JP2017044673A - Vibration measurement device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a vibration measurement device that realizes experiment mode analysis in which the effect of a natural vibration mode present in a region other than a measurement frequency region is taken into account when measuring the vibration of a structure.SOLUTION: A vibration measurement device comprises: a fast Fourier transformation unit for calculating the transfer function of a measurement object in a prescribed frequency band on the basis of an exciting force signal indicating an exciting force and an acceleration signal indicating the acceleration of the measurement object at a measurement point that is generated by the exciting force; a low order mode arithmetic unit for calculating a mode parameter of the measurement object on the basis of the transfer function; a high order mode vector estimation unit for estimating a natural vibration mode vector that corresponds to a natural frequency in a region other than the frequency band on the basis of the mode parameter; and an optimization arithmetic unit for performing arithmetic for minimizing, in the frequency band, a difference between a first high order mode acceleration response calculated on the basis of the natural vibration mode vector and a second high order mode acceleration response obtained by multiplying the acceleration response of the measurement object and the estimated natural vibration mode vector in the region other than the frequency band.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a vibration measuring apparatus for a structure.

  Experimentally grasping the natural vibration characteristics of a structure is to extract non-conformity factors such as resonance and forced vibration in machines where excitation force is applied, such as rotating machines, and reduce the vibration and noise of the equipment. It is important to plan. In the natural vibration measurement, the experimental mode analysis is widely used as a very effective experimental analysis method capable of integrally evaluating the vibration mode (mode) by adding the natural vibration characteristics to the frequency domain.

  The experimental mode analysis is basically evaluated based on the frequency domain transfer function by the FFT analyzer. Therefore, there are restrictions on the frequency range of the natural vibration mode that can be evaluated. For example, since the upper limit of the measurement frequency range is set by the measurement limit frequency (maximum frequency) of the analyzer, when performing vibration measurement using the FFT analyzer, it is necessary to specify the maximum frequency and the frequency resolution. In other words, the measurement must be performed under measurement conditions that maintain the necessary resolution and have an appropriate margin for the frequency of interest.

  However, since there are generally many natural frequencies (infinite in principle), there are multiple natural frequencies even in the high frequency range where the frequency is higher than the measurement frequency range set for measurement. Will do. Therefore, the vibration data measured by the FFT analyzer includes a response component having a natural frequency higher than the maximum frequency.

  In the experimental mode analysis, a mode parameter corresponding to the natural frequency existing in the measurement frequency range of the FFT analyzer is calculated. If the mode parameter is obtained, the vibration characteristics of the target structure can be evaluated by obtaining the vibration response of the target structure by superimposing the mode responses. On the other hand, the vibration response of the reanalyzed structure is composed of mode parameters corresponding to the natural frequency in the measurement frequency range, and the mode response of the natural frequency outside the measurement frequency range is not considered. For this reason, at the upper limit or the lower limit of the measurement frequency range, a numerical difference occurs between the actually measured vibration response and the vibration response by reanalysis. Therefore, in the experimental mode analysis, the influence of the mode response outside the measurement range is generally corrected using the residual stiffness at the upper limit and the residual mass at the lower limit.

  Since the FFT analyzer can usually measure from 0 Hz, the lower limit of the measurement frequency range is rarely a problem. On the other hand, with respect to the upper limit, the residual rigidity is only a constant although a plurality of high-frequency natural frequencies that affect the measurement range are generally inherent. Although the error between the actually measured value and the reanalyzed value can be reduced to some extent, it is difficult to completely correct the error. In particular, when there are a plurality of high-frequency natural frequencies close to the upper limit of the measurement frequency, the error increases.

JP-A-7-167736

  As described above, the conventional vibration measuring apparatus has a problem that it is difficult to perform an experimental mode analysis in consideration of the influence of the natural vibration mode existing outside the measurement frequency region. The embodiment has been made to solve such a problem, and in vibration measurement of a structure, vibration measurement that realizes experimental mode analysis in consideration of the influence of natural vibration modes existing outside the measurement frequency region, particularly in the high frequency region. An object is to provide an apparatus.

  The vibration measuring apparatus according to the embodiment is based on an excitation force signal indicating an excitation force to the excitation point of the measurement object and an acceleration signal indicating an acceleration at the measurement point of the measurement object generated by the excitation force. A fast Fourier transform unit that calculates a transfer function of the measurement object in a predetermined frequency band, and a low-order mode calculation unit that calculates a mode parameter of the measurement object in the frequency band based on the transfer function A higher-order mode vector estimation unit that estimates a natural vibration mode vector corresponding to a natural frequency outside the frequency band based on the mode parameter in the frequency band, and the frequency based on the natural vibration mode vector. A mode parameter of the measurement object outside the band is calculated, and a first higher-order mode addition expressed using the calculated mode parameter is performed. Second response obtained by multiplying the acceleration response in the transfer function of the measurement object and the natural vibration mode vector corresponding to the natural frequency outside the frequency band estimated by the higher-order mode vector estimation unit. And an optimization calculation unit that performs a calculation for minimizing the difference in higher-order mode acceleration response in the frequency band.

It is the schematic which shows the structure of the vibration measuring device of 1st Embodiment. It is the schematic which shows the structure of the structure which is a measuring object of the vibration measuring device of 1st Embodiment. It is a flowchart which shows operation | movement of the vibration measuring apparatus of 1st Embodiment. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of FIG. 2 measured. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of FIG. 2 measured. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required by the vibration measuring apparatus of 1st Embodiment. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required by the vibration measuring apparatus of 1st Embodiment. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required with the vibration measuring apparatus by a prior art. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required with the vibration measuring apparatus by a prior art. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required with the vibration measuring apparatus by a prior art. It is a frequency response function figure which shows the self-transfer function (acceleration) of the system of the structure shown in FIG. 2 calculated | required with the vibration measuring apparatus by a prior art. It is a frequency response function figure which shows the self-transfer function (compliance) explaining the mode parameter estimation method in the vibration measuring device of 4th Embodiment.

ここで、［Ｍ］、［Ｃ］、［Ｋ］は、それぞれ質量行列、減衰行列、剛性行列であり、｛ｘ｝は変位ベクトル、｛ｆ｝は外力ベクトルである。行列の大きさ（自由度）は、測定点数（応答数）Ｎ_ｏに等しい。質量行列、減衰行列および剛性行列を、総称して特性行列と呼ぶ。 (Measurement principle)
The equation of motion of the structure O to be measured can be expressed by Equation 1.

Here, [M], [C], and [K] are a mass matrix, an attenuation matrix, and a stiffness matrix, respectively, {x} is a displacement vector, and {f} is an external force vector. The size (degree of freedom) of the matrix is equal to the number of measurement points (number of responses) _No. The mass matrix, the attenuation matrix, and the stiffness matrix are collectively referred to as a characteristic matrix.

ここで、Ｎ_ｉは入力数であり、解析では採用モード数、実験では測定モード数に相当する。 Corresponding to Equation 1, the natural vibration mode vector {φ _r }; r = 1, 2,..., N _i can be obtained by solving the eigenvalue problem of Equation 2, and the size of N _o rows and N _i columns. A matrix [Φ] shown in Formula 3 is obtained.

Here, _Ni is the number of inputs, which corresponds to the number of adopted modes in the analysis and the number of measurement modes in the experiment.

ここで、記号“「」”は対角行列を意味し、「ｍ」、「ｃ」および「ｋ」の対角成分はそれぞれモード質量、モード減衰、モード剛性と呼ばれ、数式５が成り立つ。

数式５では、ｍ_ｒ＝１となるように固有振動モードベクトル｛φ_ｒ｝を正規化している。この場合、モード剛性ｋ_ｒは固有値ω_ｒ ^２と一致する。角固有振動数ω_ｒは固有値の平方根であり、固有振動数は数式６により求めることができる。

また、減衰率ζ_ｒは数式７により求めることができる。

固有振動モードベクトル、モード質量、モード減衰、モード剛性およびこれらより誘導される定数を総称してモード・パラメータと呼ぶ。 Since the natural vibration mode vector {φ _r } forms an orthonormal basis, Equation 4 is established when the attenuation matrix is a proportional attenuation matrix.

Here, the symbol ““ ”means a diagonal matrix, and the diagonal components of“ m ”,“ c ”, and“ k ”are called mode mass, mode damping, and mode stiffness, respectively, and Equation 5 is established.

In Equation 5, the natural vibration mode vector {φ _r } is normalized so that m _r = 1. In this case, mode stiffness _{k r} is consistent with the eigenvalues ω _r ^2. The angular natural frequency ω _r is the square root of the natural value, and the natural frequency can be obtained from Equation 6.

Further, the attenuation rate ζ _r can be obtained by Expression 7.

The natural vibration mode vector, mode mass, mode damping, mode stiffness and constants derived therefrom are collectively referred to as mode parameters.

ここで、行列［Ｉｄ］の各列｛Ｉｄ｝は、加振点が１、その他は０のベクトルである。実験モード解析は、数式８に基づいて周波数応答関数｛Ｈ｝にカーブ・フィッティングという技法を用いてモード・パラメータを算出する解析手法であり、原理上は入力数Ｎ_ｉ対までのモード・パラメータを特定することが可能である。 In the experimental mode analysis, the equation of motion of Equation 1 is handled in the form of a frequency response function according to the measurement result of the FFT analyzer. That is, 1 point excitation frequency response function {H} is the excitation point component of the excitation force ^{{f} f = e st (} s = jω), the response {x} to obtain the other components as zero Laplace transform. In this case, the frequency response function of multi-point excitation is a matrix of the number of responses and the number of inputs (N _o × N _i ), and Equation 1 can be expressed as Equation 8.

Here, each column {Id} of the matrix [Id] is a vector whose excitation point is 1 and the others are 0. The experimental mode analysis is an analysis method for calculating a mode parameter using a technique called curve fitting to the frequency response function {H} based on Equation 8, and in principle, mode parameters up to N _i pairs of inputs are calculated. It is possible to specify.

数式９によって得られる予測固有振動モードベクトル｛φ_ｒ｝；ｒ＝（Ｎ_ｉ＋１），（Ｎ_ｉ＋２），…，Ｎ_ｏを含めて固有振動モードベクトル｛φ_ｒ｝；ｒ＝１，２，…，Ｎ_ｏは正規直交基底をなす。 Now, it is assumed that _Ni pairs of mode parameters are obtained by experimental mode analysis. At this time, since the natural vibration mode vector {φ _r }; r = 1, 2,..., N _i forms an orthonormal basis, by applying an orthogonalization formula to these known natural vibration mode vectors, An unknown natural vibration mode vector {φ _r }; r = (N _i +1), (N _i +2),..., N _o in a higher frequency region can be predicted. That is, when a typical Gram-Schmidt technique is used as an orthogonalization expression, the calculation of Expression 9 is repeated for an arbitrary initial vector {y _r }.

Prediction obtained by Equation 9 natural mode vector _{{φ r}; r = (} N i +1), (N i +2), ..., including _{N o} natural mode vector {φ _{r}; r} = 1,2 ,..., N _o form an orthonormal basis.

すなわち、数式１０と数式１２の差が最小となるようにモード質量ｍ_ｒ、モード減衰ｃ_ｒ、モード剛性ｋ_ｒを決定する。 On the other hand, modal mass _{m r,} mode damping _{c r,} for mode stiffness _{k r, r = (N i} +1), (N i +2), ..., N o mode for excitation force {f} given by Equation 10 for With respect to the response, the one-degree-of-freedom motion equation of the mode coordinate system based on the mode mass m _r , the mode damping c _r , and the mode stiffness k _r shown in Equation 11 and the response shown in Equation 12 will be considered.

That is, the mode mass m _r , the mode damping c _r , and the mode stiffness k _r are determined so that the difference between Formula 10 and Formula 12 is minimized.

Further, when the number of inputs is equal to the number of responses, that is, when N _i = N _o , the mode matrix [Φ] forms a square matrix with N _o rows and N _o columns. Can be sought.

By the above procedure, modal mass _{m r,} mode damping _{c r,} mode stiffness _{k r,} the natural oscillation mode vector _{{φ r}; r = (} N i +1), (N i +2), ..., N o is determined It is possible to consider the influence of the natural vibration mode in the frequency range higher than the measurement frequency range. According to the notation of Expression 8, {x} corresponds to the frequency response function {H}, and the excitation force {f} corresponds to {Id}.

(First embodiment)
Hereinafter, the configuration of the vibration measuring apparatus 1 according to the first embodiment will be described with reference to FIG. As shown in FIG. 1, the vibration measuring apparatus of the embodiment includes an impulse hammer 10, a load cell 15 built in the impulse hammer 10, acceleration pickups 21... 24, a signal cable 30, an FFT analyzer 40, and a calculation unit 50. Yes.

  The impulse hammer 10 is a hammer that generates a vibration measured by the vibration measuring apparatus 1. The impulse hammer 10 includes a load cell 15 that measures its own excitation force, and can measure vibration applied by the hammer.

  The acceleration pickups 21... 24 are vibration sensors arranged in the structure O to be measured, and measure vibration responses at predetermined positions in the structure O. The signal cable 30 is a cable that guides measurement signals from the load cell 15 and the acceleration pickups 21 to 24 to the vibration measuring apparatus 1.

  The FFT analyzer 40 performs a fast Fourier transform (FFT) based on the measurement signal received from the signal cable 30 to calculate a transfer function. The calculation unit 50 is a computer that calculates a mode parameter, a mass matrix, a stiffness matrix, an attenuation matrix, and the like based on the transfer function calculated by the FFT analyzer 40.

  As shown in FIG. 1, the calculation unit 50 includes a low-order mode calculation unit 51, a high-order vector calculation unit 52, an optimization calculation unit 53, and a matrix calculation unit 54. The low-order mode calculation unit 51 is a processor that calculates mode parameters within the measurement frequency range of the FFT analyzer 40. The high-order vector calculation unit 52 is a processor that calculates a high-order natural vibration mode vector outside the measurement frequency range. The optimization calculation unit 53 is a processor that calculates parameters of all modes. The matrix calculator 54 is a processor that calculates a mass matrix, a stiffness matrix, and an attenuation matrix.

Subsequently, the operation of the vibration measuring apparatus according to the embodiment will be described with reference to FIGS. First, a measurement point and an excitation point are set for the structure O to be measured (step 100; hereinafter referred to as “S100”). In the following description, it is assumed that the structure O is a four-degree-of-freedom system including four degrees of freedom x1, x2, x3, and x4 moving in the X-axis direction as shown in FIG. In the structure O, a mass 61 having a degree of freedom x1 is connected to the fixed end 60 via a stiffness 62 and a damping 63, and a mass 64 having a degree of freedom x2 and a mass 67 having a degree of freedom x3 are stiffened by a stiffness 65 with respect to the mass 61. 66, rigidity 68, and attenuation 69 are connected in series. Further, it is assumed that the mass 70 having the degree of freedom x4 is connected to the mass 61 in parallel with the degree of freedom x2 via the stiffness 71 and the damping 72. It is assumed that the mass of each degree of freedom is m ₁ , m ₂ , m ₃ , m ₄ , the stiffness is k ₁ , k ₂ , k ₃ , k ₄ , and the attenuation is c ₁ , c ₂ , c ₃ , c ₄ .

  The impulse hammer 10 strikes and vibrates the degree of freedom x1, that is, the mass 61. Accelerations occurring at the degrees of freedom x1 to x4 according to the impact excitation are measured by the acceleration pickups 21. The excitation force signal detected by the load cell 15 and the acceleration signal of each degree of freedom detected by the acceleration pickups 21... 24 are sent to the FFT analyzer 40 via the signal cable 30. The FFT analyzer 40 calculates a transfer function using the received excitation force signal and acceleration signal (S110). The calculated transfer function is sent to the calculation unit 50.

ただし、減衰行列［Ｃ］については、比例減衰を数式１４に示すものとして、α＝５．０、β＝５．０×１０^−５とする。

このとき、数式１の運動方程式は、数式１５にて表される。

Here, the specifications of the structure O are values shown in Table 1.

However, with respect to the attenuation matrix [C], the proportional attenuation is expressed by Equation 14, and α = 5.0 and β = 5.0 × 10 ⁻⁵ .

At this time, the equation of motion of Formula 1 is expressed by Formula 15.

低次モード演算部５１は、数式１６を演算して固有値、固有振動モードベクトルなどモード・パラメータを算出する。算出結果例を表２に示す。

The eigenvalue problem of Equation 2 corresponding to Equation 15 is as shown in Equation 16.

The low-order mode calculation unit 51 calculates Equation 16 to calculate mode parameters such as eigenvalues and natural vibration mode vectors. An example of the calculation result is shown in Table 2.

  In the analysis by the low-order mode calculation unit 51, the mode parameters of all modes are obtained as shown in Table 2. However, in actual measurement, there are limitations on the measurement frequency region of the FFT analyzer 40. Therefore, when the measurement frequency range of the FFT analyzer 40 is set to 0 to 50 Hz, the low-order mode calculation unit 51 sets the mode parameter based on the measured transfer function for two natural frequencies of 50 Hz or less shown in Table 2. decide.

  As an example of the actually measured transfer function, FIG. 4A and FIG. 4B show self-acceleration (transfer function in which the response at the excitation point is evaluated by acceleration, that is, the transfer function at the degree of freedom x1 expressed as acceleration). Since FIG. 4A and FIG. 4B are actually measured, the response of the natural vibration mode outside the measurement frequency range is also included.

Since the acceleration is obtained by dividing the response acceleration of each degree of freedom by the excitation force in the dynamic range, it is equal to the response acceleration when the unit harmonic excitation force F shown in Expression 17 is input in Expression 15.

As shown in FIG. 5A and FIG. 5B, the acceleration diagram shows the peak value at the primary and secondary natural frequencies. If the experimental mode analysis is performed using a transfer function with a measurement frequency range of 0 to 50 Hz, the mode parameters for the primary and secondary modes in which the natural frequency exists in the measurement frequency range are as in Equations 18 and 19. Desired.

  As shown in Table 2, there are two third and fourth natural frequencies above 50 Hz, which is the upper limit of the measurement frequency range. However, since it is outside the measurement frequency range, the third and fourth natural frequencies cannot be obtained from the measurement result of the transfer function measured with the measurement frequency range of 0 to 50 Hz. That is, the mode parameter corresponding to the third-order and fourth-order natural frequencies is unknown.

When the self-acceleration is reanalyzed using the mode parameters obtained by Equations 18 and 19, the results are as shown in FIGS. 6A and 6B. 6A and 6B, when the actual measurement value indicated by the broken line is compared with the calculation result indicated by the solid line, the two values are close to each other in the vicinity of the peak at the primary and secondary natural frequencies, but the amplitude is increased in other bands. A big gap is seen. There is also a difference in phase between the primary and secondary natural frequencies. This difference is due to the fact that the mode response corresponding to the third and fourth natural frequencies above the measured frequency range is not considered. In order to improve the accuracy in consideration of the influence of the natural frequency higher than the measurement frequency range, the residual rigidity is generally used. The residual rigidity can be obtained by Equation 20.

  The self-acceleration taking account of the residual rigidity is as shown in FIGS. 7A and 7B. Although the difference in the intermediate portion between the primary and secondary natural frequencies is reduced by the residual rigidity, it can be seen that a large difference remains in the frequency band exceeding the secondary natural frequency. This is calculated by summing up the reciprocal of the mode rigidity corresponding to the third and fourth order natural frequencies as shown in Equation 20, in which the individual frequencies are evaluated individually. Because there is no.

  Therefore, the vibration measuring apparatus according to the embodiment includes a high-order vector calculation unit 52 that estimates natural vibration mode vectors corresponding to the third-order and fourth-order natural frequencies, and calculates respective mode parameters (S130). The high-order vector calculation unit 52 estimates the natural vibration mode vectors corresponding to the third and fourth natural frequencies, and the natural vibration mode vectors of the primary and secondary natural frequencies calculated by the low-order mode calculation unit 51. The orthogonalization formula is used. Here, a typical Gram-Schmidt equation is used as the orthogonalization equation.

｛φ_３｝^Ｔ｛φ_３｝＝１となるように正規化を施せば、数式２２のように表される。

The third-order natural vibration mode vector {φ ₃ } can be obtained as in Expression 21 if {1 1 0 1} ^T is selected as the initial vector in Expression 9.

If normalization is performed so that {φ ₃ } ^T {φ ₃ } = 1, it is expressed as Equation 22.

このように、実施形態の振動測定装置によれば、グラム・シュミットの直交化式を用いて既知の１次、２次固有振動モードベクトルに対して直交する未知の３次、４次固有振動モードベクトルを推定するので、ＦＦＴアナライザ４０の測定周波数範囲外の固有振動数を考慮した精度の高いモード・パラメータや特性行列を得ることができる。１次、２次固有振動モードベクトルと併せてモード行列を作れば、数式２４が得られる。

The fourth-order natural vibration mode vector {φ ₄ } is similarly expressed as Equation 23 if {1 1 1 1} ^T is selected as the initial vector.

As described above, according to the vibration measuring apparatus of the embodiment, the unknown third-order and fourth-order natural vibration modes orthogonal to the known first-order and second-order natural vibration mode vectors using the Gram-Schmidt orthogonalization formula. Since the vector is estimated, it is possible to obtain a highly accurate mode parameter and characteristic matrix in consideration of the natural frequency outside the measurement frequency range of the FFT analyzer 40. Formula 24 can be obtained by creating a mode matrix together with the primary and secondary natural vibration mode vectors.

一方、３次のモード・パラメータを用いて３次モード加速度応答を表すと、数式１５、数式１７より数式２６のようになる。

Further, the higher-order vector calculation unit 52 performs curve fitting with the mode response obtained by multiplying the response (transfer function) vector by the natural vibration mode vector with respect to the third-order and fourth-order mode mass, mode damping, and mode rigidity. Since the transfer function is obtained as a response to the excitation force expressed by Equation 17, as shown in Equation 25, the acceleration response obtained by measurement is multiplied by the third natural vibration mode vector {φ ₃ } ^T to obtain the third order mode. Find the acceleration response.

On the other hand, when the third-order mode acceleration response is expressed using the third-order mode parameter, the following Expression 26 is obtained from Expression 15 and Expression 17.

The optimization calculation unit 53 performs optimization so that the difference (objective function) between the third-order mode acceleration response obtained by Expression 25 and the third-order mode acceleration response obtained by Expression 26 is minimized in the range of 0 to 50 Hz. To determine the mode parameters m ₃ , ω ₃ , and ζ ₃ appearing in Equation 26 (S140).

omega _3, zeta ₃ is modal mass _{m 3,} mode damping _{c 3,} since it derived from the mode stiffness _{k 3,} Equation 26, modal mass _{m 3,} mode damping _{c 3,} is defined in the mode stiffness _{k 3.} That is, there are _three unknowns of this problem: mode mass m ₃ , mode damping c ₃ , and mode stiffness k ₃ , and an equation is calculated with values at appropriate three points (for example, 10 Hz, 30 Hz, and 50 Hz). An algebraic method can be considered first.

However, since the measured value is used for the transfer function in an actual problem, it does not always show ideal characteristics as shown in FIGS. 5A and 5B. Therefore, such an algebraic algorithm may introduce errors. There is. Therefore, the mode parameters m ₃ , c ₃ , and k ₃ are used as design variables, and the optimization problem is minimized by minimizing the sum of the objective functions (absolute values of the third-order mode acceleration response differences) in the frequency range of 0 to 50 Hz. . That is, the objective function is minimized in the range of 0 to 50 Hz as expressed by Equation 27.

Similarly, for the fourth-order mode, the fourth-order mode parameters m ₄ , ω ₄ , and ζ ₄ are obtained by minimizing the difference between the actual measurement and the analysis of the mode acceleration response. Table 3 shows an example of the mode parameter obtained in this way.

  Here, since the values of the primary and secondary modes are obtained by the experimental mode analysis, they are the same as those in Table 2 and are omitted in Table 3. The results of calculating the self-acceleration using the mode parameters in Table 3 are shown in FIGS. 5A and 5B. In FIGS. 5A and 5B, the broken line is an actually measured response curve, which is the same as that in FIGS. 4A and 4B. The calculation result indicated by the solid line is almost the same as the actual measurement result indicated by the broken line, and it can be seen that the accuracy of the estimated third-order and fourth-order mode parameters is very good. According to the vibration measurement device of the embodiment, for the natural frequency outside the measurement frequency range of the FFT analyzer 40, the higher-order natural vibration mode vector is calculated by the vector orthogonalization formula, and the residual of the mode response is minimized. It enables high-level measurement even outside the measurement frequency range of the FFT analyzer 40.

Subsequently, the matrix calculation unit 54 calculates a characteristic matrix (S150). First, the matrix calculation unit 54 calculates the matrix of Equation 13 using the values in Table 3. Examples of calculation results are shown in Equations 28 to 32.

Subsequently, the matrix calculation unit 54 calculates the characteristic matrix as shown in Expressions 33 to 35 by substituting Expressions 28 to 32 into Expression 13.

  Comparing the characteristic matrix shown in Equations 33 to 35 with the matrix of Equation 15 which is a true value, the symmetry of the matrix is maintained and the values of the main terms (components with large numerical values) are very well matched. Thus, the validity of the measurement procedure of the embodiment can be confirmed.

If only the re-analysis of the transfer function is performed, it is sufficient to overlap the inner products of the natural vibration mode vectors {φ _r } corresponding to the mode estimated as the acceleration response as in Expression 25. That is, the mode response shown in Expression 36 can be obtained from the acceleration vector shown in Expression 37.

(Second Embodiment)
In the first embodiment, the optimization calculation unit 53 uses the mean square of the real part and the imaginary part of the mode response as an objective function as shown in Expression 27. In this case, if convergence to an inappropriate local solution during the optimization process, only the real part or imaginary part may be minimized and deviate from the true optimal solution. Therefore, in the vibration measurement device according to the second embodiment, the optimization calculation unit 53 simultaneously minimizes the real part and the imaginary part.

これにより実数部の差と虚数部の差を同時に最小化することができるので、より正確な曲線適合が可能となる。 That is, the optimization calculation unit 53 of this embodiment performs the objective function expressed by the mathematical formula 39 under the constraint condition expressed by the mathematical formula 38 with respect to the design variables m ₃ , c ₃ , and k ₃ . The operation that minimizes is performed. The same applies to the fourth-order mode parameter.

As a result, the difference between the real part and the difference between the imaginary part can be minimized at the same time, so that more accurate curve fitting is possible.

これによりｍ_３、ｍ_４が決定されるので、最適化演算部５３が演算する数式２７の最適化問題における未知数を３個から２個に減らすことができる。したがって、この実施形態の振動測定装置によれば、計算時間の削減や、計算精度の向上を図ることができる。 (Third embodiment)
Since the stiffness matrix and the damping matrix are affected by the joining state between the degrees of freedom of the structure O, it is generally difficult to specify analytically. On the other hand, it is relatively easy to obtain the value of the mass matrix directly from the configuration. That is, it is possible to determine the mass matrix before fitting the curve. If the mass matrix [M] is known, the mode masses m ₃ and m ₄ can be calculated from the diagonal term of the triple product with the estimated mode vector. Here, since the mode parameters of the first and second modes are known, the optimization calculation unit 53 of this embodiment obtains only the third and fourth mode masses using the equation 40.

As a result, m ₃ and m ₄ are determined, so the number of unknowns in the optimization problem of Equation 27 calculated by the optimization calculation unit 53 can be reduced from three to two. Therefore, according to the vibration measuring apparatus of this embodiment, the calculation time can be reduced and the calculation accuracy can be improved.

  It should be noted that the present invention can also be applied to the calculations of Formula 38 and Formula 39 in the second embodiment. That is, in the second embodiment, the optimization calculation unit 53 may calculate only the third-order and fourth-order mode masses in advance, and then perform the calculations of Expressions 38 and 39.

ここで、Ω＝０とおくと、数式４２が得られる。

これは、伝達関数としてコンプライアンスの周波数軸切片の値からモード剛性ｋ_３が計算できることを意味している。 (Fourth embodiment)
When the mode displacement is considered instead of the mode acceleration of Expression 26, it can be expressed as Expression 41.

Here, when Ω = 0, Formula 42 is obtained.

This means that the mode stiffness k ₃ can be calculated from the value of the compliance frequency axis intercept as a transfer function.

ただし、コンプライアンスを測定すると０Ｈｚ近傍でノイズの影響を受けやすいので、実際には低周波領域でノイズの少ない平滑な領域を補外して０Ｈｚの値を推定することになる。 FIG. 8 shows the third-order and fourth-order mode responses in compliance. When the mode stiffnesses k ₃ and k ₄ are obtained from the values of P3 and P4 in the figure, they are as shown in Equation 43 and Equation 44, and it can be seen that the values shown in Table 2 are substantially equal.

However, since the measurement of compliance is likely to be affected by noise in the vicinity of 0 Hz, the value of 0 Hz is estimated by extrapolating a smooth region with low noise in the low frequency region.

As a result, k ₃ and k ₄ are determined, so the number of unknowns in the optimization problem of Equation 27 calculated by the optimization calculation unit 53 can be reduced from three to two. Therefore, calculation time can be reduced and calculation accuracy can be improved.

  It should be noted that the present invention can also be applied to the calculations of Formula 38 and Formula 39 in the second embodiment. That is, in the second embodiment, the optimization calculation unit 53 may calculate only the third-order and fourth-order mode stiffnesses in advance, and then perform the calculations of Expressions 38 and 39.

(Fifth embodiment)
In the first embodiment, values as shown in Equations 33 to 35 are obtained as the characteristic matrix. Here, when the attenuation matrix of Equation 34 and the stiffness matrix of Equation 35 are viewed in detail, the component (1 row 3 column, 3 row 1 column, 2 row 4 column) that should be 0 in the matrix of Equation 15 that is the true value. (4 rows, 2 columns, 3 rows, 4 columns, 4 rows, 3 columns) values are small but have errors. Since there is no coupling between the degrees of freedom that are not directly connected (degrees of freedom x1 and degrees of freedom x3, degrees of freedom x2 and degrees of freedom x4, degrees of freedom x3 and degrees of freedom x4), there is no coupling. These components can be specified from the connection configuration of the structure O. Therefore, the component that does not cause coupling in the stiffness matrix of Equation 35 is set to zero. That is, in this embodiment, the matrix calculation unit 54 calculates the mathematical formula 45.

When the eigenvalue problem of Equation 2 is solved using Equation 33 and Equation 45, Equation 46 is obtained as a mode matrix.

すなわち、非連成項の値が０に近付き精度の改善が見られた。必要に応じて行列演算部５４がこの操作を繰り返せば減衰行列［Ｃ］、剛性行列［Ｋ］を真の値に漸近させることができる。これにより計算精度のさらなる向上がはかられる。 The Gram-Schmidt method requires an initial vector as seen in Equation 9, and the accuracy increases as the initial vector approximates a true vector. Therefore, when the natural vibration mode vector obtained in Equation 45 is substituted into Equation 9 which is an orthogonalization equation as an initial value to improve the mode matrix, the damping matrix and the stiffness matrix are expressed by Equation 47 and Equation 48, respectively. expressed.

That is, the value of the uncoupled term approached zero, and the accuracy was improved. If the matrix calculation unit 54 repeats this operation as necessary, the attenuation matrix [C] and the stiffness matrix [K] can be made asymptotic to true values. As a result, the calculation accuracy can be further improved.

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the scope of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

  DESCRIPTION OF SYMBOLS 1 ... Vibration measuring apparatus, 10 ... Impulse hammer, 15 ... Load cell, 21-24 ... Accelerometer, 30 ... Signal cable, 40 ... FFT analyzer, 50 ... Calculation part, 51 ... Low-order mode calculation part, 52 ... High-order vector Calculation unit, 53 ... optimization calculation unit, 54 ... matrix calculation unit.

Claims (6)

Based on the excitation force signal indicating the excitation force to the excitation point of the measurement object and the acceleration signal indicating the acceleration at the measurement point of the measurement object generated by the excitation force, in the predetermined frequency band A fast Fourier transform unit for calculating the transfer function of the measurement object;
Based on the transfer function, a low-order mode calculation unit that calculates a mode parameter of the measurement object in the frequency band;
A higher-order mode vector estimation unit that estimates a natural vibration mode vector corresponding to a natural frequency outside the frequency band based on the mode parameter in the frequency band;
A mode parameter of the measurement object outside the frequency band is calculated based on the natural vibration mode vector, a first higher-order mode acceleration response expressed using the calculated mode parameter, and the measurement object The difference between the acceleration response in the transfer function of the object and the second higher-order mode acceleration response obtained by multiplying the natural vibration mode vector corresponding to the natural frequency outside the frequency band estimated by the higher-order mode vector estimation unit A vibration measurement device comprising an optimization calculation unit that performs a calculation for minimizing the frequency band in the frequency band.   The higher-order mode vector estimator uses, among the mode parameters in the frequency band, a natural frequency outside the frequency band by using an orthogonal expression with a natural vibration mode vector corresponding to the natural frequency in the frequency band. The vibration measurement apparatus according to claim 1, wherein a natural vibration mode vector corresponding to is estimated.   The optimization arithmetic unit individually minimizes real part minimization and imaginary part minimization of the first higher-order mode acceleration response and the second higher-order mode acceleration response, respectively. The vibration measuring device according to claim 1 or 2.   4. The vibration measuring apparatus according to claim 1, wherein the optimization calculation unit calculates a mode mass outside the frequency band prior to the calculation to be minimized. 5.   Further comprising a matrix calculation unit for calculating a characteristic matrix of the measurement object outside the frequency band and the frequency band based on mode parameters of the measurement object outside the frequency band and the frequency band. The vibration measuring device according to any one of claims 1 to 4.   The vibration measurement apparatus according to claim 5, wherein the matrix calculation unit calculates, as 0, a component that does not cause coupling in the stiffness matrix among the mode parameters of the measurement object.

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