Ball nut crack fault diagnosis method

Abstract

The present application relates to a kind of ball nut crack fault diagnosis method, comprising: S1. the radial dynamics model of ball screw nut pair in normal state is established in radial direction;S2. crack fault is introduced in the radial dynamics model, and the radial dynamics model under fault state is established;S3. the simulation result of normal operation of the ball screw nut pair is obtained based on the radial dynamics model under normal state simulation calculation;The fault operation simulation result of the ball screw nut pair under fault state is obtained based on the radial dynamics model under fault state simulation calculation;The abnormal characteristics of the ball screw nut pair under fault state are obtained by comparing the normal operation simulation result and the fault operation simulation result;S4. the actual operation result of the ball screw nut pair is collected, and the actual operation result is detected based on the abnormal characteristics, and whether the ball screw nut pair has crack fault is judged.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electromechanical actuator fault diagnosis, and particularly relates to a ball nut crack fault diagnosis method. BACKGROUND

[0002] Due to the increasing investment and technological progress in the fields of aviation, aerospace and navigation, the demand for electric drive servo technology has become urgent. Therefore, electromechanical actuators (EMA) that can directly convert electrical energy into mechanical energy have emerged as the times require. At present, countries have proposed the demand for high reliability and high safety EMA in the development of aircraft aileron control systems, new landing gear systems, spacecraft thrust vector control systems, new electric rudders for helicopter attitude control, ship steering control systems and other key systems.

[0003] EMA is an electromechanical integrated system that integrates motor, servo control, mechanical transmission and other technologies, and has the characteristics of high technical density and frequent working condition switching, which also increases the failure rate of EMA. In particular, once the ball screw pair as a motion mechanism is stuck, the entire EMA system will completely lose its motion ability. Therefore, in order to ensure the high reliability and safety of the mechanical system, it is necessary to timely detect and even prevent various faults of the electromechanical actuator.

[0004] At present, in the field of EMA state monitoring and fault diagnosis, most of the methods used by research institutes are data-driven algorithms such as artificial neural networks and deep learning. Although there have been many studies on the dynamics modeling of ball screw pairs, most of the research objects are machine tool feed mechanisms, and there are few studies on the dynamics simulation of ball screw pairs contained in EMA, the analysis of fault mechanism and fault implantation method, and the solution of EMA fault diagnosis problem from the aspect of physical modeling. SUMMARY

[0005] The purpose of the present application is to provide a ball nut crack fault diagnosis method.

[0006] In order to achieve the above-mentioned purpose of the application, the present application provides a ball nut crack fault diagnosis method, which comprises:

[0007] S1. A radial dynamics model of a ball screw nut pair in a normal state in the radial direction is established.

[0008] S2. A crack fault is introduced into the radial dynamics model to establish a radial dynamics model in a fault state.

[0009] S3. A normal operation simulation result of the ball screw nut pair is obtained by simulation calculation based on the radial dynamics model in the normal state.

[0010] obtaining a fault operation simulation result of the ball screw nut pair in the fault state based on simulation calculation of the radial dynamic model in the fault state

[0011] comparing the normal operation simulation result and the fault operation simulation result to obtain an abnormal feature of the ball screw nut pair in the fault state;

[0012] S4. Collecting an actual operation result of the ball screw nut pair, detecting the actual operation result based on the abnormal feature, and judging whether the ball screw nut pair has a crack fault.

[0013] According to one aspect of the present application, in step S1, the step of establishing a radial dynamic model of the ball screw nut pair in a normal state in the radial direction includes:

[0014] S11. Establishing a three-dimensional coordinate system based on the ball screw nut pair; wherein the axial direction of the nut in the ball screw nut pair is the z direction, the plumb radial direction of the nut in the ball screw nut pair is the y direction, and the horizontal radial direction of the nut in the ball screw nut pair is the x direction;

[0015] S12. Converting the ball screw nut pair into an equivalent model;

[0016] S13. Establishing a radial dynamic model of the ball screw nut pair based on the three-dimensional coordinate system and the equivalent model.

[0017] According to one aspect of the present application, in step S12, the step of converting the ball screw nut pair into an equivalent model includes:

[0018] equivalent to a spring damping system;

[0019] equivalent to a mass block as a whole;

[0020] The ball screw nut pair is converted into an equivalent model in which the mass block is connected to the screw through the spring damping system.

[0021] According to one aspect of the present application, in step S13, the radial dynamic model in the normal state is represented as:

[0022]

[0023] wherein c is a damping constant; F x0 , F y0 are preloads acting on the nut in the x direction and the y direction, respectively; F x , Fy They represent the radial forces acting on the nut in the x and y directions respectively; m represents the overall mass of the ball screw nut pair, δ x , δ y Respectively represent the displacement of the nut in the x direction and the y direction.

[0024] According to one aspect of the present invention, the radial force F exerted on the nut in the x-direction and the y-direction is x 、F y Obtained through the following steps, including:

[0025] An initial corresponding relationship between the radial force on the nut in the radial direction and the radial elastic restoring force on the ball is established: wherein the initial corresponding relationship is expressed as:

[0026]

[0027]

[0028]

[0029] Where n is the number of initial load balls, θ is the angle between two adjacent balls, F ni Indicates the radial elastic restoring force on the ball, d d is the ball diameter, d s is the pitch diameter of the screw, γ is the helix angle of the screw;

[0030] The initial correspondence is optimized based on the circulation process of the ball in the nut to obtain a true correspondence between the radial force on the nut in the radial direction and the radial elastic restoring force on the ball at any time; wherein the true correspondence is expressed as:

[0031]

[0032]

[0033] θ pr =π(1-mod(N s ,1))cosγ

[0034]

[0035]

[0036] Among them, T b Indicates the ball passing cycle, mod(N s , 1) is N s The remainder when divided by 1, N s Indicates the actual number of load-bearing raceways in the nut; θpr The angle between the start / end of the reverser raceway for ball circulation in the nut and the symmetrical centerline of the reverser; θ a F is the phase where the symmetrical centerline of the inverter is ahead of the y-axis when the ball nut is actually installed; nex Indicates the radial elastic restoring force on the ball when it is leaving the reverser; F nen Indicates the radial elastic restoring force on the ball when it enters the reverser; n s is the screw rotation speed; β is the contact angle; ω bs is the angular velocity of the ball center rotating around the screw;

[0037] The radial elastic restoring force F on the ball ni The radial elastic restoring force F exerted on the ball when entering and leaving the reverser is nen and F nex Solve them separately to obtain the solution formula, which can be expressed as:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] Among them, δ ni represents the radial elastic deformation of the i-th ball; δ nen Indicates the radial elastic deformation of the ball entering the reverser; δ nex represents the radial elastic deformation of the ball leaving the deflector; kn is the Hertzian contact stiffness; ∑ρ bs ,∑ρ bn are the sum of the principal curvatures of the ball and screw raceway and the ball and nut raceway respectively; r s 、r n are the curvature radii of the screw raceway and the nut raceway respectively; ν1, ν2, ν3 are the Poisson's ratios of the ball, screw, and nut respectively; E1, E2, E3 are the Young's modulus of elasticity of the ball, screw, and nut respectively.

[0045] According to one aspect of the present invention, the displacement δ of the nut in the x-direction and the y-direction x , δ y Expressed as:

[0046] δ x=|x|sin(θ a +θ pr +ω bs mod(t,T b )+iθ)

[0047] δ y =|y|cos(θ a +θ pr +ω bs mod(t,T b )+iθ)

[0048] The radial elastic deformation of the i-th ball is expressed as:

[0049]

[0050] Radial elastic deformation of the ball entering the reverser δ nen Expressed as:

[0051]

[0052] Radial elastic deformation of the ball leaving the deflector δ nex Expressed as:

[0053]

[0054] Among them, l p The distance between the center of curvature of the nut raceway and the center of curvature of the screw raceway when only the preload force is applied is expressed as l p =r s +r n -d s +δ p , r s 、r n are the curvature radii of the screw raceway and the nut raceway respectively; δ p Indicates the deformation of the ball due to the influence of preload; δ ren and δ rex Respectively represent the difference between the ball deformation when entering / exiting the reverser and the ball deformation when fully loaded.

[0055] According to one aspect of the present invention, in step S2, in the step of introducing a crack fault into the radial dynamic model and establishing the radial dynamic model under the fault state, the radial dynamic model under the fault state is expressed as:

[0056]

[0057] Among them, F xf 、F yf They represent the radial forces in the x and y directions respectively when a fault occurs in the ball nut.

[0058] According to an aspect of the present application, the radial forces Fx, Fy that the nut suffers in the x and y directions when a fault exists in the nut are obtained by combining the real correspondence between the radial force that the nut suffers in the radial direction and the radial elastic recovery force that the ball suffers at any moment and the solving formula of the radial elastic recovery force that the ball suffers when passing through a crack fault, and are expressed as: xf , Fy = -F yf x

[0059] The solving formula of the radial elastic recovery force that the ball suffers when passing through a crack fault is constructed as follows:

[0060]

[0061]

[0062]

[0063]

[0064] θ f = 2arcsin(bcosγ / d s )

[0065] wherein δ f represents the release amount of elastic deformation of the ball when passing through a crack fault; b represents the width of the crack fault, and is less than the diameter of the ball; θ f represents the corresponding radian of the crack fault on the pitch circle of the screw rod;

[0066] The radial forces Fx, Fy that the nut suffers in the x and y directions when a fault exists in the nut are obtained by combining the real correspondence between the radial force that the nut suffers in the radial direction and the radial elastic recovery force that the ball suffers at any moment and the solving formula of the radial elastic recovery force that the ball suffers when passing through a crack fault, and are expressed as: xf , Fy = -F yf x

[0067]

[0068]

[0069]

[0070]

[0071] wherein θ af represents the included angle between the fault center line and the y axis;

[0072] According to one aspect of the present application, in the step S3 of obtaining the abnormal characteristics of the ball screw nut pair under the fault state by comparing the normal operation simulation result and the fault operation simulation result, the envelope spectrum analysis method is used to process the normal operation simulation result and the fault operation simulation result respectively, and the abnormal characteristics are obtained by comparing the processed normal operation simulation result and the processed fault operation simulation result.

[0073] According to one aspect of the present application, in the step S3 of obtaining the abnormal characteristics of the ball screw nut pair under the fault state by comparing the normal operation simulation result and the fault operation simulation result, the abnormal characteristics are the acceleration abnormal response and / or displacement abnormal response of the nut in the radial direction.

[0074] According to one aspect of the present application, by establishing the dynamic model of the ball screw under the normal and fault states, the normal and fault dynamic characteristics of the ball screw are analyzed respectively, the feature performance when the fault occurs can be quickly and effectively found out, and the running state monitoring and fault diagnosis of the ball screw can be accurately realized based on the obtained feature performance.

[0075] According to one aspect of the present application, the fault diagnosis method of the present application is universal for the screw rod speed of 60-420 rpm, which greatly guarantees the practicability and effectiveness of the present application.

[0076] According to one aspect of the present application, by referring to the actual running environment of the ball screw nut pair in the EMA system, the main vibration excitation sources of the ball screw pair under the normal state and the fault state are comprehensively analyzed, and the dynamic characteristics of the ball nut are analyzed considering some unique structures of the ball nut, the displacement and acceleration response in the x and y directions of the nut are obtained, and the two-degree-of-freedom time-varying dynamic model of the ball screw pair is accurately established. Then, considering the specific performance of the nut crack fault in the nut dynamic characteristics under the actual engineering environment, the crack fault is implanted in the normal model, and the two-degree-of-freedom time-varying dynamic model of the ball screw pair under the fault state is accurately formed.

[0077] According to one aspect of the present application, the dynamic model of the present application fully meets the simulation simulation of the real object, the simulation result is accurate and effective, and the effectiveness of the real object detection is further improved.

[0078] According to one scheme of the present application, when the model is further analyzed and simulated, it is found that when the raceway of the ball nut has a crack fault, the amplitude at the three times ball passing frequency in the acceleration signal spectrum of the nut will obviously increase compared with the amplitudes at the one and two times frequencies, and this phenomenon does not change with the change of the screw rotation speed. Therefore, the characteristic performance of the ball nut raceway crack fault in the nut acceleration signal spectrum can effectively distinguish whether the ball screw nut pair has a fault, and the result is accurate.

[0079] According to one scheme of the present application, by using the simulation means to obtain the abnormal characteristic performance, the difficulty of repeated testing by using the physical object is greatly reduced, and the diagnosis efficiency is improved. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 is a schematic block diagram showing steps of a ball nut crack fault diagnosis method;

[0081] Figure 2 is a coordinate system diagram showing a ball screw pair dynamics model;

[0082] Figure 3 is an equivalent model diagram of a ball screw nut pair;

[0083] Figure 4 is a schematic diagram showing a ball screw helix projection plane relationship, wherein (a) shows a ball screw helix actual structure diagram, (b) shows a ball screw helix structure diagram projected onto the same plane, and (c) shows a ball screw helix side view projected onto the same plane;

[0084] Figure 5 is a schematic diagram showing a ball and a reverser in and out plane;

[0085] Fig. 6(a) is a schematic diagram showing the direction of action of the radial elastic restoring force on the part of the ball at 0 time;

[0086] Fig. 6(b) is a schematic diagram showing the direction of action of the radial elastic restoring force on the part of the ball at t time;

[0087] Figure 7 is a schematic diagram showing the relationship between the pre-tightening force and the ball deformation when a single ball is loaded;

[0088] Figure 8 is a schematic diagram showing the relationship between the radial elastic restoring force F ni and the radial elastic deformation δ ni of the i-th ball;

[0089] Fig. 9(a) is a schematic diagram showing the force analysis of each ball load when the nut has a radial displacement and all δ ni ≥ 0;

[0090] Fig. 9(b) is a schematic representation of the nut undergoing radial displacement and partial δ ni Fig. 8 is a schematic representation of the force analysis of each ball bearing when the nut is in the state of 0;

[0091] Figure 10 Fig. 9(a) is a schematic representation of the force analysis of each ball bearing when the nut is in the state of δ

[0092] Figure 11 Fig. 10 is a schematic representation of the analysis of the process of the ball passing through the crack failure point;

[0093] Figure 12 Fig. 11 is a schematic representation of the stress relief process when the ball passes through the crack failure point;

[0094] Figure 13 Fig. 12 is a schematic representation of the impact on the trailing edge after failure when the ball passes through the crack failure point;

[0095] Figure 14 Fig. 13 is a schematic representation of the displacement and acceleration response in the x and y directions when the lead screw speed is 30 rpm, the axial pre-tightening force is 100 N, and the simulation is performed without failure;

[0096] Figure 15 Fig. 14 is a schematic representation of the acceleration response and its spectrum in the x and y directions when the lead screw speed is 30, 60, and 90 rpm, the axial pre-tightening force is 100 N, and the simulation is performed without failure; wherein (a) is the x-direction acceleration response graph, (b) is the y-direction acceleration response graph, (c) is the x-direction acceleration spectrum graph, and (d) is the y-direction acceleration spectrum graph;

[0097] Figure 16 Fig. 15 is a schematic representation of the acceleration response and its envelope spectrum in the x and y directions when the lead screw speed is 90 rpm, the axial pre-tightening force is 100 N, and the simulation is performed without failure; wherein (a) is the x-direction acceleration response and its envelope signal graph, (b) is the y-direction acceleration response and its envelope signal graph, (c) is the x-direction envelope spectrum graph, and (d) is the y-direction envelope spectrum graph;

[0098] Figure 17 Fig. 16 is a schematic representation of the acceleration response and its envelope spectrum in the x and y directions when the lead screw speed is 30 rpm, the axial pre-tightening force is 100 N, and the simulation is performed without failure; wherein (a) is the x-direction acceleration response and its envelope signal graph, (b) is the y-direction acceleration response and its envelope signal graph, (c) is the x-direction envelope spectrum graph, and (d) is the y-direction envelope spectrum graph;

[0099] Figure 18Figure 1 schematically shows the acceleration responses and their envelope spectra in the x and y directions when the screw speed is 420 rpm, the axial preload is 100 N, and no faults are simulated. (a) shows the acceleration response and its envelope signal in the x direction, (b) shows the acceleration response and its envelope signal in the y direction, (c) shows the envelope spectrum in the x direction, and (d) shows the envelope spectrum in the y direction.

[0100] Figure 19 The diagram schematically shows the displacement response and acceleration response in the x and y directions when the screw speed is 30 rpm, the axial preload is 100 N, and a crack failure occurs in the nut.

[0101] Figure 20 The diagram schematically shows the acceleration response and its envelope spectrum in the x and y directions when the screw speed is 30 rpm, the axial preload is 100 N, and the nut has a crack fault, and compares them with the envelope spectrum of the normal signal; (a) is the acceleration response and its envelope signal diagram in the x direction, (b) is the acceleration response and its envelope signal diagram in the y direction, (c) is the envelope spectrum diagram of the fault signal in the x direction, (d) is the envelope spectrum diagram of the fault signal in the y direction, (e) is the envelope spectrum diagram of the normal signal in the x direction, and (f) is the envelope spectrum diagram of the normal signal in the y direction;

[0102] Figure 21 The figure schematically shows the comparison of normal and fault acceleration response envelope spectra in the x and y directions when the screw speeds are 90, 180, 390, and 420 rpm and the axial preload is 100 N.

[0103] Figure 22 is a diagram schematically showing a ball screw experimental platform according to an embodiment of the present invention;

[0104] Figure 23 It is a schematic diagram showing the comparison between the normal and fault signals measured by the three sensors in the experiment and the model simulation signals when the screw speed is 60 rpm;

[0105] Figure 24 It is a schematic diagram showing the comparison between the normal and fault signals measured by the three sensors in the experiment and the model simulation signals when the screw speed is 180 rpm;

[0106] Figure 25 It is a schematic diagram showing the comparison between the normal and fault signals measured by the three sensors in the experiment and the model simulation signals when the screw speed is 240 rpm;

[0107] Figure 26is a schematic representation of the comparison between the normal and fault signals measured by the three sensors in the experiment and the model simulation signals at a screw rotation speed of 420 rpm. DETAILED DESCRIPTION

[0108] The application will be described in detail below with reference to the drawings and specific embodiments, which cannot be exhaustively listed here, but the embodiments of the application are not limited to the following embodiments.

[0109] As Figure 1 shown, according to an embodiment of the application, a ball nut crack fault diagnosis method of the application comprises:

[0110] S1. Establishing a radial dynamic model of the ball screw nut pair in the radial direction under normal state;

[0111] S2. Introducing a crack fault into the radial dynamic model to establish a radial dynamic model under fault state;

[0112] S3. Performing simulation calculation based on the radial dynamic model under normal state to obtain normal operation simulation results of the ball screw nut pair;

[0113] Performing simulation calculation based on the radial dynamic model under fault state to obtain fault operation simulation results of the ball screw nut pair under fault state

[0114] Comparing the normal operation simulation results and the fault operation simulation results to obtain abnormal characteristics of the ball screw nut pair under fault state;

[0115] S4. Collecting actual operation results of the ball screw nut pair, detecting the actual operation results based on the abnormal characteristics, and determining whether the ball screw nut pair has a crack fault.

[0116] According to an embodiment of the application, before establishing the ball screw fault dynamic model, it is necessary to first analyze the characteristics of the ball screw pair under normal state, establish a normal dynamic model of the ball screw, and then implant a fault in the normal model to perform simulation under fault state.

[0117] Further, when a fault occurs at a certain point on the nut and screw of the ball screw nut pair, the internal balls can cause impact vibration when passing through the fault point, and the impact vibration direction is usually the normal direction of the fault point, i.e., the radial direction of the screw. Furthermore, in this embodiment, in order to achieve better results in the fault diagnosis of the ball screw nut pair, it is necessary to model the vibration response of the ball screw in the radial direction in detail, and simulate the vibration signal when the fault occurs, so as to collect the characteristics when the fault occurs, and based on the collected abnormal characteristics, the ball screw nut pair in actual operation can be detected.

[0118] In this embodiment, before establishing the kinetic model, the following assumptions are made:

[0119] (1) All balls in the ball nut are tightly arranged and fill the entire nut raceway;

[0120] (2) A preload must be applied to the ball nut to prevent vibration during operation, and the direction of the preload must coincide with the axis of the nut.

[0121] (3) The axial load on all balls in the nut is uniformly distributed;

[0122] (4) The raceways of the nut and the screw are rigid and do not deform;

[0123] (5) The speed at which each ball in the nut rotates around the screw is consistent;

[0124] (6) The ball screw pair studied in this paper is a ball screw pair in which the screw rotates only around its axis and the nut moves only in the direction of the screw axis;

[0125] (7) The damping value of the ball screw pair in the two radial directions is the same;

[0126] (8) Ignoring the influence of processing and assembly errors, the shape and material of all balls are exactly the same.

[0127] like Figure 2 As shown, according to one embodiment of the present invention, in step S1, the step of establishing a radial dynamic model of the ball screw nut pair in the radial direction under a normal state includes:

[0128] S11. Establish a three-dimensional coordinate system based on the ball screw nut pair; wherein the axial direction of the nut in the ball screw nut pair is the z direction, the plumb bob radial direction of the nut in the ball screw nut pair is the y direction, and the horizontal radial direction of the nut in the ball screw nut pair is the x direction;

[0129] S12. Convert the ball screw nut pair into an equivalent model;

[0130] S13. Establish a radial dynamic model for the ball screw nut pair based on the three-dimensional coordinate system and the equivalent model. In this embodiment, for the convenience of describing this solution, the subsequent dynamic model establishment and calculation description are selected in the y direction.

[0131] like Figure 3 As shown, according to one embodiment of the present invention, in step S12, the step of converting the ball screw nut pair into an equivalent model includes:

[0132] The balls in the ball screw nut pair are equivalent to a spring damping system;

[0133] The nut and additional components in the ball screw nut pair are regarded as a whole and are equivalent to a mass block;

[0134] The ball screw-nut pair is transformed into an equivalent model in which a mass block is connected to the screw through a spring-damper system.

[0135] like Figure 3 As shown, according to one embodiment of the present invention, in step S13, the radial dynamics model is expressed as:

[0136]

[0137] Where c is the damping constant; F x0 、F y0 are the preloads acting on the nut in the x and y directions respectively; F x 、F y They represent the radial forces acting on the nut in the x and y directions respectively; m represents the overall mass of the ball screw nut pair, δ x , δ y In this embodiment, it is assumed that the damping value of the system in the two radial directions is the same. To simplify the calculation process, c is directly given by the empirical value. x0 、F y0 In general, the preload in the radial direction of the plumb bob is equal to the gravity of all components installed on the nut, while the preload borne by the nut in the horizontal radial direction is generally small and can generally be ignored.

[0138] In order to further elaborate on the process of constructing the radial dynamic model under normal conditions in this solution, a further detailed description is given in conjunction with the accompanying drawings.

[0139] According to one embodiment of the present invention, an overall force analysis is performed based on the structure of the ball screw nut pair. Specifically, due to the existence of the helix angle in the ball screw nut pair, there is a certain angle difference between the actual contact direction between the ball, the screw, and the nut and the established coordinate system. Therefore, see Figure 4 As shown in the figure, in this scheme, all balls are projected into the same plane for analysis to simplify the calculation process.

[0140] like Figure 4 As shown, F x 、F y 、F z are the total horizontal radial force, total plumb radial force and total axial force on the nut, respectively, x , δ y are the displacements of the nut in the horizontal radial direction and the plumb bob radial direction, F ni is the radial elastic restoring force on the i-th ball. Figure 4It can be seen that the radial elastic restoring force F on each ball is ni The direction of F x 、F y The direction of action is different. When synthesizing the radial forces on all balls into the total radial force on the nut, the angle corresponding to each ball needs to be considered. Therefore, F x 、F y With F ni The initial correspondence is as follows:

[0141]

[0142]

[0143] Where n is the number of initial load-bearing balls, and θ is the angle between two adjacent balls.

[0144] Since the balls are closely arranged, the ball angle θ can be calculated by the following formula:

[0145]

[0146] Where, d b is the ball diameter, d s is the pitch diameter of the screw, and γ is the helix angle of the screw.

[0147] Since the ball screw pair needs to include a reverser structure for ball circulation, the ball nut raceway must leave a gap for the balls to enter and exit the reverser, that is, the first and last raceways of the nut are not a complete arc. x 、F y With F ni When the corresponding relationship is obtained, it is also necessary to locate the gap positions of the first and last raceways of the nut in order to calculate the missing part of the raceway, which is further used to optimize the initial corresponding relationship.

[0148] like Figure 5 As shown in the figure, when the center point of the reverser on the nut is installed along the y-axis, the first and last raceways in the nut are projected onto the plane of the x and y axes, and it can be seen that the inlet and outlet of the reverser are arranged symmetrically with respect to the y-axis. In this embodiment, it is assumed that the angle between the start / end of the reverser raceway and the reverser's symmetry centerline (y-axis) is θ pr Then it is expressed as:

[0149] θ pr =π(1-mod(N s ,1))cosγ (4)

[0150] Among them, N sNactual represents the actual number of loaded raceways in the ball nut (provided by the manufacturer of the ball screw nut pair), mod(N s , 1) is the remainder of N s divided by 1.

[0151] Generally, the balls in the reverser of the ball screw nut pair do not need to bear any load. Therefore, when the balls gradually leave the reverser and enter the loaded raceway, the load borne by the balls gradually increases from 0, and the elastic deformation of the balls gradually increases. In this transition stage, the radial elastic deformation of the balls is different from that of the balls in the loaded raceway, and needs to be calculated separately, and then the initial correspondence relationship can be further optimized by the obtained calculation results.

[0152] Specifically, it is assumed that the radial elastic restoring force borne by the ball in the process of leaving the reverser (i.e., the first ball in the loaded raceway) is F nex , and the radial elastic restoring force borne by the ball in the process of entering the reverser (i.e., the last ball in the loaded raceway) is F nen . The optimized results obtained after introducing the initial correspondence relationship are represented as:

[0153]

[0154]

[0155] Wherein, θ a is the phase of the center line of the reverser symmetry ahead of the y-axis when the ball nut is actually installed, and as shown in Figure 5 , the state when the center line of the reverser symmetry coincides with the y-axis.

[0156] Further, since the direction of the radial elastic restoring force borne by each ball changes with the rotation of the ball when the ball starts to rotate in the circumferential direction. Therefore, when optimizing the initial correspondence relationship of F x , F y and F ni , the change of the direction of F ni at any time needs to be calculated, and then the real correspondence relationship of F x , F y and F ni at any time can be obtained by introducing the foregoing optimization results.

[0157] Specifically, as shown in FIGS. 6(a) and 6(b), in the present embodiment, it is assumed that the instant when the No. 0 ball leaves the reverser of the nut and enters the screw-nut loaded raceway is 0 time. At this time, the direction of the radial elastic restoring force F n0 borne by the No. 0 ball is consistent with the junction line of the reverser raceway and the loaded raceway, i.e., Fn0 The included angle with the y-axis is θ a + θ pr .

[0158] After 0 time, the aforementioned 0thball rolls forward, and the n+1thball following the 0thball gradually leaves the reverser and enters the bearing raceway. At the same time, the n thball at the other end of the nut also gradually leaves the bearing raceway and enters the reverser. Therefore, when the balls fill the bearing raceway, as long as the first ball and the last ball in the bearing raceway are exactly on the junction line of the reverser raceway and the bearing raceway, the number of balls n carrying the load in the ball screw pair at any time will be a constant value and will not change with time.

[0159] However, it is difficult to achieve in engineering practice, resulting in a slight change in the number of balls n carrying the load in most ball screw nut pairs in engineering with the change of time. Specifically, the calculation method of the number of balls n carrying the load in the ball screw nut pair is described in detail in the existing literature "Mengtao Xu, Hongzhuang Zhang, Zhendong Liu, et al. A time-dependent dynamic model for ball passage vibration analysis of recirculation ball screw mechanism [J]. Mechanical Systems and Signal Processing, 2021, 157: 107632." which will not be repeated here.

[0160] At time t, the angle turned by the aforementioned 0thball relative to 0 time is:

[0161] θ t = ω bs t

[0162]

[0163] Where n s is the screw rotation speed (rpm); ω bs is the angular velocity of the ball center rotating around the screw.

[0164] Further, the aforementioned 0thball continues to rotate, and the rotation angle θ t is equal to a ball included angle θ, the n+1thball will fill the original position of the 0thball. If the n+1thball is assumed to be a new 0thball, the direction of the radial elastic restoring force F ni of each ball in the bearing raceway at this time is exactly the same as that of the aforementioned 0thball.

[0165] Further, it is known that each time the ball in the load bearing raceway of the nut rotates by a ball included angle θ, the direction of F ni of each ball will return to the direction at the time when the aforementioned No. 0 ball is in the aforementioned state, forming a periodic motion. In the present embodiment, this period is defined as the ball passing period T b , which can be expressed as:

[0166]

[0167] Further, the aforementioned optimization result can be converted into the true correspondence relationship between F x , F y and F ni at any time, which is expressed as:

[0168]

[0169]

[0170] According to an embodiment of the present application, based on the aforementioned obtained true correspondence relationship between F x , F y and F ni at any time, the radial elastic restoring force F ni borne by the ball contained therein, the radial elastic restoring force F nen borne by the ball when entering and leaving the reverser, and F nex are all key quantities in the radial dynamics model, and need to be further solved to obtain the corresponding solving formula. In the present embodiment, the force state of the ball in the nut in static and dynamic states is solved, and the radial dynamics model is further improved according to the obtained solving result.

[0171] First, the force state of the ball in the nut in static state is solved; wherein. According to the Hertz contact theory, the corresponding relationship between the preload Q p borne by the ball in the ball screw pair and the deformation δ p of the ball due to the influence of the preload is:

[0172] Q p = k n δ p 3 / 2 (10)

[0173] In the formula, k n is the Hertz contact stiffness.

[0174] To solve formula (10), the sum of the principal curvatures ∑ρ bs , ∑ρ bn of the ball and the screw raceway and the ball and the nut raceway need to be solved respectively. Referring toFigure 7 As shown in the figure, based on the relationship between the preload force and the ball deformation when a single ball is loaded, the sum of the main curvatures of the ball and the screw raceway is:

[0175]

[0176] The sum of the principal curvatures of the ball and nut raceways is:

[0177]

[0178] Among them, r s 、r n are the curvature radii of the screw and nut raceways, respectively, and β is the contact angle;

[0179] Furthermore, the Hertzian contact stiffness is expressed as:

[0180]

[0181] Among them, k bs 、k bn are the Hertzian contact stiffness of the ball and screw, and the ball and nut, respectively. ν1, ν2, and ν3 are the Poisson's ratios of the ball, screw, and nut, respectively. E1, E2, and E3 are the Young's moduli of the ball, screw, and nut, respectively. It is assumed here that the nut and screw are made of the same material, that is, ν2=ν3 and E2=E3.

[0182] See further Figure 7 As shown, the nut is subjected to an axial force F p The preload Q of the ball p There is a correlation between them. Combining formula (10), we can obtain the axial force F of the nut under the static stress state of the ball in the nut: p The deformation of the ball due to the preload δ p The corresponding relationship between them is expressed as:

[0183] F p =Nk n δ p 3 / 2 sinβcosγ (12)

[0184] Where N is the number of balls initially loaded, and the number of balls that can be loaded on the premise that the raceway is full is N. s The angle θ between the adjacent balls is calculated.

[0185] Secondly, the dynamic force state of the ball in the nut is calculated; wherein. Based on the aforementioned existing literature “Mengtao Xu, Hongzhuang Zhang, Zhendong Liu, et al. A time-dependent dynamic model for ball passage vibration analysis of recirculation ball screw mechanism [J]. Mechanical Systems and Signal Processing, 2021, 157: 107632.”, under the premise of pre-tightening force, the axial force F a The corresponding relationship between the axial displacement of the nut and the axial displacement of the nut is represented as:

[0186]

[0187] In the formula, l p is the distance between the curvature center of the nut raceway and the curvature center of the screw raceway when only the pre-tightening force acts, which can be obtained by the formula l p = r s + r n -d s + δ p r s , r n are the curvature radii of the screw raceway and the nut raceway respectively; l a is the distance between the curvature center of the nut raceway and the curvature center of the screw raceway after the axial force acts; δ a represents the displacement of the nut; β is the initial contact angle; β a is the contact angle after the axial force acts; γ is the helix angle of the screw and the nut raceway.

[0188] In this embodiment, it is assumed that all the balls in the nut uniformly bear the axial pre-tightening force, and further, according to formula (12), in formula (13), the deformation δ p of the ball affected by the pre-tightening force can be obtained by the following formula:

[0189]

[0190] Referring to Figure 8 , when the i-th ball is loaded during the movement of the nut, the radial elastic restoring force F ni of the ball and the radial deformation δ ni of the ball before the ball are obtained based on formula (13), and are specifically represented as:

[0191]

[0192] From equation (15), the radial elastic restoring force F ni of the ball is: ni In the previous corresponding relationship, the radial deformation δ ni of the ball is one of the important quantities. For this purpose, referring to Fig. 9, the radial deformation of the ball is solved while the force analysis is performed.

[0193] Referring to Fig. 9(a), the projection of the displacement of the nut in two radial directions (x direction and y direction) in the bearing direction of the i-th ball is:

[0194] δ x = |x| sin (θ a + θ pr + ω bs mod (t, T b ) + iθ) (16)

[0195] δ y = |y| cos (θ a + θ pr + ω bs mod (t, T b ) + iθ) (17)

[0196] Based on equations (16) and (17), the solving formula of the radial deformation δ ni of the ball is:

[0197]

[0198] In the present embodiment, it is assumed that the position of the screw is fixed and no displacement is generated in the ball screw nut pair. Referring to Fig. 9(b), when the nut generates a large displacement in the negative direction of the x axis and the y axis, respectively, the elastic deformation of the ball bearing in the lower left raceway due to the pre-tightening force is completely released, and the ball is separated from the contact with the raceway and the bearing. Therefore, when the radial elastic restoring force F ni of each ball in the nut is calculated, it is necessary to distinguish between the bearing ball and the non-bearing ball, and the F ni of the non-bearing ball is set to zero before the calculation.

[0199] Therefore, in combination with equation (15), the radial elastic restoring force F ni of the ball can be rewritten as:

[0200]

[0201] Similar to the solving method of the radial elastic restoring force F ni of the ball described above, the radial elastic restoring force F nen of the ball in the stage of entering and exiting the reverser is calculated.nex The analysis can also be performed by the above method, and the solving formula is:

[0202]

[0203]

[0204] wherein δ nen and δ nex are the radial elastic deformation amounts of the ball entering and leaving the recirculator ball respectively.

[0205] Since the nut does not rotate during normal operation of the ball screw nut pair, the angle between the start and end positions of the recirculator raceway in the nut and the y-axis is constant, so the radial elastic deformation amounts δ nen and δ nex of the ball entering and leaving the recirculator ball can be directly solved by the following formula, which are respectively represented as:

[0206]

[0207]

[0208] wherein δ ren and δ rex represent the difference between the ball deformation amount when entering / leaving the recirculator and the ball deformation amount when fully loaded.

[0209] It should be noted that during the transition phase of the recirculator and the connected load raceway, the actual deformation amount of the ball is less than the ball deformation amount when fully entering the load raceway, and thus when calculating the ball deformation amount during the transition phase, the additional part needs to be subtracted, that is, δ ren is subtracted in formula (22) and δ rex is subtracted in formula (23). In this embodiment, the solving method of δ ren and δ rex has been given in the aforementioned existing literature “Mengtao Xu, Hongzhuang Zhang, Zhendong Liu, et al. A time-dependent dynamic model for ball passage vibration analysis of recirculation ball screw mechanism [J]. Mechanical Systems and Signal Processing, 2021, 157: 107632.”, which will not be repeated here.

[0210] Due to the specific working environment of the electromechanical actuator, the actuator often needs to be frequently reversed, started and stopped, speed changed, or bear a larger load, so the ball screw mechanism in the EMA is also more prone to failure. The ball screw nut pair in the EMA mainly has the fault forms of partial jamming, peeling, cracking, gap and the like, and each fault form will have a great influence on the normal function, precision and noise of the EMA. In the scheme, the ball nut crack fault is mainly selected to implant the established model.

[0211] For fault implantation in the established dynamic model, the application further additionally proposes the following assumptions:

[0212] (1) Only one crack fault occurs in the nut;

[0213] (2) The damping does not change after the fault occurs;

[0214] (3) The crack fault depth is large enough to make the ball only contact the two ends of the fault, and not contact the bottom of the fault;

[0215] (4) The width of the crack fault is smaller than the diameter of the ball.

[0216] According to an embodiment of the application, in the step of introducing the crack fault in the radial dynamic model in step S2, the radial dynamic model with the crack fault is obtained, which is represented as:

[0217]

[0218] Wherein, F xf , F yf respectively represent the radial forces in the x direction and the y direction when the nut has a fault.

[0219] As shown in Figure 10 , in the embodiment, it is assumed that the nut bearing raceway region produces a crack fault with a width of b and a depth of h, and the angle between the fault center line and the y axis is θ af , which does not change with time during the rotation of the ball. Since in engineering practice, the crack fault depth is usually much larger than the width, it is assumed that the crack depth h is large enough to make the ball only contact the edge lines of the two ends of the fault, and not contact the bottom of the fault.

[0220] In the embodiment, it is assumed that the damping of the ball screw pair does not change after the fault occurs, so the motion equation of the ball screw pair in the fault state is not different from that in the normal state, and then the radial forces F xf , F yfThe radial dynamic model under the fault state can be obtained by substituting the radial dynamic model under the normal state. It can be seen that the radial force F in the x and y directions of the nut when the ball passes through the fault state is xf 、F yf It is the key quantity in the radial dynamic model under fault conditions. Therefore, the radial force F in the x and y directions of the nut when the ball passes through the fault is calculated in conjunction with the attached figure. xf 、F yf The solution process is explained in further detail.

[0221] like Figure 11 As shown, when the ball reaches the edge in front of the crack, due to the gap in the load-bearing raceway, it will move forward in a circular motion around point A. Simultaneously, as the ball gradually enters the gap created by the crack, its elastic deformation and elastic recovery force gradually decrease, indicating that the ball is in a "de-stressing process." When the ball's center reaches the centerline of the crack, it contacts the edge behind the crack, exerting a significant impact on that point. The ball then breaks contact with point A and re-enters the load-bearing raceway, experiencing an increase in its elastic deformation and elastic recovery force, indicating that the ball is in a "re-stressing process."

[0222] In this embodiment, it is assumed that the crack fault width b is smaller than the ball diameter, so only one ball can pass through the fault at the same time. The basis for determining whether the ball passes the fault position is:

[0223]

[0224] Among them, θ f =2arcsin(bcosγ / d s ) is the arc corresponding to the crack on the pitch circle of the screw.

[0225] In this embodiment, This is to facilitate the subsequent calculation of the angle of the ball when it passes through the crack failure.

[0226] Combine Figure 11 and Figure 12 As shown, the release amount of elastic deformation when the ball passes through the crack failure is δ f , then the moment the ball contacts point A, δ f = 0. During the stress relief process of the ball, δ f With (θ fs +θ fb ) increases rather than linearly, see Figure 12 As shown. Among them, θ fs It represents the angle that the ball center rotates around the screw center starting from the ball contact point A, θ fb It represents the angle that the ball center rotates around point A starting from the point where the ball contacts the ball.f The solution formula of is:

[0227]

[0228] Combining Figure 11 and Figure 12 , when the ball contacts point B, i.e. the ball center reaches the fault center line, the following is satisfied:

[0229]

[0230] When δ f reaches the maximum value , the stress relief process ends.

[0231] From the above, the deformations δ xf and δ xf of the ball in the x and y directions when passing through the fault are respectively:

[0232]

[0233]

[0234] Further, substituting the δ f , δ xf , δ yf solved by the foregoing process into equation (18), the solution formula of the elastic deformation δ nf of the ball when passing through the crack fault is as follows:

[0235]

[0236] Further, the solution formula of the radial elastic restoring force F nf experienced by the ball when passing through the crack fault is as follows:

[0237]

[0238] Combining Figure 11 and Figure 13 , when the ball center passes through the fault center line, it enters the "re-stress phase". First, the ball will impact the rear edge of the fault, as shown in Figure 13 , after the impact ends, the ball will continue to move in a circle with B point as the center, and the deformation of the ball will gradually increase, returning to the normal bearing raceway.

[0239] After the impact of the ball is completed, the impact speed v f of the ball at point B will decay to 0. According to the momentum theorem, the impact force F f of the ball on the nut fault edge can be solved by the following formula:

[0240]

[0241] Among them, m b is the ball mass, It is the fault impact time, which is actually the time it takes for the ball to break away from the fault contact.

[0242] In this embodiment, v f The direction is along the line connecting point B and the ball center O2. The solution formula is as follows:

[0243]

[0244] where θ b It is the arc corresponding to the fault crack on the outer circle of the ball.

[0245] In this embodiment, when the ball continues to make a circular motion around point B, the elastic restoring force F nf Gradually returns to the normal load-bearing state, at this time F nf and δ nf The solution method is the same as that in the stress relief process, except that the elastic deformation release δ when the ball passes the fault is f Slightly different, we get:

[0246]

[0247] Furthermore, combining formula (8), formula (9) and formula (29), the radial force F on the nut when the ball passes through the fault is xf 、F yf The solution formula is as follows:

[0248]

[0249]

[0250] It should be noted that, since the force on the ball changes when it passes through the crack fault, when the radial force dynamic model based on the fault state is simulated, the radial force F on the nut is calculated. x 、F y When solving, it is necessary to calculate the F when passing through the fault point. nf Listed separately for consideration, and under normal load ball F ni In the accumulation of , it is necessary to remove the balls that have passed the fault to avoid repeated calculation. Furthermore, when performing simulation calculation based on the radial force dynamic model of the fault state, it is assumed that the crack fault occurs at the Nth ball of the nut raceway. sf Circle, then the formula (33) and formula (34) That is, the judgment condition that the i-th ball does not pass the fault area.

[0251] According to an embodiment of the present application, in step S3, after the establishment of the dynamic model under the normal state and the fault state of the ball screw nut pair, the five-order Runge-Kutta method is used to solve the dynamic model, and the displacement and acceleration response signals of the ball screw nut pair under the normal state and the fault state are simulated respectively. In the embodiment, considering the rotating speed that the experimental table can reach, the rotating speed of the screw used in the simulation is 30-420 rpm, which is increased by 30 rpm as an interval. In order to ensure that there is enough sample data (for example, more than 5 screw rotation periods) under each rotating speed, the simulation time is set to 10 s. At the same time, in order to balance the calculation efficiency and the fidelity of the data, the rotating speed of the screw can be set to 300 rpm, the step length of the simulation is 4.8828x10 -5 s, and the simulation time is set to 10 s.

[0252] In the embodiment, in order to further illustrate the simulation results of the dynamic model under the normal state and the fault state of the present scheme, specifically, the SFV2505 ball nut produced by TBI MOTION Company and the matching screw are used, and therefore the parameters in the simulation model are also set with reference to the SFV2505 ball nut, so as to facilitate subsequent experimental verification. The main parameters are shown in Table 1.

[0253]

[0254]

[0255] Table 1

[0256] In the embodiment, the data in Table 1 is used to simulate the radial dynamic model under the normal state, and the corresponding simulation results are obtained, which are shown in FIG. 1. Figure 14 Specifically, the displacement response and the acceleration response of the nut in the x and y radial directions are collected when the rotating speed of the screw is 30 rpm, the axial pre-tightening force is 100 N, and no fault occurs. When the rotating speed of the screw is 30 rpm, the ball passes through a period T0=0.1488 s. As can be seen from the displacement response graphs in the x and y directions, in one ball passing period (T0) when the ball screw pair is normally running, there are two times of step responses, which correspond to the impact vibration caused by the ball entering and leaving the reverser respectively. Between the two times of step responses, since the ball carrying the load is always rotating around the center of the screw, the projections of the resultant external force on the x and y directions of the nut also change slightly with the rotation of the ball, and the change is not linear in nature. However, since the change of the force is very small, the change of the displacement can be approximately regarded as linear. As shown in FIG. 1, in the interval between the two times of step responses, the displacement of the nut changes in an approximately linear form. Figure 14 ​

[0257] In addition, in the acceleration response diagram in the x and y directions, the displacement response Figure 1 Similarly, corresponding impact peaks can be seen at corresponding time points, and the amplitudes of these impact peaks correspond to the amplitude of displacement changes. In the parameter settings before simulation, the nut installation angle (θ a ) is set to 0, which means that the installation position of the deflector in the ball nut is the same as Figure 5 The angle between the start / end of the reverser raceway and the y-axis (θ pr ) is 36°, so the direction in which the ball impacts the reverser is closer to the y-axis. In addition, due to the effect of gravity, the preload in the y-direction (F y0 ) is greater than that in the x-direction. The elastic deformation of the ball in the y-direction is also greater, so the impact caused by the ball in the y-direction when entering and exiting the deflector is also greater. This can be seen in the simulation results, where the amplitude of the acceleration and displacement in the y-direction are much greater than those in the x-direction. This proves that the model constructed in this article can reflect some of the dynamic characteristics of the ball screw pair to a certain extent and can also serve as a basis for selecting the sensor installation location in the experimental device.

[0258] like Figure 15 As shown in the figure, in this embodiment, the acceleration response and its spectrum in the x and y directions are further collected when the screw speed is 30, 60, and 90 rpm, the axial preload is 100 N, and no fault occurs. Through comparative analysis, it can be seen that if the simulation signal is simply fast Fourier transformed, the obtained spectrum will produce a large frequency peak in the higher frequency band (around 383.2 Hz) with more sidebands, and the position of the frequency peak is independent of the screw speed (such as Figure 15 (c) and (d)). This frequency is determined to be the natural frequency of the ball screw system. The lower-frequency ball passing frequency is completely masked by the natural frequency component. Therefore, using only the FFT method is insufficient for this research.

[0259] In order to preserve the original vibration characteristics of the system more realistically, an envelope analysis method is further used to capture the ball passing frequency. Figure 16 As shown in FIG. 1 , in this embodiment, the acceleration response and its envelope spectrum in the x and y directions are obtained when the screw speed is 90 rpm, the axial preload is 100 N, and no fault occurs. Figure 16 In (a) and (b), the image in the upper part is the envelope signal of the acceleration signal. By performing FFT on the envelope signal, we can obtain the acceleration envelope spectrum dominated by the ball passing frequency, as shown in the figure below. Figure 16(c), (d) are shown. Theoretically, when the screw rotation speed is 90 rpm, the passing frequency of the ball should be about 20.16 Hz, which corresponds to the frequency value of the first peak in the envelope spectrum. However, we can find from the envelope spectrum that there are also larger amplitude peaks at the double frequency and triple frequency of the passing frequency of the ball. This is because there are two impacts (entering and leaving the reverse device) within the same passing frequency of the ball, and the time interval between the two impacts is close to 12T0 or 13T0. Thus, the amplitude at the double frequency and triple frequency of the passing frequency of the ball in the frequency spectrum increases.

[0260] Referring to Figure 17 Fig. 6, the above phenomenon is most obvious when the screw rotation speed is 30 rpm. When the screw rotation speed is 30 rpm, the passing period of the ball is 0.1488 s, and the time interval between the two impacts is about 0.0508 s, which is almost equal to 12T0. This results in a significant increase in the amplitude at the triple frequency of the passing frequency of the ball in the envelope spectrum, even more than at the double frequency.

[0261] As Figure 18 shown in Fig. 7, when the screw rotation speed increases to 420 rpm, the time interval between the two impacts is covered by the damping oscillation of the system due to the larger passing frequency of the ball, resulting in a decrease in the amplitude at the double and triple frequencies of the passing frequency of the ball in the envelope spectrum. Moreover, due to the larger rotation speed, some small frequency components appear in the low frequency part of the envelope spectrum.

[0262] In summary, the ball screw dynamics model established in this paper under normal conditions can more realistically reflect the impact vibration caused by the ball entering and leaving the reverse device in the ball screw pair, as well as the specific performance in the displacement time domain signal, acceleration time domain signal, frequency spectrum and envelope spectrum in the x and y directions of the nut, providing a certain reference for the study of the dynamic characteristics of the ball screw pair.

[0263] In this embodiment, in order to facilitate comparison with the simulation results of the normal model and the subsequent experimental results, the basic parameters set in the simulation of the radial dynamics model under fault conditions are basically the same as those in Table 1, and the parameters of the crack fault implanted in the model are also listed in Table 1. Specifically, referring to Figure 19 Fig. 8, the simulation under fault conditions is carried out under the condition that the screw rotation speed is 30 rpm, the axial pre-tightening force is 100 N, and the nut has a crack fault, and the displacement response and acceleration response of the nut in the x and y radial directions are obtained. As can be clearly seen from the figure, there is an additional impact between the two impacts of the ball entering and leaving the reverse device, which is the impact caused by the ball passing through the crack fault. In this paper, the angle θ of the fault is set to 0°, that is, the crack is perpendicular to the direction of the ball passing through the nut. afis set to π, i.e. along the negative direction of the y-axis, in order to be consistent with the faulty nut used in the subsequent experimental verification. When θ af = π, the ball will produce a large impact force in the y direction when passing through the fault position, while in the x direction, only when the ball contacts the trailing edge of the fault will a certain impact force be produced, and the rest of the time the force acting on the x direction is small, and this phenomenon can also be found in the displacement response of x, y. In the y direction, the fault signal and the impact signal of the ball in and out of the reverse are basically the same in waveform; but in the x direction, the waveform of the fault signal is: first a relatively sharp impact, and the subsequent waveform is relatively flat, which also conforms to the theoretical analysis in the foregoing.

[0264] Further, the envelope spectrum analysis method similar to the normal state model simulation signal is adopted, and the results are shown in Figure 20 (a), (b), (c) and (d). Since the number of impacts of the same ball passing through the cycle becomes three after the fault occurs, when comparing the envelope spectrum of the normal signal with the fault signal, it can be found that the amplitude of the three times frequency of the ball passing frequency in the fault signal envelope spectrum has a significant increase. Due to the parameter setting, the effect of the fault on the y direction is larger, so Figure 20 the three times frequency amplitude increase phenomenon in the y direction is much more obvious than that in the x direction.

[0265] Since the fault position is far from the x axis, the impact of the fault on the x direction is small, so when the screw speed is continuously increased, in the x direction, the fault only shows an increase in the amplitude of each frequency in the envelope spectrum, and the image of the significant increase in the amplitude of the three times frequency mentioned in the foregoing becomes less and less obvious, as shown in Figure 21 (a), (c), (e) and (g). But in the y direction, whether in the envelope spectrum at a lower speed (90, 180 rpm) or at a higher speed (390, 420 rpm), a significant amplitude increase can be found at the three times frequency of the ball passing frequency, as well as at the 6 times frequency, 9 times frequency, etc. In summary, the simulation results of the model established in this paper can be summarized as follows: when a crack fault occurs in the ball nut, a large amplitude increase will occur at the position of the three times ball passing frequency in the nut acceleration response envelope spectrum, and the closer the fault position is to the y axis (or x axis), the more obvious this phenomenon will be.

[0266] In order to further illustrate the technical effect of the present application, an experimental verification is carried out in combination with the physical ball screw nut.

[0267] In this embodiment, the aforementioned SFV2505 ball nut produced by TBI Company and the matching screw are used, and the 1FL6042-2AF2x motor of Siemens Company is used to drive the ball screw pair to move, and the specific experimental equipment is as shown inFigure 22

[0268] Since the failure of the nut occurred at the negative direction of the y-axis in the experiment, the failure feature in the y direction is the most obvious, while the failure feature in the x direction is basically not apparent. Therefore, only the experimental data in the y direction is selected for verification in the experimental verification.

[0269] In order to better compare with the simulation results of the model, three sensor installation positions are selected as shown in Figure 22 The sensors used in the experiment are all YMC-262A05 miniature single-axis low-impedance voltage output type acceleration sensors of Yangzhou Yingmeike. Sensor No. 1 A1 is used to detect the motor output signal to obtain the frequency components related to the motor for subsequent differentiation. Sensor No. 2 A2 is installed above the ball nut support seat, which mainly serves to support the nut and add preload, and also simulates the shell of the actual electromechanical actuator (EMA) assembly. Sensor No. 2 A2 is mainly used to verify whether the vibration generated in the ball screw pair can be conducted to the outside of the shell through some components. The installation position of sensor No. 3 A3 is on the y-axis of the nut, along the plumb direction, i.e. the y-axis direction, and is in direct contact with the nut. The vibration measured by sensor No. 3 is the vibration of the ball nut, so the data measured by sensor No. 3 is also the most suitable data for verifying the simulation results of the model.

[0270] In this paper, a 1mm wide crack fault is implanted in the negative direction of the y-axis of the SFV2505 ball nut by wire cutting method, and experiments are conducted respectively using normal and fault-implanted ball nuts. The acquisition card used in the experiment is the NI 9174 acquisition card of NI company, the working mode is IEPE mode, the sampling frequency is 10.24kHz to 20.48kHz, and the sampling time is 10s. At each screw speed, 10 groups of data are collected.

[0271] As shown in Figure 23 , under the condition that the screw speed is 60rpm, the normal and fault signals measured by the three sensors are compared with the simulation signals of the model. In Figure 23 (c), it can be seen that when no failure occurs, the frequency components of the ball screw pair in the experimental signal spectrum are basically covered by noise, although they can still be found in the spectrum, but are not very obvious. When a fault occurs, as shown in Figure 23 (d), the amplitude at three times the ball passing frequency in the spectrum is observed to rise significantly, which further verifies the effectiveness of the scheme. At the same time, from Figure 23 ​As can be seen in (e) and (f), sensor No. 2, mounted on the nut support, can also detect the characteristic frequencies of the ball screw pair to a certain extent, especially the fault characteristic frequencies. However, it is also susceptible to interference from the motor and other noise sources.

[0272] Combine Figure 24 and Figure 25 As shown in the figure, normal and fault signals measured by the three sensors at screw speeds of 180 and 240 rpm are collected and compared with the model simulation signals. At all speeds, the amplitude corresponding to triple the ball passing frequency in the fault signal increases significantly relative to the amplitude corresponding to single frequency. Therefore, the figure shows that increasing the screw speed has no effect on the patterns summarized above, demonstrating that the ball screw crack fault signatures proposed in this solution can be applied to different operating conditions.

[0273] like Figure 26 As shown in the figure, when the screw speed is further increased to 420rpm, although the amplitude increase phenomenon can still be found at three times the ball passing frequency of the fault signal, due to the high speed, the interference from noise sources such as the motor is large, so the fault characteristics are masked by the increased noise, and it is even more difficult to find the characteristic frequency of the ball screw in the normal signal. Therefore, if the characteristics summarized in this scheme are to be applied to higher speed occasions, additional signal processing methods and noise reduction methods are needed to highlight the frequency components occupied by the ball screw.

[0274] The above contents are merely examples of specific solutions of the present invention. For devices and structures not described in detail, it should be understood that they can be implemented by adopting general devices and methods available in the art.

[0275] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that the present invention is susceptible to various modifications and variations. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A ball nut crack fault diagnosis method comprising: S1. Establish a radial dynamic model of the ball screw nut pair in the radial direction under normal conditions; These include: S11. Establish a three-dimensional coordinate system based on the ball screw nut pair; wherein the axial direction of the nut in the ball screw nut pair is the z direction, the plumb bob radial direction of the nut in the ball screw nut pair is the y direction, and the horizontal radial direction of the nut in the ball screw nut pair is the x direction; S12. Converting the ball screw nut pair into an equivalent model; including: The balls in the ball screw nut pair are equivalent to a spring damping system; The nut and additional components in the ball screw nut pair are regarded as a whole and are equivalent to a mass block; Converting the ball screw nut pair into an equivalent model in which a mass block is connected to the screw through a spring damping system; S13. Establishing a radial dynamic model for the ball screw nut pair based on the three-dimensional coordinate system and the equivalent model; wherein the radial dynamic model under normal conditions is expressed as: ； in, c is the damping constant; 、 are the preloads acting on the nut in the x-direction and y-direction respectively; F x 、 F y They represent the radial forces acting on the nut in the x and y directions respectively; m represents the overall mass of the ball screw nut pair, δ x 、 δ y Respectively represent the displacement of the nut in the x direction and the y direction; S2 introduces a crack fault into the radial dynamic model to establish a radial dynamic model under a fault state; S3. A simulation calculation is performed based on the radial dynamics model under normal conditions to obtain the normal operation simulation results of the ball screw nut pair; Performing simulation calculation based on the radial dynamics model under the fault state to obtain a fault operation simulation result of the ball screw nut pair under the fault state; Comparing the normal operation simulation result with the fault operation simulation result to obtain abnormal characteristics of the ball screw nut pair in the fault state; S4. Collect actual operating results of the ball screw nut pair, detect the actual operating results based on the abnormal characteristics, and determine whether the ball screw nut pair has a crack fault.

2. The ball nut crack fault diagnosis method according to claim 1, characterized in that: The radial force on the nut in the x and y directions F x 、 F y Obtained through the following steps, including: An initial corresponding relationship between the radial force on the nut in the radial direction and the radial elastic restoring force on the ball is established: wherein the initial corresponding relationship is expressed as: ； ； ； in, n is the initial number of load-bearing balls, θ is the angle between two adjacent balls, F ni Indicates the radial elastic restoring force on the ball. d b is the ball diameter, d s is the pitch diameter of the screw, γ is the screw helix angle; The initial correspondence is optimized based on the circulation process of the ball in the nut to obtain a true correspondence between the radial force on the nut in the radial direction and the radial elastic restoring force on the ball at any time; wherein the true correspondence is expressed as: ； ； ； ； ； in, T b Indicates the ball passing cycle, mod ( N s , 1) for N s The remainder when divided by 1, N s Indicates the actual number of load-bearing raceways in the nut; θ pr Indicates the angle between the start / end of the reverser raceway for ball circulation in the nut and the reverser's symmetrical centerline; θ a The phase where the symmetrical centerline of the inverter leads the y-axis when the ball nut is actually installed; F nex Indicates the radial elastic restoring force on the ball when it is in the process of leaving the reverser; F nen Indicates the radial elastic restoring force on the ball when it is in the process of entering the reverser; n s is the screw rotation speed; β is the contact angle; ω bs is the angular velocity of the ball center rotating around the screw; Radial elastic restoring force on the ball F ni The radial elastic restoring force exerted on the ball when entering and leaving the reverser is F nen and F nex Solve them separately to obtain the solution formula, which can be expressed as: ； ； ； ； ； ； in, δ ni represents the radial elastic deformation of the i-th ball; δ nen Indicates the radial elastic deformation of the ball entering the reverser; δ nex Indicates the radial elastic deformation of the ball leaving the deflector; k n is the Hertzian contact stiffness; 、 are the sum of the principal curvatures of the ball and screw raceway and the ball and nut raceway respectively; r s 、 r n are the curvature radii of the screw raceway and the nut raceway respectively; ν 1. ν 2. ν 3 are the Poisson's ratios of the ball, screw and nut respectively, E 1. E 2. E 3 are the Young's modulus of elasticity of the ball, screw and nut respectively.

3. The ball nut crack fault diagnosis method according to claim 2, characterized in that: The displacement of the nut in the x-direction and y-direction δ x 、 δ y Expressed as: ； ； The radial elastic deformation of the i-th ball is expressed as: ； Radial elastic deformation of the ball entering the reverser δ nen Expressed as: ； Radial elastic deformation of the ball leaving the deflector δ nex Expressed as: ； Among them, l p When only preload is applied, the distance between the center of curvature of the nut raceway and the center of curvature of the screw raceway is expressed as , r s 、r n are the curvature radii of the screw raceway and the nut raceway respectively; δ p Indicates the deformation of the ball due to the influence of preload; δ ren and δ rex Respectively represent the difference between the ball deformation when entering / exiting the reverser and the ball deformation when fully loaded.

4. The ball nut crack fault diagnosis method according to claim 3, characterized in that: In step S2, a crack fault is introduced into the radial dynamic model to establish the radial dynamic model under the fault state. The radial dynamic model under the fault state is expressed as: ； in, F xf 、 F yf They represent the radial forces in the x and y directions respectively when there is a fault in the nut.

5. The ball nut crack fault diagnosis method according to claim 4, characterized in that: The radial forces in the x and y directions when a fault occurs in the nut F xf 、 F yf Obtained through the following steps, including: The solution formula for the radial elastic restoring force exerted on the ball when passing through a crack failure is constructed as follows: ； ； ； ； ； in, δ f Indicates the amount of elastic deformation released when the ball passes through a crack failure; b Indicates the crack failure width, which is smaller than the diameter of the ball. θ f Indicates the arc corresponding to the crack fault on the screw pitch circle; Combined with the true correspondence between the radial force on the nut in the radial direction and the radial elastic restoring force on the ball at any time and the solution formula for the radial elastic restoring force on the ball when it passes through a crack fault, the radial forces on the nut in the x and y directions when a fault exists are obtained. F xf 、 F yf , which is expressed as: ； ； ； ； in, θ af Indicates the angle between the fault centerline and the y-axis.

6. The ball nut crack fault diagnosis method according to claim 5, characterized in that: In step S3, in the step of comparing the normal operation simulation results with the fault operation simulation results to obtain the abnormal characteristics of the ball screw nut pair in the fault state, the envelope spectrum analysis method is used to process the normal operation simulation results and the fault operation simulation results respectively, and the abnormal characteristics are obtained based on the comparison between the processed normal operation simulation results and the fault operation simulation results.

7. The ball nut crack fault diagnosis method according to any one of claims 1 to 6, characterized in that: In step S3, in the step of comparing the normal operation simulation result with the fault operation simulation result to obtain abnormal characteristics of the ball screw nut pair in the fault state, the abnormal characteristics adopt abnormal acceleration response and / or abnormal displacement response of the nut in the radial direction.

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