CN103235866A - Monte Carlo simulation based method for predicting pass percent of pull-in voltages of contactors - Google Patents
Monte Carlo simulation based method for predicting pass percent of pull-in voltages of contactors Download PDFInfo
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Abstract
The invention discloses a Monte Carlo simulation based method for predicting the pass percent of pull-in voltages of contactors and belongs to the technical field of contactor detection. The method solves the problems that methods for detecting pull-in voltage parameters during design of existing contactors are high in design and test cost and long in design period due to the fact that samples are required to be machined and manufactured. According to the method, three kinds of design values, upper limits and lower limits of parameters which affect pull-in voltages are determined according to design documents of contactors, and a matrix laboratory (MATLAB) is used for producing N groups of parameter combinations through an independent identically distributed central limit theorem; then N groups of pull-in voltage characteristic parameters are obtained according to N groups of parameter combinations; distribution characteristics of pull-in voltage parameters are obtained; and finally, the pass percent of pull-in voltages of contactors is obtained through a Simpson principle according to distribution characteristics and pull-in voltage design parameters. The method is applicable to prediction and analysis of the pass percent of pull-in voltages of contactors in the design link of contactors, so that bases are provided for correction of design parameters for designers of contactors.
Description
Technical field
The invention belongs to the contactor field, relate to a kind of pick-up voltage qualification rate computing method, just be based on the contactor pick-up voltage yield analysis method of Monte Carlo simulation specifically.
Background technology
Pick-up voltage is the most important basic parameter of contactor, is the key factor that determines contactor electric current of make-and-break ability, can directly determine according to this parameter whether contactor is qualified." TB/T2767-2010 used for rolling stock D.C. contactor " 7.2.4 bar stipulates that clearly " contactor is the minimum voltage value of adhesive reliably, and this value is minimum operate voltage, is a same environment temperature, control supply voltage and the relevant value of control air pressure.Reliably adhesive of contactor when this voltage does not allow the phenomenon of secondary pick-up and adhesive repeatedly to occur.”。But in the product development of reality, because the complicacy of real mechanism, various parameters comprise that dimensional parameters, design parameter and adjustment parameter all can produce certain influence to pick-up voltage, therefore need determine to influence the principal element of this parameter in the design phase, and can be by certain methods qualification rate with regard to its pick-up voltage of analog computation before actual product is produced, thereby pass through the qualification rate of the range of tolerable variance control pick-up voltage of change part factor, make the productivity effect of contactor reach maximum.
In the design process of existing contactor, be after the design drawing of contactor is handled, go out a plurality of samples according to the design drawing processing and fabricating, adopt testing apparatus to carry out the test of pick-up voltage to a plurality of samples of making then, and then whether the parameter that can verify design is reasonable, if unreasonable, just needs revisions on drawings, then again the processing and fabricating sample, do experiment again, this has just caused design cycle prolongation and design and testing cost than higher.
Summary of the invention
The objective of the invention is to solve in the design process of existing contactor, need come out to exist the method that the parameter of pick-up voltage is tested design cycle length and processing and fabricating sample to cause designing the problem high with testing cost sample making according to design drawing, the invention provides a kind of pick-up voltage qualification rate based on the contactor pick-up voltage qualification rate Forecasting Methodology of Monte Carlo simulation.
The step of the contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of the present invention is as follows:
Step 1: obtain the influential dimensional parameters design load of the pick-up voltage of contactor, design parameter design load and adjust the range of tolerable variance of parameter designing value and each parameter according to design document and art work sheet, utilize MATLAB to produce the N group changes and meet normal distribution in range of tolerable variance dimensional parameters, design parameter and adjustment parameter three class parameter combinations according to independent identically distributed central limit theorem, Parameter N is the integer more than or equal to 1000;
Step 2: above N is organized three class parameter combinations successively as the input parameter of contactor pick-up voltage acquisition module, obtain N group pick-up voltage characterisitic parameter;
Step 3: the N group pick-up voltage parameter that obtains is analyzed, calculated and obtain probability density function, parameter expectation and mean square deviation, and then obtain N group pick-up voltage parameter distributions characteristic;
Step 4: require to determine pick-up voltage differentiation boundary according to the performance index in the design parameter of contactor, the N group pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate of utilizing the Simpson rule to obtain according to step 3.
Described contactor pick-up voltage acquisition module adopts software engineering to realize, the course of work of this module comprises and the following is step:
Steps A, contactor model calculating parameter initialization characterisitic parameter is set;
Step B, ask the current time magnetic linkage by previous moment coil voltage, electric current and magnetic linkage integration;
Step C, obtain coil current by coil flux linkage, armature displacement check table;
Step D, the coil current, the armature displacement check table that are obtained by step C obtain electromagnetic attraction;
Step e, calculate the mechanical spring counter-force by the armature displacement
f=k·x+c
d·v
K represents spring rate in the formula, c
dThe expression spring damping, x represents the armature displacement of spring, v represents the armature speed of spring;
Step F, employing fourth-order Runge-Kutta method are found the solution the mechanical motion differential equation group, and described mechanical motion differential equation group is:
Described Y represents armature displacement, speed column vector, expression formula be Y=(x, v)
TFollowing footnote n represents sampling instant;
t
nExpression n is time corresponding constantly;
G represents armature speed, acceleration column vector, and expression formula is
F represents electromagnetic attraction; M represents the armature quality;
G (t
n, Y
n) middle t
nAnd Y
nIndependent variable for above-mentioned expression formula;
H represents step-length computing time;
The calculation result data of step G, preservation step F is also extracted the pick-up voltage characterisitic parameter from described calculation result data, finish obtaining of pick-up voltage characterisitic parameter.
The described table of comparisons be the coil flux linkage of contactor about the bivariate table of coil current and armature displacement, this table of comparisons obtains by following step:
Step H, in UG software, set up the electromagnetic mechanism three-dimensional model according to the design drawing of the electromagnetic mechanism of contactor;
Step I, by software finite element software FLUX according to the three-dimensional model of electromagnetic mechanism, calculate the coil current, armature displacement, electromagnetic attraction and the magnetic linkage that obtain many windings tentaculum;
Step J, the coil current, armature displacement, electromagnetic attraction and the magnetic linkage parameter that obtain many windings tentaculum according to step I make up the table of comparisons.
Step I is described by the three-dimensional model of software finite element software FLUX according to electromagnetic mechanism, and the process of calculating the coil flux linkage, coil current and the armature displacement that obtain many windings tentaculum is:
Step I1, employing finite element software FLUX set up geometric model according to the three-dimensional model of electromagnetic mechanism, and this geometric model are divided finite element grid;
Step I2, the physical attribute of each finite element grid among the step I1 is set according to the real physical characteristics of electromagnetic mechanism;
Step I3, the geometric model that sets up physical attribute is carried out static characteristics emulation, the coil current values of the many groups of input and corresponding dimensional parameters during emulation, described current value is obtained divided by the coil resistance in the design parameter of contactor by voltage; Obtain armature displacement, electromagnetic attraction and the magnetic linkage of every group of coil current value and dimensional parameters correspondence by emulation.
The process that the N that utilizes the Simpson rule to obtain according to step 3 described in the step 4 organizes pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate is: the expectation and the variance that at first calculate N group pick-up voltage data, determine that according to existing pick-up voltage acceptability limit the Simpson rule calculates required upper lower limit value then, adopt described rule to divide in the upper lower limit value inner product at last and obtain contactor pick-up voltage qualification rate.
Method of the present invention is applied to the design link of contactor, can just carry out quantitative assessment and judgement to the rationality of its parameter in the design link, when shortening trial-produce period, reducing testing cost, improves reliability of products.
Method of the present invention was applicable in the contactor design phase carries out forecast analysis to the qualification rate of contactor pick-up voltage, and then the foundation of correction design parameter is provided for the deviser of contactor.
This method is based on Monte Carlo simulation and proposes, and Monte Carlo (Monte Carlo) simulation is a kind of by setting stochastic process, rise time sequence repeatedly, and the calculating parameter estimator, and then study the method for its distribution characteristics.The principle of Monte Carlo simulation method is when problem or object itself have probability characteristics, can produce sampling results with the method for computer simulation, according to the value of sample calculation statistic or parameter; Along with increasing of simulation number of times, the method that can be averaging by the estimated value to each time statistic or parameter obtains stablizing conclusion.
When each parameter of contactor known, owing to relate to machine,, finding the solution of magnetic coupling equation, be difficult to directly set up according to the tolerance of each parameter the mathematical models of contactor batch products pick-up voltage qualification rate, but can (comprise dimensional parameters at each parameter of contactor, design parameter, tuning parameter) produces N numerical value that in range of tolerable variance, changes and meet normal distribution at random, from these parameters, extract a numerical value then at every turn and be used for calculating pick-up voltage, so carry out obtaining for N time the pick-up voltage of N contactor, be equivalent to produce and assembled N contactor and recorded pick-up voltage, then this N pick-up voltage is carried out statistical study, obtain its regularity of distribution and parameter, calculate its pick-up voltage qualification rate according to discrimination standard at last, N is more big, and its qualification rate that calculates more approaches with actual conditions.This computation process has been used the thought of Monte Carlo simulation.
Method of the present invention can be in the design phase of contactor, the dimensional parameters, design parameter and the adjustment parameter tolerances scope that provide according to art work sheet, utilize the approximate contactor pick-up voltage qualification rate that obtains of thought of Monte Carlo Analogue Method, can allow manufacturing enterprise that the manufacturing of contactor is had the assurance of an overall situation, lay the foundation for further improving the contactor qualification rate simultaneously.
Description of drawings
Fig. 1 is the process flow diagram of the method for the invention; Fig. 2 is the principle of work synoptic diagram of described contactor pick-up voltage acquisition module; Fig. 3 is certain model contactor construction synoptic diagram, and wherein 1 is shell, and 2 is connecting rod, and 3 is coil, and 4 is armature, and 5 is reaction spring, and 6 is iron core, and 7 is yoke, and 8 is rebound spring, and 9 is moving contact, and 10 is static contact; Fig. 4 is certain model contactor moving contact pick-up voltage distribution curve and differentiates boundary that wherein the vertical line perpendicular to horizontal ordinate is the differentiation boundary.Fig. 5 is that the present invention calculates the principle schematic that obtains the pick-up voltage qualification rate.
Embodiment
Embodiment one, referring to Fig. 1 present embodiment is described.The described a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of present embodiment, this method comprises the steps:
Step 1: obtain the influential dimensional parameters design load of the pick-up voltage of contactor, design parameter design load and adjust the range of tolerable variance of parameter designing value and each parameter according to design document and art work sheet, utilize MATLAB to produce the N group changes and meet normal distribution in range of tolerable variance dimensional parameters, design parameter and adjustment parameter three class parameter combinations according to independent identically distributed central limit theorem, Parameter N is the integer more than or equal to 1000;
Step 2: above N is organized three class parameter combinations successively as the input parameter of contactor pick-up voltage acquisition module, obtain N group pick-up voltage characterisitic parameter;
Step 3: the N group pick-up voltage parameter that obtains is analyzed, calculated and obtain probability density function, parameter expectation and mean square deviation, and then obtain N group pick-up voltage parameter distributions characteristic;
Step 4: require to determine pick-up voltage differentiation boundary according to the performance index in the design parameter of contactor, the N group pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate of utilizing the Simpson rule to obtain according to step 3.
The described independent identically distributed central limit theorem of step 1, namely row dimension one Edward Lindberg theorem is a kind of special shape of the central limit theorem in the statistics, has than widespread use in practice.
The specific implementation method of above-mentioned independent identically distributed central limit theorem in MATLAB is in MATLAB, by limiting the mode of expectation value and variance, adopt function of random variable Random to generate N group number, then this N group numerical value directly satisfies row dimension one Edward Lindberg theorem.Wherein, expectation value is the design centre value, and variance is then determined by the range of tolerable variance of design.
Embodiment two, referring to Fig. 2 present embodiment is described.The difference of the described a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of present embodiment and embodiment one is, described contactor pick-up voltage acquisition module adopts software engineering to realize, the course of work of this module comprises and the following is step:
Steps A, contactor model calculating parameter initialization characterisitic parameter is set;
Step B, ask the current time magnetic linkage by previous moment coil voltage, electric current and magnetic linkage integration;
Step C, obtain coil current by coil flux linkage, armature displacement check table;
Step D, the coil current, the armature displacement check table that are obtained by step C obtain electromagnetic attraction;
Step e, calculate the mechanical spring counter-force by the armature displacement
f=k·x+c
d·v
K represents spring rate in the formula, c
dThe expression spring damping, x represents the armature displacement of spring, v represents the armature speed of spring;
Step F, employing fourth-order Runge-Kutta method are found the solution the mechanical motion differential equation group, and described mechanical motion differential equation group is:
Described Y represents armature displacement, speed column vector, expression formula be Y=(x, v)
TFollowing footnote n represents sampling instant;
t
nExpression n is time corresponding constantly;
G represents armature speed, acceleration column vector, and expression formula is
F represents electromagnetic attraction; M represents the armature quality;
G (t
n, Y
n) middle t
nAnd Y
nIndependent variable for above-mentioned expression formula;
H represents step-length computing time;
The calculation result data of step G, preservation step F is also extracted the pick-up voltage characterisitic parameter from described calculation result data, finish obtaining of pick-up voltage characterisitic parameter.
The difference of the described a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of embodiment three, present embodiment and embodiment two is, the described table of comparisons be the coil flux linkage of contactor about the bivariate table of coil current and armature displacement, this table of comparisons obtains by following step:
Step H, in UG software, set up the electromagnetic mechanism three-dimensional model according to the design drawing of the electromagnetic mechanism of contactor;
Step I, by software finite element software FLUX according to the three-dimensional model of electromagnetic mechanism, calculate the coil current, armature displacement, electromagnetic attraction and the magnetic linkage that obtain many windings tentaculum;
Step J, the coil current, armature displacement, electromagnetic attraction and the magnetic linkage parameter that obtain many windings tentaculum according to step I make up the table of comparisons.
The difference of the described a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of embodiment four, present embodiment and embodiment three is, step I is described by the three-dimensional model of software finite element software FLUX according to electromagnetic mechanism, and the process of calculating the coil flux linkage, coil current and the armature displacement that obtain many windings tentaculum is:
Step I1, employing finite element software FLUX set up geometric model according to the three-dimensional model of electromagnetic mechanism, and this geometric model are divided finite element grid;
Step I2, the physical attribute of each finite element grid among the step I1 is set according to the real physical characteristics of electromagnetic mechanism;
Step I3, the geometric model that sets up physical attribute is carried out static characteristics emulation, the coil current values of the many groups of input and corresponding dimensional parameters during emulation, described current value is obtained divided by the coil resistance in the design parameter of contactor by voltage; Obtain armature displacement, electromagnetic attraction and the magnetic linkage of every group of coil current value and dimensional parameters correspondence by emulation.
Embodiment five, the difference of the described a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of present embodiment and embodiment one is, the process that the N that utilizes the Simpson rule to obtain according to step 3 described in the step 4 organizes pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate is: the expectation and the variance that at first calculate N group pick-up voltage data, determine that according to existing pick-up voltage acceptability limit the Simpson rule calculates required upper lower limit value then, adopt described rule to divide in the upper lower limit value inner product at last and obtain contactor pick-up voltage qualification rate.
Illustrate that referring to Fig. 5 present embodiment calculating obtains the principle of pick-up voltage qualification rate, among Fig. 5, curve is represented the pick-up voltage family curve, and horizontal ordinate is represented pick-up voltage, and ordinate is represented probability density, and vertical curve is represented boundary, then according to formula
Can obtain the probability of pick-up voltage.
Embodiment six, present embodiment are concrete cases of a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation of the present invention, and in the present case, described step is as follows:
Step 1: the parameter ginseng that obtains dimensional parameters design load, the design parameter design load of contactor and adjust the range of tolerable variance of parameter designing value and each parameter according to the design document of certain model contactor construction shown in Figure 3 and art work sheet is shown in Table 1:
Table 1
| Code name | Meaning | Scope | Design load |
| x1 | Coil resistance (Ω) | 5.50±0.55 | 5.50 |
| x2 | Clearance between open contacts (mm) | 1.30±0.13 | 1.3 |
| x3 | Armature travel (mm) | 2.20±0.06 | 2.20 |
| x4 | Rebound spring decrement (mm) | 0.45±0.03 | 0.45 |
| x5 | Reaction spring decrement (mm) | 8.54±0.10 | 8.54 |
| x6 | Rebound spring rigidity (kN/m) | 16.27±0.30 | 16.27 |
| x7 | Reaction spring rigidity (kN/m) | 0.250±0.019 | 0.250 |
| x8 | Moving contact quality (g) | 7.74±0.74 | 7.74 |
| x9 | Armature quality (g) | 8.88±0.18 | 8.88 |
| x10 | Contact colliding stiffness (10 9N/m） | 4.20±0.84 | 4.20 |
| x11 | The contact collision punishment degree of depth (mm) | 0.10±0.01 | 0.10 |
| x12 | Contact collisional damping (10 4Ns/m） | 3.5±0.7 | 3.5 |
Utilize MATLAB to produce the N group changes and meet normal distribution in range of tolerable variance dimensional parameters, design parameter and adjustment parameter three class parameter combinations according to independent identically distributed central limit theorem, Parameter N is the integer more than or equal to 1000;
Step 2: above N is organized three class parameter combinations successively as the input parameter of contactor pick-up voltage acquisition module, obtain N group pick-up voltage characterisitic parameter;
Step 3: the N group pick-up voltage parameter that obtains is analyzed, calculated and obtain probability density function, parameter expectation and mean square deviation, and then obtain N group pick-up voltage parameter distributions characteristic N (3.4926,0.04);
Step 4: require to determine that according to the performance index in the design parameter of contactor pick-up voltage differentiates boundary for being specification product less than 4V, the N group pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate of utilizing the Simpson rule to obtain according to step 3, as shown in Figure 4, curve is that contact is inhaled and the voltage distribution curve among the figure, the vertical line vertical with horizontal ordinate is that voltage is the differentiation boundary of 4V, and utilizing the Simpson rule to calculate contactor pick-up voltage qualification rate is 86.9%.
Claims (5)
1. contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation, it is characterized in that: step is as follows:
Step 1: obtain the influential dimensional parameters design load of the pick-up voltage of contactor, design parameter design load and adjust the range of tolerable variance of parameter designing value and each parameter according to design document and art work sheet, utilize MATLAB to produce the N group changes and meet normal distribution in range of tolerable variance dimensional parameters, design parameter and adjustment parameter three class parameter combinations according to independent identically distributed central limit theorem, Parameter N is the integer more than or equal to 1000;
Step 2: above N is organized three class parameter combinations successively as the input parameter of contactor pick-up voltage acquisition module, obtain N group pick-up voltage characterisitic parameter;
Step 3: the N group pick-up voltage parameter that obtains is analyzed, calculated and obtain probability density function, parameter expectation and mean square deviation, and then obtain N group pick-up voltage parameter distributions characteristic;
Step 4: require to determine pick-up voltage differentiation boundary according to the performance index in the design parameter of contactor, the N group pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate of utilizing the Simpson rule to obtain according to step 3.
2. a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation according to claim 1 is characterized in that: described contactor pick-up voltage acquisition module adopts software engineering to realize, the course of work of this module comprises and the following is step:
Steps A, contactor model calculating parameter initialization characterisitic parameter is set;
Step B, ask the current time magnetic linkage by previous moment coil voltage, electric current and magnetic linkage integration;
Step C, obtain coil current by coil flux linkage, armature displacement check table;
Step D, the coil current, the armature displacement check table that are obtained by step C obtain electromagnetic attraction;
Step e, calculate the mechanical spring counter-force by the armature displacement
f=k·x+c
d·v
K represents spring rate in the formula, c
dThe expression spring damping, x represents the armature displacement of spring, v represents the armature speed of spring;
Step F, employing fourth-order Runge-Kutta method are found the solution the mechanical motion differential equation group, and described mechanical motion differential equation group is:
Described Y represents armature displacement, speed column vector, expression formula be Y=(x, v)
TFollowing footnote n represents sampling instant;
t
nExpression n is time corresponding constantly;
G represents armature speed, acceleration column vector, and expression formula is
F represents electromagnetic attraction; M represents the armature quality;
G (t
n, Y
n) middle t
nAnd Y
nIndependent variable for above-mentioned expression formula;
H represents step-length computing time;
The calculation result data of step G, preservation step F is also extracted the pick-up voltage characterisitic parameter from described calculation result data, finish obtaining of pick-up voltage characterisitic parameter.
3. a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation according to claim 2, it is characterized in that: the described table of comparisons be the coil flux linkage of contactor about the bivariate table of coil current and armature displacement, this table of comparisons obtains by following step:
Step H, in UG software, set up the electromagnetic mechanism three-dimensional model according to the design drawing of the electromagnetic mechanism of contactor;
Step I, by software finite element software FLUX according to the three-dimensional model of electromagnetic mechanism, calculate the coil current, armature displacement, electromagnetic attraction and the magnetic linkage that obtain many windings tentaculum;
Step J, the coil current, armature displacement, electromagnetic attraction and the magnetic linkage parameter that obtain many windings tentaculum according to step I make up the table of comparisons.
4. a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation according to claim 3, it is characterized in that: step I is described by the three-dimensional model of software finite element software FLUX according to electromagnetic mechanism, and the process of calculating the coil flux linkage, coil current and the armature displacement that obtain many windings tentaculum is
Step I1, employing finite element software FLUX set up geometric model according to the three-dimensional model of electromagnetic mechanism, and this geometric model are divided finite element grid;
Step I2, the physical attribute of each finite element grid among the step I1 is set according to the real physical characteristics of electromagnetic mechanism;
Step I3, the geometric model that sets up physical attribute is carried out static characteristics emulation, the coil current values of the many groups of input and corresponding dimensional parameters during emulation, described current value is obtained divided by the coil resistance in the design parameter of contactor by voltage; Obtain armature displacement, electromagnetic attraction and the magnetic linkage of every group of coil current value and dimensional parameters correspondence by emulation.
5. a kind of contactor pick-up voltage qualification rate Forecasting Methodology based on Monte Carlo simulation according to claim 1, it is characterized in that: the process that the N that utilizes the Simpson rule to obtain according to step 3 described in the step 4 organizes pick-up voltage parameter distributions property calculation contactor pick-up voltage qualification rate is: the expectation and the variance that at first calculate N group pick-up voltage data, determine that according to existing pick-up voltage acceptability limit the Simpson rule calculates required upper lower limit value then, adopt described rule to divide in the upper lower limit value inner product at last and obtain contactor pick-up voltage qualification rate.
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