End-toothed disc positioning and indexing precision reliability optimization method of wear model based on multi-factor coupling

Abstract

The invention relates to an end-fluted disc positioning and indexing precision reliability optimization method based on a multi-factor coupling wear model. An end-fluted disc comprises a fixed fluted disc and a locking fluted disc; a fixed tooth opening surrounding the fixed fluted disc is formed in the fixed fluted disc; a locking tooth opening is formed in the locking fluted disc; under the action of hydraulic pressure, the locking fluted disc moves in the vertical direction, and the locking fluted disc slides in the tooth surface direction to the final state that the fixed tooth opening and the locking tooth opening are completely locked. The optimization method comprises the following steps: step 1, modeling an initial state error of the end-toothed disc; 2, a single-time abrasion model of the end-toothed disc is established; 3, a multi-time abrasion model of the end-toothed disc is established; 4, calculating the abrasion loss of the end-toothed disc and representing the indexing precision; 5, optimizing design parameters of the end-toothed disc, an assembly chain of the end-toothed disc and a transmission chain of the end-toothed disc; according to the method, the whole process of the end-toothed disc from the initial stage of contact to elastic deformation is considered in combination with the assembly error and the random effect, the abrasion process of the end-toothed disc is reflected more comprehensively, and the mapping relation between the indexing error and the positioning error and the abrasion frequency of the end-toothed disc is established.

Description

Technical Field

[0001] The invention belongs to the technical field of end gear disc design, and in particular relates to a method for optimizing the reliability of end gear disc positioning and indexing accuracy based on a wear model coupled with multiple factors. Background Art

[0002] The end gear disc, also called the rat tooth disc or the end face gear disc, is the core and key component of the mechanical indexing equipment. It can ensure the orderly operation of high-precision indexing of CNC machinery and other equipment. In engineering, the two end gear discs are often used to realize the functions of CNC tool holder tool change and indexing attachment head angle change. The end gear discs need to grind each other quickly and repeatedly during use, and the tooth surface is seriously worn, causing the end gear disc indexing accuracy to decline. The meshing of the end gear discs is a typical high-speed and heavy-load friction pair. The interacting tooth surfaces form an alternating process of adhesion-destruction-adhesion-destruction, so the tooth surfaces of the end gear discs will produce adhesion wear. In order to characterize the amount of wear, Archard theory is usually used for calculation. In Archard theory, the amount of wear is proportional to the relative motion distance. Calculating the amount of wear is equivalent to calculating the slip distance between the two end gear discs.

[0003] The research on end gears mainly focuses on the fitting of end gear experimental data based on data-driven, which cannot reveal the wear law of end gears from a mechanistic perspective. The current wear model of end gears only considers the wear caused by the elastic deformation after the two end gears are fully engaged, and ignores the wear caused by the sliding distance generated by the end gears from the initial contact to the full engagement. In addition, the current wear model assumes that the wear amount is the same each time, ignoring the randomness of the angle deviation of the two end gears in the initial state and the change in the single wear amount caused by the change in sliding distance caused by the cumulative wear error, which has limitations in practical applications. Existing research is limited to the manufacturing accuracy of the end gear itself, ignoring the manufacturing error and assembly error of its assembly chain and the transmission error of the transmission chain, and cannot directly guide the evaluation and design of the end gear guidance equipment.

[0004] Existing technical solutions:

[0005] [1] Wang Xingang, Zhang Heng, Wang Baoyan, et al. Study on dynamic reliability and sensitivity of end gear indexing accuracy considering wear error[J]. China Mechanical Engineering, 2018, 29(01): 2-7.

[0006] Wang Xingang provided a reliability evaluation method for the indexing accuracy of the end gear disc taking into account the wear error. The method takes the relative slip of the two end gear discs during the meshing process as the wear amount, and considers that the relative slip distance is proportional to the cumulative load time. The wear position is only in the same side area of ​​the end gear disc, ignoring the centering principle of the end gear disc. A tooth thickness wear model under the unilateral wear condition of the end gear disc is established. The indexing accuracy error calculated based on the wear model is monotonically increasing, which is different from the accuracy change trend during the actual working process of the end gear disc.

[0007] [2] Song Xincheng. Reliability evaluation of CNC tool holder considering end gear wear[D]. Jilin University, 2023. DOI: 10.27162 / d.cnki.gjlin.2023.003401.

[0008] Song Xincheng analyzed the wear amount of the end gear by combining the wear model under the unilateral wear condition of the end gear engagement, characterized the division accuracy of the end gear based on the variable gamma process, and fitted the mathematical model of repeatability accuracy error with time as the independent variable through experimental data.

[0009] The gamma process is an important process in the theory of random processes and is a type of Markov process. Its increments follow an independent gamma distribution and can be used to describe a monotonically increasing change process. This model cannot reflect the accuracy fluctuation caused by the centering effect of the end gear (the indexing accuracy may become higher or lower).

[0010] [3] Wang Siqi. Reliability evaluation of CNC tool holder based on accelerated degradation test[D]. Jilin University, 2022. DOI: 10.27162 / d.cnki.gjlin.2022.004307.

[0011] Wang Siqi established a reliability model for CNC tool holders based on the reliability test data of CNC tool holders and the Wiener process. The model is a random process model that can fluctuate (not limited to monotonically increasing or monotonically decreasing). The degradation trajectory reflects the fluctuation process of the repeatability accuracy of the CNC tool holder. The accuracy of the end gear disk is the factor that has the greatest impact on the repeatability accuracy of the CNC tool holder, that is, the indexing accuracy of the end gear disk is fluctuating. However, the model is data-driven and cannot establish the influence of the wear amount of the end gear disk on the reliability of the indexing accuracy from the perspective of wear mechanism. Among them, the Wiener process is a continuous-time random process, also often called a Brownian motion process or simply Brownian motion. It is the most famous type of Levy process (a stationary independent incremental random process with left limit and right continuity), and has important applications in pure mathematics, applied mathematics, economics and physics.

[0012] From the basic characteristics of the above reliability design methods and processes, it can be seen that the existing technologies have the following shortcomings:

[0013] 1. The above methods all ignore the wear process of the toothed discs at both ends from the initial contact to before elastic deformation, assuming that the relative slip distance of wear is only caused by the elastic deformation of the toothed discs at both ends, and the wear model is not accurate enough.

[0014] 2. The above methods all ignore the impact of accumulated wear on the next wear of the end gear disc, assuming that the wear of the end gear disc is the same each time, and the wear model is not accurate enough.

[0015] 3. The above methods only consider the wear on one side of the end gear disc. The end gear disc indexing accuracy model calculated based on the wear model is a monotonically increasing model, which does not conform to the accuracy fluctuation caused by the centering effect of the end gear disc.

[0016] 4. The above method does not take into account the manufacturing error and assembly error between the end gear disc and its assembly chain and the transmission chain, and cannot directly optimize its indexing accuracy or positioning accuracy.

[0017] In view of the above technical problems, improvements need to be made. Summary of the invention

[0018] The present invention aims to overcome the defects in the above-mentioned prior art and provide a method for optimizing the reliability of end toothed disc positioning and indexing accuracy based on a wear model with multi-factor coupling; the present invention is mainly aimed at end toothed discs used for indexing or positioning, and intends to provide a method for evaluating and optimizing the reliability of indexing accuracy of double-sided wear of end toothed discs taking into account the errors of assembly chain and transmission chain, and determines the initial state of the end toothed disc by error analysis of assembly chain and transmission chain, establishes a cumulative double-sided wear model of the end toothed disc taking into account random effects through mechanical analysis of the end toothed disc, establishes a mapping between the number of uses and indexing accuracy, and then evaluates the indexing accuracy reliability of the end toothed disc or applicable equipment, thereby scientifically guiding the design and verification of the end toothed disc, solving the problems of the current end toothed disc wear research such as the lack of wear process model, neglect of initial state, random effects and error accumulation, and proposes a direct end toothed disc reliability optimization design method.

[0019] In order to achieve the above purpose, the technical solution adopted by the present invention is: a method for optimizing the reliability of end gear plate positioning and indexing accuracy based on a wear model with multi-factor coupling, wherein the end gear plate comprises a fixed gear plate and a locking gear plate; the fixed gear plate is formed with a fixed tooth opening arranged around the fixed gear plate; the locking gear plate is formed with a locking tooth opening; wherein, under the action of the hydraulic pressure, the locking gear plate first moves in the vertical direction, and then slides along the tooth surface direction until the fixed tooth opening and the locking tooth opening are completely locked; the optimization method comprises the following steps:

[0020] Step 1: Modeling the initial state error of the end gear disc;

[0021] Step 2: Single wear model of end gear disc;

[0022] Step 3: Multiple wear model of end gear disc;

[0023] Step 4: Calculation of end gear wear and characterization of indexing accuracy;

[0024] Step 5: Optimize the design parameters of the end gear plate and its assembly chain and transmission chain.

[0025] As a preferred embodiment of the present invention, in step 1, the fixed gear plate is connected to other parts by screws; there are manufacturing errors and assembly errors in the fixed gear plate and the fixed parts, and the errors are characterized by multiple methods such as traditional tolerance analysis, small displacement screw method, reliability index method, and hybrid convolution method; the locking gear plate is connected to other parts by screws, and the part drives the locking gear plate to move axially and rotate around the axis; similarly, there are manufacturing errors and assembly errors in the locking gear plate and the fixed parts, and the errors are characterized by multiple methods such as traditional tolerance analysis, small displacement screw method, reliability index method, and hybrid convolution method; if the transmission chain is closed-loop control, the manufacturing and assembly accuracy of feedback components such as encoders can be used to calculate the error distribution at the locking fixed gear plate.

[0026] As a preferred embodiment of the present invention, in step 2, the specific steps of the end gear plate single wear model include:

[0027] Step 2.1: Single rigid body wear model of end gear disc;

[0028] Step 2.2: Single elastic wear model of end gear.

[0029] As a preferred embodiment of the present invention, in step 2.1, the locking toothed disc and the fixed toothed disc are both rigid bodies, that is, neither of them is deformed; when the locking toothed disc is not in contact with the fixed toothed disc, the locking toothed disc moves in the vertical direction and contacts with the fixed toothed disc; when the locking toothed disc is in contact with the fixed toothed disc, a positive pressure F perpendicular to the tooth surface is generated between the two toothed discs. N and the friction force parallel to the tooth surface, under the action of the friction force, a slip distance S1 is generated on the tooth surface; the slip distance can be expressed as:

[0030]

[0031] Wherein, Δh1 is the height difference from the contact between the locking sprocket and the fixed sprocket to the end of the rigid body motion stage, and α is the tooth profile angle of the fixed sprocket and the locking sprocket.

[0032] The surface pressure of the end gear contact surface can be expressed as:

[0033]

[0034] In the formula, F N is the positive pressure, A is the contact area, T is the vertical force, Z is the number of teeth on the fixed gear and the locking gear, b iis the final contact length during single contact, s i is the total distance of a single move, and s is the displacement distance coordinate during the movement.

[0035] As a preferred embodiment of the present invention, in step 2.2, both the locking toothed disc and the fixed toothed disc are elastic bodies, that is, both can be deformed; when the fixed toothed disc and the locking toothed disc are elastically deformed and locked after a single rigid body wear process, a slip distance S2 is generated at this time; the slip distance can be expressed as:

[0036]

[0037] Wherein, Δh2 is the elastic deformation wear after the rigid body motion stage ends, and α is the tooth profile angle of the fixed gear disc (1) and the locking gear disc (2).

[0038] As a preferred embodiment of the present invention, in step 3, the multiple wear model of the end tooth plate specifically includes: the angular error between the locking tooth opening on the locking tooth plate and the fixed tooth opening on the fixed tooth plate along the axial direction is the initial state error of the fixed tooth plate; the error probability distribution of the end tooth plate is fitted by the calculated initial error; when multiple wear occurs, the past wear amount of the fixed tooth plate and the locking tooth plate will affect the rigid wear process and the spatial position of the elastic wear of the tooth plate, that is, affect the subsequent single wear amount, so the wear amount parameters on both sides of the upper locking tooth plate are introduced.

[0039] As a preferred embodiment of the present invention, the final length of the fixed toothed disc before multiple wear can be expressed as:

[0040]

[0041] In the formula, h 1ls is the wear thickness of the left side of the fixed gear disc bevel, h 1rs h is the wear thickness on the right side of the fixed gear disc bevel, 2ls h is the wear thickness of the left side of the locking gear bevel, 2rs It is the wear thickness on the right side of the locking sprocket bevel.

[0042] As a preferred embodiment of the present invention, the wear amount calculation formula of the fixed toothed disc after multiple wear can be expressed as:

[0043]

[0044] In the formula, s i is the total distance of a single move, b i is the final contact length in single contact, σ s is the material yield limit, K s is the adhesive wear coefficient, sis the displacement distance coordinate during the movement, T is the vertical upward force, Z is the number of teeth on the fixed gear plate and the locking gear plate, and α is the tooth angle of the fixed gear plate and the locking gear plate.

[0045] As a preferred embodiment of the present invention, in step 4, based on the initial state error calculated in step 1 and the multiple wear model of the end gear disc in step 3, a mathematical relationship between the number of wear times and the dividing accuracy / positioning accuracy is established by the Monte Carlo method.

[0046] As a preferred embodiment of the present invention, in step 5, the optimization interval of the design parameters of the fixed gear plate and its assembly chain and the transmission chain is set, the simulation parameters are constructed by Latin hypercube sampling, a response surface model is established based on the parameters, and optimization algorithms such as gradient descent method, Newton method and quasi-Newton method, conjugate gradient method or intelligent control algorithm are used to perform optimization to obtain the optimal solution.

[0047] The beneficial effects of the present invention are:

[0048] 1. The present invention takes into account the entire process of the end toothed disc from the initial contact to the occurrence of elastic deformation, reflects the wear process of the end toothed disc more comprehensively, and establishes a mathematical model of the wear amount of a single wear process.

[0049] 2. The present invention takes into account the impact of the accumulated wear of the end gear disc on subsequent wear. Each wear amount calculated by the wear model has a certain difference, which is more in line with the actual wear process.

[0050] 3. The present invention takes into account the randomness of the initial position of the end toothed disc, so that the end toothed disc wear model can reflect the wear on any side of the end toothed disc. The wear model has accuracy fluctuations, which is consistent with the centering effect of the end toothed disc.

[0051] 4. The present invention may only consider the initial indexing error caused by the manufacturing error and assembly error of the end gear disc, and may also introduce its assembly chain and transmission chain through the error modeling method, and finally directly optimize the indexing accuracy or positioning accuracy of the structure or equipment of the end gear disc through the intelligent control algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 The embodiment of the present invention is a meshing diagram of a fixed gear disc and a locking gear disc.

[0053] Figure 2 is a flow chart of an embodiment of the present invention.

[0054] Reference numerals in the figures: fixed toothed disc 1 , locking toothed disc 2 , fixed tooth opening 10 , locking tooth opening 20 . DETAILED DESCRIPTION

[0055] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0056] Example:

[0057] like Figure 1-Figure 2 As shown, Figure 1 is a meshing diagram of a fixed toothed disc and a locking toothed disc in an embodiment of the present invention; Figure 2 is a flow chart of an embodiment of the present invention.

[0058] A method for optimizing the reliability of end gear positioning and indexing accuracy based on a wear model with multi-factor coupling, wherein the wear model of the end gear is based on the wear between a fixed gear 1 and a locking gear 2, and the end gear comprises a fixed gear 1 and a locking gear 2; the fixed gear 1 is provided with a fixed tooth opening 10 arranged around the fixed gear 1; the locking gear 2 is provided with a locking tooth opening 20; wherein, under the action of the hydraulic pressure, the locking gear 2 moves in the vertical direction, and the locking gear 2 slides along the tooth surface direction until the fixed tooth opening 10 and the locking tooth opening 20 are completely locked.

[0059] According to the end gear indexing accuracy test method mentioned in the mechanical industry standard JB / T4316.2-2011, the test principle is to test the difference between the actual rotation error and the theoretical rotation angle, and use this as the basis for determining the end gear indexing accuracy. Therefore, when the wear causes the tooth width to change, if the impact of the manufacturing error on the end gear size is not considered and it is assumed that each meshing tooth surface is evenly worn, the angular error studied is the error value between the actual angle after rotating a certain angle θ and the theoretical required angle.

[0060] Movement process of the locking gear disc: During a single meshing (wear) process, the fixed gear disc 1 remains stationary in space and does not move; during a single (wear) process, the locking gear disc 2 moves upward in the vertical direction; the tooth surface of the fixed gear disc 1 is an inclined surface, and under the action of the hydraulic pressure, the locking gear disc 2 first moves in the vertical direction, and then slides along the tooth surface direction until the final fixed tooth mouth 10 and the locking tooth mouth 20 are completely locked; the slip distance may include a single rigid body slip distance S1 and a slip distance S2 caused by elastic deformation; because the rigidity of the fixed gear disc is relatively large, it can be equivalent to a rigid body in actual calculations, and the rigid body slip distance S1 can be calculated in this state; considering that the elastic deformation of the fixed gear disc will also cause a slip distance, the slip distance S2 caused by elastic deformation is introduced.

[0061] The centering effect of the end toothed disc: the two toothed discs need to be locked in the final state, that is, in the final state, all the mating tooth surfaces need to fit together; when the left and right sides of the tooth grooves of the fixed toothed disc 1 are worn equally, the teeth of the locking toothed disc 2 only need to move slightly in the axial direction, and the axis error of the tooth and the axis error of the tooth groove have not changed, so the indexing accuracy or positioning accuracy of the fixed toothed disc 1 has not changed. This phenomenon will cause the indexing accuracy of the fixed toothed disc 1 to show a regression trend or a fluctuation trend, which may not necessarily be a monotonically decreasing trend; similarly, the wear of the locking toothed disc will also produce the same effect. All current studies have not considered this issue, which is also the core innovation of the present invention.

[0062] The optimization method includes the following steps:

[0063] Step 1: Modeling the initial state of the end gear disc; the specific steps include:

[0064] Step 1.1: Modeling the initial state error of fixed gear disc 1;

[0065] The fixed gear plate 1 is connected to other parts by screws; the fixed gear plate 1 and the fixed parts have manufacturing errors and assembly errors, which are characterized by traditional tolerance analysis method, small displacement screw method, reliability index method, and mixed convolution method.

[0066] Step 1.2: Modeling the initial state error of locking gear disc 2;

[0067] The initial error state of the locking sprocket 2 is modeled; the locking sprocket 2 is connected to other parts by screws, and the parts drive the locking sprocket 2 to move axially and rotate around the axis; similarly, there are manufacturing errors and assembly errors in the locking sprocket 2 and the fixed parts, and the errors are characterized by various methods such as traditional tolerance analysis, small displacement screw method, reliability index method, and mixed convolution method; if the transmission chain is closed-loop control, the manufacturing and assembly accuracy of feedback components such as encoders can be used to calculate the error distribution at the locking end sprocket.

[0068] Among them, the transmission error can be calculated by referring to CB / Z 178-1980 "Calculation and Inspection Method of Torque Backlash and Rotation Error of Precision Gear Transmission Chain".

[0069] The small displacement screw method is a mathematical tool used to describe the small motion or deformation of a rigid body in three-dimensional space. It consists of two three-dimensional vectors: one represents the change in position and the other represents the change in direction.

[0070] Step 1.3: Indexing / positioning accuracy model of fixed gear disc 1 and locking gear disc 2

[0071] According to the geometric error between the fixed gear disc 1 and the locking gear disc 2, the indexing / positioning error after the two gear discs are engaged is established, mainly the indexing / positioning error caused by the tooth thickness direction error and the angular error.

[0072]

[0073] In the formula, is the indexing / positioning error, x1 is the initial tooth thickness error of the fixed tooth disc 1, x2 is the initial tooth thickness error of the locking tooth disc, x′1 is the tooth thickness error caused by wear of the fixed tooth disc 1, x′2 is the tooth thickness error caused by wear of the locking tooth disc 2, is the angular error of the fixed gear disc 1 in the initial state, is the rotation angle error of the locking gear disc 2 in the initial state, and d is the pitch circle diameter of the fixed gear disc.

[0074] Step 2: Single wear model of end gear disc; the specific steps include:

[0075] Step 2.1: Single rigid body wear model of end gear disc;

[0076] Assume that the locking toothed disc 2 and the fixed toothed disc 1 are both rigid bodies, that is, neither of them is deformed; when the locking toothed disc 2 is not in contact with the fixed toothed disc 1, the locking toothed disc 2 moves in the vertical direction and contacts with the fixed toothed disc 1; when the locking toothed disc 2 contacts with the fixed toothed disc 1, a positive pressure F perpendicular to the tooth surface is generated between the two toothed discs. N and the friction force parallel to the tooth surface, under the action of the friction force, a slip distance S1 is generated on the tooth surface; the slip distance can be expressed as:

[0077]

[0078] Wherein, Δh1 is the height difference from the contact between the locking gear disc 2 and the fixed gear disc 1 to the end of the rigid body motion stage, and α is the tooth profile angle of the fixed gear disc 1 and the locking gear disc 2;

[0079] The surface pressure of the contact surface between the fixed gear disc 1 and the locking gear disc 2 can be expressed as:

[0080]

[0081] In the formula, F N is the positive pressure, A is the contact area, T is the vertical force, Z is the number of teeth of the fixed gear plate 1 and the locking gear plate 2, b i is the final contact length during single contact, s i is the total distance of a single move, and s is the displacement distance coordinate during the movement.

[0082] Archard proposed a computational model for adhesive wear.

[0083]

[0084] Where Ks is the adhesive wear coefficient, P is the surface pressure of the contact surface, s is the wear distance coordinate along the surface, and σ sis the yield limit of the material.

[0085] According to Archard theory, the single wear depth of the fixed gear plate and the locking gear plate is h 1i It can be expressed as:

[0086]

[0087] Where b i is the final contact length during single wear, s i is the total distance of a single move, s1 is the rigid body sliding distance, σ s is the material yield limit, K s is the adhesive wear coefficient, T is the vertical upward force, Z is the number of teeth of the fixed gear plate 1 and the locking gear plate 2, and α is the tooth profile angle of the fixed gear plate 1 and the locking gear plate 2 (usually 60°).

[0088] Since the initial position of the locking gear may have positive or negative deviation, that is, the difference Δy between the axis of a tooth of the locking gear and the axis of the tooth groove where the tooth finally meshes can be obtained. 1i Determine whether the friction surface is the left tooth surface or the right tooth surface.

[0089] Step 2.2: Single elastic wear model of end gear disc;

[0090] Assume that both the fixed toothed disc 1 and the locking toothed disc 2 are elastic bodies, that is, both can be deformed; when the fixed toothed disc 1 and the locking toothed disc 2 complete a single rigid body wear process, the fixed toothed disc 1 undergoes elastic deformation and locks, and a slip distance S2 is generated at this time; the slip distance can be expressed as:

[0091]

[0092] Wherein, Δh2 is the elastic deformation wear after the rigid body motion stage, and α is the tooth profile angle of the fixed gear disc 1 and the locking gear disc 2 (usually 60°).

[0093] According to Archard theory, the single wear depth of the fixed gear plate and the locking gear plate is h 2i It can be expressed as:

[0094]

[0095] Where b i is the final contact length during single wear, s i is the total distance of a single move, s1 is the rigid body sliding distance, σ s is the material yield limit, K sis the adhesive wear coefficient, T is the vertical upward force, Z is the number of teeth of the fixed gear plate 1 and the locking gear plate 2, and α is the tooth profile angle of the fixed gear plate 1 and the locking gear plate 2 (usually 60°).

[0096] Step 3: Multiple wear model of end tooth discs; including: the angular error between the locking tooth opening 20 on the locking tooth disc (2) and the fixed tooth opening 10 on the fixed tooth disc (1) along the axial direction is the initial state error between the end tooth discs; the error probability distribution of the fixed tooth disc 1 and the locking tooth disc 2 is fitted by the calculated initial errors; when multiple wear occurs, the past wear amount of the fixed tooth disc 1 and the locking tooth disc 2 will affect the rigid wear process and the spatial position of the elastic wear of the end tooth disc, that is, affect the subsequent single wear amount, so the wear amount parameters on both sides of the upper fixed tooth disc 1 and the locking tooth disc 2 are introduced.

[0097] The final length of the end gear disc before multiple wear can be expressed as:

[0098]

[0099] In the formula, h 1ls is the wear thickness of the left side of the inclined surface of the fixed toothed disc 1, h 1rs is the wear thickness of the right side of the inclined surface of the fixed toothed disc 1, h 2ls is the wear thickness of the left side of the bevel of locking gear disc 2, h 2rs It is the wear thickness of the right side of the inclined surface of locking gear disc 2.

[0100] The calculation formula of the wear amount of the end gear disc after multiple wear can be expressed as:

[0101]

[0102] In the formula, s i is the total distance of a single move, b i is the final contact length in single contact, σ s is the material yield limit, K s is the adhesive wear coefficient, s is the displacement distance coordinate during the movement, T is the vertical upward force, Z is the number of teeth of the fixed gear disc 1 and the locking gear disc 2, and α is the tooth profile angle of the fixed gear disc 1 and the locking gear disc 2.

[0103] Step 4: Calculation of end gear wear and characterization of indexing accuracy; Based on the initial state error calculated in step 1 and the multiple wear model of the fixed gear in step 3, the mathematical relationship between the number of wear times and indexing accuracy / positioning accuracy is established through the Monte Carlo method.

[0104] Step 5: Optimize the design parameters of the end sprocket and its assembly chain and transmission chain; set the optimization range of the design parameters of the fixed sprocket and its assembly chain and transmission chain, construct the simulation parameters through Latin hypercube sampling, establish a response surface model based on the parameters, and perform optimization through optimization algorithms such as gradient descent method, Newton method and quasi-Newton method, conjugate gradient method or intelligent control algorithm to obtain the optimal solution.

[0105] Among them, Latin hypercube sampling is a method of approximate random sampling from a multivariate parameter distribution. It belongs to a stratified sampling technique and is often used in computer experiments or Monte Carlo integration. Assuming there are N variables (dimensions), each variable can be divided into M intervals with the same probability. At this time, M sample points that meet the Latin hypercube conditions can be selected. It should be noted that Latin hypercube sampling requires the same number of partitions M for each variable. However, this method does not require that the number of samples M increases as the number of variables increases.

[0106] 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.

[0107] Although this article uses the following terms more frequently: fixed tooth plate 1, locking tooth plate 2, fixed tooth opening 10, locking tooth opening 20, etc., it does not exclude the possibility of using other terms; these terms are used only to more conveniently describe and explain the essence of the present invention; interpreting them as any additional limitations is contrary to the spirit of the present invention.

Claims

1. A reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling, characterized in that: The end toothed disc comprises a fixed toothed disc (1) and a locking toothed disc (2); the fixed toothed disc (1) is formed with a fixed tooth opening (10) arranged around the fixed toothed disc (1); the locking toothed disc (2) is formed with a locking tooth opening (20); wherein, under the action of the hydraulic pressure, the locking toothed disc (2) first moves in a vertical direction, and then the locking toothed disc (2) slides in the tooth surface direction until the fixed tooth opening (10) and the locking tooth opening (20) are completely locked; the optimization method comprises the following steps: Step 1: Modeling the initial state error of the end gear disc; Step 2: Single wear model of end gear disc; Step 3: Multiple wear model of end gear disc; Step 4: Calculation of end gear wear and characterization of indexing accuracy; Step 5: Optimize the design parameters of the end gear plate and its assembly chain and transmission chain.

2. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 1 is characterized in that: In the step 1, The fixed gear plate (1) is connected to other parts by screws; the fixed gear plate (1) and the fixed parts have manufacturing errors and assembly errors, and the errors are characterized by a variety of methods such as traditional tolerance analysis method, small displacement screw method, reliability index method, and mixed convolution method; The locking toothed disc (2) is connected to other parts by screws, and the parts drive the locking toothed disc (2) to move along the axial direction and rotate around the axis; similarly, the locking toothed disc (2) and the fixed parts have manufacturing errors and assembly errors, and the errors are characterized by various methods such as traditional tolerance analysis method, small displacement screw method, reliability index method, mixed convolution method, etc.; if the transmission chain is closed-loop controlled, the manufacturing and assembly accuracy of feedback components such as encoders can be used to calculate the error distribution at the locking fixed toothed disc.

3. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 1 is characterized in that: In step 2, the specific steps of the end gear plate single wear model include: Step 2.1: Single rigid body wear model of end gear disc; Step 2.2: Single elastic wear model of end gear.

4. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 3 is characterized in that: In step 2.1, it is assumed that the locking toothed disc (2) and the fixed toothed disc (1) of the end toothed disc are both rigid bodies, that is, neither of them is deformed; when the locking toothed disc (2) is not in contact with the fixed toothed disc (1), the locking toothed disc (2) moves in the vertical direction and contacts with the fixed toothed disc (1); when the locking toothed disc (2) contacts with the fixed toothed disc (1), a positive pressure F perpendicular to the tooth surface is generated between the two toothed discs. N and the friction force parallel to the tooth surface, under the action of the friction force, a slip distance S1 is generated on the tooth surface; the slip distance can be expressed as: Wherein, Δh1 is the height difference between the locking gear disc (2) and the fixed gear disc (1) from contact to the end of the rigid body motion stage, and α is the tooth profile angle of the fixed gear disc (1) and the locking gear disc (2); The surface pressure of the end gear contact surface can be expressed as: In the formula, F N is the positive pressure, A is the contact area, T is the vertical upward force, Z is the number of teeth on the fixed gear plate (1) and the locking gear plate (2), b i is the final contact length during single contact, s i is the total distance of a single move, s is the displacement distance coordinate during the movement.

5. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 4 is characterized in that: In step 2.2, it is assumed that the locking toothed disc (2) and the fixed toothed disc (1) of the end toothed disc are both elastic bodies, that is, both can be deformed; when the fixed toothed disc (1) and the locking toothed disc (2) undergo elastic deformation and lock after a single rigid body wear process, a slip distance S2 is generated at this time; the slip distance can be expressed as: Wherein, Δh2 is the elastic deformation wear after the rigid body motion stage ends, and α is the tooth profile angle of the fixed gear disc (1) and the locking gear disc (2).

6. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 1 is characterized by: In step 3, the multiple wear model of the end tooth disc specifically includes: the angular error between the locking tooth opening (20) on the locking tooth disc (2) and the fixed tooth opening (10) on the fixed tooth disc (1) along the axial direction is the initial state error of the fixed tooth disc (1) and the locking tooth disc (2); the error probability distribution is fitted by the calculated initial error of the end tooth disc; when multiple wear occurs, the past wear amount of the fixed tooth disc (1) and the locking tooth disc (2) will affect the rigid wear process and the spatial position of the elastic wear of the tooth disc, that is, affect the subsequent single wear amount, so the wear amount parameters on both sides of the fixed tooth disc and the locking tooth disc are introduced.

7. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 6 is characterized in that: The final length of the end gear disc before multiple wear can be expressed as: In the formula, h 1ls is the wear thickness of the left side of the fixed gear disc bevel, h 1rs h is the wear thickness of the right side of the fixed gear disc bevel, 2ls h is the wear thickness of the left side of the locking gear bevel, 2rs It is the wear thickness on the right side of the locking sprocket bevel.

8. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 6 is characterized in that: The calculation formula of the wear amount of the end gear disc after multiple wear can be expressed as: In the formula, s i is the total distance of a single move, b i is the final contact length in single contact, σ s is the material yield limit, K s is the adhesive wear coefficient, s is the coordinate of the displacement distance during the movement, T is the vertical upward resultant force, Z is the number of teeth of the fixed gear disc (1) and the locking gear disc (2), and α is the tooth profile angle of the fixed gear disc (1) and the locking gear disc (2).

9. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 6 is characterized by: In step 4, based on the initial state error calculated in step 1 and the multiple wear model of the end gear disc in step 3, a mathematical relationship between the number of wear times and the indexing accuracy / positioning accuracy is established through the Monte Carlo method.

10. The reliability optimization method for end gear positioning and indexing accuracy based on a wear model with multi-factor coupling according to claim 1 is characterized by: In the step 5, the design parameter optimization intervals of the fixed toothed disc (1) and the locking toothed disc (2) of the end toothed disc and their assembly chain and transmission chain are set, simulation parameters are constructed by Latin hypercube sampling, a response surface model is established based on the parameters, and optimization is carried out by optimization algorithms such as gradient descent method, Newton method and quasi-Newton method, conjugate gradient method or intelligent control algorithm to obtain the optimal solution.

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