SU1287116A1 - Device for determining non-linear characteristics of oscillating systems - Google Patents

Abstract

The invention relates to a test technique and can be used in cases where high accuracy and speed are required to determine the non-linear characteristics of the tested oscillatory systems. The purpose of the invention is to increase the informativity of determining the characteristics of the system - the device, besides the voltage source 1 at the first output 2, of which the signal is proportional to the movement, is a bandpass filter 4, first 7 and second 7 quadrants, adder 8, two-coordinate recorder 11, block 12 executions of the oscillation decrement and the second two-coordinate recorder, comprises a Hilbert transform unit 5, a differentiator 6, a square root extraction unit 9 and an instantaneous frequency calculation unit 10. 2 hp f-ly, 3 ill. (L

Description

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The invention relates to a test technique and can be used to determine the dynamic properties of structures, machines, mechanisms and other objects under the action of short-term shock loads, for example, when designing robotic manipulators, aircraft, etc., where high accuracy and speed are required. Determination of non-linear characteristics of the tested oscillatory - systems.

The purpose of the invention is the higher accuracy and informativeness of the experimental study of oscillatory systems.

FIG. 1 shows a block diagram of the proposed device; in fig. 2 is a block diagram of an instantaneous frequency calculation unit; in fig. 3 is a block diagram of an oscillation decrement calculation unit.

The device (Fig. 1) includes a mechanical oscillatory system with a source of voltage 1, a first output 2 proportional to speed, and a second output 3 proportional to displacement, a band-pass filter 4, a block 5 a transform, a Gilbert guide, a differentiator 6, the first 7 and a second squaring block, an adder 8, a square root extracting unit 9, an instantaneous frequency calculating unit 10, a first two coordinate recorder 11, a fluctuation decrement calculating unit 12, a second two-coordinate recorder 13. FIG. 1 is indicated: 14 and 15 — the inputs of the first 7 and second 7 squaring block; 16-18 are the second, third and fourth inputs of the instant frequency calculation unit 10; 19 and 20, respectively, its first and fifth inputs; 21 and. 22, respectively, the second and first inputs of the first two-coordinate recorder 11; 23 and 24 - the second and first input of the unit 12 for calculating the vibration decrement; 25 and 26 — the second and first inputs of the second two-coordinate register 13. In FIG. 2 denotes: 27 and 28 — the first and the second multiplier, 29 — the subtractor, 30 — the divider J by fi. 3 - 31 — the memory element of the maximum bend, 32 — the logarithmic divider, 33 — the divider.

The device works as follows.

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A shock mechanism (not shown) with a short pulse excites free oscillations in a mechanical oscillatory system. And the duration of the impact is much less than the period of natural oscillations of the system.

The voltage source 1 converts the mechanical oscillations into an electrical signal x (t) proportional to the displacement, on the second 3 and to an electrical signal x (t) proportional to the velocity on the first output 2.

The signal x (t) coming from the output of the bandpass filter 4 passes through the elements of the device, where it is converted and recorded.

On two-coordinate devices 13 and 11, the dependence of the instantaneous frequency of the signal f (t) and the decrement of oscillation 5 (t) on the instantaneous amplitude (envelope) of the signal A (t) is recorded.

The so-called skeleton curve of the oscillatory system, expressing the relationship between the instantaneous frequency f (t and the instantaneous amplitude (envelope) of the signal A (t.) During free oscillations, contains information about its own nonlinear elastic, i.e., its rigidity .

The skeletal curve in graphic form expresses the connection between the natural frequency of a nonlinear system and the amplitude of oscillations.

 To calculate the instantaneous amplitude (envelope) A (t), the device performs a calculation according to the formula

A (t) Hx (t) + x (t),

(one)

where x (t) is the Hilbert transform of the signal x (t), and the instantaneous frequency f (t) is calculated by the formula

, 1 x (t) x; (t) -x (t) Xr (t),,. f (t) 2. (2)

The calculation of these formulas is carried out in blocks and elements of the device as follows.

The signal x (t) is fed to the input 14 of the first squaring block, where x (t) is calculated. At the same time, this signal is fed to the input of the Hilbert transform unit 5, where X (t) is calculated.

The Hilbert transform block is made according to the algorithm specified in 43.

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The signal from the output of block 5 of the Hilbert transform occurs at the input of the second, block 15, squaring, the output of which will be the signal X (t) .. Then the signals from the blocks

The 7 squares are input to the adder 8, where x (t) + xVt is calculated. This signal is fed to the input of the square-root extraction unit 9 and then fed to the second input 21 of the first two-channel recorder 11 in the form (1) This is the instantaneous amplitude (envelope) of the signal.

To form the instantaneous frequency signal f (t), the second input 16 of the instant frequency calculation unit 10 is fed from the output of the adder 8 X (t) + x |. (T), to the third input 17 - the output of the Gilbert transform unit 5 X;. (T), to the fourth input 18 - the output 6 of the differentiator xj. (T), to the first input 19 - the signal x (t) from the output of the band-pass filter 4, to the fifth 20 - to the signal from the output 2 of the source 1 - zhenny, proportional to the speed x (t). In block 10, the calculation of the instantaneous frequency is carried out according to the formula (2).

The first product of the numerator is performed in the second multiplier 28 (FIG. 2), the second product. In the first multiplier 27, the product difference is calculated in subtractor 29. The difference is divided by the sum of squares and multiplied by a constant factor is performed in divider 30 .

The signal from the output of block 10 is fed to the first input 22 of the first two-coordinate recorder 11, where the skeleton curve of the oscillatory process is recorded.

Recording the dependence of the decrement of oscillations S (t) on the instantaneous amplitude (envelope) of the signal A (t). carried out in the second two-coordinate recorder 13.

L The decrement of oscillations. (T) is calculated in block 12 and is fed to the second input 26 of the second two-coordinate recorder 13. On-block 12, the envelope signal A (t) is received (FIG. 3).

8, the memory element 31 of the maximum envelope (peak detector) records, with the maximum value.

In the logarithmic divider 32, the maximum of the envelope is divided by the current value of the envelope in time, followed by the calculation

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logarithm of the private and the division by the current time, i.e. calculation

attenuation coefficient h (t) ln dt-gx /

/ t. - Then, in divider 33, the division of the signal from the output of the rhymic divider 32 log (attenuation coefficient h (t)) to the instantaneous frequency f (t) is stopped. Thus, the decrement of oscillations S (t) is calculated.

In the proposed device, the oscillation decrement determination block used in 21 is used as an oscillation decrement calculating unit.

Thus, the proposed device makes it possible to determine the degree of non-linearity of the structure. This facilitates and refines the calculation of the oscillatory system, taking into account its nonlinear properties. In a real construction, non-linear elastic forces and non-linear friction forces almost always work. The magnitude of the non-linearity is quantified for both non-linear damping (e.g., structural damping, dry friction), and non-linear elasticity (contact stiffness).

Claims (3)

Formula one . A device for determining the nonlinear characteristics of oscillating systems, comprising a voltage source connected by the first and second outputs respectively to the first and second inputs of a bandpass filter, an adder connected by the first and second inputs respectively to the outputs of the first and second squaring blocks, the first input of which is connected to the first input of the first two-coordinate registrar-. pa, and the output - with the first input of the second two-coordinate recorder, characterized in that, in order to increase the informativity of characterization of the system, the device comprises an instantaneous frequency calculating unit, a square root extraction unit, a differentiator and a Hilbert transform unit, the input of which is connected to the input of the first squaring unit, and the first 512 the input of the instantaneous frequency calculation unit, the second input of which is connected to the output of the adder and the input of the square root extraction unit, the third input to the output of the Hubert transform unit, the inputs of the second squaring unit and the differentiator, the fourth input to the differentiator output, the fifth input - with the second output of the bandpass filter, and the output - with the first input of the oscillation decrement calculator; the output of the square root calculator is connected to the second inputs of the first and second two-coordinate recorders and calculating the decrement of vibrations. 2, a device according to claim 1, of tl and h ayuschees. by that the instantaneous frequency calculation unit contains the first multiplier and the second multiplier connected in series, calculated 166 a divider and a divider connected by the output to the output of the block, and the second input to the first input of the block, the second and third inputs of the block are connected respectively to the first and second inputs of the first multiplier connected by the output to the second input of the subtractor, and the fourth and fifth inputs are connected respectively with the first and second inputs of the second multiplier. 3. The device according to claim 1, characterized in that the unit for calculating the vibration decrement contains serially connected memory elements of a maximum envelope, a logarithmic divider and a divider connected by an output to the output of the block, and -BTopbW input - to the first input of the block5 the second input of the block is connected with the second input of the logarithmic divider and the input of the memory element of the maximum envelope. 3 Fi, & FIG. five