Double-arc harmonic reducer transmission error modeling method considering fault factors

Abstract

The invention belongs to the technical field of gear transmission error modeling, and aims to solve the problems that at present, research on the influence of faults on transmission errors is not thorough, and a transmission error model of a harmonic reducer with faults does not exist. The double-arc harmonic reducer transmission error modeling method considering the fault factors comprises the following steps that an error source of a harmonic reducer is analyzed, and eccentric vector angular displacement errors related to a rigid gear, a flexible gear and a wave generator are obtained; different types of error sources are regarded as meeting the normal distribution relation, the error homogenization effect is considered, and the comprehensive transmission error of the harmonic reducer is obtained; based on the change condition of the amplitude of the transmission error component of each error source in the transmission error when the harmonic reducer breaks down, a transmission error model of the harmonic reducer influenced by the fault is obtained. According to the method, the transmission error change of each error source can be analyzed according to the fault influence, and a more accurate error model under the fault is provided.

Description

Technical Field

[0001] The invention belongs to the technical field of gear transmission error modeling, and specifically relates to a double arc harmonic reducer gear transmission error modeling method. Background Art

[0002] The harmonic reducer consists of a wave generator, a flexible bearing, a flexible wheel, and a rigid wheel, and transmits motion and force through the deformation of the flexible wheel. The harmonic reducer has the advantages of compact structure, small size, light weight, large transmission ratio and load capacity, and high transmission accuracy. Transmission error is one of the important indicators to measure the transmission performance of the harmonic reducer, which represents the angular difference between the ideal position and the actual position of the output gear. The input and output angles are collected by the encoder installed on the input and output shafts, and the transmission error signal can be obtained by calculation. Compared with commonly used fault diagnosis signals such as vibration and temperature, the transmission error signal contains rich operating status information, and because the encoder has high accuracy and the transmission path is simpler and more direct, the transmission error signal is less interfered by the external environment and is more suitable for fault diagnosis.

[0003] However, the research on the influence of faults on transmission errors is not thorough, and there is no transmission error model of harmonic reducers with faults. Summary of the invention

[0004] In order to solve at least one of the above-mentioned technical problems existing in the prior art, the present invention provides a double-arc harmonic reducer transmission error modeling method taking fault factors into consideration.

[0005] The present invention is implemented by the following technical solution: a double arc harmonic reducer transmission error modeling method considering fault factors, comprising the following steps:

[0006] Based on the transmission principle and structural composition of the double arc harmonic reducer, the error source that affects the transmission error of the harmonic reducer is obtained; the structure of the harmonic reducer includes a rigid wheel, a flexible wheel and a wave generator;

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

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

[0009] Different types of error sources are considered to satisfy the normal distribution relationship, and the error averaging effect is considered to obtain the comprehensive transmission error of the harmonic reducer.

[0010] When a fault occurs in the harmonic reducer, the change in the amplitude of the transmission error component of each error source in the comprehensive transmission error is used to obtain a transmission error model of the harmonic reducer affected by the fault. The transmission error model reflects the degree to which the eccentricity 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, wherein the manufacturing errors include the comprehensive eccentricity vector of the rigid wheel, the comprehensive eccentricity vector of the flexible wheel, and the comprehensive tangential error of one tooth; the assembly errors include the assembly error of the rigid wheel, 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 integrated eccentricity vector of the rigid wheel is expressed as:

[0013]

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

[0015] The angular displacement error caused by the flexspline's comprehensive eccentricity vector is expressed as:

[0016]

[0017] Where, ΔF p2 ΔF is the cumulative error of the flexible wheel pitch; p2 The initial phase angle is φ 12 ;e 21n is the comprehensive eccentricity vector of the flexible wheel; z CS is the number of teeth on the steel wheel; z FS is the number of flexspline teeth;

[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 f2They represent the tangential comprehensive error of one tooth of the rigid wheel and the flexible wheel respectively; N is the number of teeth meshing at the same time.

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

[0022]

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

[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 Represents the eccentric vector that does not rotate with the flexible wheel; φ 22 Denotes ΔE 22 The initial phase angle of

[0027] The angular displacement error caused by the eccentric vector rotating with the flexible wheel is expressed as:

[0028]

[0029] Where, ΔE 23 represents the eccentric vector rotating with the flexspline, φ 23 Denotes ΔE 23 The initial phase angle of

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

[0031]

[0032] Where, ΔE 31 is the eccentric vector rotating with the wave generator; θ1 represents the eccentric vector ΔE 31 Angle with respect to the long axis of the wave generator;

[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 is the eccentric vector that does not rotate with the wave generator; φ 32 is ΔE 32 The initial phase angle.

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

[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 the eccentric vector that does not rotate with the flexible wheel. The output error frequency is the input frequency of the wave generator. times;

[0039] The third type is the transmission error caused by the integrated eccentricity vector of the rigid wheel, the assembly error of the rigid wheel and the eccentricity 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 eccentric vector of the flexible wheel and the eccentric vector rotating with the flexible wheel. The output error frequency is the input frequency of the wave generator. times;

[0041] The fifth type is the transmission error caused by the tangential comprehensive error of one tooth. The output frequency is the input frequency. times.

[0042] Preferably, the calculation formula of the comprehensive transmission error is:

[0043]

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

[0045] Preferably, when a fault occurs in the harmonic reducer, the change in the amplitude of the transmission error component of each error source in the comprehensive transmission error can be expressed as:

[0046] Among them, Δ′F pj , j = 1, 2 is the cumulative error of the cycle under fault conditions; k pj is the cumulative error increment of the cycle under fault conditions; Δ′E xy , x=2,3; y=1,2,3 is the assembly error under fault conditions; k xy is the assembly error increment under fault conditions; Δ′f fi , i = 1, 2 is the tangential adjacent comprehensive error under fault conditions; k fi is the tangential adjacent comprehensive error increment under fault conditions; p is the gear meshing process; P is the faulty gear tooth participating in the meshing process.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention provides a transmission error modeling method for a double arc harmonic reducer that takes fault factors into consideration. The method first analyzes the manufacturing and assembly errors of the wave generator, rigid wheel, and flexible wheel, and calculates the angular displacement error generated thereby. Afterwards, according to the distribution form of different error terms, the comprehensive transmission error of the assembled harmonic reducer is regarded as the sum of the transmission errors caused by the eccentric vectors of the assembly error and the manufacturing error. When a fault occurs, the method can analyze the transmission error changes of each error source according to the impact of the fault, provide a more accurate error model under fault, and provide a theoretical basis for improving the transmission accuracy of the harmonic reducer and the accuracy of life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0050] Figure 1 is a flow chart of the method of the present invention;

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

[0052] Figure 3 It is a schematic diagram of the meshing of the teeth of the harmonic reducer in the coordinate axis in the present invention;

[0053] Figure 4 It is a schematic diagram of the comprehensive eccentricity vector in the present invention;

[0054] Figure 5 It is a schematic diagram of assembly error in the present invention;

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

[0056] Figure 7 This is a transmission error signal diagram when the harmonic reducer in the present invention fails. DETAILED DESCRIPTION

[0057] In conjunction with the drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0058] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by 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] The present invention provides an embodiment:

[0060] like Figure 1 As shown, a double arc harmonic reducer transmission error modeling method considering fault factors includes the following steps:

[0061] Based on the transmission principle and structural composition of the double-arc harmonic reducer, the error sources that affect 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; the error sources of the harmonic reducer are analyzed to obtain the eccentric vector angular displacement errors related to the rigid wheel, the flexible wheel and the wave generator; based on the error frequency of each eccentric vector angular displacement error, different types of error sources are classified; different types of error sources are regarded as satisfying the normal distribution relationship, and the error averaging effect is considered to obtain the comprehensive transmission error of the harmonic reducer; based on the change in the amplitude of the transmission error component of each error source in the comprehensive transmission error when a fault occurs in the harmonic reducer, combined with the harmonic transmission principle and the cause of its error generation, a transmission error model of the harmonic reducer affected by the fault is obtained, and the 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, wherein the manufacturing errors include the rigid wheel comprehensive eccentricity vector, the flexible wheel comprehensive eccentricity vector, and the one-tooth tangential comprehensive error, and 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. Under normal circumstances, the manufacturing and assembly errors of each key component of the harmonic reducer will cause the actual meshing point to deviate from the theoretical meshing point, thereby generating a transmission error. In order to facilitate calculation, each error is converted into a corresponding eccentricity vector.

[0063] like Figure 2As shown in the figure, for dual-wave transmission, the harmonic reducer will have two meshing areas at the same time. Without considering the manufacturing and assembly errors, the meshing conditions of the two meshing areas should be completely consistent. However, in actual situations, due to manufacturing and assembly errors, the meshing areas are not completely symmetrical, and the meshing degree will be deepened on one side of the meshing area, while the meshing degree on the other side will be relatively weakened, so the influence of the dominant area is mainly analyzed. This also shows that the transmission error caused by the manufacturing error of the rigid-flexible wheel is based on half a turn of the wave generator as one cycle.

[0064] Figure 3 The figure shows the gear meshing situation, where K is the theoretical meshing point. The comprehensive 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 meshing line t .

[0065] like Figure 4 As shown, in the manufacturing error, for the rigid wheel comprehensive eccentricity vector e 11 , whose component along the meshing line is recorded as e 11n , whose changing frequency is twice the rotation frequency of the wave generator, can be expressed as:

[0066]

[0067] Among them, e 11 is the integrated 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 integrated eccentricity vector of the rigid wheel is expressed as:

[0069]

[0070] Among them, r bCS is the base circle radius of the rigid wheel; r CS is the pitch radius of the rigid wheel; r bCS =r CS cosα n ; α n is the meshing angle; ω is the speed of the wave generator; t is the time; ΔF p1 is the cumulative error of the rigid wheel pitch; φ 11 ΔF p1 The initial phase angle of e 11n It is the component of the comprehensive eccentricity vector of the rigid wheel along the meshing line.

[0071] For the flexspline comprehensive eccentricity vector e 21n , similar to the rigid wheel, the angular displacement error caused by the comprehensive eccentricity vector of the flexible wheel can be derived as:

[0072]

[0073] Where, ΔF p2 ΔF is the cumulative error of the flexible wheel pitch; p2 The initial phase angle is φ 12 ;e 21n is the comprehensive eccentricity vector of the flexible wheel; z CS is the number of teeth on the steel wheel; z FS is the number of flexspline teeth;

[0074] The tangential comprehensive error of one tooth is jointly determined by the tooth profile error of the meshing teeth of the rigid wheel and the flexible wheel. When the rigid and flexible wheels mesh once, the tooth profile error will have an impact on the harmonic drive, so it affects the harmonic transmission in each meshing cycle. During the operation of the harmonic reducer, multiple pairs of teeth are meshed at the same time. Considering that their effects on the harmonic drive are similar, in order to simplify the model, their effects on the harmonic drive are regarded as the same. The angular displacement error caused by the tangential comprehensive error of one tooth of the rigid wheel and the flexible wheel is expressed as:

[0075]

[0076] Where Δf f1 and Δf f2 They represent the tangential comprehensive error of one tooth of the rigid wheel and the flexible wheel respectively; N is the number of teeth meshing at the same time.

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

[0078]

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

[0080] The assembly error of the flexspline can be divided into two categories: the assembly error caused by the eccentric vector that does not rotate with the flexspline and the assembly error caused by the eccentric vector that rotates with the flexspline.

[0081] The first type of assembly error is fixed. As the flexible wheel rotates slowly, it affects the meshing of the flexible wheel and the rigid wheel at different positions, which leads to the generation of transmission error. That is, this assembly error will produce a periodic change during the process of the flexible wheel rotating one circle. The angular displacement error caused by the eccentric vector that does not rotate with the flexible wheel is expressed as:

[0082]

[0083] Where, ΔE 22 Represents the eccentric vector that does not rotate with the flexible wheel; φ 22 Denotes ΔE 22 The initial phase angle of

[0084] The second type of assembly error is affected by the position of the meshing area. Its changing frequency corresponds to the rotation frequency of the flexspline relative to the wave generator. The angular displacement error caused by the eccentric vector rotating with the flexspline is expressed as:

[0085]

[0086] Where, ΔE 23 represents the eccentric vector rotating with the flexspline, φ 23 Denotes ΔE 23 The initial phase angle of

[0087] The error of the wave generator mainly comes from processing error and assembly error. According to its influence on the meshing of rigid-flexible gear, it 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 in Figure 1, the first type of eccentricity vector will have 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 eccentricity vector rotating with the wave generator is expressed as:

[0089]

[0090] Where, ΔE 31 is the eccentric vector rotating with the wave generator; θ1 represents the eccentric vector ΔE 31 Angle with respect to the long axis of the wave generator;

[0091] When the wave generator is assembled, the second type of eccentricity vector is fixed. It can be equivalent to the opposite eccentricity vector acting on the rigid wheel. The angular displacement error caused by the eccentricity vector that does not rotate with the wave generator is expressed as:

[0092]

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

[0094] In summary, the angular displacement errors of harmonic reducers under normal conditions can be divided into several categories, 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] According to the different error frequencies, the error sources are divided into five categories: the first category 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 category is the transmission error caused by the eccentric vector that does not rotate with the flexible wheel, and the output error frequency is the input frequency of the wave generator. The third type is the transmission error caused by the integrated eccentricity vector of the rigid wheel, the assembly error of the rigid wheel and the eccentricity 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 integrated eccentricity vector of the flexible wheel and the eccentricity vector that rotates with the flexible wheel. The output error frequency is times the input frequency of the wave generator. times; the fifth type is the transmission error caused by the tangential comprehensive error of one tooth, and the output frequency is the input frequency times.

[0098] Different types of error sources satisfy different probability distribution forms. If they are all considered to satisfy the normal distribution relationship, the comprehensive transmission error can be expressed as the sum of the transmission errors caused by the eccentric vectors of assembly error and processing error. Considering the error averaging effect, the calculation formula of the comprehensive transmission error is:

[0099]

[0100] Among them, K b is the operating coefficient, generally 0.8 to 1.0, here it is 1.0; N is the total number of meshing teeth; Δ ij is the transmission error caused by each error source; ξ is the conversion coefficient from linear to angle; d is the pitch diameter of the flexspline.

[0101] Since the transmission error caused by the tangential combined error of one tooth of the rigid wheel and the flexible wheel is determined by their tooth shape error, each gear meshing will introduce an error into the harmonic drive, and its period corresponds to one meshing cycle. Other error sources affect the harmonic drive with a period close to the input frequency, resulting in one or more effects per revolution of the wave generator.

[0102] The influence of local fault on transmission error is mainly reflected in the change of each eccentricity vector amplitude, which is specifically manifested as follows:

[0103]

[0104] Among them, Δ′F pj , j = 1, 2 is the cumulative error of the cycle under fault conditions; k pjis the cumulative error increment of the cycle under fault conditions; Δ′E xy , x=2,3; y=1,2,3 is the assembly error under fault conditions; k xy is the assembly error increment under fault conditions; Δ′f fi , i = 1, 2 is the tangential adjacent comprehensive error under fault conditions; k fi is the tangential adjacent comprehensive error increment under fault conditions; p is the gear meshing process; P is the faulty gear tooth participating in the meshing process.

[0105] Figure 7 The transmission error signal diagram of the harmonic reducer when there is a local fault. The results show that the transmission error signal has obvious periodicity. Due to the different error sources, the transmission error signal contains a series of frequency components. It is mainly composed of Figure 7 (a) shows the constant component, 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, resulting in periodic shocks. Short-period fluctuations are caused by the tangential comprehensive error deviation of one tooth of multiple meshing tooth pairs. This error fluctuates at a high frequency in each meshing cycle.

[0106] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A transmission error modeling method for a double arc harmonic reducer considering fault factors, characterized in that , including the following steps: Based on the transmission principle and structural composition of the double arc harmonic reducer, the error sources that affect 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; Analyze the error sources of the harmonic reducer to obtain the angular displacement errors of the eccentric vectors related to the rigid wheel, the flexible wheel and the wave generator; Based on the error frequency of each eccentricity vector angular displacement error, different types of error sources are classified; Different types of error sources are considered to satisfy the normal distribution relationship, and the error averaging effect is considered to obtain the comprehensive transmission error of the harmonic reducer. When a fault occurs in the harmonic reducer, the change in the amplitude of the transmission error component of each error source in the comprehensive transmission error is used to obtain a transmission error model of the harmonic reducer affected by the fault. The transmission error model reflects the degree to which the eccentricity vector of each error source is affected by the fault.

2. A double arc harmonic reducer transmission error modeling method considering fault factors according to claim 1, characterized in that: The error sources of the harmonic reducer include manufacturing errors and assembly errors, wherein the manufacturing errors include the comprehensive eccentricity vector of the rigid wheel, the comprehensive eccentricity vector of the flexible wheel, and the comprehensive tangential error of one tooth; the assembly errors include the assembly error of the rigid wheel, 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.

3. A double arc harmonic reducer transmission error modeling method considering fault factors according to claim 2, characterized in that: In the manufacturing error, the angular displacement error caused by the integrated eccentricity vector of the rigid wheel is expressed as: Among them, r bCS is the base circle radius of the rigid wheel; r CS is the pitch radius of the rigid wheel; r bCS =r CS cosα n ; α n is the meshing angle; ω is the speed of the wave generator; t is the time; ΔF p1 is the cumulative error of the rigid wheel pitch; 11 ΔF p1 The initial phase angle of e 11n is the component of the integrated eccentricity vector of the rigid wheel along the meshing line; The angular displacement error caused by the flexspline's comprehensive eccentricity vector is expressed as: Where, ΔF p2 ΔF is the cumulative error of the flexible wheel pitch; p2 The initial phase angle is φ 12 ;e 21n is the comprehensive eccentricity vector of the flexible wheel; z CS is the number of teeth on the steel wheel; z FS is the number of flexspline teeth; The angular displacement error caused by the combined tangential error of one tooth of the rigid wheel and the flexible wheel is expressed as: Where Δf f1 and Δf f2 They represent the tangential comprehensive error of one tooth of the rigid wheel and the flexible wheel respectively; N is the number of teeth meshing at the same time.

4. The method for modeling transmission errors of a double arc harmonic reducer considering fault factors according to claim 3 is characterized in that: In the assembly error, the angular displacement error caused by the rigid wheel assembly error is expressed as: Where, ΔE 21 is the rigid wheel assembly error, e 21 =ΔE 21 / 2;φ 21 ΔE 21 The initial phase angle of The angular displacement error caused by the eccentric vector that does not rotate with the flexible wheel is expressed as: Where, ΔE 22 Represents the eccentric vector that does not rotate with the flexible wheel; φ 22 Denotes ΔE 22 The initial phase angle of The angular displacement error caused by the eccentric vector rotating with the flexible wheel is expressed as: Where, ΔE 23 represents the eccentric vector rotating with the flexspline, φ 23 Denotes ΔE 23 The initial phase angle of The angular displacement error caused by the eccentric vector rotating with the wave generator is expressed as: Where, ΔE 31 is the eccentric vector rotating with the wave generator; θ1 represents the eccentric vector ΔE 31 Angle with respect to the long axis of the wave generator; The angular displacement error caused by the eccentric vector that does not rotate with the wave generator is expressed as: Where, ΔE 32 is the eccentric vector that does not rotate with the wave generator; φ 32 is ΔE 32 The initial phase angle.

5. The method for modeling transmission errors of a double arc harmonic reducer considering fault factors according to claim 4 is characterized in that: According to the different error frequencies, the 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 the eccentric vector that does not rotate with the flexible wheel. The output error frequency is the input frequency of the wave generator. times; The third type is the transmission error caused by the integrated eccentricity vector of the rigid wheel, the assembly error of the rigid wheel and the eccentricity 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 eccentric vector of the flexible wheel and the eccentric vector rotating with the flexible wheel. The output error frequency is the input frequency of the wave generator. times; The fifth type is the transmission error caused by the tangential comprehensive error of one tooth. The output frequency is the input frequency. times.

6. A double arc harmonic reducer transmission error modeling method considering fault factors according to claim 5, characterized in that: The calculation formula of comprehensive transmission error is: Among them, K b is the operating coefficient; N is the total number of meshing teeth; Δ ij is the transmission error caused by each error source; ξ is the conversion coefficient from linear to angle; d is the pitch diameter of the flexspline.

7. A double arc harmonic reducer transmission error modeling method considering fault factors according to claim 6, characterized in that: When a harmonic reducer fails, the change in the amplitude of the transmission error component of each error source in the comprehensive transmission error can be expressed as for: Among them, Δ′F pj , j = 1, 2 is the cumulative error of the cycle under fault conditions; k pj is the cumulative error increment of the cycle under fault conditions; Δ′E xy , x=2,3; y=1,2,3 is the assembly error under fault conditions; k xy is the assembly error increment under fault conditions; Δ′f fi , i = 1, 2 is the tangential adjacent comprehensive error under fault conditions; k fi is the tangential adjacent comprehensive error increment under fault conditions; p is the gear meshing process; P is the faulty gear tooth participating in the meshing process.

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