Rotational inertia high-precision measuring method and measuring device

Abstract

The invention relates to a rotational inertia high-precision measuring method and measuring device, and belongs to the technical field of inertia measurement. According to the scheme, a magnetic grid sensor is used for reading a displacement change signal generated by torsional pendulum motion of a to-be-measured disc; identifying the wave crests of the displacement change signals to obtain a wave crest point moment sequence, intercepting sampling subinterval data in a set sampling interval before and after each wave crest point moment, carrying out curve fitting on the sampling subinterval data to obtain function expressions, taking first-order derivatives about time from all the function expressions, and calculating the first-order derivatives of all the function expressions; calculating an accurate wave crest time point when the first-order derivative is zero in the corresponding sampling subinterval; and substituting each accurate wave crest time point into the corresponding function expression to obtain a wave crest point amplitude sequence, and calculating a torsional pendulum period value for calculating the rotational inertia of the torsional pendulum motion according to a time difference between two adjacent wave crests in the wave crest point amplitude sequence. The problem that the position repeated triggering precision of a position sensor or a photoelectric coupler is low is solved, and high-precision measurement of the rotational inertia is achieved.

Description

Technical Field

[0001] The invention relates to a high-precision measurement method and a measurement device for moment of inertia, belonging to the technical field of inertial measurement. Background Art

[0002] The moment of inertia is a physical quantity that characterizes the size of a rigid body's rotational inertia and measures the inertia of a rigid body against rotational motion. In the fields of aerospace and weapons and equipment, the moment of inertia is an important characteristic parameter of various aircraft, and the measurement of the moment of inertia requires high precision.

[0003] The moment of inertia is generally measured using the torsion pendulum method based on a vertical rotating axis. In a given single-degree-of-freedom vibration system, if the damping is very small, ignoring the effects of air and mechanical friction damping, the system vibration equation is simplified to the first-order constant coefficient vibration differential equation shown below:

[0004]

[0005] In the formula, J is the moment of inertia of the object being measured, and k is the elastic stiffness coefficient of the torsion bar. Solving the equation yields:

[0006] J=kT 2

[0007] That is, the moment of inertia J of the oscillating part of the system is proportional to the square of its vibration period T. The moment of inertia of the workpiece to be measured can be calculated by measuring the oscillation period of the product and comparing it with the standard sample.

[0008] From the calculation formula of the moment of inertia measured by the torsion pendulum method, it can be seen that the acquisition accuracy of the torsion pendulum period is crucial. The most commonly used method for acquiring the moment of inertia torsion pendulum period is to place a position sensor (proximity switch or Hall sensor) or a slit-type photoelectric coupling sensor within the range of the torsion pendulum movement. During the torsion pendulum process, the sensor is periodically triggered to generate a pulse signal, and then the torsion pendulum period is acquired by a high-speed pulse counter.

[0009] The above method is difficult to achieve high-precision acquisition of the torsion pendulum cycle due to the low position repetition triggering accuracy of the position sensor or photoelectric coupler. In addition, due to the influence of air and mechanical damping, the torsion pendulum amplitude will gradually decrease, and the installation position of the sensor cannot be accurately in the static equilibrium position (maximum angular velocity position), which will also affect the accurate acquisition of the torsion pendulum cycle. Summary of the invention

[0010] The purpose of the present invention is to provide a high-precision measurement method and device for the moment of inertia, so as to solve the problem that the torsion pendulum period is difficult to measure with high precision due to the low measurement precision of the torsion pendulum period.

[0011] To achieve the above object, the solution of the present invention includes:

[0012] The invention discloses a technical solution for a method for measuring the moment of inertia with high precision. The method comprises the following steps: using a magnetic grating sensor to read a displacement change signal generated by the torsion pendulum motion of a disk to be measured; identifying the peak of the displacement change signal to obtain a peak point time sequence; intercepting sampling sub-interval data in a sampling interval set before and after each peak point time; performing curve fitting on the sampling sub-interval data to obtain a function expression; taking the first-order derivative with respect to time for all the function expressions, and obtaining the precise peak time point at which the first-order derivative is zero in the corresponding sampling sub-interval; substituting each precise peak time point into the corresponding function expression to obtain a peak point amplitude sequence; and calculating the torsion pendulum period value for calculating the moment of inertia of the torsion pendulum motion according to the time difference between two adjacent peaks in the peak point amplitude sequence.

[0013] Furthermore, the time difference between multiple groups of two adjacent peaks in the peak point amplitude sequence is taken and the average is calculated as the time difference value.

[0014] Furthermore, the torsion swing period value T is calculated by the following formula: c :

[0015]

[0016] Among them, T0 is the direct measurement period value of the time difference, ξ is the system damping ratio, and the system damping includes the damping caused by mechanical friction and air resistance.

[0017] Furthermore, the system damping ratio ξ is calculated using the ratio of two amplitudes separated by a positive integer N periods:

[0018]

[0019] Among them, a i is the i-th peak point amplitude in the peak point amplitude sequence, a i+N is the i+Nth peak point amplitude in the peak point amplitude sequence.

[0020] Furthermore, a second-order differential discrimination method is used to identify the peak of the displacement change signal; and the function expression is obtained by curve fitting according to a polynomial function.

[0021] A technical solution of a high-precision moment of inertia measurement device of the present invention comprises a magnetic scale tape arranged on the outer peripheral surface of a disk to be measured and a corresponding magnetic scale reader, wherein the magnetic scale tape and the magnetic scale reader constitute a magnetic scale sensor; the magnetic scale reader is connected to a signal acquisition device, and the signal acquisition device is used to acquire a displacement change signal generated by the magnetic scale sensor when the disk to be measured is in torsional swing motion.

[0022] Furthermore, the signal acquisition device also identifies the peak of the displacement change signal to obtain a peak point time sequence, intercepts sampling sub-interval data within a sampling interval set before and after each peak point, performs curve fitting on the sampling sub-interval data to obtain a function expression, takes the first-order derivative with respect to time for all function expressions, and obtains the precise peak time point at which the first-order derivative is zero in the corresponding sampling sub-interval; substitutes each precise peak time point into the corresponding function expression to obtain a peak point amplitude sequence, and calculates the torsion pendulum period value used to calculate the moment of inertia of the torsion pendulum motion based on the time difference between two adjacent peaks in the peak point amplitude sequence.

[0023] Furthermore, the time difference between multiple groups of two adjacent peaks in the peak point amplitude sequence is taken and the average is calculated as the time difference value.

[0024] Furthermore, the torsion swing period value T is calculated by the following formula: c :

[0025]

[0026] Among them, T0 is the direct measurement period value of the time difference, ξ is the system damping ratio, and the system damping includes the damping caused by mechanical friction and air resistance.

[0027] Furthermore, the system damping ratio ξ is calculated using the ratio of two amplitudes separated by a positive integer N periods:

[0028]

[0029] Among them, a i is the i-th peak point amplitude in the peak point amplitude sequence, a i+N is the i+Nth peak point amplitude in the peak point amplitude sequence.

[0030] The beneficial effects of the present invention are:

[0031] The present invention adopts a magnetic grating displacement sensor to continuously collect the torsion swing periodic signal at high speed, solving the problem of low position repetitive triggering accuracy of position sensors or photoelectric couplers. At the same time, the collected data is analyzed and processed, and the measured values ​​of the period under different damping ratio conditions and different swing amplitude conditions are corrected, so as to achieve high-precision measurement of the swing period value, thereby improving the accuracy of the moment of inertia measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a structural principle diagram of a high-precision moment of inertia measuring device of the present invention;

[0033] Figure 2 It is a schematic diagram of a curve obtained by fitting each sampling sub-interval data according to a polynomial function;

[0034] Figure 3 It is a schematic diagram of the effect of system damping on the swing period. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is described in detail in a clear and complete manner in conjunction with the accompanying drawings and embodiments.

[0036] The present invention adopts a magnetic grating displacement sensor to continuously collect torsion swing periodic signals at high speed, analyzes and processes the collected data, and can correct the measured values ​​of the period under different damping ratio conditions and different swing amplitude conditions to achieve high-precision measurement of the swing period value, thereby improving the accuracy of the moment of inertia measurement.

[0037] Device Example:

[0038] Figure 1 The structure principle diagram of a high-precision moment of inertia measuring device of the present invention is shown, which includes a central rotating shaft 5 fixed on a base 6, a disk 4 to be measured for moment of inertia is fixed on the rotating shaft 5, a magnetic scale tape 2 is arranged on the outer circumference of the disk 4, and a magnetic grid reader 1 is arranged at a position corresponding to the magnetic scale tape 2 through a mounting bracket 3, which is used to read the oscillating motion cycle through the relative movement between the magnetic grid reader 1 and the magnetic scale tape 2 when the disk 4 performs oscillating motion around the rotating shaft 5. The magnetic grid reader 1 is further connected to a signal acquisition device to acquire oscillating motion signals, and further extract the oscillating motion cycle based on the oscillating motion signals. In order to improve the accuracy, the oscillating motion cycle can be further corrected.

[0039] Specifically, the disk 1 can perform torsional swing motion around the central rotating axis 5 under the action of the elastic force of the elastic element, and the magnetic scale tape 2 is fixedly installed in the circumferential direction close to the outer edge of the disk. When the disk 1 is stationary, the magnetic scale reader 1 is installed toward the magnetic scale tape 2 at the middle position corresponding to the magnetic scale tape 2 and a certain gap is maintained between the two. The magnetic scale tape 2 and the magnetic scale reader 1 constitute a magnetic scale sensor.

[0040] In the magnetic grating sensor, the magnetic scale tape does not contact the magnetic grating reader. According to the working requirements of the magnetic grating sensor, the spacing is generally greater than 0 and less than 1.2mm.

[0041] Considering that the yaw angle of general yaw motion is within ±5 degrees, the length of the magnetic scale tape only needs to cover approximately 10 degrees of the outer edge of the disk of rotational inertia to be measured.

[0042] A method for measuring the moment of inertia with high precision of the present invention can be implemented based on the above-mentioned device for measuring the moment of inertia with high precision.

[0043] The disk 1 is pushed by the pushing mechanism to a certain angle, and after being released, it performs a torsional swing motion around the central axis 5; the signal acquisition device acquires the displacement change signal S(t) of the disk torsional swing motion generated by the magnetic grid sensor.

[0044] The collected oscillating motion signal S(t) is processed by calculation according to the following steps to extract the oscillating motion period:

[0045] Step 1: Use the second-order difference discrimination method in the prior art to identify all the peaks of the sampled data S(t) and obtain the peak point time sequence P = [p1, p2, ..., p n ], (n≥2); Due to the influence of the sampling time interval and the disturbance of the sampling signal, the peak point time sequence P is difficult to accurately represent the peak time of the torsion pendulum motion, so it is necessary to further improve the measurement accuracy through the following curve fitting steps;

[0046] Step 2: Divide the interval between two adjacent peak points according to a predetermined equal division ratio K, and the sampling window length is W = (p n -p n-1 ) / K, (K≥4 and W≥2);

[0047] Step 3: At each peak point t n The sampling sub-interval data Sn(t) is intercepted in each of the W width intervals before and after (the sampling time t satisfies: p n -W≤p n +W, that is, the sampling times beyond the start and end times are not included in this sub-interval);

[0048] Step 4: Perform curve fitting on each sampling sub-interval data Sn(t) according to the polynomial function to obtain the function expression fn(t);

[0049] Step 5: Take the first-order derivative of each fn(t) with respect to time t, and find the time point z at which the first-order derivative expression is zero in the subinterval. n , we can get the precise peak point sequence of the torsion pendulum motion Z = [z1, z2, …, z n ], the time point z of a certain (for example, the nth) peak point n and p n The relationship is as Figure 2 As shown; z n Substitute the subinterval function expression fn(t) into the peak point amplitude sequence A=[a1,a2,…,a n ];

[0050] Step 6: The time difference between two adjacent wave peaks of the torsion pendulum motion is the period value, and the average value of the difference between multiple adjacent points in sequence Z is taken as the directly measured period value T0 of the torsion pendulum motion;

[0051] Step 7: Theoretically, the period value of each swing cycle of the torsion pendulum motion is equal, but considering factors such as mechanical friction and air resistance, the period value will vary slightly, such as Figure 3There will be a slight change between the period values ​​T1 and T2 of two adjacent periods. Considering these factors, the period value T0 is corrected according to the system damping ratio to obtain the system's accurate undamped period value T c .

[0052] Specifically, the system undamped period value T c :

[0053]

[0054] Where T0 is the period value directly measured by the torsion pendulum motion signal, and ξ is the system damping ratio.

[0055] The system damping ratio ξ can be obtained by calculating the instantaneous amplitude ratio of adjacent cycles. To improve the measurement accuracy, the two amplitude ratios separated by N cycles can usually be used for calculation:

[0056]

[0057] Where N is a positive integer, a i is the i-th peak amplitude in the peak amplitude sequence A, a i+N is the i+Nth peak point amplitude in the peak point amplitude sequence A.

[0058] When analyzing and calculating the moment of inertia under air damping conditions, the damped vibration period measured can be converted into an undamped vibration period through the damping ratio, and the moment of inertia value of the workpiece to be measured is calculated under undamped conditions, which can further improve the measurement accuracy of the moment of inertia.

[0059] Method Example:

[0060] The method for high-precision measurement of moment of inertia of the present invention has been clearly introduced in the device embodiment and will not be repeated here.

Claims

1. A high-precision measurement method for moment of inertia, characterized in that: The displacement change signal generated by the torsion swing motion of the disk to be tested is read by using a magnetic grating sensor; the peak of the displacement change signal is identified to obtain a peak point time sequence, sampling sub-interval data is intercepted in a sampling interval set before and after each peak point, and a function expression is obtained by curve fitting of the sampling sub-interval data, the first-order derivative with respect to time is taken for all function expressions, and the precise peak time point at which the first-order derivative is zero in the corresponding sampling sub-interval is obtained; Substituting each precise peak time point into the corresponding function expression to obtain a peak point amplitude sequence, the pendulum period value used to calculate the moment of inertia of the pendulum motion is calculated according to the time difference between two adjacent peaks in the peak point amplitude sequence.

2. The high-precision measurement method of moment of inertia according to claim 1 is characterized in that: The time difference between two adjacent peaks in the peak point amplitude sequence is taken and the average is calculated as the time difference.

3. The high-precision measurement method of moment of inertia according to claim 2 is characterized in that: The torsion period value T is calculated by the following formula c : Among them, T0 is the direct measurement period value of the time difference, ξ is the system damping ratio, and the system damping includes the damping caused by mechanical friction and air resistance.

4. The high-precision measurement method of moment of inertia according to claim 3 is characterized in that: The damping ratio ξ of the system is calculated using the ratio of two amplitudes separated by a positive integer N cycles: Among them, a i is the i-th peak point amplitude in the peak point amplitude sequence, a i+N is the i+Nth peak point amplitude in the peak point amplitude sequence.

5. The high-precision measurement method of moment of inertia according to claim 1 is characterized in that: The second-order difference discrimination method is used to identify the peak of the displacement change signal; and the function expression is obtained by curve fitting according to the polynomial function.

6. A high-precision moment of inertia measuring device, characterized in that: It includes a magnetic scale tape arranged on the outer peripheral surface of the disc to be measured and a corresponding magnetic scale reader, wherein the magnetic scale tape and the magnetic scale reader constitute a magnetic scale sensor; the magnetic scale reader is connected to a signal acquisition device, and the signal acquisition device is used to acquire the displacement change signal generated by the magnetic scale sensor when the disc to be measured is in torsional motion.

7. The high-precision moment of inertia measuring device according to claim 6, characterized in that: The signal acquisition device further identifies the peak of the displacement change signal to obtain a peak point time sequence, intercepts sampling sub-interval data in a sampling interval set before and after each peak point, performs curve fitting on the sampling sub-interval data to obtain a function expression, takes the first-order derivative with respect to time for all function expressions, and obtains the precise peak time point at which the first-order derivative is zero in the corresponding sampling sub-interval; Substituting each precise peak time point into the corresponding function expression to obtain a peak point amplitude sequence, the pendulum period value used to calculate the moment of inertia of the pendulum motion is calculated according to the time difference between two adjacent peaks in the peak point amplitude sequence.

8. The high-precision moment of inertia measuring device according to claim 7, characterized in that: The time difference between two adjacent peaks in the peak point amplitude sequence is taken and the average is calculated as the time difference.

9. The high-precision moment of inertia measuring device according to claim 8, characterized in that: The torsion period value T is calculated by the following formula c : Among them, T0 is the direct measurement period value of the time difference, ξ is the system damping ratio, and the system damping includes the damping caused by mechanical friction and air resistance.

10. The high-precision moment of inertia measuring device according to claim 9, characterized in that: The damping ratio ξ of the system is calculated using the ratio of two amplitudes separated by a positive integer N cycles: Among them, a i is the i-th peak point amplitude in the peak point amplitude sequence, a i+N is the i+Nth peak point amplitude in the peak point amplitude sequence.

Images