CN103674425A - Rotational inertia measuring method and device - Google Patents

Abstract

The invention discloses a rotational inertia measuring method including the steps of 1), rotationally mounting an object on two fulcrums 2), providing auxiliary supporting to the object by springs; 3), applying force to the object and then releasing the force to enable the object to do torsional vibration; 4), acquiring the natural frequency of the object; 5), setting additional standard mass blocks in sequence and then repeating the step 3) and the step 4) after each setting so as to acquire data; 6), performing linear regression analysis to the data to acquire the rotational inertia of the object. The invention further discloses a rotational inertial measuring device comprising the additional standard mass blocks, a vibration sensor, a data acquisition system and a supporting mechanism, wherein the data acquisition system is connected with the vibration sensor, and the supporting mechanism is used for supporting the object. As the object is rotationally mounted on the two fulcrums to do torsional vibration, the rotational inertia of the object can be acquired rapidly and accurately by means of existing vibration measurement process and the regression analysis. In addition, the object can be of non-symmetrical structure; the rotational inertia measuring method and the rotational inertia measuring device have wide application range.

Description

A kind of method of testing of moment of inertia and device

Technical field

The present invention relates to mechanical characteristic field, be specifically related to a kind of method of testing and device of moment of inertia, be applicable to the test of the moment of inertia of aerocraft system, satellite system, vessel etc.

Background technology

Moment of inertia (Moment of Inertia) is rigid body while swaying the measuring of inertia (revolution object keeps its uniform circular motion or static characteristic).The moment of inertia of rigid body has important physical significance, at industrial circles such as scientific experiment, engineering, space flight, electric power, machinery, instrument, is also an Important Parameters.The indication mechanism of electromagnetic instrument, different because of the moment of inertia of coil, can be respectively used to measure Weak current (galvanometer) or electric weight (ballistic galvanometer).In the configuration design of engine blade, flywheel, gyro and artificial satellite, accurately measure moment of inertia, be all very necessary.

Moment of inertia is only decided by the position of shape, mass distribution and the rotating shaft of rigid body, and irrelevant around the rotary state (as the size of angular velocity) of axle with rigid body.The homogeneous rigid body of regular shape, its moment of inertia can directly calculate with formula.And for the moment of inertia of irregular rigid body or heterogeneous body rigid body, general method is by experiment measured, thereby experimental technique just seems very important.

In engineering reality, need to survey the moment of inertia of general structure, for example aircraft and spacecraft, in flight course, need to adjust control parameter according to its moment of inertia.Each assembling parts is converted and often can accurately do not obtained system-level rotational inertia data by theory.If the system of certain type unmanned plane is a subassembly that has different task load, has middle control computer, oil plant, by the attitude that drives aileron to complete unmanned plane, control, be a comparatively servo-drive system for complicated mechanical-electric coupling, its driving force size is directly proportional to the moment of inertia of system.Actual use finds that such unmanned plane has certain gap according to design-calculated moment of inertia and actual test, must carry out the moment of inertia test of standard, and also to moment of inertia, test has special code requirement to air line.

The method of testing of moment of inertia is conventional three-line pendulum test generally, and the method has advantage quickly and easily.The principle of three-line pendulum test: two different disks of radius (upper disk and lower disc) are connected with three isometric lines.Two disks are all transferred to level, and the center of circle is on same perpendicular line, and upper disc radius is less than lower disc radius.Lower disc can reverse (doing simple harmonic oscillation) around the center line of two disks, and it turns round and by the moment of inertia of lower disc, is determined cycle turnover.When the moment of inertia change (as additional jobbie on lower disc) of lower disc, its torsion cycle will change.Three-line pendulum is exactly by measuring its torsion cycle, to draw the moment of inertia of any mass objects.

The principle of three-line pendulum test moment of inertia derives many devices.As Granted publication number discloses a kind of three line Inertia Based on Torsion Pendulum Method rotational inertia test apparatus for the patent documentation of CN200996883Y, comprise a support with upper cross plate and lower cross plate, a upper disk, a lower swinging disc, three wire rope, three wire rope adjusting mechanisms that are fixed on adjustable steel wire rope length on disk, be arranged on the fixture that can fix tested article on lower swinging disc, upper disk and lower swinging disc center coaxially arrange, one end of wire rope is fixedly connected on wire rope adjusting mechanism, the other end is successively by upper disk and lower swinging disc serial connection, on upper cross plate, be fixedly connected with the reducing gear of output shaft free end precision drive downward and that vertically arrange, the central horizontal of upper disk is fixedly connected on the free end of output shaft, a side that is positioned at lower swinging disc on lower cross plate is fixedly connected with the detent mechanism with scalable thimble, offers and the corresponding recess of thimble head on lower swinging disc edge, and thimble stretches out state can snap in this recess.Utilize that this patent tests that the moment of inertia of tested article is easy to operate, test accurately.

But because three-line pendulum adopts flexible suspension, tested object does not often have symmetry, generally has when rotated and rotates and rock two kinds of aggregate motions, has a strong impact on test result.Especially for the aerocraft system with fuel oil etc., the apparatus for vertical placing of three-line pendulum and aircraft conventionally closely the state of tangential movement be not inconsistent.For Large Scale Space Vehicle system, as fighter plane and airline carriers of passengers, the pendulum length of three-line pendulum requires large to being difficult to realization, reaches the magnitude of hundreds of meters.

Summary of the invention

For the problems referred to above, the invention provides a kind of method of testing of moment of inertia.With solving three-line pendulum method of testing, easily rotate and rock two kinds of aggregate motions and affect the problem of test result, and to inapplicable problems such as aircraft.

A method of testing for moment of inertia, comprises the following steps:

1) provide two fulcrums, tested object is rotatably installed on corresponding fulcrum, and the line of two fulcrums is the turning axle of tested object.

2) by spring, provide two elastic supports in order to the tested object of supplemental support, the position of two elastic supports is about the axisymmetry of tested object;

3) to a side application of force of tested object, tested object is rotated, release force, makes tested object do twisting vibration around the turning axle of self;

4) obtain the natural frequency of tested system;

Tested system refers to tested object and spring, if added additional standard mass, tested system is tested object, spring and additional standard mass.

5) in a side of tested object, successively place additional standard mass, after each placement, all repeat step 3) to 4), the natural frequency of tested system after the each placement of acquisition additional standard mass;

6) natural frequency of some groups of tested systems that obtain according to step 4) and step 5) and the corresponding additional standard mass of this frequency are around the moment of inertia of the turning axle of tested object, by these data are carried out to linear regression analysis, obtain the moment of inertia of tested object again.

While not placing additional standard mass, the natural frequency f of tested system:

$f=\frac{1}{2\mathrm{\π}}\sqrt{\frac{\mathrm{nkD}}{J}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J}}---\left(1\right)$

The elasticity coefficient that wherein k is spring; When tested object bilateral all has spring, n is 2, and when tested object only has a side to have spring, n is 1; D is that spring center line is to the distance of the turning axle of tested object; K ₀for coefficient of colligation, its value is the product of nkD; J is that tested object is around the moment of inertia of turning axle;

While placing additional standard mass, the natural frequency f of tested system _i:

$f_i=\frac{1}{2\mathrm{\π}}\sqrt{\frac{\mathrm{nkD}}{J+m_i{D}_i}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J+m_i{D}_i}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J+J_i}}---\left(2\right)$

M wherein _iquality for additional standard mass; D _ifor the distance of additional standard mass center of gravity to the turning axle of tested object; J _ifor the moment of inertia of additional standard mass around turning axle;

Formula (2) transition form can obtain formula (2.1):

J _i＝K ₀/(2πf _i) ²-J (2.1)

According to formula (2.1), determine linear fit equation (3):

$J_i=\stackrel{\_}{K_o}/{\left(2\mathrm{\π}{f}_i\right)}^2-J---\left(3\right)$

Wherein

for equivalent stiffness, it is the slope of linear fit equation; Every group of J _iwith 1/ (2 π f _i) ²form a bit, when not placing additional standard mass, corresponding additional standard mass is 0kgm around the moment of inertia of turning axle ².Several points are carried out to least square linear fit, obtain the moment of inertia J of tested object.

As preferably, step 2) in, the spring at two elastic support places all compressed 15%～30%.Spring keeps a suitable initial compression amount can promote the precision of test, makes tested object have rotatablely moving of better quality.

As preferably, step 3) angle of tested object rotation is 5 °～15 °.The anglec of rotation is larger or littlely all can affect gyrating mass, affects the precision of test data.

As preferably, step 4) in, by some vibration transducers that are connected with data acquisition system (DAS) are installed in the structure of tested object, record the vibration signal of tested object, and the vibration signal of record is processed to obtain the natural frequency of tested system by data acquisition system (DAS).

The kind of vibration transducer has multiple, and the type of selecting determines according to test request, and as preferably, described vibration transducer is laser displacement sensor or acceleration transducer.Laser sensor is more accurate, is applicable to the less accurate measurement of structural vibration displacement, and laser sensor do not produce additional mass, is used for gathering displacement signal; Acceleration transducer, uses extensively, and service band is wider, gathers acceleration signal.

As preferably, the described data acquisition system sampling time is 10～20s.Sampling time determines according to the frequency of tested object, and the low sampling time of frequency is long, frequency height the sampling time short.

As preferably, sample frequency is 100～200Hz.Sample frequency is relevant with the frequency of measurand, and sample frequency is 5～12 times of measurand frequency.

The present invention also provides a kind of proving installation of moment of inertia.With solving, adopt the device of three-line pendulum principle because easily rotating and rocking the problem that two kinds of aggregate motions affect test result, and to inapplicable problems such as aircraft.

A kind of proving installation of moment of inertia, comprise for being arranged on additional standard mass and the vibration transducer on tested object, and the data acquisition system (DAS) being connected with described vibration transducer, also comprise that this supporting mechanism comprises for supporting the supporting mechanism of tested object:

Bearing;

Be arranged on two bearings on described bearing;

Be fixed on two springs on described bearing, the both sides that are arranged in bearing axis of described two spring symmetries.

Described two bearings and two springs provide four strong points for tested object.

As preferably, described two coaxial bearing are arranged.

Also comprise an inclinometer and telemeter rod.The angle that inclinometer is pressed in order to test; The pre compressed magnitude of measuring spring for telemeter rod, spring center line, additional standard mass center of gravity be the distance of the turning axle of tested object extremely.

The invention has the beneficial effects as follows: by tested object being rotatably installed on two fulcrums, the spring that coordinates two supplemental support, make tested object can rotate freely vibration, attenuation due to vibration, the frequency of vibration is pure, test period is very short, in conjunction with the method for testing vibration of existing system, and can obtain accurately fast the moment of inertia of measurand by regretional analysis; Tested can be unsymmetric structure, applied widely.

Accompanying drawing explanation

Fig. 1 is the schematic diagram of the method for testing of moment of inertia of the present invention;

Fig. 2 is the linear fit rectilinear of the embodiment of the present invention;

Fig. 3 is the structural representation of the proving installation of moment of inertia of the present invention.

1. bearing, 2. bearing, 3. spring, 4. vibration transducer, 5. additional standard mass.

Embodiment

The present embodiment is to utilize the method for testing of moment of inertia of the present invention to test model plane, and model plane weight is 150kg, and length is 2.5m, because of the needs that flight is controlled, now measures model plane around the moment of inertia of its central shaft.As shown in Figure 1, concrete steps are as follows:

1) provide two bearings as fulcrum, model plane head and the tail two ends are arranged on corresponding bearing, and the line of two bearing axis is the turning axle of model plane.

The line of two bearing axis can not be the central axis of tested object, and this method can be tested unsymmetric structure.

2) by spring, provide two elastic supports in order to supplemental support model plane; the position of spring is at the thriving nose part of model airplane machine, and the position of two elastic supports is about the axisymmetry of model plane, and spring initial length is 20cm; the elastic coefficient is 200N/cm, spring compressed 20% after installing.

3) to a side application of force of model plane, make 10 ° of model plane rotations, release force, makes model plane do twisting vibration around the turning axle of self.

4) 3 acceleration transducers are installed on model plane, be arranged on successively on port wing, fuselage (position aligns turning axle), starboard wing, and acceleration transducer is connected with data acquisition system (DAS), by data acquisition system (DAS), record the vibration signal of model plane, the sampling time of acquisition system is 13s, sample frequency is 100Hz, again gathered vibration signal is carried out to digital signal processing after having gathered the vibration signal of unmanned plane, obtains the natural frequency of tested system.

Tested system refers to tested object and spring, if added additional standard mass, tested system is model plane, spring and additional standard mass.

5) in a side of model plane wing, successively place additional standard mass; after each placement, all repeat step 3) to 4); the natural frequency of tested system after the each placement of acquisition additional standard mass; as shown in table 1; for each test sequence number corresponding parameter list, comprise that the distance, additional standard mass of additional standard mass quality, additional standard mass center of gravity and model plane turning axle are around the moment of inertia of turning axle and the natural frequency of tested system.

Table 1

6) according to step 4) and step 5), obtain four groups of data in table 1, every group of data comprise that the natural frequency of tested system and the corresponding additional standard mass of this frequency are around the moment of inertia of turning axle, by these data are carried out to linear regression analysis, obtain the moment of inertia of model plane again.

While not placing additional standard mass, the natural frequency f of tested system is shown in formula (1):

$f=\frac{1}{2\mathrm{\π}}\sqrt{\frac{\mathrm{nkD}}{J}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J}}---\left(1\right)$

The elasticity coefficient that wherein k is spring; When model plane bilateral all has spring, n is 2, and when model plane only have a side to have spring, n is 1; D is that spring center line is to the distance of the turning axle of model plane; K ₀for coefficient of colligation, its value is the product of nkD; J is that model plane are around the moment of inertia of turning axle;

While placing additional standard mass, the natural frequency f of tested system _isee formula (2):

$f_i=\frac{1}{2\mathrm{\π}}\sqrt{\frac{\mathrm{nkD}}{J+m_i{D}_i}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J+m_i{D}_i}}=\frac{1}{2\mathrm{\π}}\sqrt{\frac{K_0}{J+J_i}}---\left(2\right)$

M wherein _iquality for additional standard mass; D _ifor the distance of additional standard mass center of gravity to the turning axle of model plane; J _imoment of inertia for the turning axle of additional standard mass deviation from voyage route mould;

Formula (2) transition form can obtain formula (2.1):

J _i＝K ₀/(2πf _i) ²-J （2.1）

According to formula (2.1), determine linear fit equation (3):

$J_i=\stackrel{\_}{K_0}/{\left(2\mathrm{\π}{f}_i\right)}^2-J---\left(3\right)$

Wherein

for equivalent stiffness, it is the slope of linear fit equation; Every group of J _iwith 1/ (2 π f _i) ²form a bit, altogether four point (J _i, f _ivalue in Table 1), when not placing additional standard mass, i is 0, m ₀be 0, J ₀be 0.

Four points are carried out to least square linear fit, as shown in Figure 2, obtain linear fit equation

J _i＝201.1453(2πf _i) ²-5.6622

Finally obtain the moment of inertia J=5.6622kgm of model plane ².

The present invention also provides a kind of proving installation of moment of inertia.With solving, adopt the device of three-line pendulum principle because easily rotating and rocking the problem that two kinds of aggregate motions affect test result, and to inapplicable problems such as aircraft.

As shown in Figure 3, a proving installation for moment of inertia, comprises for being arranged on additional standard mass 5 and the vibration transducer 4 on tested object, and the data acquisition system (DAS) being connected with vibration transducer, also comprise that this supporting mechanism comprises for supporting the supporting mechanism of tested object:

Bearing 2;

Be arranged on two coaxially arranged bearings 1 on bearing;

Be fixed on the both sides that are arranged in bearing axis of 3, the two spring symmetries of two springs on bearing.

Two bearings and two springs provide four strong points for tested object.

Two bearings of proving installation and two springs provide four strong points for tested object.

This bearing can also be designed with liftable mechanism, and two bearings are fixed in liftable mechanism, can regulate the position of bearing by liftable mechanism, with this, improve the applicability of the proving installation of moment of inertia.

The proving installation of moment of inertia also comprises an inclinometer and telemeter rod.The angle that inclinometer is pressed in order to test; The pre compressed magnitude of measuring spring for telemeter rod, spring center line, additional standard mass center of gravity be the distance of the turning axle of tested object extremely.

Claims (8)

1. a method of testing for moment of inertia, is characterized in that, comprises the following steps:

1) provide two fulcrums, tested object is rotatably installed on corresponding fulcrum, and the line of two fulcrums is the turning axle of tested object;

2) by spring, provide two elastic supports in order to the tested object of supplemental support, the position of two elastic supports is about the axisymmetry of tested object;

3) to a side application of force of tested object, tested object is rotated, release force, makes tested object do twisting vibration around the turning axle of self;

4) obtain the natural frequency of tested system;

5) in a side of tested object, successively place additional standard mass, after each placement, all repeat step 3) to 4), the natural frequency of tested system after the each placement of acquisition additional standard mass;

6) natural frequency of some groups of tested systems that obtain according to step 4) and step 5) and the corresponding additional standard mass of this frequency are around the moment of inertia of the turning axle of tested object, by these data are carried out to linear regression analysis, obtain the moment of inertia of tested object again.

2. the method for testing of moment of inertia according to claim 1, is characterized in that step 2) in the spring all compressed 15%～30% at two elastic support places.

3. the method for testing of moment of inertia according to claim 1, is characterized in that step 3) angle of tested object rotation is 5 °～15 °.

4. the method for testing of moment of inertia according to claim 1, it is characterized in that, step 4) in, by some vibration transducers that are connected with data acquisition system (DAS) are installed in the structure of tested object, record the vibration signal of tested object, and the vibration signal of record is processed to obtain the natural frequency of tested system by data acquisition system (DAS).

5. the method for testing of moment of inertia according to claim 4, is characterized in that, described vibration transducer is laser displacement sensor or acceleration transducer.

6. the method for testing of moment of inertia according to claim 4, is characterized in that, the described data acquisition system sampling time is 10～20s, and sample frequency is 100～200Hz.

7. the proving installation of a moment of inertia, comprise for being arranged on additional standard mass and the vibration transducer on tested object, and the data acquisition system (DAS) being connected with described vibration transducer, it is characterized in that, also comprise that this supporting mechanism comprises for supporting the supporting mechanism of tested object:

Bearing;

Be arranged on two bearings on described bearing;

Be fixed on two springs on described bearing, the both sides that are arranged in bearing axis of described two spring symmetries,

Described two bearings and two springs provide four strong points for tested object.

8. the proving installation of moment of inertia according to claim 7, is characterized in that, described two coaxial bearing are arranged.

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