A calculation method for the non-adjustment rate of the pull-in voltage of an electromagnetic relay based on the cooperation of the attraction and repulsion forces

Abstract

The present invention discloses a calculation method for the non-adjustment rate of the pull-in voltage of an electromagnetic relay based on the cooperation of the pull-in and counter-force. The method is as follows: Step 1, determination of part dimensions, distribution of assembly parameters, and definition of key positions during the pull-in process; Step 2, single-factor analysis of the electromagnetic pull-in force at key positions during the pull-in process and screening of key influencing factors; Step 3, solution of the pull-in and counter-force distribution at the value of a single point position in each key position distribution and calculation of the non-conformance rate of matching; Step 4, calculation of the non-conformance rate of pull-in and counter-force matching under the influence of each key position distribution; Step 5, calculation of the non-adjustment rate of the relay operating voltage under the comprehensive influence of each key position distribution. Based on the specified pull-in voltage as a benchmark, the present invention comprehensively considers the matching qualification of the pull-in and counter-force distributions under this voltage, under the influence of the distributions of various key parameters, and at the key positions of the armature during the pull-in process, so as to calculate the non-adjustment rate of the pull-in voltage, and can accurately and efficiently calculate the non-adjustment rate of the pull-in voltage of the electromagnetic relay.

Description

Technical Field

[0001] The present invention relates to a calculation method for the non-adjustment rate of an electromagnetic relay, and more particularly to a calculation method for the non-adjustment rate of the pull-in voltage of an electromagnetic relay based on the cooperation of the attraction and repulsion forces. Background Art

[0002] As a core component of the power system and the automatic control system, the electromagnetic relay is widely used in high-tech industries and the national defense field due to its high conversion depth and strong anti-interference ability, and plays roles such as circuit conversion and safety protection.

[0003] During the production and assembly process of the electromagnetic relay, the meaning of the non-adjustment rate is generally defined as the probability that the product directly meets the requirements of various output characteristic indicators without debugging after assembly. However, electromagnetic relays applied to some special occasions need to have strict output characteristics, which greatly increases the difficulty of their assembly without adjustment. Some links need to rely on manual debugging to make the product have the required performance, thus prolonging the production cycle and increasing the labor cost. To reduce costs and increase efficiency, it is usually considered to optimize the design of part sizes, assembly parameters, etc. in the design stage, and use these parameters to calculate the non-adjustment rate of batch products before the prototype machining to ensure that the design results meet the expectations. The pull-in voltage is one of the key output characteristic indicators of the electromagnetic relay. The non-adjustment rate of the pull-in voltage refers to the probability that the product directly meets the pull-in voltage requirement without debugging after assembly. The calculation of the non-adjustment rate of the pull-in voltage can verify and evaluate the design and optimization scheme of the relay, and is one of the important processes in the optimal design of the relay.

[0004] Currently, there is little research on the calculation method of the non-adjustable rate of the pull-in voltage in the industry. The main idea is as follows: First, considering all influencing parameters, a parameter sample of batch products is obtained by using the random sampling method. Second, the electromagnetic force characteristics of all samples at the armature release position and under the full-range coil voltage are directly solved by using the finite element simulation method combined with interpolation and extrapolation, and it is directly considered that the reaction force of all samples at the armature release position is the same fixed value. Third, in each sample, the coil voltage corresponding to the equal electromagnetic force and reaction force is searched as the pull-in voltage of each sample, and the interpolation and extrapolation are performed on the above pull-in voltage results to obtain the probability density function of the pull-in voltage distribution of batch products. Finally, the probability density area higher than the pull-in voltage index in the pull-in voltage distribution is directly calculated by the integral method as the non-adjustable rate of the pull-in voltage. The above method has the following problems: First, the pull-in voltage is the result of the matching of the pull and reaction forces. If the pull-in voltage distribution is to be directly solved, it is necessary to complete the matching of the pull and reaction forces of each sample one by one. And the matching of the pull and reaction forces is a process of adjusting the coil voltage so that the suction force is just higher than the reaction force. If this process is realized by simulation, it is necessary to obtain the electromagnetic suction force of each sample at different voltages by using the finite element simulation method, then obtain the electromagnetic force characteristics of each sample by interpolation and extrapolation one by one, and then calculate the pull-in voltage by searching and comparing the pull and reaction forces one by one, which makes such methods have the problems of large calculation amount and low calculation efficiency. Second, it is considered that the reaction force of each sample at the armature release position is the same fixed value, which does not conform to the actual production and processing situation. Affected by the deviations of part sizes, assembly parameters, etc., the reaction forces of the relays will also have a distribution. Considering it as the same fixed value may make the calculation results inaccurate. Third, it is considered that the coil voltage when the suction force at the armature release position is just greater than the reaction force is the pull-in voltage, and this understanding is not comprehensive enough. If the electromagnetic suction force of the armature at other positions is lower than the reaction force, there will be a two-step pull-in problem for the relay, and such products also do not belong to the non-adjustable products, which may lead to inaccurate calculation results of the existing methods. Fourth, considering all influencing factors to generate samples and calculate the probability density area of the pull-in voltage distribution as the non-adjustable rate of the pull-in voltage only considers the direct reasons affecting the non-adjustable rate of the pull-in voltage, and does not consider its fundamental reasons in the working principle of the relay. Therefore, the calculation results can only roughly evaluate the non-adjustable rate situation of the pull-in voltage under the current design, and cannot provide guiding suggestions for subsequent optimization designs. Summary of the Invention

[0005] Aiming at the problems of low calculation efficiency and incomplete consideration in the current calculation method of the non-adjustable rate of the pull-in voltage of relays, the present invention provides a calculation method for the non-adjustable rate of the pull-in voltage of electromagnetic relays based on the cooperation of the pull and reaction forces.

[0006] The object of the present invention is achieved by the following technical solutions:

[0007] A calculation method for the non - adjustable rate of the pull - in voltage of an electromagnetic relay based on the cooperation of the pulling and repulsive forces, comprising the following steps:

[0008] Step 1: Determination of part dimensions, distribution of assembly parameters, and definition of key positions during the pull - in process:

[0009] Step 1.1: According to the technological characteristics of the processing and assembly processes of each part of the electromagnetic relay, combined with the analysis of the working principle of the electromagnetic relay, determine the main influencing parameters affecting its pull - in voltage, and express the pull - in voltage as:

[0010] U(z i ), i ∈ [1, 2, 3, …, n];

[0011] where z i represents the i - th parameter, and n represents the total number of the main influencing parameters affecting the pull - in voltage;

[0012] Step 1.2: Considering the technological characteristics of the relay production and assembly process, for each z i , where and respectively represent the distribution mean and standard deviation of the i - th parameter;

[0013] Step 1.3: To meet the conditions of Step 1.2, two key positions need to be determined in the armature stroke during the pull - in process, defined as Point A and Point B. Among them, Point A is the armature position in the released state, and Point B is the armature position when the stationary contact spring and the moving contact spring just separate during the pull - in process. The distributions of the two key positions affected by the parameters are respectively expressed as:

[0014] x A (z i ) ∼ N A (μ A , σ A 2 ) and x B (z i ) ∼ N B (μ B , σ B 2 );

[0015] where μ A and μ B respectively represent the distribution means of Point A and Point B, and σ A and σ B respectively represent the distribution standard deviations of Point A and Point B. Thus, the non - adjustable rate of the pull - in voltage is defined as:

[0016] ρ=(1 - P A )·(1 - P B );

[0017] Among them, P A and P B Represents the unqualified rate of batch products at point A and point B respectively;

[0018] Step 2: Single factor analysis of electromagnetic suction force at key positions during the suction process and screening of key influencing factors:

[0019] Step 2.1: Combine finite element simulation analysis to solve each main influencing parameter z i Probability density function of electromagnetic attraction distribution at each key position and The impact of F EMF Indicates the magnitude of electromagnetic attraction, F SF Indicates the magnitude of the reaction force. The values ​​of the simulation parameters are taken according to the principle of 3 times the standard deviation:

[0020]

[0021] Step 2.2: Analyze the influence of each parameter on suction and select the most important key influencing parameter z k ,k∈[1,2,3,…m], where z k represents the kth key influencing parameter, and m represents the total number of key influencing parameters;

[0022] Step 3: Solve the suction reaction force distribution and calculate the matching failure rate under the single point position value in each key position distribution:

[0023] Step 3.1: Use exponential sampling to obtain the sampling point value set of each key position and in, and denote the sampling points of point A and point B, respectively; α and β denote the uniformly changing value parameters of the exponential sampling of point A and point B, respectively; h∈{1,2,3,…,c} denotes the hth sampling point, and c denotes the total number of sampling points;

[0024] Step 3.2: Use random sampling to select each and Multiple groups of z k Value combination, for z that follows a normal distribution k , define the sampling distance d(Z j ) and weight value w(Z j ):

[0025]

[0026] Among them, Z j represents the jth group of samples, Denote the value of the k-th key influencing parameter in the j-th group of samples, and implement random sampling of the key influencing parameter combination according to its weight value;

[0027] Step 3.3: Conduct finite element simulation calculations of the electromagnetic suction and reaction force for each key influencing parameter combination sample one by one to obtain the and probability density functions of the electromagnetic suction and reaction force distributions under each

[0028]

[0029] Among them, and respectively represent the probability density functions of the electromagnetic suction and reaction force at point A changing with the position distribution of point A and the key influencing parameter distribution. and respectively represent the probability density functions of the electromagnetic suction and reaction force at point B changing with the position distribution of point B and the key influencing parameter distribution. μ EMF () and σ EMF () represent the distribution mean and standard deviation of the electromagnetic suction changing with the armature position, and μ SF () and σ SF () represent the distribution mean and standard deviation of the reaction force changing with the armature position;

[0030] Step 3.4: Calculate the functions g A and x B changing with their respective values x A (x A ) and g B (x B ) of the nonconforming rates of point A and point B respectively. According to the existing sampling points, obtain the nonconforming rate at each sampling point through numerical integration:

[0031]

[0032] Step 4: Calculate the nonconforming rate of the suction and reaction force matching under the influence of the distribution of each key position:

[0033] Step 4.1: Use the calculation results of the nonconforming rates of the sampling points to establish a fast calculation model of g A (x A ):

[0034]

[0035] Among them, φ() represents the basis function, ε represents the Gaussian parameter, r represents the distance, represents the h-th sampling point, and s h represents the interpolation weight of the h-th sampling point; to solve the interpolation weight at each sampling point, solve the following linear equations:

[0036]

[0037] Among them, represents the δ-th sampling point, and from this, the interpolation weight s of each known sampling point is calculated h , and then a rapid calculation model for the unqualified rate at point A is obtained:

[0038] g A (x A ) = V A (x A );

[0039] Step 4.2: Using the calculation results of the unqualified rate of the sampling points, establish a rapid calculation model for g B (x B ):

[0040]

[0041] Among them, φ() represents the basis function, ε represents the Gaussian parameter, r represents the distance, represents the h-th sampling point, and s h represents the interpolation weight of the h-th sampling point; to solve the interpolation weight at each sampling point, solve the following linear equations:

[0042]

[0043] Among them, represents the δ-th sampling point, and from this, the interpolation weight s of each known sampling point is calculated h , and then a rapid calculation model for the unqualified rate at point B is obtained:

[0044] g B (x B ) = V B (x B );

[0045] Step 4.3: Based on Step 4.2 and Step 4.2, obtain the unqualified rate under the influence of the distributions at points A and B:

[0046]

[0047] Step 5: Calculate the non-adjustment rate of the relay operating voltage under the comprehensive influence of the distributions at each key position:

[0048] According to the calculation formula for the non-adjustment rate of the pick-up voltage, solve the non-adjustment rate of the pick-up voltage of the electromagnetic relay:

[0049] ρ = (1 - P A ) · (1 - P B ).

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] The present invention defines the key positions in the armature suction process that affect the non-adjustment rate of the suction voltage. Considering combining the finite element simulation method to conduct a single-factor analysis on multiple part size parameters and assembly parameters, etc., the key influencing factors of the electromagnetic suction force are obtained; since there are distributions for each key position itself, and there are distributions for the electromagnetic suction force and the reaction force under the distribution values of each key position, the calculation of the non-adjustment rate of the suction voltage is regarded as a three-dimensional probability distribution problem. By gradually solving the matching situation of the suction and reaction forces under the above influences, combining the sampling method and the finite element simulation method, a rapid calculation model for the non-adjustment rate of the suction voltage is established, and the non-adjustment rate of the suction voltage of the overall batch of products is solved by integral method. In summary, compared with other calculation methods, the present invention starts from the working principle of the relay, takes the specified suction voltage as the benchmark, comprehensively considers the matching qualification of the suction and reaction force distributions under this voltage, under the influence of the distribution of each key parameter, and at the key positions of the armature during each suction process, so as to calculate and obtain the non-adjustment rate of the suction voltage, which can accurately and efficiently calculate the non-adjustment rate of the suction voltage of the electromagnetic relay, and can provide guiding suggestions for subsequent optimization design. Description of the Drawings

[0052] Figure 1 is the calculation flow chart of the non-adjustment rate of the suction voltage of the electromagnetic relay;

[0053] Figure 2 is an example of the electromagnetic suction force distribution results at each value of point A. Detailed Embodiments

[0054] The technical solution of the present invention will be further described below in conjunction with the drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0055] The present invention provides a method for calculating the non-adjustment rate of the suction voltage of an electromagnetic relay based on the matching of the suction and reaction forces, as Figure 1 shown, the method includes the following steps:

[0056] Step 1. The non-adjustment rate of the suction voltage of the electromagnetic relay refers to the probability that the relay product directly meets the suction voltage requirement without debugging after assembly. According to the process characteristics of each part processing and assembly process of the electromagnetic relay, combined with the analysis of the working principle of the electromagnetic relay, the main influencing parameters affecting its suction voltage are determined, and the suction voltage is expressed as:

[0057] U(z i ), i ∈ [1, 2, 3,..., n];

[0058] Among them, z i represents the i-th parameter, and n represents the total number of main influencing parameters affecting the pull-in voltage.

[0059] Considering the characteristics of the relay production and assembly process, for each z i there is a distribution. In engineering, it is generally considered that the parameters of machine processing follow a normal distribution, that is:

[0060]

[0061] Among them, and respectively represent the distribution mean and standard deviation of the i-th parameter.

[0062] Since the pull-in voltage is the result of the matching of the pull and release forces, the non-adjustment rate of the pull-in voltage can essentially be understood as that after the relay product is assembled, its static suction force characteristic curve is completely higher than the static release force characteristic curve under the specified pull-in voltage. Analyzing in combination with the working principle of the relay, it can be known that to meet the above conditions, only two key positions need to be determined in the armature stroke during the pull-in process, defined as point A and point B. Among them, point A is the armature position in the release state, and the matching situation of the pull and release forces at this key position determines whether the product can be pulled in under the pull-in voltage; point B is the armature position when the static contact spring and the moving contact spring just separate during the pull-in process, and the matching situation of the pull and release forces at this key position determines whether there is a two-step pull-in problem for the product. The distributions of the two key positions affected by the parameters are respectively expressed as:

[0063] x A (z i )~N A (μ A ,σ A 2 ) and x B (z i )~N B (μ B ,σ B 2 );

[0064] Among them, μ A and μ B respectively represent the distribution means of point A and point B, and σ A and σ B respectively represent the distribution standard deviations of point A and point B.

[0065] Thus, the non-adjustment rate of the pull-in voltage can be defined as:

[0066] ρ=(1 - P A )·(1 - P B );

[0067] Among them, PA and P B represent the unqualified rates of batch products at points A and B respectively, and the probability that the product's pull-in voltage is adjustable-free means that both point A and point B are qualified.

[0068] Step 2: Combine the finite element simulation analysis method to solve each main influencing parameter z i The probability density function of the electromagnetic suction force distribution at each key position and of the influence situation, where F EMF represents the magnitude of the electromagnetic suction force, and F SF represents the magnitude of the reaction force. Each simulation parameter is taken according to the 3-fold standard deviation principle as:

[0069]

[0070] By analyzing the influence of each parameter on the suction force, the most important key influencing parameter z k , k ∈ [1, 2, 3, … m], can be screened out, thereby reducing the computational complexity of the subsequent work, where z k represents the k-th key influencing parameter, and m represents the total number of key influencing parameters.

[0071] Step 3: Use the exponential sampling method to obtain the sampling point value sets at each key position and where, and represent the sampling points at points A and B respectively, α and β represent the uniformly varying value parameters during exponential sampling at points A and B respectively, h ∈ {1, 2, 3, …, c} represents the h-th sampling point, and a total of c sampling points are generated as the value parameters change. At each key position sampling point and below, the electromagnetic suction force and the reaction force are mainly affected by the distribution of the key influencing parameter . Therefore, both the electromagnetic suction force and the reaction force will follow a normal distribution.

[0072] To solve the above distribution and at the same time consider reducing the computational complexity of the finite element simulation, a random sampling method is given to extract multiple groups of z and value combinations below each k For z k that follows a normal distribution, define the value distance d(Z j ) and the weight value w(Z j ) of its sampling sample:

[0073]

[0074] where, Z jDenote the j-th group of samples, Denote the value of the k-th key influencing parameter in the j-th group of samples. Random sampling of the combination of key influencing parameters is implemented according to their weight values.

[0075] Perform finite element simulation calculations of the electromagnetic attraction and reaction force for each of these combinations of key influencing parameters one by one to obtain the and probability density functions of the electromagnetic attraction and reaction force distributions under each

[0076]

[0077] Among them, and respectively represent the probability density functions of the electromagnetic attraction and reaction force at point A changing with the distribution of the position of point A and the distribution of key influencing parameters, and respectively represent the probability density functions of the electromagnetic attraction and reaction force at point B changing with the distribution of the position of point B and the distribution of key influencing parameters, μ EMF () and σ EMF () represent the distribution mean and standard deviation of the electromagnetic attraction changing with the armature position, μ SF () and σ SF () represent the distribution mean and standard deviation of the reaction force changing with the armature position. Taking the electromagnetic attraction distribution at point A as an example, the results that can be obtained are as shown in Figure 2 shown.

[0078] Since the condition for the relay pull-in voltage to be free of adjustment is that the electromagnetic attraction at points A and B is greater than the reaction force under the specified pull-in voltage, first calculate the functions g A and x B changing with the respective values x A (x A ) and g B (x B ) of the unqualified rates of points A and B respectively. According to the existing sampling points, the unqualified rates under each sampling point can be obtained through numerical integration:

[0079]

[0080] Step 4: Use the calculated results of the unqualified rates of the above sampling points to establish fast calculation models of g A (x A ) and g B (x B ). Taking point A as an example:

[0081]

[0082] Among them, φ() represents the basis function, ε represents the Gaussian parameter, and r represents the distance, represents the h-th sampling point, s h represents the interpolation weight of the h-th sampling point, and c represents the total number of sampling points. To solve for the interpolation weight at each sampling point, solve the following system of linear equations:

[0083]

[0084] where, represents the δ-th sampling point, from which the interpolation weight s of each known sampling point can be calculated h , and then obtain the rapid calculation model for the nonconforming rate at point A:

[0085] g A (x A ) = V A (x A ).

[0086] The method for establishing the rapid calculation model of the nonconforming rate at point B is the same as that at point A.

[0087] Thus, obtain the nonconforming rate under the influence of the distributions at points A and B:

[0088]

[0089] Step 5: According to the calculation formula for the non-adjustment rate of the pull-in voltage, solve for the non-adjustment rate of the pull-in voltage of the electromagnetic relay:

[0090] ρ = (1 - P A )·(1 - P B );

[0091] Thus, the calculation of the non-adjustment rate of the pull-in voltage of the electromagnetic relay is completed.

[0092] Combined with an example, calculate that the nonconforming rate at point A of a certain model of electromagnetic relay is P A = 26.3%, and the nonconforming rate at point B is P B = 22.3%. Then the non-adjustment rate of the pull-in voltage ρ = 57.26%. Actually process a batch of samples of this design, and the measured non-adjustment rate of the pull-in voltage of the batch of products is 58%. Calculate the relative error as:

[0093] E R = (58% - 57.26%) / 58% × 100% ≈ 1.28%.

Claims

1. A method for calculating the non-adjustment rate of the electromagnetic relay's pull-in voltage based on pull-in and pull-back force coordination, characterized in that The method comprises the following steps: Step 1: Determine the part size, assembly parameter distribution and define the key positions of the pull-in process: Step 1.1, according to the process characteristics of the processing and assembly process of each part of the electromagnetic relay, combined with the working principle of the electromagnetic relay, determine the main influencing parameters affecting its pull-in voltage, and express the pull-in voltage as: U(z i ),i∈[1,2,3,…,n]; Among them, z i represents the i-th parameter, and n represents the total number of main influencing parameters affecting the pull-in voltage; Step 1.2: Consider the characteristics of relay production and assembly process, for each z i In terms of in, and Respectively represent the distribution mean and standard deviation of the i-th parameter; Step 1.3: To meet the conditions of step 1.2, it is necessary to determine two key positions in the armature stroke during the pull-in process, which are defined as point A and point B. Point A is the armature position in the released state, and point B is the armature position when the static contact spring and the dynamic contact spring are just separated during the pull-in process. The distribution of the two key positions affected by the parameters is expressed as: x A (z i )~N A (μ A ,σ A 2 ) and x B (z i )~N B (μ B ,σ B 2 ); Among them, μ A and μ B Represent the distribution means of point A and point B respectively, σ A and σ B They represent the distribution standard deviations of point A and point B respectively, and the pull-in voltage adjustment-free rate is defined as: ρ=(1-P A )·(1-P B ); Among them, P A and P B Represents the unqualified rate of batch products at point A and point B respectively; Step 2: Single factor analysis of electromagnetic suction force at key positions during the suction process and screening of key influencing factors: Step 2.1: Combine finite element simulation analysis to solve each main influencing parameter z i Probability density function of electromagnetic attraction distribution at each key position and The impact of F EMF Indicates the magnitude of electromagnetic attraction, F SF Indicates the size of the reaction force; Step 2.2: Analyze the influence of each parameter on suction and select the most important key influencing parameter z k ,k∈[1,2,3,…m], where z k represents the kth key influencing parameter, and m represents the total number of key influencing parameters; Step 3: Solve the suction reaction force distribution and calculate the matching failure rate under the single point position value in each key position distribution: Step 3.1: Use exponential sampling to obtain the sampling point value set of each key position and in, and denote the sampling points of point A and point B, respectively; α and β denote the uniformly changing value parameters of the exponential sampling of point A and point B, respectively; h∈{1,2,3,…,c} denotes the hth sampling point, and c denotes the total number of sampling points; Step 3.2: Use random sampling to select each and Multiple groups of z k Value combination, for z that follows a normal distribution k , define the sampling distance d(Z j ) and weight value w(Z j ): Among them, Z j represents the jth group of samples, Indicates the value of the kth key influencing parameter in the jth group of samples, and implements random sampling of key influencing parameter combinations according to their weight values; Step 3.3: Perform finite element simulation calculations on the electromagnetic attraction and reaction force for each key influencing parameter combination sample to obtain and The probability density function of the electromagnetic attraction and reaction force distribution under: in, and They represent the probability density functions of the electromagnetic attraction and reaction force at point A as the position distribution of point A and the distribution of key influencing parameters change, respectively. and They represent the probability density functions of the electromagnetic attraction and reaction force at point B as the position distribution of point B and the distribution of key influencing parameters, μ EMF () and σ EMF () represents the mean and standard deviation of the distribution of electromagnetic attraction force as the armature position changes, μ SF () and σ SF () represents the distribution mean and standard deviation of the reaction force as the armature position changes; Step 3.4: Calculate the failure rates of point A and point B as their respective values ​​x A and x B The function of the change g A (x A ) and g B (x B ), according to the existing sampling points, the unqualified rate at each sampling point is obtained by numerical integration: Step 4: Calculation of the failure rate of suction and reaction force matching under the influence of distribution of each key position: Step 4.1: Use the unqualified rate calculation results of the sampling points to establish g A (x A )’s fast calculation model: Among them, φ() represents the basis function, ε represents the Gaussian parameter, and r represents the distance. represents the hth sampling point, s h represents the interpolation weight of the hth sampling point; to solve the interpolation weight at each sampling point, solve the following linear equations: in, Represents the δth sampling point, from which the interpolation weight s of each known sampling point is calculated h , and then get the fast calculation model of the unqualified rate of point A: g A (x A )=V A (x A ); Step 4.2: Use the unqualified rate calculation results of the sampling points to establish g B (x B )’s fast calculation model: Among them, φ() represents the basis function, ε represents the Gaussian parameter, and r represents the distance. represents the hth sampling point, s h represents the interpolation weight of the hth sampling point; to solve the interpolation weight at each sampling point, solve the following linear equations: in, Represents the δth sampling point, from which the interpolation weight s of each known sampling point is calculated h , and then get the fast calculation model of the failure rate of point B: g B (x B )=V B (x B ); Step 4.3, based on step 4.2 and step 4.2, obtain the unqualified rate under the influence of the distribution of point A and point B: Step 5: Calculation of relay action voltage free adjustment rate under the comprehensive influence of distribution of key positions: According to the calculation formula of the pick-up voltage free adjustment rate, solve the pick-up voltage free adjustment rate of the electromagnetic relay.

2. The method for calculating the electromagnetic relay pull-in voltage adjustment-free rate based on pull-in and pull-out force coordination according to claim 1 is characterized in that In step 2.1, the values ​​of the simulation parameters are taken according to the principle of three times standard deviation:

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