A pick system reliability analysis method

Abstract

The application provides a pick system reliability analysis method, by considering the influence of environment, area and aggregation on the pick system reliability, respectively constructing the pick system reliability model under the influence of environment, area, aggregation alone and the comprehensive influence of the three factors. The pick system reliability model considering the influence of environment, area and aggregation conforms to the engineering practice, provides effective guidance for the design optimization and reliability improvement of the pick system, and provides a theoretical basis and scientific basis for the maintenance and spare parts management of the pick system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of coal rock cutting machinery, in particular to a pick system reliability analysis method. BACKGROUND

[0002] As the most critical actuator of the boom-type roadheader, the pick system undertakes the task of breaking rock, and its reliability directly determines the working performance and service life of the roadheader, and has a direct impact on the tunneling efficiency and the economic benefits generated thereby in the coal mine. Generally, the reliability of the pick system can be improved in two ways: one is to improve the reliability of the pick in the pick system; and the other is to study a more reasonable internal structure of the pick system. The reliability of the pick is bottlenecked by the performance of raw materials, heat treatment methods, welding quality and other technical levels. Therefore, scientific evaluation of the reliability of the pick system is an important basis for guiding the optimal design, maintenance decision and spare parts management of the pick system. At present, although the evaluation method of the reliability of the pick system has been widely studied, there is still no technical solution that considers the influence of environment, region and aggregation on the reliability of the pick system. SUMMARY

[0003] In order to solve the above technical problems or at least partially solve the above technical problems, the present application provides a pick reliability analysis method.

[0004] According to a first aspect, a pick system reliability analysis method, the method comprising:

[0005] S1: obtaining coal rock hardness, determining the corresponding pick allowable failure number under different coal rock hardness according to the coal rock hardness, and establishing a pick system environmental reliability model based on the coal rock hardness and the pick allowable failure number corresponding to different coal rock hardness;

[0006] S2: dividing the pick system into different regions according to a preset division condition, determining the pick allowable failure number in each region after division and the pick system overall pick allowable failure number, and establishing a pick system regional reliability model based on the failure pick number, the pick allowable failure number in each region and the pick system overall pick allowable failure number;

[0007] S3: obtaining pick real-time position information, determining the allowable failure number under the aggregation effect according to the pick real-time position information and a distance threshold, and establishing a pick system aggregation degree reliability model based on the failure pick number and the maximum allowable failure number of the pick under the aggregation effect;

[0008] S4: combining the pick system environmental reliability model, the pick system regional reliability model and the pick system aggregation degree reliability model to establish a pick system reliability analysis model.

[0009] Preferably, in step S1, different coal rock environments are divided according to coal rock hardness, the allowable failure number of the pick in any coal rock environment and the reliability of a single component are defined, the environment reliability model of the pick system is established according to the total probability formula, and the reliability formula of the environment reliability model of the pick system is:

[0010]

[0011] In the formula, E j is the jth environment in which the system is located, is the allowable failure number of the pick in the jth environment, is the reliability of a single component in the jth environment, P(E j ) is the total probability formula, e is the maximum number of different environments contained, is the combination number of selecting i components from n components, and n is the total number of components.

[0012] Preferably, in step S2, the pick system is divided into different regions according to the order of drilling into coal rock under the preset division condition, and the reliability probability formula of the region reliability model of the pick system is:

[0013]

[0014] In the formula, n f is the number of failed components; S is the number of regions divided by the pick system according to the preset division condition; is the number of allowable failures of components in the lth region; S l is the lth region of the system; is the total number of components in the lth region; k is the total allowable failure number of the pick system; and g is the number of any components in the lth region of the system.

[0015] Based on the reliability probability formula of the region reliability model of the pick system, the reliability of the region reliability model of the pick system is:

[0016]

[0017] Preferably, the sum of the allowable failure numbers of the picks in the divided regions is greater than the total allowable failure number of the pick system, and the allowable failure number of the pick in each divided region is less than the total allowable failure number of the pick system.

[0018] Preferably, in step S3, the aggregation effect is formed when the distance between any two of the failed picks is less than the distance threshold, and the certain number refers to the allowable failure number under the aggregation effect.

[0019] Preferably, the reliability probability formula of the aggregation degree reliability model of the pick system is:

[0020]

[0021] wherein, is the total number of cases of failure components forming aggregation, n f is the number of failure components; R is the reliability of a single component, n is the total number of system components, n a is the minimum number of failure components that can cause system failure due to aggregation;

[0022] Based on the reliability probability formula of the pick system aggregation reliability model, the reliability of the pick system aggregation reliability model is obtained as follows:

[0023]

[0024] Preferably, the pick tooth coordinates are obtained according to the real-time position information of the pick tooth and the spatial coordinate system; the distance model between any two pick teeth is established based on the pick tooth coordinates; the relative distance matrix of all components of the pick system is constructed based on the distance model between any two pick teeth; and the total number of cases of failure components forming aggregation is determined based on the distance threshold and the relative distance matrix.

[0025] Preferably, the reliability formula of the pick system reliability model is as follows:

[0026]

[0027] The probability formula of the pick system reliability model is as follows:

[0028]

[0029] wherein, E j is the jth environment in which the system is located, is the reliability of a single component under the jth environment, n f is the number of failure components, S is the number of regions divided by the pick system according to the preset division condition, is the number of components allowed to fail in the lth region, S l is the lth region of the system, n a is the minimum number of failure components that can cause system failure due to aggregation.

[0030] Compared with the prior art, the technical scheme provided by the embodiments of the present disclosure has the following advantages:

[0031] The embodiment of the present application considers the influence of environment, region and concentration on the reliability of the cutting tooth system, and respectively constructs the reliability models of the cutting tooth system under the influence of environment, region and concentration respectively and the comprehensive influence of the three factors. The reliability model of the cutting tooth system considering the influence of environment, region and concentration conforms to the engineering practice, provides effective guidance for the design optimization and reliability improvement of the cutting tooth system, and provides a theoretical basis and scientific basis for the maintenance and spare parts management of the cutting tooth system. BRIEF DESCRIPTION OF DRAWINGS

[0032] In order to more clearly illustrate the technical solutions in the specific embodiments or prior art, the drawings needed to be used in the specific embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0033] Figure 1 is a flowchart of a cutting tooth system reliability analysis method according to an embodiment of the present application;

[0034] Figure 2 is a reliability block diagram of a k / n(F) system according to an embodiment of the present application;

[0035] Figure 3.1 is a drilling working condition diagram of a cutting tooth system in coal rock according to an embodiment of the present application;

[0036] Figure 3.2 is a region division diagram of a cutting tooth system in coal rock according to an embodiment of the present application;

[0037] Figure 4.1 is a cutting tooth coordinate diagram of a cutting tooth system according to an embodiment of the present application;

[0038] Figure 4.2 is a cutting tooth arrangement unfolding diagram of a cutting tooth system according to an embodiment of the present application;

[0039] Figure 5 is a reliability curve diagram of a single cutting tooth under different coal rock hardness conditions according to a verification experiment of the present application;

[0040] Figure 6 is a reliability curve diagram of a cutting tooth system according to a verification experiment of the present application;

[0041] Figure 7 is a sensitivity analysis diagram of the reliability of a cutting tooth system under different n values according to a verification experiment of the present application;

[0042] Figure 8This is a schematic diagram of the sensitivity analysis of the reliability of the cutting tooth system under different k values ​​according to the verification experiment of the present invention;

[0043] Figure 9 This is a verification experiment based on the present invention at different n a A schematic diagram of sensitivity analysis of the reliability of the cutting tooth system under certain conditions;

[0044] Figure 10 This is a verification experiment based on the present invention at different D... H A schematic diagram of sensitivity analysis of the reliability of the cutting tooth system under certain conditions. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] The cutting tooth system consists of n cutting teeth arranged in a spiral. Powered by a cutting motor, the system rotates, causing the distributed cutting teeth to rotate and cut the coal and rock. Under specific coal and rock conditions, when the number of failed cutting teeth is less than k, the tunneling machine can maintain a certain cutting efficiency and complete the rock-breaking work; in this case, the cutting tooth system is within its normal operating range. When the number of failed cutting teeth is greater than or equal to k, the cutting continuity is disrupted due to the insufficient number of cutting teeth, and the tunneling machine loses its cutting ability and cannot complete the rock-breaking work; in this case, the cutting tooth system fails. In reliability theory, if k or more of the n components of a system fail, the system cannot function properly; this is denoted as a k / n(F) redundant system. The k / n(F) reliability block diagram of the cutting tooth system is shown below. Figure 2 As shown. The failure of the cutting tooth system is affected by the environment, region, and degree of clustering, specifically manifested as follows:

[0047] (1) The failure of the cutting tooth system is affected by the hardness of coal and rock. Under different environments, the hardness of coal and rock is different, the reliability of a single cutting tooth is different, and the number of cutting teeth that can fail in the cutting tooth system is different. That is, the system k value is different under different environments, and the system reliability is affected by the environment.

[0048] (2) The failure of the cutting tooth system is affected by the working area. The cutting tooth system can be divided into different working areas, and each area is an independent k / n(F) system. Therefore, the entire cutting tooth system forms a multi-level k / n(F) system. Due to different positions and different job responsibilities, the number of cutting teeth that can fail in different areas is also different, that is, the k value of different areas is different. If any area fails, the entire cutting tooth system will fail. The system reliability is affected by the area.

[0049] (3) The failure of the cutting tooth system is affected by the degree of clustering of failed cutting teeth. When the distance between any two failed cutting teeth in the cutting tooth system is less than the distance threshold, that is, when the failed cutting teeth form a clustering effect, the entire cutting tooth system fails, and the reliability of the system is affected by the degree of clustering.

[0050] The above situation is consistent with the actual application of the cutting tooth system of the tunnel boring machine. If these processes are simplified, it will lead to inaccurate reliability assessment of the cutting tooth system. Therefore, the present invention provides a reliability analysis method for the cutting tooth system, which comprehensively considers the influence of environment, region and concentration on the cutting tooth system.

[0051] For a completely new cutting tooth system, each cutting tooth is independently and identically distributed in R(t), and the cutting teeth are new at the initial moment. Therefore, the reliability R of the cutting tooth system in the new state is... S (t) is:

[0052]

[0053] Among them, R S R(t) represents the reliability of the cutting tooth system, R(t) represents the reliability of the cutting tooth, n represents the total number of cutting teeth in the cutting tooth system, and k represents the number of cutting teeth that the cutting tooth system can fail.

[0054] According to an embodiment of the present invention, a method for reliability analysis of a cutting tooth system is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0055] This embodiment provides a reliability analysis method for a cutting tooth system, which can be used in the aforementioned mobile terminals, such as mobile phones and tablet computers. Figure 1 This is a flowchart of a reliability analysis method for a cutting tooth system according to an embodiment of the present invention, such as... Figure 1 As shown, the process includes the following steps:

[0056] S1: Obtain the hardness of the coal and rock, determine the allowable number of cutter failures corresponding to different coal and rock hardnesses, and establish an environmental reliability model for the cutter system based on the coal and rock hardness and the allowable number of cutter failures corresponding to different coal and rock hardnesses.

[0057] In this embodiment, when the cantilever tunneling machine is performing cutting operations, the cutting efficiency of the cutting tooth system is closely related to its environment. The most important factor determining the working environment of the cutting tooth system is the hardness of the coal and rock being cut. Coal and rock hardness refers to the comprehensive concept of the ease or difficulty of breaking coal and rock under various coal and rock breaking methods. Under different coal and rock breaking methods, the hardness of the same type of coal and rock is basically consistent, possessing the same proportionality coefficient, i.e., the Protodyakonov hardness coefficient. Based on the Protodyakonov hardness coefficient f, coal and rock can be classified into coal (f < 4), semi-coal and rock (4 ≤ f ≤ 8), and rock (f > 8).

[0058] When cutting coal and rock of varying hardness, the cutting tooth system experiences different loads, resulting in varying natural wear and degradation rates, different probabilities of random load impacts, and different amplitudes of these impacts. Consequently, the reliability of individual cutting teeth varies, leading to differences in the overall reliability of the entire cutting tooth system. Furthermore, to ensure the cutting performance and continuity of tunneling operations, the allowable number of failed cutting teeth varies depending on the hardness of the coal and rock. Higher coal and rock hardness results in greater loads and fewer allowable failed cutting teeth; conversely, lower coal and rock hardness results in smaller loads and more allowable failed cutting teeth. Therefore, coal and rock hardness are inversely correlated with the allowable number of failed cutting teeth. Table 1 shows the k-value and component reliability of the k / n(F) system under different environments.

[0059] Table 1

[0060]

[0061] In the table, E j For the j-th environment in which the system is located, Let be the number of allowable failure teeth of the system under the j-th environment.

[0062] Let be the reliability of a single component under the j-th environment, where

[0063] Optionally, in step S1, different coal and rock environments are classified according to the hardness of the coal and rock. The allowable number of failures and the reliability of a single component for cutting teeth corresponding to different coal and rock hardnesses under any given coal and rock environment are defined. Based on the law of total probability, an environmental reliability model for the cutting tooth system is established. The reliability formula for the environmental reliability model of the cutting tooth system is:

[0064]

[0065] In the formula, E j For the j-th environment in which the system is located, Let be the number of allowable failure teeth of the system under the j-th environment.

[0066] Let P(E) be the reliability of a single component under the j-th environment. j () represents the law of total probability, and e represents the maximum number of distinct environments included. Let be the number of combinations of choosing i parts from n parts, where n is the total number of parts.

[0067] S2: Divide the cutting tooth system into different regions according to preset division conditions, determine the number of allowable failures of cutting teeth in each region and the total number of allowable failures of cutting teeth in the cutting tooth system, and establish a regional reliability model of the cutting tooth system based on the number of failed cutting teeth, the number of allowable failures of cutting teeth in each region and the total number of allowable failures of cutting teeth in the cutting tooth system.

[0068] Optionally, the sum of the allowable failure numbers of cutting teeth in each region after division is greater than the total allowable failure number of cutting teeth in the cutting tooth system, and the allowable failure number of cutting teeth in each region after division is less than the total allowable failure number of cutting teeth in the cutting tooth system.

[0069] In this embodiment, the drilling conditions and area division of the cantilever tunneling machine cutting tooth system in coal and rock are as follows: Figure 3.1 and Figure 3.2 As shown, based on the drilling sequence of the cutting tooth system into the coal and rock, the system is divided into three working areas: front, middle, and rear. During the cutting process, if a certain number of cutting teeth in any area fail, that area fails, leading to the failure of the entire cutting tooth system. That is, by dividing the system into areas, the cutting tooth system is transformed into a hierarchical k / n(F) system, where different areas contain different numbers of components and allowable failure numbers of cutting teeth. Furthermore, even if the number of failed cutting teeth in each area does not reach the allowable failure number for that area, but the total number of failed cutting teeth reaches the overall allowable failure number for the entire cutting tooth system, the cutting tooth system still fails.

[0070] During drilling, the cutting tooth system first cuts through the coal and rock in the front region. Because the coal and rock have well-developed bedding and joints before fracturing, and their structure is relatively intact, the front region experiences the greatest impact and vibration during drilling, resulting in the greatest rock-breaking effect and the highest requirement for the integrity of the cutting teeth. Therefore, the number of cutting teeth that can fail in this region is the smallest. After drilling through the front region, rock breaking begins in the middle region. Since the integrity of the coal and rock structure has been disrupted, and the cutting teeth from the front region also participate in cutting, the impact and vibration in the middle region decrease, resulting in a moderate number of cutting teeth that can fail. As drilling through the middle region is completed, the integrity of the coal and rock structure is further disrupted, and the number of cutting teeth participating in cutting further increases. Therefore, the rear region experiences the least impact and vibration during rock breaking, resulting in the least rock-breaking effect and the lowest requirement for the integrity of the cutting teeth. Thus, the number of cutting teeth that can fail in this region is the largest. Table 2 shows the number of components and the number of cutting teeth that can fail in different regions of the k / n(F) system.

[0071] Table 2

[0072]

[0073] Among them, region S l For the l-th region of the system, The total number of components in the l-th region. The number of allowable failures for the cutting teeth in the l-th region.

[0074] The reliability of a k / n(F) system affected by regional factors can be calculated using the following steps:

[0075] (1) When the number of failed parts The system will not fail at that time.

[0076] (2) When the number of failed parts When the system fails, it can only fail due to the failure of region S1. In this case, the probability of the system being reliable is:

[0077]

[0078] The expression within the square brackets means that when the system has n f When a component fails, there is no probability that region S1 will fail.

[0079] (3) When the number of failed parts In this case, the system may fail not only due to the failure of region S1, but also due to the failure of region S2. The probability of system reliability in this situation is:

[0080]

[0081] The expression within the square brackets means that when the system has n f The probability that neither region S1 nor region S2 fails when a component fails.

[0082] (4) And so on, when the number of failed parts In this scenario, all regions may fail, and the system may fail due to the failure of any one region. In this case, the probability of the system being reliable is:

[0083]

[0084] The expression within the square brackets means that when the system has n f When one component fails, there is no probability of failure in any area.

[0085] Optionally, different regions can be divided according to the drilling sequence of the cutting tooth system into the coal and rock. The reliability probability formula for the regional reliability model of the cutting tooth system is as follows:

[0086]

[0087] In the formula, n f S represents the number of failed components; S represents the number of regions divided by the cutting tooth system according to preset division conditions. S represents the number of components allowed to fail in the l-th region; l This is the l-th region of the system; is the total number of components in the l-th region; k is the total number of allowable failures of the cutting teeth in the overall cutting tooth system; g is the number of arbitrary components in the l-th region of the system;

[0088] Based on the reliability probability formula of the regional reliability model of the cutting tooth system, the reliability of the regional reliability model of the cutting tooth system is obtained as follows:

[0089]

[0090] S3: Obtain the real-time position information of the cutting teeth, determine the number of allowable failures under the clustering effect based on the real-time position information of the cutting teeth and the distance threshold, and establish a clustering reliability model of the cutting tooth system based on the number of failed cutting teeth and the maximum allowable number of failures of cutting teeth under the clustering effect.

[0091] Optionally, in step S3, the clustering effect is formed when the distance between any two of the failed cutting teeth is less than the distance threshold. The "certain number" refers to the allowable number of failures under the clustering effect.

[0092] Optionally, the coordinates of the cutting teeth are obtained based on the real-time position information of the cutting teeth and the spatial coordinate system; a distance model between any two cutting teeth is built based on the cutting tooth coordinates; a relative distance matrix of all components of the cutting tooth system is constructed based on the distance model between any two cutting teeth; and the total number of cases in which failed components form clusters is determined based on the distance threshold and the relative distance matrix.

[0093] In this embodiment, the cantilever tunneling machine's cutting tooth system consists of n cutting teeth arranged in a spiral pattern, and the relative positions of the cutting teeth in the system are determined. During the cutting process, if any of the n teeth fail... a Make sure the distance between any two cutting teeth is less than a certain distance threshold D. H If a failed cutting tooth accumulates in a localized area of ​​the cutting tooth system, a clustering effect occurs. The vacuum region created by this clustering of failed cutting teeth causes the cutting tooth system to operate in a discontinuous cutting state. This results in uneven stress distribution, increased load fluctuations, and intensified vibrations, ultimately leading to a loss of cutting performance and system failure. A schematic diagram of the coordinates of a single cutting tooth and the position of teeth within the cutting tooth system is shown below. Figure 4.1 and Figure 4.2 As shown.

[0094] The spatial coordinates of components in the k / n(F) system are shown in Table 3. iy i z i These are the horizontal, vertical, and axial coordinates of the component, respectively.

[0095] Table 3

[0096]

[0097] Based on the data shown in Table 2, the distance D between any two components i,j for:

[0098]

[0099] The relative distance matrix D of all components in the system can be represented as:

[0100]

[0101] In this embodiment, let S i The relative distance between component i and subsequent components is less than the distance threshold D. H The total number of cases. For example, S1 represents the number of components whose relative distance to component 1 is less than the distance threshold. Then, the relative distance between two components in the system is less than the distance threshold D. H There are a total of kind.

[0102] In this embodiment, the reliability of a k / n(F) system affected by the clustering degree of failed components can be calculated according to the following steps:

[0103] (1) When the number of failed parts n f <n a The system will not fail at this time, among which,

[0104] (2) When the number of failed parts n f ≥n a At this time, the system may fail due to the accumulation of faulty components. In this case, the probability of the system being reliable is:

[0105]

[0106] in, This represents the total number of cases where failed components form a cluster. The expression in square brackets means that when there are n... f When an individual component fails, there is no probability that the components will cluster together.

[0107] In this embodiment, when there are n f When one component fails, the probability that the k / n(F) system is reliable due to the clustering degree of the failed components is:

[0108]

[0109] In the formula, n f R represents the number of failed components, R represents the reliability of a single component, and n represents the total number of components in the system. a The minimum number of faulty components that could cause system failure due to aggregation.

[0110] Based on the reliability probability formula of the clustering reliability model of the cutting tooth system, the reliability of the clustering reliability model of the cutting tooth system is obtained as follows:

[0111]

[0112] S4: By combining the environmental reliability model, regional reliability model, and clustering reliability model of the cutting tooth system, a reliability analysis model for the cutting tooth system is established.

[0113] In this embodiment, considering the combined effects of environment, region, and clustering degree, when there are n f When one component fails, the probability that the k / n(F) system is reliable is:

[0114]

[0115] In the formula, E j For the j-th environment in which the system is located, Let n be the reliability of a single component under the j-th environment. f S represents the number of failed components, and S represents the number of regions divided by the cutting tooth system according to preset division conditions. S represents the number of components allowed to fail in the l-th region. l For the l-th region of the system, n a The minimum number of faulty components that could cause system failure due to aggregation.

[0116] The reliability formula for the reliability model of the cutting tooth system is:

[0117]

[0118] This invention describes the structural characteristics and failure modes of a cutting tooth system, modeling it as a k / n(F) system. Secondly, by describing the influence of coal and rock hardness, working area, and the degree of clustering of failed cutting teeth on the failure of the cutting tooth system, reliability models of the cutting tooth system under the individual influences of environment, region, and clustering degree, as well as the combined influence of all three, are constructed. The reliability model of the cutting tooth system considering the influences of environment, region, and clustering degree in this invention conforms to engineering practice, providing effective guidance for the design optimization and reliability improvement of cutting tooth systems, and also providing a theoretical basis and scientific foundation for the maintenance and spare parts management of cutting tooth systems.

[0119] This invention uses n aLet's take 3 as an example to illustrate. The solution method is as follows: when the relative distance between any two of the three failed components is less than a distance threshold, the k / n(F) system fails due to the clustering effect of the failed components. First, select one component from the system; this component can be any one of the n components. Second, select a second component, assuming its relative distance to the first component is less than the distance threshold. After the selection, n new relative distance matrices D are formed. i Each matrix is ​​composed of the relative distances between the i-th component and each component whose relative distance to the i-th component is less than a distance threshold. For example, there are three components whose relative distance to the i-th component is less than the distance threshold: components 5, 8, and 10. The new relative distance matrix D1, composed of the relative distances of these three components, is:

[0120]

[0121] Let S 1j For component j, whose relative distance to component j is less than the distance threshold, and whose relative distance to component j after component j is less than the distance threshold D,... H The total number of cases. For example, S 15 This represents the number of components whose relative distance to both components 1 and 5 is less than the distance threshold. Therefore, in the system, the relative distance between any two of the three components is less than the distance threshold D. H There are a total of species, that is Among them, i min The component with the smallest relative distance to component i that is less than a distance threshold is called component i. max The component with the largest relative distance to component i, which is less than the distance threshold. Therefore, when n... a >3, The above method can be used for recursive calculation.

[0122] To further verify the effectiveness and feasibility of the method of the present invention, a cutting test was conducted using a small-section rock tunnel boring machine with a cutting power of 260kW manufactured by a certain tunnel boring machine manufacturer.

[0123] The longitudinal axis cutting tooth system consists of 51 cutting teeth arranged in three helical lines. If 12 cutting teeth fail, the entire system fails. The coal and rock environment in which the cutting tooth system operates is mainly composed of grayish-white medium-grained sandstone and grayish-black sandy mudstone, with an average Protodyakonov hardness of f6.8, accompanied by high-hardness gangue and faults. The cutting tooth system is divided into three regions: front, middle, and rear, forming a multi-level k / n(F) system. Furthermore, if the distance between any two of the three failed cutting teeth is less than 10 mm, the cutting tooth system fails due to the aggregation effect of the failed cutting teeth. The spatial coordinates of the cutting teeth in the system, the n-value of each region, and the k-value of each region are shown in Table 4.

[0124] Table 4

[0125]

[0126] Based on the hardness of coal and rock, the working environment of the cutting tooth system is divided into coal (f < 4), semi-coal and rock (4 ≤ f ≤ 8), and rock (f > 8). Based on engineering data, the reliability model parameters of the cutting tooth system can be obtained by fitting, as shown in Table 5. Furthermore, the reliability curves of a single cutting tooth under different coal and rock hardness conditions are plotted on... Figure 5 middle.

[0127] Table 5

[0128]

[0129] Depend on Figure 5 It is evident that when the cutting system cuts whole coal, the natural degradation rate of the cutting teeth is lowest due to the lowest hardness of the coal. Furthermore, whole coal lacks high-hardness gangue and faults, so the degradation of the cutting teeth is unaffected by random load impacts and only experiences soft failures due to natural wear. Therefore, its reliability level is the highest. However, when the cutting system cuts semi-coal, the natural degradation rate of the cutting teeth increases with the increase in coal hardness. Simultaneously, due to the presence of high-hardness gangue and faults, the degradation of the cutting teeth also includes instantaneous degradation caused by random load impacts and variable-rate accelerated degradation over the impact duration. The cutting teeth are more prone to soft failures, thus reducing their reliability level. When the coal and rock being cut by the cutting tooth system is whole rock, the cutting tooth does not undergo a natural degradation process because the rock has the highest hardness. The cutting tooth is always in a variable-rate accelerated degradation process within the duration of the impact caused by high-hardness gangue and faults. At the same time, when the gangue and faults reach a certain hardness, the cutting tooth may also experience hard failure caused by random load impact. Therefore, in the competing failure modes of soft failure and hard failure, its reliability level is the lowest.

[0130] To account for the impact of environment, region, and clustering on the failure of the cutting tool system and to verify the model's generality, the established reliability model of the cutting tool system was transformed into a reliability model considering different factors by setting different parameter values. Table 6 compares the main factors considered in these models.

[0131] Table 6

[0132]

[0133] To illustrate the impact of environment, region, and clustering on the reliability of the cutting tool system, reliability curves for the four models listed in Table 5 were plotted based on the parameter values ​​given in Table 6. Figure 6 From this, we can draw the following conclusions:

[0134] (1) The impact of the environment on the reliability of the cutting tooth system can be obtained by comparing the reliability curves of Model 1 and Model 2. As shown in the figure, the cutting tooth system without considering the environmental impact has a high stability reliability stage of 7 days, that is, the cutting tooth system will not fail within 7 days, which is quite different from the actual application of the cutting tooth system. However, the cutting tooth system considering the environmental impact has a high stability reliability stage of 5 days, and the reliability is 0.52 at 8 days, that is, the probability that the cutting tooth system will not fail within 8 days is 52%, which is consistent with the actual degradation trend of the cutting tooth system. This is because when the environmental impact is not considered, the working environment of the cutting tooth system is only for the full coal working condition. There are no high-hardness gangue and faults in the coal seam, the natural wear of the cutting tooth is the slowest, and it is not affected by random load impact, so the reliability is the highest. At the same time, the system k value of the cutting tooth system is the largest under the full coal working condition. However, in engineering practice, the cutting tooth system cannot be in a constant working environment. Under different coal and rock hardness conditions, the reliability of a single cutting tooth and the number of cutting teeth that can fail in the cutting tooth system will change accordingly. If the impact of environmental changes on system failure is ignored, the system reliability calculation will be inaccurate. Therefore, models that consider environmental impact always have a more accurate reliability level than models that do not consider environmental impact.

[0135] (2) The impact of regions on the reliability of the cutting tooth system can be obtained by comparing the reliability curves of Model 2 and Model 3. As shown in the figure, the cutting tooth system without considering the regional impact has a high stable reliability stage of 5 days, and the reliability is 0.52 at 8 days. The cutting tooth system considering the regional impact has a high stable reliability stage of 4.5 days, and the reliability is 0.3 at 8 days. The probability of failure of the cutting tooth system increases by 22%. This is because each region of the cutting tooth system has different responsibilities and functions under specific working conditions. The failure of a certain number of cutting teeth in any region will cause the loss of function in that region, thus leading to the failure of that region and ultimately causing the failure of the entire cutting tooth system. That is, the cutting tooth system and its various regions form a hierarchical k / n(F) system. If the impact of regional failure on system failure is ignored, the reliability of the system will be overestimated. Therefore, the model considering the regional impact always has a lower reliability level than the model without considering the regional impact.

[0136] (3) The impact of clustering on the reliability of the cutting tooth system can be derived by comparing the reliability curves of Model 3 and Model 4. As shown in the figure, the cutting tooth system without considering the impact of clustering has a high-stability reliability stage of 4.5 days, with a reliability of 0.3 at 8 days. The cutting tooth system considering the impact of clustering only has a high-stability reliability stage of 4 days, with a reliability of 0.22 at 8 days, indicating an 8% increase in the probability of system failure. This is because although the cutting tooth system as a whole and in each region does not fail, the failure of the cutting teeth clusters locally, forming a vacuum area. This causes uneven stress on the cutting tooth system during the cutting process, increased load fluctuations, and intensified vibration, leading to the loss of cutting performance and ultimately causing the entire system to fail. Ignoring the impact of the clustering of failure of the cutting teeth on system failure will overestimate the reliability of the system. Therefore, the model considering the impact of clustering always has a lower reliability level than the model without considering the impact of clustering.

[0137] (4) The reliability curve of the cutting tooth system, which is affected by the combined factors of environment, region, and concentration, is shown in Model 4. As can be seen from the figure, unlike the cutting tooth itself, which does not have a high-stability reliability stage throughout its entire life cycle, the cutting tooth system has a 4-day high-stability reliability stage throughout its entire life cycle, after which it enters a rapid degradation stage, with a reliability of 0.5 for 7 days. At this reliability level, the need for safe and efficient production is still not met, which is an important reason why the cutting tooth system needs to adopt a reasonable maintenance and spare parts inventory strategy.

[0138] To verify the reliability model of the cutting tooth system and guide its optimized design to improve reliability, it is necessary to analyze the sensitivity of the model parameters to study their impact on reliability. Specifically, the parameters n, k, and n0 are considered. a and D H These are key parameters that determine the reliability of the system. Therefore, based on engineering data, the sensitivity of the above parameters was analyzed, and the specific parameter ranges are shown in Table 7.

[0139] Table 7

[0140]

[0141] Sensitivity analysis of the total number of cutting teeth n and the system failure threshold k of the cutting tooth system is as follows: Figure 7 and Figure 8 As shown, when the value of n decreases from 57 to 45, the reliability of the cutting tooth system improves by 0.48 after 7 days. When the value of k increases from 10 to 14, the reliability of the cutting tooth system improves by 0.39 after 7 days. Therefore, decreasing the system's n value or increasing the system's k value both improve the system's reliability. In practice, n and k reflect the redundancy structure of the cutting tooth system. Therefore, under the premise of meeting the overall design requirements of the tunnel boring machine, the system's cutting capacity can be increased, thereby reducing the total number of cutting teeth n or increasing the system's failure threshold k, i.e., reducing the system's redundancy, and ultimately improving the overall reliability of the cutting tooth system.

[0142] The number n of failed cutting teeth that cause a clustering effect on the cutting tooth system a and distance threshold D H Sensitivity analysis such as Figure 9 , Figure 10 As shown. When n a When the value increased from 3 to 5, the reliability of the cutting tooth system improved by 0.32 over 7 days; when D H Increasing the value of n from 8 to 12 improved the reliability of the cutting tooth system by 0.33 over 7 days. Therefore, decreasing n increases the reliability. a Or D H With a higher value of n, the system's reliability is improved. a and D H This reflects the arrangement design of the cutting teeth in the cutting tooth system. Therefore, the design of the cutting tooth arrangement, including the outline, number of helical lines, helix angle, and section spacing, should be continuously optimized to improve the cutting capability of the cutting tooth system and thus reduce the number of failed cutting teeth (n) that form a clustering effect. a and distance threshold D H This ultimately improves the reliability of the entire cutting tooth system.

[0143] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A reliability analysis method for a cutting tooth system, characterized in that, The method includes: S1: Obtain the hardness of coal and rock, determine the allowable number of cutter failures corresponding to different coal and rock hardnesses based on the coal and rock hardness, and establish an environmental reliability model for the cutter system based on the coal and rock hardness and the allowable number of cutter failures corresponding to different coal and rock hardnesses. S2: Divide the cutting tooth system into different regions according to the preset division conditions, determine the number of cutting teeth failures in each region and the total number of cutting teeth failures in the cutting tooth system, and establish a regional reliability model of the cutting tooth system based on the number of failed cutting teeth, the number of cutting teeth failures in each region and the total number of cutting teeth failures in the cutting tooth system. S3: Obtain the real-time position information of the cutting teeth, determine the number of cutting teeth that can fail under the clustering effect based on the real-time position information of the cutting teeth and the distance threshold, and establish a clustering reliability model of the cutting teeth system based on the number of failed cutting teeth and the number of cutting teeth that can fail under the clustering effect. S4: Combining the environmental reliability model, regional reliability model, and clustering reliability model of the cutting tooth system, establish a reliability analysis model for the cutting tooth system; The reliability formula for the reliability analysis model of the cutting tooth system is: In the formula, Indicates the reliability of the cutting teeth; Indicates the maximum number of distinct environments included; Indicates the first The number of allowable failure teeth of the system under such conditions; Indicates the system's current position. This environment; This represents the law of total probability. Indicates components; The number of failed components; The probability formula for the reliability analysis model of the cutting tooth system is: In the formula, Indicates from Select from components The number of combinations of components; For the first The reliability of a single component under various conditions; The system is in the first This environment; This represents the total number of cases where failed components form clusters. The minimum number of failed components that cause system failure due to aggregation; For the first The number of components allowed to fail in each region; For the first The total number of components in each region; For the system's first One region; The cutting tooth system is divided into a number of regions according to preset division conditions; For the system's first The number of any number of components in each region.

2. The reliability analysis method for a cutting tooth system according to claim 1, characterized in that: In step S1, different coal and rock environments are classified according to the hardness of the coal and rock. The allowable number of failures and the reliability of a single component for cutting teeth corresponding to different coal and rock hardnesses under any given coal and rock environment are defined. Based on the law of total probability, an environmental reliability model for the cutting tooth system is established. The reliability formula for the environmental reliability model of the cutting tooth system is: In the formula, The system is in the first This kind of environment, For the first The number of permissible failures of the system's cutting teeth under this environment. For the first The reliability of a single component under such conditions. This is the law of total probability. This represents the maximum number of distinct environments included. From Select from components The number of combinations of components This represents the total number of components.

3. The reliability analysis method for a cutting tooth system according to claim 2, characterized in that: In step S2, based on the drilling sequence of the cutting tooth system into the coal and rock, the cutting tooth system is divided into different regions according to preset division conditions. The reliability probability formula of the regional reliability model of the cutting tooth system is: In the formula, The number of failed components; The cutting tooth system is divided into a number of regions according to preset division conditions; For the first The number of components allowed to fail in each region; For the system's first One region; For the first The total number of components in each region; This represents the total allowable number of cutter failures in the cutter system. For the system's first The number of any number of components in each region; For the reliability of a single component; Based on the reliability probability formula of the regional reliability model of the cutting tooth system, the reliability of the regional reliability model of the cutting tooth system is obtained as follows: 。 4. The reliability analysis method for a cutting tooth system according to claim 3, characterized in that: After the division, the sum of the allowable failure numbers of the cutting teeth in each region is greater than the total allowable failure number of the cutting teeth in the entire cutting tooth system, while the allowable failure numbers of the cutting teeth in each region are less than the total allowable failure number of the cutting teeth in the entire cutting tooth system.

5. The reliability analysis method for a cutting tooth system according to claim 1, characterized in that: In step S3, the clustering effect is formed when the distance between any two of the failed cutting teeth is less than the distance threshold. The "certain number" refers to the number of cutting teeth that are allowed to fail under the clustering effect.

6. The reliability analysis method for a cutting tooth system according to claim 5, characterized in that: The reliability probability formula for the clustering reliability model of the cutting tooth system is: In the formula, This represents the total number of cases where failed components cluster together. The number of failed parts. For the reliability of individual components, This represents the total number of system components. The minimum number of failed components that cause system failure due to aggregation; Based on the reliability probability formula of the clustering reliability model of the cutting tooth system, the reliability of the clustering reliability model of the cutting tooth system is obtained as follows: 。 7. The reliability analysis method for a cutting tooth system according to claim 5, characterized in that: Based on the real-time position information of the cutting tooth and the spatial coordinate system, the coordinates of the cutting tooth are obtained; A model of the distance between any two cutting teeth is constructed based on the aforementioned cutting tooth coordinates; Construct a relative distance matrix for all components of the cutting tooth system based on the distance model between any two cutting teeth; The total number of cases where failed components form clusters is determined based on the distance threshold and the relative distance matrix.

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