CN104792405B - A kind of pipeline flexibility connection pipe reverses mechanical impedance measurement method - Google Patents

Abstract

Mechanical impedance measurement method is reversed the invention provides a kind of pipeline flexibility connection pipe, is comprised the following steps：First, the impedance matrix about the flexibility connection pipe 12 × 12 is set up：The equal direct measurement of impedance parameter wherein related to translational degree of freedom is obtained；2nd, impedance matrix is resolved：If axisymmetric flexibility connection pipe, then lower end is will take over first and is fixed, exerted a force and measure in upper end, resolve and obtain respective impedance；Then two adapters are symmetrically installed, to eliminate the rotation around y-axis, exert a force and measure in joint, calculated and obtain respective impedance；If elbow form flexible connecting pipe, then lower end is fixed first, exert a force and measure in upper end, resolve and obtain respective impedance；Then two adapters are symmetrically installed respectively and are installed with antisymmetry, the speed of the rotation and z-axis around y-axis is eliminated respectively, exerted a force and measure in joint, calculated and obtain respective impedance.Other impedance parameters related to rotational freedom are obtained by the peer-to-peer of impedance matrix.

Description

A kind of pipeline flexibility connection pipe reverses mechanical impedance measurement method

Technical field

The invention belongs to vibration reduction of ship noise reduction technology field, and in particular to a kind of pipeline flexibility connection pipe reverses mechanical impedance and surveys Amount method.

Background technology

Structure vibration and structure borne noise, the suppression fluid transmitted along pipe-line system can not only be isolated and be decayed to flexibility connection pipe in pipeline Noise, moreover it is possible to because the big displacement that vibration, impact cause deforms between compensation equipment and pipe-line system.Therefore it is big on ship both at home and abroad Amount uses flexibility connection pipe.The mechanical impedance property of flexibility connection pipe is the main evaluation parameter for weighing its anti-vibration performance, is also to carry out The important initial parameter of pipe-line system acoustical behavior forecast.

The translation mechanical impedance measuring method of current three change in coordinate axis direction may be referred to international standard ISO10846.Wang Suo Spring etc. (tested and its 12nd ship underwater noise science of vibration isolating effect prediction research is begged for by elbow form flexible connecting pipe mechanical impedance By can collection of thesis, 2009) three translation directions are obtained using symmetrical or antisymmetry mounting means to elbow form flexible connecting pipe Mechanical impedance.

Because pipe-line system is generally elongated space structure, pipeline section can contemplate in the forecast of pipe-line system acoustical behavior Three translations and three torsions, totally 6 mechanical impedances of the free degree, and flexibility connection pipe is because cannot measure around three reference axis Reverse impedance and often ignored, the mechanical impedance test data for only introducing three change in coordinate axis direction is calculated.Current It has also been found that there is the coupling between translation and torsion in pipeline, and ignoring torsion impedance will cause calculation error in research.Yin Zhiyong Deng (the 11st ship underwater noise academic discussions of acceleration partition method of the mechanical impedance measurement of pipeline flexible support torsion Collection of thesis, 2007) propose and produce torque with the mode of eccentric annular flow, the method for acceleration separate is obtained rotating and accelerated Degree, obtains pipe-support and reverses mechanical impedance, and the method is tested mainly for the input impedance of support member.

In sum, the measuring method that flexibility connection pipe reverses mechanical impedance is lacked at present, pipeline acoustics is seriously constrained Can forecast and calculate, breakthrough is needed in the lifting of influence pipe-line system acoustics design and control technology badly.

The content of the invention

In view of this, mechanical impedance measurement method is reversed the invention provides a kind of pipeline flexibility connection pipe, can be utilized T-shaped Mass applies moment of torsion and measurement angular speed, power ring measurement power and moment of torsion, and direct access flexibility connection pipe reverses mechanical impedance.

To reach above-mentioned purpose, the technical scheme is that：A kind of pipeline flexibility connection pipe reverses mechanical impedance measurement side Method, the method comprises the following steps：

Step one, for flexibility connection pipe, its upper and lower side has 6 motions of the free degree, the relevant flexibility is set up accordingly and is connect The impedance matrix of pipe 12 × 12：

It is 1 end with the upper end of flexibility connection pipe, lower end is 2 ends, and coordinate system Ox is set up respectively for 1 end and 2 ends₁y₁z₁With Ox₂y₂z₂If the flexibility connection pipe is axisymmetric flexibility connection pipe, wherein Ox₁y₁z₁Using the end face at 1 end as x₁oy₁Face, to scratch Property adapter axis be z₁Axle, Ox₂y₂z₂Using the end face at 2 ends as x₂oy₂Face, the axis with flexibility connection pipe is as z₂Axle；If described Flexibility connection pipe is elbow form flexible connecting pipe, wherein Ox₁y₁z₁Using the end face at 1 end as x₁oy₁Face, the axis with flexibility connection pipe is as z₁ Axle, Ox₂y₂z₂Using the end face at 2 ends as y₂oz₂Face, the axis with flexibility connection pipe is as x₂Axle.

Wherein F_1x、F_1yAnd F_1z1 end is illustrated respectively in along x₁、y₁And z₁The excitation that direction applies, M_1x、M_1yAnd M_1zDifference table Show 1 end around x₁、y₁And z₁The excitation that axle applies, v_1x、v_1yAnd v_1z1 end is illustrated respectively in x₁、y₁And z₁The point-to-point speed in direction is rung Should, θ_1x、θ_1yAnd θ_1zRepresent 1 end around x respectively₁、y₁And z₁The angular velocity of rotation response of axle.

Wherein F_2x、F_2yAnd F_2zRepresent respectively and be applied to 2 end x₂、y₂And z₂The excitation in direction, M_2x、M_2yAnd M_2z2 are represented respectively End is around x₂、y₂And z₂The excitation that axle rotation applies, v_2x、v_2yAnd v_2z2 ends are illustrated respectively in x₂、y₂And z₂The point-to-point speed in direction Response, θ_2x、θ_2yAnd θ_2zRepresent 2 ends around x respectively₂、y₂And z₂The angular velocity of rotation response of axle.

Be impedance parameter, wherein in subscript have numeral 11 in 1 end input impedance parameter, subscript have numeral 22 Be 2 end input impedance parameters, have numeral 12 in subscript is 1 end to the transfer impedance parameter at 2 ends, has numeral in subscript 21 is 2 ends to the transfer impedance parameter at 1 end；Numeral 1~3 in subscript represents that translational degree of freedom, 4~6 represent rotatably mounted Degree, the impedance parameter wherein in subscript with 4~6 is the impedance parameter related to rotational freedom, only 1~3 in subscript Impedance parameter is the impedance parameter related to translational degree of freedom.

The equal direct measurement of impedance parameter wherein related to translational degree of freedom is obtained.

Step 2, the impedance matrix for resolving flexibility connection pipe 12 × 12:

If the flexibility connection pipe is axisymmetric flexibility connection pipe, the step is as follows：

S201, the lower end of axisymmetric flexibility connection pipe is fixed on mounting platform through power and torque sensor, by one Individual T-shaped mass is perpendicularly fixed at the upper end outer circumferential side of the axisymmetric flexibility connection pipe, two ends point on the arm of T-shaped mass Not Fang Zhi sensor be used to measure power, translational velocity and angular speed, wherein one end is installed exciting rod and is used to exert a force.

S202, exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end along x₁The excitation that axle applies F_1xAnd 1 end around y₁The excitation M that axle applies_1y, by 1 end of the sensor acquisition on T-shaped mass along x₁The translational velocity of axle v_1xWith along y₁The rotational angular velocity θ of axle_1y；It is related to the excitation of 1 end and response by being chosen in described 12 × 12 impedance matrix relation Relational expression：

WhereinIt is the 1 end input impedance parameter related to translational degree of freedom, direct measurement is obtained；

Had by principle of reciprocity：Above formula is resolved to obtainWith

S203, transfer impedance parameter

S204, two axisymmetric flexibility connection pipes of selection, the end of two of which axisymmetric flexibility connection pipe 2 passes through power and torsion Square sensor is fixed on mounting platform, and 1 end of the two is docked by connector, and T-shaped mass is perpendicularly fixed at the company of the two Fitting side；Exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end around z₁The excitation M that axle applies_1zWith And 2 end around z₂The excitation M that axle applies_2z, by 1 end of the sensor acquisition on T-shaped mass along z₁The rotational angular velocity θ of axle_1z。

Then input impedance parameterWith transfer impedance parameter

S205, calculate what is obtained according to above step S201~S204WithBy with Lower reciprocal relation obtains other impedance parameters related to rotational freedom： Remaining impedance parameter related to rotational freedom is zero；So far, all of axisymmetric flexibility connection pipe are completed The measurement of impedance parameter.

If the flexibility connection pipe is elbow form flexible connecting pipe, the step is as follows：

S2001,2 ends of elbow form flexible connecting pipe are fixed on mounting platform by power and torque sensor, it is T-shaped by one Mass is perpendicularly fixed on the end face at 1 end of the elbow form flexible connecting pipe, and sensor is placed at two ends respectively on the arm of T-shaped mass For measuring power, translational velocity and angular speed, wherein one end is placed exciting rod and is used to exert a force.

S2002, exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end along x₁What axle applied swashs Encourage F_1xAnd 1 end around y₁The excitation M that axle applies_1y, the 1 end edge obtained by the speed on T-shaped mass and angular-rate sensor x₁The translational velocity v of axle_1xWith along y₁The rotational angular velocity θ of axle_1y；Then chosen and 1 by described 12 × 12 impedance matrix relation The end excitation relational expression related to response：

WhereinWithThe input impedance related to translational degree of freedom is, direct measurement is obtained.

Had by principle of reciprocity：Calculate and obtainWithTransfer impedance parameter

S2003, two elbow form flexible connecting pipes of selection, the end of two of which elbow form flexible connecting pipe 2 passes through power and torque sensing Device is fixed on mounting platform, and 1 end of the two is docked by connector, and the two formation is symmetrically installed, and T-shaped mass is vertically fixed In the connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end around x₁Axle applies Excitation M_1xAnd 2 end around x₂The excitation M that axle applies_2x, 1 obtained by the speed on T-shaped mass and angular-rate sensor End is along x₁The rotational angular velocity θ of axle_1x；Then input impedance parameterTransfer impedance parameter

S2004, two elbow form flexible connecting pipes of selection, the end of two of which elbow form flexible connecting pipe 2 passes through power and torque sensing Device is fixed on mounting platform, and 1 end of the two is docked by connector, and the two forms antisymmetry and installs, and T-shaped mass is vertically solid Due to the connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end around y₁Axle is applied Plus excitation F_1yAnd 1 end around z₁The excitation M that axle applies_1z, obtained by the speed on T-shaped mass and angular-rate sensor 1 end is along z₁The rotational angular velocity θ of axle_1z。

Then by choosing the relational expression related to the excitation of 1 end and response in described 12 × 12 impedance matrix relation：

WhereinIt is the input impedance parameter related to translational degree of freedom, directly test is obtained,Above formula is resolved to obtain With

S2005, transfer impedance parameter

S2006, calculate what is obtained according to above step S2001~S2005 Other impedances related to rotational freedom are obtained according to following reciprocal relation to join Number The remainder impedance parameter related to rotational freedom is 0；So far, elbow is completed The measurement of all impedance parameters of flexibility connection pipe.

Further, the sensor that two ends are placed on the arm of T-shaped mass is respectively reluctance head and velocity sensor, wherein Reluctance head measures speed for v₂, it is v that velocity sensor measures speed₁, spacing is △ between reluctance head and velocity sensor.

1 end for then being obtained by the sensor on T-shaped mass in the step S202 is along x₁The translational velocity v of axle_1xWith Along y₁The rotational angular velocity θ of axle_1yMethod be specially：

Beneficial effect：

The present invention applies moment of torsion and measurement angular speed, power ring measurement power and moment of torsion using T-shaped mass, being capable of direct access Flexibility connection pipe reverses mechanical impedance, can be used to evaluating the anti-vibration performance of flexibility connection pipe, the forecast of pipe-line system acoustical behavior, acoustics sets Meter and vibration isolator reverse the measurement of mechanical impedance.

Brief description of the drawings

Fig. 1 is illustrated for the axisymmetric adapter of one embodiment of the invention and elbow form flexible connecting pipe two ends power and moment of torsion；

Fig. 2 reverses diagram for the T-shaped mass measurement of one embodiment of the invention；

Fig. 3 is the axisymmetric adapter impedance of one embodiment of the inventionTest schematic diagram is illustrated. In figure：Acceleration transducer 1, exciting rod 2, reluctance head 3, T-shaped mass 4, flexibility connection pipe 5, power and torque sensor 6, install Platform 7；

Fig. 4 is symmetrically installed axisymmetric adapter impedance for one embodiment of the inventionMeasurement diagram；

Fig. 5 is the elbow form flexible connecting pipe impedance of one embodiment of the inventionMeasurement diagram；

Fig. 6 is symmetrically installed elbow form flexible connecting pipe impedance for one embodiment of the inventionMeasurement diagram；

Fig. 7 installs elbow form flexible connecting pipe impedance for the antisymmetry of one embodiment of the inventionMeasurement figure Show.

Specific embodiment

Develop simultaneously embodiment below in conjunction with the accompanying drawings, and the present invention will be described in detail.

Embodiment 1, a kind of pipeline flexibility connection pipe reverse mechanical impedance measurement method, and the method comprises the following steps：

Step one, for flexibility connection pipe, its upper and lower side has 6 motions of the free degree, the relevant flexibility is set up accordingly and is connect The impedance matrix of pipe 12 × 12：

It is 1 end with the upper end of flexibility connection pipe, lower end is 2 ends, and coordinate system Ox is set up respectively for 1 end and 2 ends₁y₁z₁With Ox₂y₂z₂If the flexibility connection pipe is axisymmetric flexibility connection pipe, wherein Ox₁y₁z₁Using the end face at 1 end as x₁oy₁Face, to scratch Property adapter axis be z₁Axle, Ox₂y₂z₂Using the end face at 2 ends as x₂oy₂Face, the axis with flexibility connection pipe is as z₂Axle；If described Flexibility connection pipe is elbow form flexible connecting pipe, wherein Ox₁y₁z₁Using the end face at 1 end as x₁oy₁Face, the axis with flexibility connection pipe is as z₁ Axle, Ox₂y₂z₂Using the end face at 2 ends as y₂oz₂Face, the axis with flexibility connection pipe is as x₂Axle.

Wherein F_1x、F_1yAnd F_1z1 end is illustrated respectively in along x₁、y₁And z₁The excitation that direction applies, M_1x、M_1yAnd M_1zDifference table Show 1 end around x₁、y₁And z₁The excitation that axle applies, v_1x、v_1yAnd v_1z1 end is illustrated respectively in x₁、y₁And z₁The point-to-point speed in direction is rung Should, θ_1x、θ_1yAnd θ_1zRepresent 1 end around x respectively₁、y₁And z₁The angular velocity of rotation response of axle.

Wherein F_2x、F_2yAnd F_2zRepresent respectively and be applied to 2 end x₂、y₂And z₂The excitation in direction, M_2x、M_2yAnd M_2z2 are represented respectively End is around x₂、y₂And z₂The excitation that axle rotation applies, v_2x、v_2yAnd v_2z2 ends are illustrated respectively in x₂、y₂And z₂The point-to-point speed in direction Response, θ_2x、θ_2yAnd θ_2zRepresent 2 ends around x respectively₂、y₂And z₂The angular velocity of rotation response of axle.

Axisymmetric takes over as shown in Figure 1 with elbow form flexible connecting pipe two ends power and torque diagram.

It is impedance matrix, whereinIt is impedance parameter, wherein Have numeral 11 in subscript is 2 end input impedance parameters, subscript for have numeral 22 in 1 end input impedance parameter, subscript In to have numeral 12 and 21 be transfer impedance parameter；Numeral 1~3 in subscript represents that translational degree of freedom, 4~6 represent and rotates The impedance parameter in the free degree, wherein subscript with 4~6 is the impedance parameter related to rotational freedom, only 1 in subscript~ 3 impedance parameter is the impedance parameter related to translational degree of freedom.

In linear system, impedance matrix is symmetrical relative to leading diagonal, i.e., the element with subscript 12 in above formula With the element correspondent equal with subscript 21.The present invention only provides the measuring method of the impedance parameter related to rotational freedom.

The equal direct measurement of the impedance parameter related to translational degree of freedom is obtained；

Step 2, the impedance matrix for resolving flexibility connection pipe 12 × 12:

If the flexibility connection pipe is axisymmetric flexibility connection pipe, the step is as follows：

S201, the lower end of axisymmetric flexibility connection pipe is fixed on mounting platform by power and torque sensor, by one Individual T-shaped mass is perpendicularly fixed at the upper side of the axisymmetric flexibility connection pipe, and two ends are placed respectively on the arm of T-shaped mass Sensor is used to measure power, translational velocity and angular speed, and wherein one end is placed exciting rod and is used to exert a force.

T-shaped mass of the present invention is as shown in Fig. 2 as can be seen that can be applied by T-shaped mass in Fig. 2 Different power, while corresponding sensor is placed on T-shaped mass can then measure power and moment of torsion and speed, acceleration etc. Amount.

Fig. 3 is then axisymmetric adapter impedanceTest schematic diagram is illustrated.In figure：Acceleration transducer 1, exciting rod 2, reluctance head 3, T-shaped mass 4, flexibility connection pipe 5, power and torque sensor 6, mounting platform 7.

S202, exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end along x₁The excitation that axle applies F_1xAnd 1 end around y₁The excitation M that axle applies_1y, by 1 end of the sensor acquisition on T-shaped mass along x₁The translational velocity of axle v_1xWith along y₁The rotational angular velocity θ of axle_1y；Then there is following relation between the excitation of 1 end and response：

This is the relational expression related to the excitation of 1 end and response chosen in impedance matrix model by above-mentioned 12 × 12；Its InIt is the input impedance related to translational degree of freedom, direct measurement is obtained；Had according to principle of reciprocity：

Above formula is resolved to obtainWith

S203, transfer impedance parameter

S204, two axial symmetry type flexibility connection pipes of selection, the end of two of which axial symmetry type flexibility connection pipe 2 passes through power and torsion Square sensor is fixed on mounting platform, and 1 end of the two is docked by connector, and connector is used to dock the two fixation, T-shaped Mass is perpendicularly fixed at the connector side of the two；Exerted a force using exciting rod, obtained by power and torque sensor measurement 1 end is obtained around z₁The excitation M that axle applies_1zAnd 2 end around z₂The excitation M that axle applies_2z, obtained by the sensor on T-shaped mass 1 end along z₁The rotational angular velocity θ of axle_1z；

For axisymmetric adapter, two flexibility connection pipes can be eliminated into θ to dress_1y, as shown in Figure 4, it is ensured that in excitation Only θ_1zAnd v_1x, due to θ_1zAnd v_1xIn the absence of coupling, it is possible to directly obtain input impedance parameterAnd biography Pass impedance parameter

S205, calculate what is obtained according to above step S201~S204WithBy with Lower reciprocal relation obtains other impedance parameters related to rotational freedom： The remainder impedance parameter related to rotational freedom is zero；So far, the institute of axial symmetry type flexibility connection pipe is completed There is the measurement of impedance parameter.

If flexibility connection pipe is elbow form flexible connecting pipe, the step is as follows：

S2001,2 ends of elbow form flexible connecting pipe are fixed on mounting platform by power and torque sensor, it is T-shaped by one Mass is perpendicularly fixed on the end face at 1 end of the elbow form flexible connecting pipe, and sensor is placed at two ends respectively on the arm of T-shaped mass For measuring power, translational velocity and angular speed, wherein one end is placed exciting rod and is used to exert a force；It is specific to install as shown in Figure 5.

S2002, exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end along x₁What axle applied swashs Encourage F_1xAnd 1 end around y₁The excitation M that axle applies_1y, the 1 end edge obtained by the speed on T-shaped mass and angular-rate sensor x₁The translational velocity v of axle_1xWith along y₁The rotational angular velocity θ of axle_1y；Then there is following relation between the excitation of 1 end and response：

This is the relational expression related to the excitation of 1 end and response chosen in impedance matrix model by above-mentioned 12 × 12；Its InWithThe input impedance related to translational degree of freedom is, direct measurement is obtained；Had according to principle of reciprocity

It is possible thereby to resolve above formula, obtainWith

Transfer impedance parameter

S2003, two elbow form flexible connecting pipes of selection, the end of two of which elbow form flexible connecting pipe 2 passes through power and torque sensing Device is fixed on mounting platform, and 1 end of the two is docked by connector, and the two formation is symmetrically installed, and T-shaped mass is vertically fixed In the connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end around x₁Axle applies Excitation M_1xAnd 2 end around x₂The excitation M that axle applies_2x, 1 obtained by the speed on T-shaped mass and angular-rate sensor End is along x₁The rotational angular velocity θ of axle_1x。

For elbow form flexible connecting pipe, two flexibility connection pipes can be eliminated into θ to dress_1y, as shown in Figure 6, it is ensured that in excitation Only θ_1xAnd v_1z, due to θ_1xAnd v_1zIn the absence of coupling, it is possible to directly obtain input impedance parameterTransmission Impedance parameter

S2004, two elbow form flexible connecting pipes of selection, the end of two of which elbow form flexible connecting pipe 2 passes through power and torque sensing Device is fixed on mounting platform, and 1 end of the two is docked by connector, and the two forms antisymmetry and installs, and T-shaped mass is vertically solid Due to the connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain 1 end around y₁Axle is applied Plus excitation F_1yAnd 1 end around z₁The excitation M that axle applies_1z, obtained by the speed on T-shaped mass and angular-rate sensor 1 end is along z₁The rotational angular velocity θ of axle_1z；

For elbow form flexible connecting pipe, as shown in fig. 7, install v can be eliminated by antisymmetry_1z, then 1 end encourage and respond it Between there is following relation：

This is the relational expression related to the excitation of 1 end and response chosen in impedance matrix model by above-mentioned 12 × 12；Its InIt is the input impedance parameter related to translational degree of freedom, directly test is obtained,Above formula is resolved to obtainWith

S2005, transfer impedance parameter

S2006, calculate what is obtained according to above step S2001~S2005 Other impedances related to rotational freedom are obtained according to following reciprocal relation to join Number The remainder impedance parameter related to rotational freedom is 0；So far, elbow is completed The measurement of all impedance parameters of flexibility connection pipe.

In impedance measurement method in embodiment 2, above-described embodiment 1, the sensor that two ends are placed on the arm of T-shaped mass Respectively reluctance head and velocity sensor, wherein reluctance head measure speed for v₂, it is v that velocity sensor measures speed₁, reluctance head Spacing is △ between velocity sensor.

1 end for then being obtained by the sensor on T-shaped mass in step S202 is along x₁The translational velocity v of axle_1xWith along y₁ The rotational angular velocity θ of axle_1yMethod be specially：

In sum, presently preferred embodiments of the present invention is these are only, is not intended to limit the scope of the present invention. All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., should be included in of the invention Within protection domain.

Claims (2)

1. a kind of pipeline flexibility connection pipe reverses mechanical impedance measurement method, it is characterised in that the method comprises the following steps：

Step one, for flexibility connection pipe, its upper and lower side has 6 motions of the free degree, and the relevant flexibility connection pipe 12 is set up accordingly × 12 impedance matrix：

It is a1 ends with the upper end of flexibility connection pipe, lower end is a2 ends, and coordinate system Ox is set up respectively for a1 ends and a2 ends₁y₁z₁With Ox₂y₂z₂If the flexibility connection pipe is axisymmetric flexibility connection pipe, wherein Ox₁y₁z₁Using the end face at a1 ends as x₁oy₁Face, to scratch Property adapter axis be z₁Axle, Ox₂y₂z₂Using the end face at a2 ends as x₂oy₂Face, the axis with flexibility connection pipe is as z₂Axle；If described Flexibility connection pipe is elbow form flexible connecting pipe, wherein Ox₁y₁z₁Using the end face at a1 ends as x₁oy₁Face, the axis with flexibility connection pipe is as z₁ Axle, Ox₂y₂z₂Using the end face at a2 ends as y₂oz₂Face, the axis with flexibility connection pipe is as x₂Axle；

Wherein F_1x、F_1yAnd F_1zA1 ends are illustrated respectively in along x₁、y₁And z₁The excitation that direction applies, M_1x、M_1yAnd M_1zA1 is represented respectively End is around x₁、y₁And z₁The excitation that axle applies, v_1x、v_1yAnd v_1zA1 ends are illustrated respectively in x₁、y₁And z₁The point-to-point speed in direction is rung Should, θ_1x、θ_1yAnd θ_1zRepresent a1 ends around x respectively₁、y₁And z₁The angular velocity of rotation response of axle；

Wherein F_2x、F_2yAnd F_2zRepresent respectively and be applied to a2 ends x₂、y₂And z₂The excitation in direction, M_2x、M_2yAnd M_2zA2 ends are represented respectively Around x₂、y₂And z₂The excitation that axle rotation applies, v_2x、v_2yAnd v_2zA2 ends are illustrated respectively in x₂、y₂And z₂The point-to-point speed in direction is rung Should, θ_2x、θ_2yAnd θ_2zRepresent a2 ends around x respectively₂、y₂And z₂The angular velocity of rotation response of axle；

Be impedance parameter, have wherein in subscript numeral 11 to have numeral 22 in a1 ends input impedance parameter, subscript It is a2 ends input impedance parameter, have numeral 12 in subscript is a1 ends to the transfer impedance parameter at a2 ends, there is number in subscript Word 21 is a2 ends to the transfer impedance parameter at a1 ends；Numeral 1~3 in subscript represents that translational degree of freedom, 4~6 represent and rotates The impedance parameter in the free degree, wherein subscript with 4~6 is the impedance parameter related to rotational freedom, only 1 in subscript~ 3 impedance parameter is the impedance parameter related to translational degree of freedom；

The equal direct measurement of impedance parameter wherein related to translational degree of freedom is obtained；

Step 2, the impedance matrix for resolving flexibility connection pipe 12 × 12:

If the flexibility connection pipe is axisymmetric flexibility connection pipe, the step is as follows：

S201, the lower end of axisymmetric flexibility connection pipe is fixed on mounting platform through power and torque sensor, it is T-shaped by one Mass is perpendicularly fixed at the upper end outer circumferential side of the axisymmetric flexibility connection pipe, and two ends are put respectively on the arm of T-shaped mass Put sensor and exciting rod is installed and is used to exert a force for measuring power, translational velocity and angular speed, wherein one end；

S202, exerted a force using exciting rod, measured by power and torque sensor and obtain a1 ends along x₁The excitation F that axle applies_1x And a1 ends are around y₁The excitation M that axle applies_1y, by the a1 ends of the sensor acquisition on T-shaped mass along x₁The translational velocity of axle v_1xWith along y₁The rotational angular velocity θ of axle_1y；It is related to the excitation of a1 ends and response by being chosen in described 12 × 12 impedance matrix relation Relational expression：

$\left(\begin{array}{c}{F}_{1x}\\ M_{1y}\end{array}\right)=\left[\begin{array}{cc}{Z}_{11}^{11}& Z_{15}^{11}\\ Z_{51}^{11}& Z_{55}^{11}\end{array}\right]\left(\begin{array}{c}{v}_{1x}\\ {\mathrm{\θ}}_{1y}\end{array}\right)$

WhereinIt is the a1 end input impedance parameter related to translational degree of freedom, direct measurement is obtained；

Had by principle of reciprocity：

Above formula is resolved to obtainWith

S203, transfer impedance parameter

S204, two axisymmetric flexibility connection pipes of selection, two of which axisymmetric flexibility connection pipe a2 ends pass through power and moment of torsion Sensor is fixed on mounting platform, and the a1 ends of the two are docked by connector, and T-shaped mass is perpendicularly fixed at the connection of the two Part side；Exerted a force using exciting rod, measured by power and torque sensor and obtain a1 ends around z₁The excitation M that axle applies_1zWith And a2 ends are around z₂The excitation M that axle applies_2z, by the a1 ends of the sensor acquisition on T-shaped mass along z₁The rotational angular velocity of axle θ_1z；

Then input impedance parameterWith transfer impedance parameter

S205, calculate what is obtained according to above step S201~S204WithBy following mutual Easy relation obtains other impedance parameters related to rotational freedom： Remaining impedance parameter related to rotational freedom is zero；So far, all impedances ginseng of axisymmetric flexibility connection pipe is completed Several measurements；

If the flexibility connection pipe is elbow form flexible connecting pipe, the step is as follows：

S2001, the a2 ends of elbow form flexible connecting pipe are fixed on mounting platform by power and torque sensor, by a T-shaped matter Gauge block is perpendicularly fixed on the end face at a1 ends of the elbow form flexible connecting pipe, and sensor is placed at two ends respectively on the arm of T-shaped mass For measuring power, translational velocity and angular speed, wherein one end is placed exciting rod and is used to exert a force；

S2002, exerted a force using exciting rod, measured by power and torque sensor and obtain a1 ends along x₁The excitation F that axle applies_1x And a1 ends are around y₁The excitation M that axle applies_1y, by the a1 ends of the speed on T-shaped mass and angular-rate sensor acquisition along x₁ The translational velocity v of axle_1xWith along y₁The rotational angular velocity θ of axle_1y；Then chosen and a1 ends by described 12 × 12 impedance matrix relation The excitation relational expression related to response：

$\left\{\begin{array}{c}\left(\begin{array}{c}{F}_{1x}\\ M_{1y}\end{array}\right)=\left[\begin{array}{cc}{Z}_{11}^{11}& Z_{15}^{11}\\ Z_{51}^{11}& Z_{55}^{11}\end{array}\right]\left(\begin{array}{c}{v}_{1x}\\ {\mathrm{\θ}}_{1y}\end{array}\right)\\ \left(\begin{array}{c}{F}_{1z}\\ M_{1y}\end{array}\right)=\left[\begin{array}{cc}{Z}_{33}^{11}& Z_{35}^{11}\\ Z_{53}^{11}& Z_{55}^{11}\end{array}\right]\left(\begin{array}{c}{v}_{1z}\\ {\mathrm{\θ}}_{1y}\end{array}\right)\end{array}\right.;$

WhereinWithThe input impedance related to translational degree of freedom is, direct measurement is obtained；

Had by principle of reciprocity：

Calculate and obtain With

Transfer impedance parameter

S2003, two elbow form flexible connecting pipes of selection, two of which elbow form flexible connecting pipe a2 ends are solid by power and torque sensor Due on mounting platform, the a1 ends of the two are docked by connector, and the two formation is symmetrically installed, and T-shaped mass is perpendicularly fixed at The connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain a1 ends around x₁Axle applies Excitation M_1xAnd a2 ends are around x₂The excitation M that axle applies_2x, obtained by the speed on T-shaped mass and angular-rate sensor A1 ends are along x₁The rotational angular velocity θ of axle_1x；

Then input impedance parameterTransfer impedance parameter

S2004, two elbow form flexible connecting pipes of selection, two of which elbow form flexible connecting pipe a2 ends are solid by power and torque sensor Due on mounting platform, the a1 ends of the two are docked by connector, and the two forms antisymmetry and installs, and T-shaped mass is vertically fixed In the connector side of the two；Exerted a force using exciting rod, measured by power and torque sensor and obtain a1 ends around y₁Axle is applied Plus excitation F_1yAnd a1 ends are around z₁The excitation M that axle applies_1z, obtained by the speed on T-shaped mass and angular-rate sensor A1 ends along z₁The rotational angular velocity θ of axle_1z；

Then by choosing the relational expression related to the excitation of a1 ends and response in described 12 × 12 impedance matrix relation：

$\left(\begin{array}{c}{F}_{1y}\\ M_{1z}\end{array}\right)=\left[\begin{array}{cc}{Z}_{22}^{11}& Z_{26}^{11}\\ Z_{62}^{11}& Z_{66}^{11}\end{array}\right]\left(\begin{array}{c}{v}_{1y}\\ {\mathrm{\θ}}_{1z}\end{array}\right)$

WhereinIt is the input impedance parameter related to translational degree of freedom, directly test is obtained,Above formula is resolved to obtain With

S2005, transfer impedance parameter

S2006, calculate what is obtained according to above step S2001~S2005 Other impedances related to rotational freedom are obtained according to following reciprocal relation to join Number The remainder impedance parameter related to rotational freedom is 0；So far, elbow is completed The measurement of all impedance parameters of flexibility connection pipe.

2. a kind of pipeline flexibility connection pipe as claimed in claim 1 reverses mechanical impedance measurement method, it is characterised in that the T The sensor that two ends are placed on the arm of type mass is respectively reluctance head and velocity sensor, and wherein reluctance head measures speed and is v₂, it is v that velocity sensor measures speed₁, spacing is △ between reluctance head and velocity sensor；

The a1 ends for then being obtained by the sensor on T-shaped mass in the step S202 are along x₁The translational velocity v of axle_1xWith along y₁ The rotational angular velocity θ of axle_1yMethod be specially：

$v_{1x}=\frac{1}{2}(v_1+v_2)$

${\mathrm{\θ}}_{1y}=\frac{1}{2\mathrm{\Δ}}(v_2-v_1).$