JPH0357416B2 - - Google Patents

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a damping ratio measuring device, and particularly to a damping ratio measuring device that can accurately measure the damping ratio even from periodic data of a vibration system with poor coherence characteristics, such as a round bar. This article relates to a damping ratio measuring device that can be used.

[Conventional technology]

Conventionally, a vibration system is vibrated to detect periodic data regarding time changes such as acceleration, and output A and input F are detected.
The transfer characteristic A/F expressed as the ratio of , that is, the change in mobility (level) with respect to frequency freq is determined, and as shown in Figure 2, the mobility frequency is 3 dB lower than the mobility of the focused frequency (e.g., resonance point) fi. fu, f _L was determined, and the damping ratio ζ was determined based on the following formula.

ζ=2C/Cc=fu−f _L /fi...(1) [Problem to be solved by the invention] However, in such conventional attenuation ratio measurement methods, it is found that the coherence characteristic is poor at the focused frequency. Since the mobility at fi cannot be determined accurately, the frequency fu, f _L is 3 dB lower.
There was also a problem in that the accuracy of the value of was also poor, resulting in poor accuracy of the damping ratio. In other words, in Fig. 2, the coherence function represented by the broken line at the resonance point has a value close to 0, indicating a state in which the coherence characteristics are poor, but the coherence characteristics become extremely poor at the frequency fi, so The accuracy of the mobility is poor, and therefore the accuracy of the damping ratio is also poor.

[Means for solving problems]

In order to solve the above problems, the present invention was made by focusing on frequencies unrelated to mobility, and includes a detection means for detecting periodic data of a vibration system related to time changes, and a Fourier transform of the periodic data. A conversion means for calculating a transfer characteristic, a means for extracting real part data from the transfer characteristic, and a band pass means for passing only data in a predetermined frequency band whose center frequency is a focused frequency among the real part data of the transfer characteristic. and a calculating means for calculating a frequency representing a maximum value and a frequency representing a minimum value of the data passed through the band pass means and calculating an attenuation ratio based on the frequency representing the maximum value and the frequency representing the minimum value. We propose a damping ratio measuring device that includes

[Effect]

Next, the principle of the present invention will be explained. As shown in FIG. 3, the equation of motion of the spring-mass-dashpot system with one degree of freedom is expressed as follows.

Mx¨+cx〓+Kx=f...(2) where M is the mass, c is the damping coefficient, K is the spring constant, f is the external force, x is the displacement, x〓 and x¨ are each the first order of x with respect to time t. Differential, second-order differential.

Here, if we transform equation (2) by setting x=Xe ^jwt (where j=√−1 and w is the frequency), we get the following (3)
It becomes a ceremony.

(−Mw ² +K)×e ^jwt +jcw×e ^jwt =F (3) Next, when A=x¨, A/F is calculated as follows.

A/F= ^-w2 ×e ^jwt /(- ^Mw2 +K)×e ^jwt +jcw×
e ^jwt =Mw ⁴ −Kw ² +jcw ³ /(−Mw ² +K) ² +C ² w ² ……(4
) The above equation (4) is expressed as a function with the frequency w as a variable, and since A corresponds to the output and F corresponds to the input, the above equation (4) is the Fourier transform form of the output. It represents a transfer function G expressed as a ratio to the Fourier transform form of the input.

Let p be the real part of the above equation (4), and differentiate this real part p with respect to the frequency w, as follows.

dp／dw＝−2w{M(KM−C ² ) ⁴ −2MK ² w ² +K ³ }／{(
−Mw ² +K) ² +C ² w ² } ² (5) Here, find w such that dp/dw=0. Since the vibration system is vibrating, w≠0,
In order for dp/dw to be 0, the following equation must be satisfied.

M(KM−C ² )w ⁴ −2M ² w ² +K ³ = 0 ...(6) When w ² = r, finding the roots r ₁ and r ₂ of the quadratic equation, r ₁ = MK ² +√MK ³ C ² /M (KM−C ² ) …(7) r ₂ =MK ² −√MK ³ C ² /M (KM−C ² ) …(8) Above (7), (8) ) From the formula, r ₁ − r ₂ / r ₁ + r ₂ = C/√MK ...(9) By the way, the critical damping coefficient Cc is expressed as Cc=2√ ...(10), so the above (9) The formula becomes:
It represents the damping ratio.

r ₁ − r ₂ / r ₁ + r ₂ = C/√MK = 2C/Cc...(11) In the above equation (11), r ₁ = w ₁ ² and r ₂ = w ₂ ² , so the damping ratio ζ is expressed as follows.

ζ＝w ₁ ² −w ₂ ² /w ₁ ² +w ₂ ² ...(12) In the above, we considered a vibration system with one degree of freedom, but the vibration characteristics of a general vibration system with multiple degrees of freedom are It can be considered as a superposition of the vibration characteristics of a multi-degree-of-freedom vibration system, and conversely, if we focus on the transmission characteristics of a specific frequency band of a multi-degree-of-freedom vibration system, it can be considered as a vibration system with one degree of freedom. The damping ratio can be determined by applying the above principle.

The present invention measures the damping ratio based on the above-mentioned principle, in which periodic data of a vibration system related to time changes is detected by a detection means, and the periodic data is Fourier-transformed by a conversion means, as described in (4) above. Calculate the transfer characteristic shown in the formula, and pass only data in a predetermined frequency band whose center frequency is the focused frequency among the real part data of the transfer characteristic by a band pass means,
The frequency indicating the maximum value and the frequency indicating the minimum value of the data passed through the band pass means are determined by the calculating means, and the attenuation ratio is calculated using the above equation (12). Here, in order to calculate the transfer characteristic, it is necessary to use acceleration data as input, but when the detection means detects periodic data of displacement, by second-order differentiation, When detecting data, it can be converted into acceleration data by first-order differentiation.

〔Example〕

An embodiment of the present invention will be described in detail below with reference to FIG. This embodiment is suitable for measuring the damping ratio of an automobile body, etc.

The accelerometer 2 is attached to the vibration system and detects acceleration as periodic data regarding time changes.
The signal output from this accelerometer 2 is A in Fig. 1.
The data is on a time axis as shown in . This accelerometer 2 is connected to a Fourier transformer 4 made up of a microprocessor. This Fourier transformer 4 has the same configuration as the conventional one, and performs a fast Fourier transform on input time axis data and calculates a transfer characteristic as frequency axis data, and the real part data of this transfer characteristic is The result is as shown in Figure 1B. A bandpass filter 6 whose center frequency fi can be variably set is connected to the real part data output terminal of the Fourier transformer 4. By setting the center frequency of the bandpass filter to the frequency of interest,
As shown in FIG. 1C, the bandpass filter 6 outputs a predetermined band signal whose center frequency is the frequency of interest. A central processing unit (CPU) 8 is connected to the output end of the bandpass filter 6, and the CPU 8 differentiates the frequency axis data input from the bandpass filter 6 with respect to frequency, and the differential coefficient becomes 0. The frequencies w ₁ and w ₂ are determined, and the damping ratio ζ is calculated based on the above equation (12). Then, the damping ratio ζ calculated by CPU8 is
Displayed on display device 12 or printer 10.

That is, by setting the frequency for determining the damping ratio (the frequency of interest) in the bandpass filter and inputting time axis data, the damping ratio will be displayed.

Although the above example uses an accelerometer, it is also possible to use a displacement meter or speedometer.
In this case, the data is converted into acceleration data using a Fourier transformer and processed. Also, a Fourier transformer,
The band bus filter and the CPU may be configured in one computer.

〔Effect of the invention〕

As explained above, since the present invention measures the damping ratio using a frequency that is not related to mobility, the present invention has the advantage that the damping ratio can be easily and accurately determined in a vibration system with poor coherence characteristics. It will be done.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing one embodiment of the present invention;
FIG. 2 is an explanatory diagram for explaining a conventional method of determining a damping ratio, and FIG. 3 is a diagram showing a spring-mass dumppot system. 2...accelerometer, 4...Fourier transformer, 6...bandpass filter, 8...CPU.

Claims (1)

[Scope of Claims] 1: a detection means for detecting periodic data of a vibration system related to time changes; a conversion means for Fourier transforming the periodic data to calculate a transfer characteristic; and extracting real part data from the transfer characteristic. means, a band pass means for passing only data in a predetermined frequency band centered on a frequency of interest among the real part data, and a frequency indicating a maximum value and a frequency indicating a minimum value of the data passed through the band pass means. A damping ratio measuring device comprising: a calculation means for calculating a damping ratio based on;