CN103413185A - Optimal arrangement method of coal mining machine rocker arm vibration sensors - Google Patents

Abstract

The invention discloses an optimal arrangement method of coal mining machine rocker arm vibration sensors. The optimal arrangement method of the coal mining machine rocker arm vibration sensors comprises the following steps that firstly, a finite element model of a coal mining machine rocker arm shell body is established; secondly, regional division of optimal arrangement points is conducted based on the power flow method; thirdly, monitoring points of the sensor are selected primarily; fourthly, optimal calculation is conducted on the number of the sensors and the specific monitoring points according to the particle swarm optimization algorithm and based on the modal assurance criterion, and therefore an optimal arrangement result of the vibration sensors is obtained. The optimal arrangement method of the coal mining machine rocker arm vibration sensors has universality. According to the optimal arrangement method of the coal mining machine rocker arm vibration sensors, on one hand, the effectiveness of each sensor measurement signal is guaranteed and on the other hand, the purpose that the modal vector of each monitoring point has a large space intersection angle is guaranteed. The optimal arrangement method of the coal mining machine rocker arm vibration sensors can meet the requirements for on-line monitoring and fault diagnosis of a coal mining machine rocker arm.

Description

A kind of rocker arm of coal mining machine vibration transducer optimization placement method

Technical field

The present invention relates to a kind of rocker arm of coal mining machine vibration transducer optimization placement method, especially a kind of rocking arm vibration transducer optimization placement method that adopts power stream and particle swarm optimization algorithm to combine of combining, be mainly used in coalcutter condition monitoring and fault diagnosis field.

Background technology

Coalcutter, as realizing that coal mine machinery melts the visual plant of adopting, is a large-scale complicated system that integrates mechanical, electric and hydraulic pressure, and the interruption of whole coal work appears causing in its fault, causes huge economic loss.The temperature sensor that detects Rocker arm-motor on existing coalcutter, only is equipped with, there is no the vibration transducer of monitoring rocking arm vibration, the duty of monitoring rocking arm from the angle of vibration is a kind of effective approach, the method for arranging of existing rocking arm vibration transducer is all near by feat of experience, sensor being positioned over to bearing seat, and reckons without the optimization problem that single-sensor collects signal between the validity of signal and a plurality of sensor.

The power stream description be the bang path of vibrational energy in structure, when vibration is transmitted on research one continuous structure, by the independent measurement transport function, be only to can not determine the bang path of vibration in structure.Use Power Flow to come the vibration transfer path in description scheme to consider simultaneously structural power and two values of speed, thereby also considered the impedance operator of structure simultaneously.In analytical structure, at first the distribution character of power stream will obtain the stressed and speed on each node according to the mechanical characteristic of structure, then according to the definition of power stream, obtain the power stream on each node, by the stream of the power in structure, just can know the strong and weak situation of vibrating in structure, thereby learn the layout area of sensor.

With modal assurance criterion, determine that the sensor layout points does not need to consider mass matrix and the stiffness matrix of structure, and can estimate very how well the angle between moments of vibration.The natural mode of vibration of each node of structure is mutually orthogonal from theory, but due to the degree of freedom of the degree of freedom in actual measurement much smaller than structural model, also be subject in addition the impact of measuring accuracy and the neighbourhood noise of sensor, the actual modal vector recorded is difficult to guarantee its orthogonality, sometimes even there will be and because the space angle of cut between vector is too small, lose important modal information.Thereby to guarantee that at first the modal vector of each measuring point has the larger space angle of cut, retains the characteristic of master mould as far as possible aspect the choosing of sensor layout points.Then one group of measuring point of primary election adds measuring point in this group survey shop, according to modal assurance criterion, making that measuring point of modal assurance criterion MAC matrix off-diagonal element minimum is the measuring point finally added, and knows that and so forth choosing satisfied detection counts.But use modal assurance criterion can't determine the position and the position that adds measuring point of initial measuring point.

Particle swarm optimization algorithm (PSO) is a kind of random class optimized algorithm based on global search, but the PSO algorithm is initialization a group particle in analytic space at first, each particle represents a potential optimum solution of extremal optimization problem, with position, speed and three these particle characteristicses of index expression of fitness value, fitness value is calculated by fitness function, and the quality of its value means the quality of particle.Up to the present, the analytical approach of PSO is system not very also, how with effective mathematical tool to operation action, convergence, speed of convergence, the parameter of PSO select, parameter robustness and computational complexity analysis need further research.

Summary of the invention

The present invention considers quantity and the position thereof of sensor, provides a kind of the associating to use power flow theory and modal assurance criterion the rocker arm of coal mining machine vibration transducer optimization placement method that uses particle swarm optimization algorithm to be in optimized selection sensor.Power stream by the housing to rocking arm transmits the optimum layout zone that analysis can draw sensor, in conjunction with modal assurance criterion, make the quantity of sensor and position further be optimized, and can guarantee the larger space angle of cut between the vibration signal measured of the sensor of finally selecting.

Technical solution of the present invention is:

A kind of rocker arm of coal mining machine vibration transducer optimization placement method comprises the following steps:

(1) set up the finite element model of rocking arm housing;

(2) but based on the layout area of Power Flow, divide;

21) use finite element analysis software to carry out humorous response analysis to the rocking arm housing, obtain the stressed of each unit;

22) extract the stressed of each unit, calculate power flow point cloth in the rocking arm housing according to plate shell power flow theory;

23) according to the power flowmeter, calculate result, but mark off the layout area of vibration transducer;

(3) based on number of sensors and the position optimization of particle cluster algorithm

31) according to step 21) but the sensor layout area analyzed is chosen m monitoring point as initial monitoring point;

32) use finite element analysis software to carry out model analysis to the rocking arm housing, obtain De Ge rank, m monitoring point Mode Shape, and resulting each first order mode is formed to the modal vector matrix;

33) according to modal assurance criterion MAC, from m monitoring point, choosing the monitoring point of n monitoring point as the rocking arm housing.

Described method, step 21) in humorous response analysis, can regard the power that other axle applies housing as a kind of prestress, after housing is first had to prestressed static analysis, more prestressed humorous response analysis be arranged.

Described method, step 32) the modal vector matrix dimension formed in is determined according to the expectation number of sensors.

Described method, step 33) according to modal assurance criterion, optimize the Sensor monitoring point, using MAC matrix off-diagonal element maximal value as optimization object, the measuring point number of take is particle, the application particle swarm optimization algorithm carries out the sensing station optimizing.

Described method, the power stream expression formula of plate shell unit transverse vibration is as follows:

$\left\{\begin{array}{c}{P}_{x1}=<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_{y1}=<Q_y\stackrel{\&CenterDot;}{w}{>}_t+<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t-<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _X1For the lateral direction power stream in x direction cross section, P _Y1For _yThe lateral direction power stream in direction cross section, w is the displacement of the z direction of unit, Q _x, Q _yBe respectively the shearing force of unit x direction and y direction, M _x, M _yBe respectively the moment of flexure of unit x direction and y direction, θ _x, θ _yBe respectively the x of unit, the angular displacement of y direction;

The power stream expression formula of plate shell unit extensional vibration is as follows:

$\left\{\begin{array}{c}{P}_{x2}=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t\\ P_{y2}=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t\end{array}\right.$

In formula, P _X2For vertical power stream in x direction cross section, P _Y2For vertical power stream in y direction cross section, u, v are respectively the x of unit and the displacement of y direction, N _x, N _yAnd N _Xy=N _YxFor the suffered film power in unit;

Plate shell unit global vibration power stream expression formula is:

$\left\{\begin{array}{c}{P}_x=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t+<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_y=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t+<Q_y\stackrel{\&CenterDot;}{w}{>}_t-<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t+<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _xFor the total power flow in x direction cross section, P _yFor the total power flow in y direction cross section,

But by Analysis of Power Flow rocking arm housing sensor layout area, at first in the ANSYS preprocessor, program and extract the stress of each cell node, then respectively according to plate shell unit lateral direction power stream, vertical power stream and total power flow factorization, calculate the power stream in housing, finally draw power stream cloud atlas and polar plot.

Described method, with the sensor of particle swarm optimization algorithm to the rocking arm housing, be optimized, at first to set up the finite element model of housing, then housing is carried out to model analysis, but in the sensor layout area that the power flowmeter is calculated, sensor is numbered, result according to modal calculation, list the displacement modes of all numbered nodes and form modal vector, according to actual conditions and requirement, choose at random and select m monitoring point as initial monitoring point, according to modal assurance criterion, calculate the MAC matrix, then with particle swarm optimization algorithm, be optimized, finally draw the sensor combinations of an optimum n monitoring point,

The MAC matrix representation is:

${\mathrm{MAC}}_{\mathrm{ij}}=\frac{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_j)}{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_i)\&CenterDot;({\mathrm{\&phi;}}_j^T\&CenterDot;{\mathrm{\&phi;}}_j)}$

In formula, φ _j, φ _jBe respectively the modal vector on i rank and j rank; MAC matrix off-diagonal element MAC _Ij(i ≠ j) should be between 0 and 1, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 1 o'clock, show that the angle of cut between two modal vector is 0, and now two modal vector can not be differentiated, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 0 o'clock, show that two modal vector are mutually orthogonal, and now two modal vector will be easy to identification, in addition, and MAC matrix off-diagonal element MAC _Ij(i ≠ j) be less than two modal vector of 0.25 expression more easily to differentiate therefore, in the sensor optimization placement process, should make MAC matrix nondiagonal element minimum as far as possible.

Integrated use power flow theory of the present invention and modal assurance criterion are optimized layout to coal mining rocking arm vibration transducer, at first use Power Flow to analyze the optimum layout zone of housing upper sensor, then according to modal assurance criterion, use particle swarm optimization algorithm to be optimized quantity and the position of sensor.The method has solved the sensor initial option point problem of modal assurance criterion on the one hand, but has overcome on the other hand the sensor layout area problems of too of simple utilization power flow method.The vibration signal that the sensor group of utilization the method optimization records can comprise the vibration information of rocking arm all sidedly, is conducive to rocking arm is carried out to status monitoring and fault diagnosis.

The accompanying drawing explanation

Fig. 1 is schematic flow sheet of the present invention.

Fig. 2 is plate and shell structure transverse vibration element stress.

Fig. 3 is plate and shell structure extensional vibration element stress.

Fig. 4 is the process flow diagram that particle group optimizing is selected the sensor layout points.

Fig. 5 is the numbering of rocker arm of coal mining machine front housing upper sensor.

Fig. 6 is the numbering of rocker arm of coal mining machine back housing upper sensor.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in detail.

As shown in Figure 1, a kind of sensor optimization method for arranging of monitoring the rocker arm of coal mining machine vibration signal of the present invention comprises following step:

(1) foundation of rocker arm of coal mining machine Shell Finite Element Method model, applying three-dimensional modeling software (SolidWorks, Pro/E, UG etc.) is set up three-dimensional model according to the physical size of rocking arm particularly, then imports to the finite element model of setting up the rocking arm housing in finite element analysis software ANSYS;

(2) but based on the sensor layout area of Power Flow, divide, in finite element analysis software ANSYS, the rocking arm housing is carried out to humorous response analysis particularly, then use post processor to extract the stressed of each unit, according to the theoretical formula of power stream, write calculation procedure, calculate power stream cloud atlas and the polar plot of rocking arm housing, finally according to power, flow the optimum layout zone of cloud atlas and polar plot analyte sensors;

(3) based on number of sensors and the position optimization of particle cluster algorithm, but the sensor layout area gone out according to Analysis of Power Flow particularly, choose m monitoring point as initial monitoring point, then use finite element analysis software ANSYS to carry out model analysis to the rocking arm housing, obtain De Ge rank, this m monitoring point Mode Shape, and resulting each first order mode is formed to the modal vector matrix, finally according to modal assurance criterion (MAC), from m monitoring point, choosing the monitoring point of n monitoring point as the rocking arm housing.

Because the kinematic train of rocker arm of coal mining machine is stage-geared, excitation frequency on every axle can be regarded the meshing frequency of gear as, excitation frequency on every axle is unequal under normal conditions, in order to simulate better the stressing conditions of rocking arm, before humorous response analysis, also can do statics Analysis to the rocking arm housing, and then do prestressed humorous response analysis.

As shown in Figure 2, the power of plate shell unit transverse vibration stream expression formula is as follows:

$\left\{\begin{array}{c}{P}_{x1}=<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_{y1}=<Q_y\stackrel{\&CenterDot;}{w}{>}_t+<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t-<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _X1For the lateral direction power stream in x direction cross section, P _Y1For the lateral direction power stream in y direction cross section, w is the displacement of the z direction of unit, Q _x, Q _yBe respectively the shearing force of unit x direction and y direction, M _x, M _yBe respectively the moment of flexure of unit x direction and y direction, θ _x, θ _yBe respectively the x of unit, the angular displacement of y direction.

As shown in Figure 3, the power of plate shell unit extensional vibration stream expression formula is as follows:

$\left\{\begin{array}{c}{P}_{x2}=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t\\ P_{y2}=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t\end{array}\right.$

In formula, P _X2For vertical power stream in x direction cross section, P _Y2For vertical power stream in y direction cross section, u, v are respectively the x of unit and the displacement of y direction, N _x, N _yAnd N _Xy=N _YxFor the suffered film power in unit.

Plate shell unit global vibration power stream expression formula is:

$\left\{\begin{array}{c}{P}_x=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t+<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_y=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t+<Q_y\stackrel{\&CenterDot;}{w}{>}_t-<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t+<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _xFor the total power flow in x direction cross section, P _yFor the total power flow in y direction cross section,

But by Analysis of Power Flow rocking arm housing sensor layout area, at first in the ANSYS preprocessor, program and extract the stress of each cell node, then respectively according to plate shell unit lateral direction power stream, vertical power stream and total power flow factorization, calculate the power stream in housing, finally draw power stream cloud atlas and polar plot.But the layout area according to power flow chart and polar plot analyte sensors.

As shown in Figure 4, with the sensor of particle swarm optimization algorithm to the rocking arm housing, be optimized, at first to set up the finite element model of housing, then housing is carried out to model analysis, but in the sensor layout area that the power flowmeter is calculated, sensor being numbered, is the sensor number at front and the back side on the rocking arm housing as shown in Figure 5 and Figure 6.Result according to modal calculation, list the displacement modes of all numbered nodes and form modal vector, according to actual conditions and requirement, choose at random and select m monitoring point as initial monitoring point, according to modal assurance criterion, calculate the MAC matrix, then with particle swarm optimization algorithm, be optimized, finally draw the sensor combinations of an optimum n monitoring point.

The MAC matrix representation is:

${\mathrm{MAC}}_{\mathrm{ij}}=\frac{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_j)}{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_i)\&CenterDot;({\mathrm{\&phi;}}_j^T\&CenterDot;{\mathrm{\&phi;}}_j)}$

In formula, φ _j, φ _jBe respectively the modal vector on i rank and j rank.MAC matrix off-diagonal element MAC _Ij(i ≠ j) should be between 0 and 1, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 1 o'clock, show that the angle of cut between two modal vector is 0, and now two modal vector can not be differentiated, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 0 o'clock, show that two modal vector are mutually orthogonal, and now two modal vector will be easy to identification, in addition, and MAC matrix off-diagonal element MAC _Ij(i ≠ j) be less than two modal vector of 0.25 expression more easily to differentiate therefore, in the sensor optimization placement process, should make MAC matrix nondiagonal element minimum as far as possible.

Before the modal calculation of housing, must set and solve collection.At first choose the boundary condition setting, choose the alternative manner of suitable eigenwert and proper vector, the frequency exponent number solved is set, and storage and printing model frequency and Mode Shape.

The power stream description be the bang path of vibrational energy in the plate shell, the large place of power stream is exactly to vibrate violent place, but is the layout area of sensor.According to the result of model analysis, extract the displacement modes of respective nodes, according to field requirement, choose arbitrarily n monitoring point, and calculate the MAC matrix of this n monitoring point modal vector, make the respective sets monitoring point of MAC matrix off-diagonal element minimum be the Sensor monitoring point of choosing.

Each Sensor monitoring point can be regarded the particle of search volume as, the MAC matrix can be regarded fitness function as, with MATLAB software, calculate according to the ultimate principle programming of particle swarm optimization algorithm, in order to make particle swarm optimization algorithm that better speed of convergence be arranged, also can apply band inertia weight particle swarm optimization algorithm or band converging factor particle swarm optimization algorithm.

By above method, just can obtain the optimum layout scheme of vibration transducer on rocker arm of coal mining machine, by the least possible sensor, just can monitor the vibration signal of all gears of rocking arm and bearing through preferred sensor arrangement.Through preferred sensor arrangement, not only have the economy of monitoring, and be conducive to further signal analysis and processing, reduce the difficulty that signal is processed.

Should be understood that, for those of ordinary skills, can be improved according to the above description or conversion, and all these improve and conversion all should belong to the protection domain of claims of the present invention.

Claims (6)

1. a rocker arm of coal mining machine vibration transducer optimization placement method, is characterized in that, comprises the following steps:

(1) set up the finite element model of rocking arm housing;

(2) but based on the layout area of Power Flow, divide;

21) use finite element analysis software to carry out humorous response analysis to the rocking arm housing, obtain the stressed of each unit;

22) extract the stressed of each unit, calculate power flow point cloth in the rocking arm housing according to plate shell power flow theory;

23) according to the power flowmeter, calculate result, but mark off the layout area of vibration transducer;

(3) based on number of sensors and the position optimization of particle cluster algorithm

31) according to step 21) but the sensor layout area analyzed is chosen m monitoring point as initial monitoring point;

32) use finite element analysis software to carry out model analysis to the rocking arm housing, obtain De Ge rank, m monitoring point Mode Shape, and resulting each first order mode is formed to the modal vector matrix;

33) according to modal assurance criterion MAC, from m monitoring point, choosing the monitoring point of n monitoring point as the rocking arm housing.

2. method according to claim 1, it is characterized in that, step 21) in humorous response analysis, can regard the power that other axle applies housing as a kind of prestress, after housing is first had to prestressed static analysis, more prestressed humorous response analysis be arranged.

3. method according to claim 1, is characterized in that step 32) in the modal vector matrix dimension that forms according to the expectation number of sensors, determine.

4. method according to claim 1, it is characterized in that step 33) according to modal assurance criterion, optimize the Sensor monitoring point, using MAC matrix off-diagonal element maximal value as optimization object, the measuring point number of take is particle, and the application particle swarm optimization algorithm carries out the sensing station optimizing.

5. method according to claim 1, is characterized in that, the power stream expression formula of plate shell unit transverse vibration is as follows:

$\left\{\begin{array}{c}{P}_{x1}=<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_{y1}=<Q_y\stackrel{\&CenterDot;}{w}{>}_t+<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t-<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _X1For the lateral direction power stream in x direction cross section, P _Y1For the lateral direction power stream in y direction cross section, w is the displacement of the z direction of unit, Q _x, Q _yBe respectively the shearing force of unit x direction and y direction, M _x, M _yBe respectively the moment of flexure of unit x direction and y direction, θ _x, θ _yBe respectively the x of unit, the angular displacement of y direction;

The power stream expression formula of plate shell unit extensional vibration is as follows:

$\left\{\begin{array}{c}{P}_{x2}=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t\\ P_{y2}=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t\end{array}\right.$

In formula, P _X2For vertical power stream in x direction cross section, P _Y2For vertical power stream in y direction cross section, u, v are respectively the x of unit and the displacement of y direction, N _x, N _yAnd N _Xy=N _YxFor the suffered film power in unit;

Plate shell unit global vibration power stream expression formula is:

$\left\{\begin{array}{c}{P}_x=<N_x\stackrel{\&CenterDot;}{u}{>}_t+<N_{\mathrm{xy}}\stackrel{\&CenterDot;}{v}{>}_t+<Q_x\stackrel{\&CenterDot;}{w}{>}_t+<M_x{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t-<M_{\mathrm{xy}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t\\ P_y=<N_y\stackrel{\&CenterDot;}{v}{>}_t+<N_{\mathrm{yx}}\stackrel{\&CenterDot;}{u}{>}_t+<Q_y\stackrel{\&CenterDot;}{w}{>}_t-<M_y{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_x{>}_t+<M_{\mathrm{yx}}{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_y{>}_t\end{array}\right.$

In formula, P _xFor the total power flow in x direction cross section, P _yFor the total power flow in y direction cross section,

But by Analysis of Power Flow rocking arm housing sensor layout area, at first in the ANSYS preprocessor, program and extract the stress of each cell node, then respectively according to plate shell unit lateral direction power stream, vertical power stream and total power flow factorization, calculate the power stream in housing, finally draw power stream cloud atlas and polar plot.

6. method according to claim 1, it is characterized in that, with the sensor of particle swarm optimization algorithm to the rocking arm housing, be optimized, at first to set up the finite element model of housing, then housing is carried out to model analysis, but in the sensor layout area that the power flowmeter is calculated, sensor is numbered, result according to modal calculation, list the displacement modes of all numbered nodes and form modal vector, according to actual conditions and requirement, choose at random and select m monitoring point as initial monitoring point, according to modal assurance criterion, calculate the MAC matrix, then with particle swarm optimization algorithm, be optimized, finally draw the sensor combinations of an optimum n monitoring point,

The MAC matrix representation is:

${\mathrm{MAC}}_{\mathrm{ij}}=\frac{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_j)}{({\mathrm{\&phi;}}_i^T\&CenterDot;{\mathrm{\&phi;}}_i)\&CenterDot;({\mathrm{\&phi;}}_j^T\&CenterDot;{\mathrm{\&phi;}}_j)}$

In formula, φ _j, φ _jBe respectively the modal vector on i rank and j rank; MAC matrix off-diagonal element MAC _Ij(i ≠ j) should be between 0 and 1, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 1 o'clock, show that the angle of cut between two modal vector is 0, and now two modal vector can not be differentiated, as MAC matrix off-diagonal element MAC _Ij(i ≠ j) equal at 0 o'clock, show that two modal vector are mutually orthogonal, and now two modal vector will be easy to identification, in addition, and MAC matrix off-diagonal element MAC _Ij(i ≠ j) be less than two modal vector of 0.25 expression more easily to differentiate therefore, in the sensor optimization placement process, should make MAC matrix nondiagonal element minimum as far as possible.

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