth of the rigid and flexible gears is determined by their tooth profile errors, each gear mesh introduces an error into the harmonic drive, with its period corresponding to one meshing cycle. Other error sources affect the harmonic drive with a period close to the input frequency, causing the wave generator to produce one or more effects per revolution.

[0102] The impact of local faults on transmission errors is mainly reflected in the changes in the amplitude of each eccentric vector, specifically as follows:

[0103]

[0104] Where, Δ′F pj j = 1, 2 represents the cumulative error of the cycle under fault conditions; k pjThis represents the cumulative error increment during fault conditions; Δ′E xy x = 2, 3; y = 1, 2, 3 represent assembly errors under fault conditions; k xy Δ′f represents the assembly error increment under fault conditions. fi , i = 1, 2 represent the tangential adjacent combined error under fault conditions; k fi denoted as the tangential adjacent comprehensive error increment under fault conditions; p represents the gear meshing process; P represents the meshing process of the faulty gear tooth.

[0105] Figure 7 This is a diagram of the transmission error signal during a partial fault in a harmonic reducer. The results show that the transmission error signal exhibits significant periodicity, containing a series of frequency components due to different error sources. It is mainly composed of… Figure 7 (a) shows the constant components, Figure 7 The low-frequency long-period fluctuations shown in (b)-(c) and Figure 7 (d) shows the high-frequency short-period fluctuations. Local faults have a significant impact on the high-frequency components, leading to periodic impacts. The short-period fluctuations are caused by the combined tangential error deviation of one tooth in multiple meshing tooth pairs. This error fluctuates at a high frequency within each meshing cycle.

[0106] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for modeling transmission errors of a dual-circular-arc harmonic reducer considering fault factors, characterized in that... This includes the following steps: Based on the transmission principle and structural composition of the double circular arc harmonic reducer, the error sources affecting the transmission error of the harmonic reducer are identified. The structure of a harmonic reducer includes a rigid wheel, a flexible wheel, and a wave generator; Analyzing the error sources of the harmonic reducer, we obtain the angular displacement errors of each eccentric vector related to the rigid wheel, flexible wheel, and wave generator; Based on the error frequency of the angular displacement error of each eccentric vector, different types of error sources are classified. By treating different types of error sources as satisfying a normal distribution relationship and considering the error averaging effect, the comprehensive transmission error of the harmonic reducer is obtained. Based on the changes in the amplitude of the transmission error components of each error source in the comprehensive transmission error when a harmonic reducer fails, a transmission error model of the harmonic reducer affected by the fault is obtained. The transmission error model reflects the degree to which the eccentric vector of each error source is affected by the fault. The error sources of the harmonic reducer include manufacturing errors and assembly errors. Manufacturing errors include the combined eccentricity vector of the rigid wheel, the combined eccentricity vector of the flexible wheel, and the combined tangential error of one tooth. Assembly errors include the rigid wheel assembly error, the eccentricity vector that does not rotate with the flexible wheel, the eccentricity vector that rotates with the flexible wheel, the eccentricity vector that rotates with the wave generator, and the eccentricity vector that does not rotate with the wave generator. Among the manufacturing errors, the angular displacement error caused by the combined eccentricity vector of the rigid wheel is expressed as: in, Let be the base circle radius of the rigid wheel; Let be the pitch circle radius of the rigid wheel; ; The engagement angle; The rotational speed of the wave generator; For time; This refers to the cumulative pitch error of the rigid wheel; for The initial phase angle; The component of the combined eccentricity vector of the rigid wheel along the meshing line; The angular displacement error caused by the combined eccentricity vector of the flexible wheel is expressed as: in, This refers to the cumulative error of the flexible wheel pitch. The initial phase angle is ; The eccentric vector of the flexible wheel; The number of teeth on the rigid wheel; This refers to the number of teeth on the flexible gear. The angular displacement error caused by the combined tangential error of one tooth of the rigid wheel and the flexible wheel is expressed as: in, and These represent the combined tangential error of one tooth of the rigid wheel and the flexible wheel, respectively; N is the number of teeth meshing simultaneously. In assembly errors, the angular displacement error caused by the assembly error of the rigid wheel is expressed as: in, For rigid wheel assembly error, ; for The initial phase angle; The angular displacement error caused by the eccentric vector that does not rotate with the flexible wheel is expressed as: in, This represents the eccentric vector that does not rotate with the flexspline; express The initial phase angle; The angular displacement error caused by the eccentric vector as the flexure rotates is expressed as: in, This represents the eccentric vector that rotates with the flexure. express The initial phase angle; The angular displacement error caused by the eccentric vector rotating with the wave generator is expressed as: in, It is the eccentric vector that rotates with the wave generator; Represents the eccentric vector The angle between the wave generator and its major axis; The angular displacement error caused by the eccentric vector that does not rotate with the wave generator is expressed as: in, It is an eccentric vector that does not rotate with the wave generator; yes The initial phase angle.

2. The method for modeling transmission errors of a dual circular arc harmonic reducer considering fault factors according to claim 1, characterized in that: Based on the different error frequencies, error sources are divided into five categories: The first type is the transmission error caused by the eccentric vector that rotates with the wave, and the output error frequency is a constant value; The second type is the transmission error caused by an eccentric vector that does not rotate with the flexspline; the output error frequency is the same as the input frequency of the wave generator. times; The third type is the transmission error caused by the combined eccentric vector of the rigid wheel, the assembly error of the rigid wheel, and the eccentric vector that does not rotate with the wave generator. The output error frequency is twice the input frequency of the wave generator. The fourth type is the transmission error caused by the combined eccentric vector of the flex wheel and the eccentric vector that rotates with the flex wheel. The output error frequency is equal to the input frequency of the wave generator. times; The fifth type is the transmission error caused by the combined error of a single tooth tangential direction, with the output frequency being equal to the input frequency. times.

3. The method for modeling transmission errors of a dual circular arc harmonic reducer considering fault factors according to claim 2, characterized in that: The formula for calculating the overall transmission error is: in, This is the operating condition coefficient; The total number of meshing teeth; Transmission errors caused by various error sources; These are the conversion coefficients from linear to angular. Let be the pitch circle diameter of the flexure.

4. The method for modeling transmission errors of a dual circular arc harmonic reducer considering fault factors according to claim 3, characterized in that: When a harmonic reducer malfunctions, the changes in the amplitudes of the transmission error components from each error source in the overall transmission error can be expressed as: in, ， j=1,2 represents the cumulative error of the cycle under fault conditions; This represents the cumulative error increment during fault conditions. ， x=2,3; y=1,2,3 represent assembly errors under fault conditions; This represents the assembly error increment under fault conditions; ， i=1,2 represents the tangential adjacent comprehensive error under fault conditions; This represents the incremental tangential adjacent composite error under fault conditions; This refers to the gear meshing process; The faulty gear tooth participates in the meshing process.

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