Strain reconstruction method for non-contact conduit strain measurement system

Abstract

The invention relates to the technical field of sensors, in particular to a strain reconstruction method for a non-contact catheter strain measurement system, which comprises the following steps of: 1, calculating any two-degree-of-freedom transfer ratio function of a catheter according to inherent characteristics of the catheter; step 2, calculating a modal shape when there is concentrated mass or not at the position carrying the strain test device; step 3, calculating an output response ratio when the loading test device has the concentrated mass and does not have the concentrated mass; and step 4, combining any two-degree-of-freedom transfer ratio function of the conduit with the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam to obtain a reconstruction proportional function of the strain of any point of the conduit on the measuring device. Data are collected through the non-contact strain measurement system, the strain value of any point of the conduit is reconstructed based on the modal analysis theory and the cantilever beam bending free vibration differential equation, and the method is good in universality, high in practicability and high in calculation efficiency.

Description

Technical Field

[0001] The present invention relates to the field of sensor technology, and in particular to a strain reconstruction method for a non-contact catheter strain measurement system. Background Art

[0002] The hydraulic system plays an extremely critical role in the safe and normal operation of equipment and ensuring the design performance, especially in the maintenance of large equipment. Most hydraulic pipeline failures are caused by abnormal vibration. Therefore, vibration stress monitoring and analysis of power hydraulic and other pipelines are particularly important for avoiding sudden catastrophic accidents caused by structural failure, reducing maintenance costs, and extending service life. The traditional wired strain testing system needs to paste strain gauges at each test point, wait for solidification, and then connect the wires to the acquisition equipment. Once the paste is not firm or there is damage, the process needs to be repeated. With the measurement workload of hundreds of test points, the whole operation has low efficiency, high labor intensity, and is very time-consuming.

[0003] After searching, Zhao Xuechuan, Lei Yongjun, Tang Guojin, etc., in "Application of transfer function method in dynamic analysis of non-local elastic beams [J]. Vibration and Shock, 2007, (05)", obtained the vibration equation of non-local elastic beams in state space by Laplace transform and defining the state vector, and used the transfer function method to solve the natural frequency problem of non-local elastic beams. The natural frequency and corresponding vibration mode of the beam under the boundary condition of one end fixed and the other end free were calculated, and the relationship between the stress at a point in the non-local elastic beam and the strain at any point in a certain area of ​​the beam was solved.

[0004] After further searching, Xia Ji, Zhu Mucheng, Ma Deyi et al. gave an accurate analysis method for the lateral natural vibration of a beam with concentrated mass and elastic support and its bending free vibration differential equation in "Analysis of lateral natural vibration of a beam with concentrated mass and elastic support [J]. Mechanics and Practice, 2000, (05)". The examples show that this method has a wide range of applicability for the analysis of the natural vibration of beams.

[0005] Therefore, after obtaining the measurement data, the strain value of any point on the catheter can be reconstructed based on the transfer function method on the elastic beam and the differential equation of the bending free vibration of the cantilever beam with concentrated mass, which has a theoretical basis. At the same time, this method can provide strong support for the non-contact strain measurement system. Therefore, it is of great significance to establish a strain reconstruction method for non-contact catheter strain measurement system. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a strain reconstruction method for a non-contact catheter strain measurement system, which has good versatility, strong practicality, high calculation efficiency and high reconstruction accuracy.

[0007] The technical problem to be solved by the present invention is achieved by adopting the following technical solutions:

[0008] A strain reconstruction method for a non-contact catheter strain measurement system comprises the following steps:

[0009] Step 1: Calculate the transfer ratio function of any two degrees of freedom of the catheter based on the inherent characteristics of the catheter;

[0010] Step 2: Calculate the modal vibration shape with and without concentrated mass at the strain test device;

[0011] Step 3: Calculate the output response ratio when there is a concentrated mass and when there is no concentrated mass at the mounting test device;

[0012] Step 4: Combining the transfer ratio function of any two degrees of freedom of the catheter with the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam, the reconstruction proportional function of the strain at any point of the catheter on the measuring device is obtained.

[0013] As a further improvement of the present invention, the process of step 1 is specifically as follows:

[0014] Assuming that the catheter system has n degrees of freedom, the output response ratio of any two degrees of freedom p and q of the catheter in the frequency domain is T Pq (ω) is:

[0015]

[0016] In the formula, X p (ω) is the output response of the system at point p under any excitation; X q (ω) is the output response of the system at point q under arbitrary excitation.

[0017] As a further improvement of the present invention, the process of step 2 is specifically as follows:

[0018] The entire measuring device is equivalent to a concentrated mass of size m. Combined with the installation of the catheter, the system is regarded as a homogeneous cantilever beam structure with a length of 1 and a concentrated mass, with one end fixed and the other end free. The measuring device is equivalent to a concentrated mass block attached to the beam at position x. Combined with the boundary conditions of the beam, the modal vibration type Y of the catheter at the nth order natural frequency can be obtained. n (μ 1 ).

[0019] As a further improvement of the present invention, the process of step 3 is specifically as follows:

[0020] By setting the parameters of the homogeneous beam length, material and concentrated mass position, μ is calculated with or without concentrated mass. 1 The output response ratio of the concentrated mass at the position and the corresponding position of the homogeneous beam is:

[0021]

[0022] Where: τ1 μ 1 The concentrated mass at the position is τ 1 Response; τ2 μ 1 The concentrated mass at the position is τ 2 Response.

[0023] As a further improvement of the present invention, the process of step 4 is specifically as follows:

[0024] The ratio T(ω) between the strain at any point of a concentrated mass conduit and the strain collected by the measuring device is defined as:

[0025]

[0026] Where: Tpq(ω) is the transfer ratio function of any two degrees of freedom of the catheter described in step 1; T τ1τ2 (ω) is the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam described in step 3; ε1 is the strain value of the non-contact measurement device; ε1 is the original strain value of the catheter.

[0027] The beneficial effects of the present invention are:

[0028] The present invention utilizes the principle of frequency response function and combines the dynamic characteristics of the component to be measured to reconstruct the vibration signal transmitted from the component to be measured to the measuring device, and indirectly obtains the stress and strain conditions of the catheter to be measured. Compared with the traditional patch measurement strain method, the present invention provides a strain reconstruction method with good versatility, strong practicality and high computational efficiency, which helps to realize non-contact strain measurement, simplifies the measurement process and saves measurement time. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The present invention is further described below in conjunction with the accompanying drawings and embodiments:

[0030] Figure 1 It is the overall flow chart of the present invention. DETAILED DESCRIPTION

[0031] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further described below with reference to the accompanying drawings and embodiments.

[0032] like Figure 1 As shown, a strain reconstruction method for a non-contact catheter strain measurement system comprises the following steps:

[0033] Step 1: Calculate the transfer ratio function of any two degrees of freedom of the catheter based on the inherent characteristics of the catheter.

[0034] First, assuming that the degree of freedom of the catheter system is n, the matrix and vector representation of the system displacement output response are:

[0035]

[0036] Where: X n is the displacement of the nth element; f n is the nth order natural frequency; H 1k The element is the frequency response function of the system's k-coordinate relative to the l-coordinate.

[0037] Combined with the displacement output response of the catheter system, the system can be approximately regarded as a linear steady-state system. Then the output response ratio of any two degrees of freedom p and q of the catheter in the frequency domain is T Pq (ω) is:

[0038]

[0039] Where: X p (ω) is the output response of the system at point p under any excitation; X q (ω) is the output response of the system at point q under arbitrary excitation; is the i-th order strain mode shape at point p; is the i-th order displacement mode shape at point q; k i The i-th order principal stiffness; λ i is the ratio of the excitation frequency to the i-th order natural frequency of the system; ξ i is the i-th order modal damping ratio of the system.

[0040] Step 2: Calculate the modal vibration shapes with and without concentrated mass at the strain gauge.

[0041] The entire measuring device is equivalent to a concentrated mass of size m. Combined with the installation of the conduit, the system is regarded as a homogeneous cantilever beam structure with a length of l and a concentrated mass, with one end fixed and the other end free. The measuring device is equivalent to a concentrated mass block attached to the beam at position x. Combining the bending free vibration differential equation with the beam lateral displacement formula, the following can be simplified:

[0042] Y″″(μ)-σ 4 Y(μ)=σ 4 τY(μ)δ(μ-μ 1 ) (6)

[0043] Where Y(μ) is the lateral displacement amplitude; μ is the relative position of the concentrated mass on the beam, which can be expressed mathematically as δ is the pulse function;

[0044]

[0045] Where: k is the mass per unit length of the beam; E is the elastic modulus of the material; J is the principal moment of inertia of the centroid of the cross section of the beam; ω nis the natural frequency of the beam;

[0046] Combined with the boundary conditions of the beam, one end is fixed and the other end is free, and after Laplace transformation and inverse transformation of equation (6), we can get:

[0047] Y(μ 1 )=Y″(0)R(σμ 1 )+Y″′(0)N(σμ 1 ) (9)

[0048] And the characteristic equation:

[0049]

[0050] In the formula, μ 1 For x=x 1 When μ is taken, u(μ-μ 1 ) is the unit step function,

[0051]

[0052] The modal vibration type Y of the duct at the nth order natural frequency can be obtained from formula (9): n (μ 1 ).

[0053] Step 3: Calculate the output response ratio when there is a concentrated mass and when there is no concentrated mass at the test device.

[0054] Using the mode superposition method, the response of the concentrated mass in the homogeneous cantilever beam with equal cross-section in the dynamic model is calculated as follows:

[0055]

[0056] Where, Yn(μ1) is the nth order natural frequency μ 1 Mode shape of position; Φ n is the nth-order steady-state response of the beam under forced vibration, and we can obtain:

[0057]

[0058] Where ω is the excitation frequency, F is the excitation force, and the constant b is:

[0059]

[0060] By setting the parameters of the homogeneous beam length, material and concentrated mass position, μ is calculated with or without concentrated mass. 1 The output response ratio of the concentrated mass at the position and the corresponding position of the homogeneous beam is:

[0061]

[0062] Where: τ1 μ 1 The concentrated mass at the position is τ 1 The response of τ2 μ 1 The concentrated mass at the position is τ 2 Response.

[0063] Step 4: Combining the transfer ratio function of any two degrees of freedom of the catheter with the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam, the reconstruction proportional function of the strain at any point of the catheter on the measuring device is obtained.

[0064] The ratio T(ω) between the strain at any point of a concentrated mass conduit and the strain collected by the measuring device is defined as:

[0065]

[0066] Where: Tpq(ω) is the transfer ratio function of any two degrees of freedom of the catheter described in step 1; T τ1τ2 (ω) is the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam described in step 3; ε1 is the strain value of the non-contact measurement device; ε1 is the original strain value of the catheter.

[0067] In the experiment, the excitation signal is set by the signal generator, which is amplified by the power amplifier and then transmitted to the hydraulic conduit through the vibrator. The conduit is installed in the form of a cantilever beam, one end of the conduit is fixedly connected to the vibrator through a right-angle connector, and the other end is suspended. The strain measurement device is installed near the vibration source. The strain is fixed on the sensing beam of the measuring device, and the non-contact strain measurement device is installed on the hydraulic conduit through a fixing fixture. After measuring the strain value ε1 on the sensing beam, the original strain reconstruction value ε2 of the conduit can be obtained by substituting it into the formula.

[0068] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A strain reconstruction method for a non-contact catheter strain measurement system, characterized in that: The following steps are involved: Step 1: Calculate the transfer ratio function of any two degrees of freedom of the catheter based on the inherent characteristics of the catheter; Step 2: Calculate the modal vibration shape with and without concentrated mass at the strain test device; Step 3: Calculate the output response ratio when there is a concentrated mass and when there is no concentrated mass at the mounting test device; Step 4: Combining the transfer ratio function of any two degrees of freedom of the catheter with the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam, the reconstruction proportional function of the strain at any point of the catheter on the measuring device is obtained.

2. The strain reconstruction method for a non-contact catheter strain measurement system according to claim 1, characterized in that: The process of step 1 is specifically as follows: Assuming that the catheter system has n degrees of freedom, the output response ratio of any two degrees of freedom p and q of the catheter in the frequency domain is T Pq (ω) is: Where, X p (ω) is the output response of the system at point p under any excitation; X q (ω) is the output response of the system at point q under arbitrary excitation.

3. The strain reconstruction method for a non-contact catheter strain measurement system according to claim 1, characterized in that: The process of step 2 is specifically as follows: The entire measuring device is equivalent to a concentrated mass of size m. Combined with the installation of the catheter, the system is regarded as a homogeneous cantilever beam structure with a length of 1 and a concentrated mass, with one end fixed and the other end free. The measuring device is equivalent to a concentrated mass block attached to the beam at position x. Combined with the boundary conditions of the beam, the modal vibration type Y of the catheter at the nth order natural frequency can be obtained. n (μ1).

4. The strain reconstruction method for a non-contact catheter strain measurement system according to claim 1, characterized in that: The process of step 3 is specifically as follows: By setting the parameters such as the length, material and concentrated mass position of the homogeneous beam, the output response ratio of the concentrated mass at the μ1 position to the corresponding position of the homogeneous beam is calculated with or without concentrated mass, that is: Where: τ1 is the response of the concentrated mass τ1 at the position μ1; Ψ τ2 is the response of the concentrated mass τ2 at the position μ1.

5. The strain reconstruction method for a non-contact catheter strain measurement system according to claim 1, characterized in that: The process of step 4 is specifically as follows: The ratio T(ω) between the strain at any point of a concentrated mass conduit and the strain collected by the measuring device is defined as: Where: T pq (ω) is the transfer ratio function of any two degrees of freedom of the catheter in step 1; T τ1τ2 (ω) is the output response ratio function of the concentrated mass and the corresponding position of the homogeneous beam described in step 3; ε1 is the strain value of the non-contact measurement device; ε1 is the original strain value of the catheter.

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