Spring impact test device and spring residual life analysis method

Abstract

The invention discloses a spring impact test device and a spring residual life analysis method, the spring impact test device comprises a base, a top plate, a guide rod, a pressing block and a positioning plate, the top plate is located above the base, the guide rod and the positioning plate are both connected between the top plate and the base, and a spring test piece sleeves the guide rod and falls on the base; the pressing block sleeves the guide rod, and the pressing block has a degree of freedom of displacement along the length direction of the guide rod, so that the pressing block can freely fall down to impact the spring test piece; a switch mechanism is arranged on the positioning plate and is used for fixing the pressing block at a set position on the guide rod; the positioning plate is provided with an anti-springback mechanism, so that secondary impact on the spring test piece in the falling process of the pressing block is avoided. The method is applied to the field of spring impact test analysis, secondary impact on the spring in the impact test process can be effectively avoided, impact damage to the spring is reproduced to the maximum extent, and the accuracy of spring residual life analysis is improved.

Description

Technical Field

[0001] The invention relates to the technical field of spring impact test analysis, in particular to a spring impact test device and a spring remaining life analysis method. Background Art

[0002] A spring is an elastic mechanical part that can deform when subjected to an external force and return to its original shape when the external force is removed. Springs can be divided into many types according to their uses and working principles, including compression springs, extension springs, torsion springs, etc. Each type of spring has its specific design and application. As an important mechanical part, springs play an important role in various mechanical systems, and their performance and quality directly affect the operation and stability of the entire system.

[0003] In various types of buffer devices, springs will be impacted at a certain speed during operation. The quality of the spring performance has a direct impact on the performance and safety of the device. The service life and reliability of the spring are very important to ensure the stable operation of the equipment. Studying the accumulated damage of the spring is of great significance to improving the reliability of the mechanism.

[0004] Most of the existing spring testing devices are used to perform fatigue tests on springs, and there are relatively few testing devices that study the impact damage accumulation of springs. In fatigue tests, both ends of the spring are always in contact with the testing device. The impact damage accumulation test requires that the spring is impacted at a certain speed, and at least one end of the spring is in motion. At the same time, during the test, the problem of the spring being subjected to secondary impact should also be avoided. Therefore, it is necessary to develop a testing device that can achieve high-speed impact of the spring and prevent secondary impact. By simulating its actual working state, the impact damage to the spring can be reproduced to the greatest extent, and relatively accurate test data can be obtained.

[0005] The existing methods for predicting the remaining life of springs are mainly divided into two categories: physical modeling and data-driven modeling. Since most of the current equipment has a complex structure and is difficult to solve with physical equations, data-driven modeling has been widely used. The data-driven method uses observed data to derive the remaining life model. The models are divided into random coefficient regression model, Wiener process model, Gamma process model and inverse Gaussian process model. Compared with other random process models, the Wiener process is a type of non-monotonic degradation process with Gaussian independent distribution increments. With its good mathematical properties, it has been widely used in the fields of reliability analysis and life prediction.

[0006] For the Wiener process model, the average degradation amount and degradation progress of the spring are controlled by the drift coefficient. The existing Wiener process model is divided into a drift coefficient determination model and a drift coefficient variable model. The drift coefficient determination model assumes that the drift coefficient is constant throughout the degradation process, and the parameter estimation can be directly solved by the maximum likelihood function. However, in the actual degradation process, due to the differences between each spring, the drift coefficient of each spring is not exactly the same. The drift coefficient variable model assumes that the drift coefficient obeys a Gaussian distribution. The existing drift coefficient variable model assumes that the drift coefficient only differs between products, and does not consider the differences in drift parameters of a product at different degradation moments. Summary of the invention

[0007] In view of the deficiencies in the above-mentioned prior art, the present invention provides a spring impact test device and a spring remaining life analysis method, which can effectively avoid secondary impact on the spring during the impact test, reproduce the impact damage to the spring to the greatest extent, and improve the accuracy of the spring remaining life analysis.

[0008] To achieve the above-mentioned object, the present invention provides a spring impact test device, comprising a base, a top plate, a guide rod, a pressure block and a positioning plate, wherein the top plate is located above the base, the guide rod and the positioning plate are connected between the top plate and the base, and the spring specimen is sleeved on the guide rod and falls on the base;

[0009] The pressing block is sleeved on the guide rod, and the pressing block has the freedom to move along the length direction of the guide rod, so that the pressing block can fall freely to impact the spring test piece;

[0010] The positioning plate is provided with a switch mechanism for fixing the pressing block at a set position on the guide rod;

[0011] The positioning plate is provided with an anti-rebound mechanism to avoid secondary impact on the spring test piece during the falling process of the pressing block.

[0012] To achieve the above object, the present invention also provides a method for analyzing the remaining life of a spring, using the above spring impact test device, comprising the following steps:

[0013] Step 1, establishing a degradation model consisting of an observation equation and a state equation, and establishing a remaining life prediction model for the spring;

[0014] Step 2, using the spring impact test device, impacting the spring specimen N0 times as one cycle, and obtaining the degradation amount of the spring specimen stiffness through a spring dynamometer after one cycle, and using it as an observation amount;

[0015] Step 3, the degradation model is combined with the entire historical observation data, and the estimated value of the state quantity is obtained by using Kalman filtering. The maximum likelihood estimate of the unknown parameters in the degradation model is obtained based on the EM algorithm of the nested RTS smoothing algorithm, and the state quantity of the degradation model is updated;

[0016] Step 4: Obtain the remaining life of the spring specimen based on the state quantity of the degradation model and the remaining life prediction model.

[0017] Compared with the prior art, the present invention has the following beneficial technical effects:

[0018] 1. The spring impact test device of the present invention can use the gravity of the pressing block to do work to realize the impact test of the spring, and can achieve different impact speeds and impact forces by changing the mass of the pressing block or adjusting the height of the pressing block, thereby increasing the test effect of the device;

[0019] 2. The spring impact test device of the present invention is provided with an anti-rebound mechanism to avoid secondary impact on the spring test piece during the falling process of the pressure block, thereby minimizing the impact of the secondary impact and improving the detection effect of the device;

[0020] 3. In the preferred embodiment of the spring impact test device of the present invention, a guide shaft is provided to constrain the pressing block, so that the spring test piece is only subjected to a vertical downward force, which facilitates the analysis of the test results;

[0021] 4. The remaining life analysis method of the spring in the present invention takes into account the differences in drift parameters of a product at different degradation moments, combines historical observation data, uses a random walk model to update the drift parameters, obtains an estimated value of the state quantity through Kalman filtering, and uses the EM algorithm based on the nested RTS smoothing algorithm to obtain the maximum likelihood estimate of the unknown parameters in the degradation model, updates the state quantity of the degradation model, and the proposed degradation model is more in line with the actual degradation process and makes full use of the observation data, thereby effectively improving the accuracy of parameter vector estimation and improving the accuracy of the remaining life analysis of the spring. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0023] Figure 1 It is a schematic diagram of the overall structure of a spring impact test device in an embodiment of the present invention;

[0024] Figure 2An enlarged schematic diagram of a switch structure in an embodiment of the present invention;

[0025] Figure 3 is an enlarged schematic diagram of the anti-rebound mechanism in an embodiment of the present invention;

[0026] Figure 4 It is a structural schematic diagram of a spring impact test device in a working state according to an embodiment of the present invention;

[0027] Figure 5 It is an enlarged schematic diagram of the anti-rebound mechanism in the working state in the embodiment of the present invention;

[0028] Figure 6 The present invention is a flowchart of a method for analyzing the remaining life of a spring in an embodiment of the present invention.

[0029] Figure numbers: 1-base, 2-positioning plate, 3-guide shaft, 4-guide rod, 5-top plate, 6-mounting hole, 7-stop block, 8-block switch, 9-linear bearing, 10-pressure block, 11-spring specimen.

[0030] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0033] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0034] In the present invention, unless otherwise clearly specified and limited, the terms "connection", "fixation", etc. should be understood in a broad sense. For example, "fixation" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0035] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0036] Example 1

[0037] like Figure 1 The figure shows a spring impact test device disclosed in the present embodiment, which mainly includes a base 1, a top plate 5, a guide rod 4, a pressure block 10 and a positioning plate 2. The top plate 5 is located directly above the base 1, the guide rod 4 and the positioning plate 2 are connected between the top plate 5 and the base 1, the spring specimen 11 is sleeved on the guide rod 4 and falls on the base 1, the pressure block 10 is sleeved on the guide rod 4, and the pressure block 10 has the freedom to move along the length direction of the guide rod 4, so that the pressure block 10 can fall freely under the action of gravity to impact the spring specimen 11. Among them, both ends of the spring specimen 11 are tightened and ground, and the guide rod 4, the positioning plate 2 and the top plate 5, the base 1 are fixed by bolts to facilitate the replacement of the pressure block 10 and the spring specimen 11. There is a clearance fit between the pressure block 10 and the guide rod 4, so that the pressure block 10 can fall freely under the action of gravity, thereby impacting the spring specimen 11.

[0038] The positioning plate 2 is provided with a switch mechanism to fix the pressing block 10 at a set position on the guide rod 4, so that the pressing block 10 can fall from the same height multiple times to ensure the accuracy of the test data. At the same time, the positioning plate 2 is provided with an anti-rebound mechanism to avoid secondary impact on the spring test piece 11 during the falling process of the pressing block 10, thereby minimizing the impact of the secondary impact and improving the test effect.

[0039] In this embodiment, the switch mechanism includes a block switch 8 arranged on the positioning plate 2. The block switch 8 has a travel on the positioning plate 2 that can slide in a direction close to or away from the pressure block 10, and the end of the block switch 8 has a support portion that can support the bottom end of the pressure block 10. In the specific implementation process, a slide groove is provided on the positioning plate 2, and the block switch 8 is installed on the slide groove by a thick-rod half-thread bolt, so that the block switch 8 can slide in the slide groove. At the same time, there is a groove on the top of the block switch 8, and the positioning plate 2 has a thick-rod half-thread bolt threadedly connected to the groove. When the block switch 8 slides along the slide groove until the support portion is supported at the bottom of the pressure block 10, the groove and the corresponding thick-rod half-thread bolt are embedded and matched, thereby fixing the block switch 8 to prevent the pressure block 10 from falling, that is, Figure 2 Preferably, a plurality of switch mechanisms can be arranged on the positioning plate 2 at intervals along the height direction, so that the baffle can fall from different heights to achieve different impact speeds and impact forces, thereby increasing the test effect of the device.

[0040] It is worth noting that in the specific application process, the switch mechanism is not limited to the structure shown in the figure, and other structures with the same function can also be used. For example, a horizontal through hole is directly opened on the positioning plate 2, and then the stopper switch 8 is slidably connected in the through hole, so as to achieve the limit or release of the pressing block 10.

[0041] In this embodiment, the anti-rebound mechanism includes a stop block 7, a first stop rod and a second stop rod, which are arranged on the positioning plate 2. The stop block 7 is rotatably connected to the positioning plate 2, the first stop rod is located below the stop block 7, the second stop rod is located above the second stop rod, and the second end of the stop block 7 is heavier than the first end. When the lower side of the stop block 7 abuts against the first stop rod, the upper side of the stop block 7 is separated from the second stop rod, and the first end of the stop block 7 is located in the falling path of the pressure block 10. When the upper side of the stop block 7 abuts against the second stop rod, the lower side of the stop block 7 is separated from the first stop rod, and the first end of the stop block 7 avoids the falling path of the pressure block 10. Preferably, grooves are provided on the upper and lower sides of the stop block 7 to cooperate with the first stop rod and the second stop rod, that is, Figure 3 shown.

[0042] In the specific application process, the position of the stop block 7 needs to be calibrated, and the process is as follows: first, the pressure block 10 is dropped on the spring test piece 11, so that the elastic force of the spring test piece 11 is the same as the gravity of the pressure block 10. Then, the stop block 7, the first stop rod and the second stop rod are installed on the positioning plate 2, so that the lower side of the first end of the stop block 7 contacts the top of the pressure block 10, and the lower side of the stop block 7 abuts the first stop rod, and the position of the stop block 7 is calibrated. In the process of the pressure block 10 falling, the stop block 7 rotates on the positioning plate 2 under the impact of the pressure block 10, so that the lower side of the stop block 7 is separated from the first stop rod, and the upper side of the stop block 7 abuts the second stop rod, and the first end of the stop block 7 avoids the falling direction of the pressure block 10, so that the pressure block 10 smoothly impacts the spring test piece 11. Due to the falling impact force, the spring specimen 11 is compressed to a length shorter than the calibrated length. When the spring specimen 11 is compressed to the shortest length, it starts to rebound. The second end of the stop block 7 is heavier than the first end, so that the stop block 7 can be quickly reset, thereby reducing the impact of the secondary impact. Figure 4 , Figure 5 shown.

[0043] In the specific implementation process, two rows of mounting holes 6 can be installed on the positioning plate 2, and the stop block 7 can be rotatably connected to the inner mounting hole 6 through a thick rod half-thread bolt, and at the same time, a thick rod half-thread bolt is respectively set on the mounting hole 6 above or below the stop block 7 as the first stop rod and the second stop rod. The height adjustment of the anti-rebound mechanism can be achieved by making the mounting holes 6 matched with the stop block 7, the first stop rod and the second stop rod have different heights, so as to adapt to different types of springs and pressure blocks 10.

[0044] As a preferred embodiment, the upper side of the first end of the stop block 7 is a rounded structure to reduce the blocking effect of the stop block 7 on the pressing block 10 falling.

[0045] As a preferred embodiment, there are two positioning plates 2, and the two positioning plates 2 are symmetrically located on both sides of the guide rod 4. At the same time, the two positioning plates 2 are also provided with symmetrical switching mechanisms and anti-rebound mechanisms, thereby improving the falling release and anti-rebound stability of the pressure block 10.

[0046] As a preferred embodiment, the spring impact test device also includes two guide shafts 3, which are connected between the top plate 5 and the base 1. The two guide shafts 3 are symmetrically located on both sides of the guide rod 4, and the pressure block 10 and the guide shaft 3 are slidably matched through linear bearings 9 to constrain the pressure block 10 so that the spring specimen 11 is only subjected to vertical downward force, which facilitates the analysis of the test results.

[0047] The working principle and working process of the spring impact test device in this embodiment are described below.

[0048] When in use, the original length x0, stiffness coefficient k and working stroke x of the spring specimen 11, and the height c of the pressing block 10 are known. If the impact velocity of the spring specimen 11 is required to be v, it can be expressed as follows according to the uniformly accelerated linear motion formula:

[0049] v=gt

[0050] Wherein, g represents the acceleration due to gravity, and t is the falling time of the pressing block 10;

[0051] According to the formula of free fall motion:

[0052]

[0053] Wherein, h is the distance between the position of the stopper switch 8 and the upper surface of the spring test piece 11;

[0054] From the law of conservation of energy we get:

[0055]

[0056] Wherein, m is the total mass of the linear bearing 9 and the pressing block 10;

[0057] From the two-force balance formula we get:

[0058] mg=kx1

[0059] The distance between the stop block 7 and the base 1 is x0-x1+c.

[0060] After the above parameters are set, the test is carried out. Place the pressure block 10 at the stop switch 8, pull the stop switch 8, and the pressure block 10 falls downward under the action of gravity. During the descent, it passes through the stop block 7. Under the action of the pressure block 10, the upper groove of the stop block 7 contacts the thick rod half-thread bolt. After the pressure block 10 is separated, the stop block 7 returns to its original state. Then the pressure block 10 impacts the spring specimen 11 at a speed v. The spring specimen 11 is compressed to x. The pressure block 10 moves upward under the action of the elastic force. Under the action of the stop block 7, the pressure block 10 is blocked at the equilibrium position. At this time, the secondary impact of the spring is minimal.

[0061] Example 2

[0062] Based on the spring impact test device in Example 1, this embodiment discloses a method for analyzing the remaining life of a spring, which analyzes and predicts the remaining life of a spring specimen through the test time measured by the spring impact test device, referring to Figure 6 The spring remaining life analysis method in this embodiment specifically includes the following steps.

[0063] Step 1, establishing a degradation model consisting of an observation equation and a state equation, and establishing a remaining life prediction model for the spring;

[0064] Step 2, using a spring impact test device, impacting the spring specimen 50 times as one cycle, and obtaining the degradation amount of the spring specimen stiffness through a spring dynamometer after one cycle, and using it as an observation amount;

[0065] Step 3: The degradation model is combined with the entire historical observation data, and the estimated value of the state quantity is obtained by using the Kalman filter. The maximum likelihood estimate of the unknown parameters in the degradation model is obtained by the EM algorithm based on the nested RTS smoothing algorithm, and the state quantity of the degradation model is updated;

[0066] Step 4: Based on the state quantity of the degradation model and the remaining life prediction model, the remaining life of the spring specimen is obtained.

[0067] In the specific implementation process, the construction process of the degradation model is:

[0068] First, the degradation equation is established with random process, using Wiener process, which is:

[0069] X(t) = x i +λ(tt i )+σB(tt i ) (1)

[0070] Among them, X(t) is the degradation amount, λ is the drift parameter, σ is the diffusion coefficient, B(tt i ) is the Brownian motion at time t and t i The difference in time;

[0071] In order to combine the observed historical data, the random walk model λ i =λ i-1 +η to update the drift parameter λ, where η~N(0,Q) represents the noise of λ with mean 0 and variance Q. The trend of spring degradation is determined by the drift parameter λ, while the diffusion coefficient σ affects the noise and can be considered as a constant;

[0072] Therefore, the degradation equation can be reconstructed through the linear state space model as:

[0073] λ i =λ i-1 +η (2)

[0074] x i =x i-1 +λ i-1 (t i -t i-1 )+σε i (3)

[0075] Among them, formula (2) is the system equation, formula (3) is the observation equation, λ i , i-1is the state quantity (i.e. drift parameter) after the i-th and i-1-th cycles, x i 、x i-1 is the observed value after the i-th and i-1-th cycles, t i ,t i-1 is the time after the i-th and i-1-th cycles, ε i is the Brownian motion at t i Time and t i-1 The difference in time; t0 = 0, x0 = 0, ε i =B(t i )-B(t i-1 )~N(0,t i -t i-1 ), we can get ε from the properties of Brownian motion i .

[0076] Assuming that the initial drift parameter λ0 follows a normal distribution with mean a0 and variance P0, the drift parameter is considered to be a hidden “state” and can be calculated based on the time until t i The observed value is estimated and expressed as the degraded data X 0:i =[x0,x1,x2,...,x i ](that is, from 0 to t i Therefore, the model establishes the connection between drift parameters and historical observation data. In formula (1), λ i Can be updated by recursive filters. Definition Represented as X-based 0:i Estimated λ i ,λ i The variance P i|i =Var(λ i |X 0:i ).

[0077] To calculate and P i|i , we need to know the known X 0:i When i The probability density function of i-1 |X 0:i-1 ) recursively estimates p(λ i |X 0:i ),for:

[0078]

[0079] Among them, p(λ i |X 0:i ) is X 0:i When λ is known, i The probability density function of i|λ i-1 ) is λ i-1 When λ is known, i The probability density function of i-1 |X 0:i ) is X 0:i When λ is known, i-1 The probability density function of i |λ i-1 ,X 0:i ) is X 0:i and λ i-1 When x is known i The joint probability density function of i-1 |X 0:i-1 ) is X 0:i-1 When λ is known, i-1 The probability density function of i |X 0:i-1 ) is X 0:i-1 When x is known i The probability density function of

[0080] From equations (2) and (3), we can see that p(λ i |X 0:i ) is the mean value of Variance is P i|i The Gaussian distribution of can be calculated by Kalman filtering. Use the entire historical observation data to recursively update This is the advantage of the state space. The process of Kalman filtering is:

[0081] Step 1), initialize a0 and P0;

[0082] Step 2), t i State estimation at time:

[0083] P i|i-1 =P i-1|i-1 +Q (5)

[0084] K i =(t i -t i-1 ) 2 P i|i-1 +σ 2 (t i -t i-1 ) (6)

[0085]

[0086] Step 3), variance update:

[0087] P i|i =P i|i-1-P i|i-1 (t i -t i-1 ) 2 K i -1 P i|i-1 (8)

[0088] Among them, P i|i-1 Based on P i-1 The estimated P i , K i is the Kalman filter gain.

[0089] In the specific implementation process, the construction process of the remaining life prediction model of the spring is as follows:

[0090] When the degradation value X(t) reaches the stiffness degradation value threshold w for the first time, it is considered that the system has reached the end of its service life. i RULR at time i Defined as:

[0091] R i = inf{r i :X(r i +t i )≥w|X 0:i} (9)

[0092] Among them, R i t i The remaining life at time r i t i The time difference between the moment-to-moment degradation amount reaching the threshold;

[0093] From formula (1), we can get t i R at time i The probability density function of and distribution function for:

[0094]

[0095] in, for The normal distribution cumulative function value of , for The normal distribution cumulative function value of ;

[0096] In formula (10), Replace λ i , however, in formula (2), the drift parameter is a random variable, so using p(λ i |X 0:i ) to derive R iThe remaining life prediction model of the spring can be obtained by the distribution of:

[0097]

[0098] Among them, E(·) is the mean, X 1:k From 1 to t k The historical observation quantity at time, x k t k The observed quantity at the moment, u is the integral variable, About Dawson points.

[0099] According to formula (12), to solve the remaining life of the spring based on the remaining life prediction model, it is necessary to first calculate With P i|i According to the aforementioned Kalman filtering process, we can calculate With P i|i The process has unknown parameters a0, P0, Q, σ 2 In this embodiment, let the parameter vector θ = [a0, P0, Q, σ 2 ] and estimate the parameter vector θ based on the EM algorithm nested with the RTS smoothing algorithm.

[0100] θ is a parameter vector. Once a new degenerate observation x is generated i , that is, θ can be estimated by maximum likelihood estimation. When the degraded data is X 0:i When , the maximum likelihood estimate of θ can be written as:

[0101] L i (θ) = logp(X 0:i |θ) (13)

[0102] Among them, L i (θ) is the maximum likelihood estimate, p(X 0:i |θ) is the degradation data X 0:i The joint probability density of

[0103] definition For X 0:i The maximum likelihood estimate of θ under the condition of is:

[0104]

[0105] Because λ i It is a hidden variable, so the maximum likelihood estimation cannot be used directly for parameter estimation. Therefore, a more effective method needs to be found to deal with this problem. The idea of ​​the EM algorithm is to replace the hidden variable with the expectation of the observed data. Then the parameter estimation can be expressed as maximizing the joint likelihood function, which is:

[0106] L i (θ) = l i (θ)-logp(γ i |X 0:i ,θ) (15)

[0107] Among them, l i (θ) = logp(X 0:i ,γ i |θ) is expressed as X when θ is known 0:i ,γ i The log-log probability density of i ={λ0,λ1,...,λ i-1} is represented as a set of drift coefficients;

[0108] Then, take the expectation operator on both sides of equation (15), for γ i |X 0:i ,θ', we have:

[0109] L i (θ) = l i (θ|θ')-K(θ|θ') (16)

[0110] in, Represented as l i The mean of (θ), Expressed as logp(γ i |X 0:i ,θ) mean;

[0111] Finally, through formula (16), we can get:

[0112]

[0113] Among them, θ' is θ at the previous moment, L i (θ') is the maximum likelihood estimate of θ', l i (θ'|θ') is l i (θ'), K(θ'|θ') is the mean of logp(γ i |X 0:i ,θ');

[0114] In formula (17), the positivity of the last term is given by p(γ i |X 0:i ,θ) and p(γ i |X 0:i ,θ'). Obviously, if l i (θ|θ')>l i (θ'|θ'), then L i (θ)>L i(θ') holds. The EM algorithm can be used to achieve l i (θ|θ')>l i (θ'|θ'), and it is estimated that It can satisfy formula (14). Therefore, the EM algorithm The estimation is divided into two steps:

[0115] Step E: Calculation in, For X 0:i Under the condition of , the parameter estimation of the kth step;

[0116] Step M: Calculation

[0117] Iterate the E and M steps until the convergence criterion is met. The convergence criterion can be set to reach a maximum number of iterations.

[0118] In the calculation process of the EM algorithm, the joint log-likelihood function can be expressed as:

[0119]

[0120] Among them, p(γ i |θ) is γ when θ is known i probability, p(λ0|θ) is the probability of λ0 when θ is known, and p(λ j |λ j-1 ,θ) is λ j-1 , when θ is known, j The probability, p(x j |λ j-1 ,θ) is λ j-1 ,θ is known when x j probability;

[0121] From equation (2) and equation (3), we can know that j |λ j-1 ~N(λ j-1 ,Q),x j |λ j-1 ~N(x j-1 +λ j-1 (t j -t j-1 ),σ 2 (t j -t j-1 )), λ0~N(a0,P0), and substituting into equation (18), we get:

[0122]

[0123] To calculate Formula (19) can be written as:

[0124]

[0125] Obviously, in order to calculate the expectation of formula (20), we need to obtain the value of γ based on the given historical observation data. i Expectations In this embodiment, the RTS smoothing algorithm is used to obtain The best estimate includes:

[0126] Step 1: forward iteration of Kalman filter;

[0127] Step 2, backward iteration:

[0128]

[0129] Among them, S j is the variance gain, P j|j t j The variance of the moment, P j+1|j Based on P j The estimated P j+1 , For X-based 0:i The obtained smoothing filter drift coefficient is t j The drift parameter estimate at time t, P j|i For X-based 0:i The obtained j The moment smoothing filter variance, P j+1|i For X-based 0:i The obtained j+1 Step 3: Initialize M i|i :

[0130] M i|i =(1-K i (t i -t i-1 ))P i-1|i-1 (twenty four)

[0131] Among them, M j|i = Cov(λ j ,λ j-1 |X 0:i ) is represented by λ j With λ j-1 The covariance between

[0132] Step 4: Backward iterative smoothing of the covariance:

[0133] M j|i =P j|j S j-1 +S j (M j+1|i-P j|j )S j-1 (25)

[0134] Among them, M j+1|i is the smoothed covariance;

[0135] at last:

[0136]

[0137] in, is j The mean of is j 2 The mean of is j λ j-1 The mean of

[0138] based on The best estimate of Then, the Mth step of the EM algorithm is performed, and the estimated parameters in the k+1th step are The result can be expressed as:

[0139]

[0140] in, Denoted as λ j 2 The mean of Represents the initial value of the drift parameter,

[0141] Denoted as λ j λ j-1 The mean of

[0142] Iterate the E and M steps of the EM algorithm until the convergence criterion is met, that is, the estimation of the parameter vector is completed;

[0143] Finally, the parameter estimation result obtained by the EM algorithm is substituted into formula (12) to predict the remaining service life of the spring after the current cycle. At the same time, the probability density function of the reliability of the predicted remaining service life can be calculated by formula (10).

[0144] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A spring impact test device, It is characterized in that It includes a base, a top plate, a guide rod, a pressure block and a positioning plate, wherein the top plate is located above the base, the guide rod and the positioning plate are connected between the top plate and the base, and the spring test piece is sleeved on the guide rod and falls on the base; The pressing block is sleeved on the guide rod, and the pressing block has the freedom to move along the length direction of the guide rod, so that the pressing block can fall freely to impact the spring test piece; The positioning plate is provided with a switch mechanism for fixing the pressing block at a set position on the guide rod; The positioning plate is provided with an anti-rebound mechanism to avoid secondary impact on the spring test piece during the falling process of the pressing block.

2. The spring impact test device according to claim 1, It is characterized in that The switch mechanism comprises a stopper switch provided on the positioning plate; The stopper switch has a travel on the positioning plate for sliding close to or away from the pressing block, and an end of the stopper switch has a supporting portion capable of supporting the bottom end of the pressing block.

3. The spring impact test device according to claim 1, It is characterized in that The anti-rebound mechanism comprises a stop block, a first stop rod and a second stop rod arranged on the positioning plate; The stop block is rotatably connected to the positioning plate, the first stop rod is located below the stop block, and the second stop rod is located above the second stop rod; When the lower side of the stop block abuts against the first stop rod, the upper side of the stop block is separated from the second stop rod, and the first end of the stop block is located in the falling path of the pressing block; When the upper side of the stop block abuts against the second stop rod, the lower side of the stop block is separated from the first stop rod, and the first end of the stop block avoids the falling path of the pressing block.

4. The spring impact test device according to claim 3, It is characterized in that The upper side of the first end of the stop block is a rounded structure.

5. The spring impact test device according to any one of claims 1 to 4, It is characterized in that The number of the positioning plates is two, and the two positioning plates are symmetrically located on both sides of the guide rod.

6. The spring impact test device according to any one of claims 1 to 4, It is characterized in that Also included are two guide shafts; The guide shaft is connected between the top plate and the base, the two guide shafts are symmetrically located on both sides of the guide rod, and the pressing block is slidably matched with the guide shaft.

7. A method for analyzing the remaining life of a spring. It is characterized in that The spring impact test device according to any one of claims 1 to 6 comprises the following steps: Step 1, establishing a degradation model consisting of an observation equation and a state equation, and establishing a remaining life prediction model for the spring; Step 2: Use the spring impact test device to test the spring specimen with N 0 One impact is one cycle. After one cycle, the degradation of the spring specimen stiffness is obtained by the spring dynamometer and used as the observed value. Step 3, the degradation model is combined with the entire historical observation data, and the estimated value of the state quantity is obtained by using the Kalman filter, and the maximum likelihood estimate of the unknown parameters in the degradation model is obtained based on the EM algorithm of the nested RTS smoothing algorithm, and the state quantity of the degradation model is updated; Step 4: Obtain the remaining life of the spring specimen based on the state quantity of the degradation model and the remaining life prediction model.

8. The remaining life analysis method of the spring according to claim 7, It is characterized in that In step 1, the degradation model is: l i =λ i-1 +n x i =x i-1 +λ i-1 (t i -t i-1 )+σε i Among them, λ i , i-1 is the state quantity after the i-th and i-1-th cycles, λ 0 The mean is a 0 , the variance is P 0 Normal distribution, η~N(0,Q) is the noise of λ, x i 、x i-1 is the observed value after the i-th and i-1-th cycles, t i ,t i-1 is the time after the i-th and i-1-th cycles, σ is the diffusion coefficient, ε i ~N(0,t i -t i-1 ) is the Brownian motion at t i Time and t i-1 The difference in time; The remaining life prediction model is: Among them, E(·) is the mean, R i is the remaining life, X 0:i From 0 to t i The historical observation at the time, w is the threshold of stiffness degradation, X 1:k From 1 to t k The historical observation quantity at time, x k t k The observed quantity at time, P i|i =Var(λ i |X 0:i ) is based on X 0:i Estimated λ i The variance of For X-based 0:i Estimated λ i , u is the integral variable, For about Dawson points.

9. The remaining life analysis method of the spring according to claim 8, It is characterized in that In step 3, the Kalman filtering process is: Initialize a 0 , P 0 ; t i State estimation at time: P i|i-1 =P i-1|i-1 +Q, K i =(t i -t i-1 ) 2 P i|i-1 +σ 2 (t i -t i-1 ), Among them, P i|i-1 Based on P i-1 The estimated P i , P i-1|i-1 P i-1 , K i is the Kalman filter gain; Variance Update: P i|i =P i|i-1 -P i|i-1 (t i -t i-1 ) 2 K i -1 P i|i-1 .

10. The remaining life analysis method of the spring according to claim 9, It is characterized in that In step 3, the EM algorithm based on the nested RTS smoothing algorithm obtains the maximum likelihood estimate of the unknown parameters in the degradation model, specifically: Define parameter vector θ = [a 0 ,P 0 ,Q,σ 2 ], and define For X 0:i The maximum likelihood estimate of θ under the condition of ; In the E step of the EM algorithm: calculate in, For X 0:i Under the condition of , the parameter estimation of the kth step includes: Will Written as: Among them, l i (θ) is X when θ is known 0:i ,γ i The logarithmic probability density of i ={λ 0 ,λ 1 ,...,λ i } is the set of drift coefficients; The RTS smoothing algorithm is used to obtain the i Expectations The best estimate of is: Forward iteration of Kalman filter; Backward iteration: Among them, S j is the variance gain, P j|j t j The variance of the moment, P j+1|j Based on P j The estimated P j+1 , For X-based 0:i The obtained smoothing filter drift coefficient is t j The drift parameter estimate at time t, P j|i For X-based 0:i The obtained j The moment smoothing filter variance, P j+1|i For X-based 0:i The obtained j+1 Moment smoothing filter variance; Initialize M i|i :M i|i =(1-K i (t i -t i-1 ))P i-1|i-1 , where M i|i is i With λ i-1 The covariance between Backward iterative smoothing of covariance: M j|i =P j|j S j-1 +S j (M j+1|i -P j|j )S j-1 , where M j|i = Cov(λ j ,λ j-1 |X 0:i ) is λ j With λ j-1 The covariance between j+1|i is the smoothed covariance; in, is j The mean of for The mean of is j λ j-1 The mean of based on The best estimate of After that, the M-step of the EM algorithm is: in, The E and M steps of the EM algorithm are iterated until the convergence criteria are met, that is, the estimation of the parameter vector is completed.

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