CN103674425B - A kind of method of testing of moment of inertia and device - Google Patents

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

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CN103674425B
CN103674425B CN201310600962.6A CN201310600962A CN103674425B CN 103674425 B CN103674425 B CN 103674425B CN 201310600962 A CN201310600962 A CN 201310600962A CN 103674425 B CN103674425 B CN 103674425B
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moment
inertia
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testing
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CN103674425A (en
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罗银淼
陶伟明
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Zhejiang University ZJU
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Abstract

The invention discloses a kind of method of testing of moment of inertia, comprise the following steps: 1) object moment is arranged on two; 2) supplemental support is provided by spring to object; 3) to object force also release force, it is made to do twisting vibration; 4) natural frequency of object is obtained; 5) successively place additional standard mass, after each placement, all repeat step 3) to 4) obtain some data; 6) linear regression analysis is carried out to these data, obtain the moment of inertia of object.The invention also discloses a kind of proving installation of moment of inertia, comprise additional standard mass and vibration transducer, and the data acquisition system (DAS) be connected with described vibration transducer, also comprise the supporting mechanism for supporting object.By being arranged on by object moment on two fulcrums, making it do whirling vibration, in conjunction with existing method for testing vibration, and the moment of inertia of object can be obtained fast accurately by regretional analysis; And object can be unsymmetric structure, applied widely.

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 (MomentofInertia) is rigid body when 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, is also an Important Parameters at industrial circles such as scientific experiment, engineering, space flight, electric power, machinery, instrument.The indication mechanism of electromagnetic instrument, because the moment of inertia of coil is different, can be respectively used to measure Weak current (galvanometer) or electricity (ballistic galvanometer).In the configuration design of engine blade, flywheel, gyro and artificial satellite, accurately measuring moment of inertia, is all very necessary.
Moment of inertia is only decided by the position of the shape of rigid body, mass distribution and rotating shaft, and has nothing to do with the rotary state (size as angular velocity) of rigid body around axle.The homogeneous rigid body of regular shape, its moment of inertia can obtain by direct formulae discovery.And for the moment of inertia of irregular rigid body or heterogeneous body rigid body, generally method by experiment measures, and thus experimental technique just seems very important.
In engineering reality, need the moment of inertia of surveying general structure, such as aircraft and spacecraft, in flight course, need to adjust control parameter according to its moment of inertia.Each assembling parts often can not accurately be obtained system-level rotational inertia data by theoretical conversion.System as certain type unmanned plane is one to be had different task load, has the subassembly of middle control computer, oil plant, by the gesture stability driving aileron to complete unmanned plane, be the servo-drive system of a comparatively 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 tests certain gap according to design-calculated moment of inertia with actual, and must carry out the moment of inertia test of specification, air line also has special code requirement to moment of inertia test.
The method of testing generally conventional three-line pendulum test of moment of inertia, the method has advantage quickly and easily.The principle of three-line pendulum test: different for radius two disks (upper disk and lower disc) three isometric lines are connected.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 is determined by the moment of inertia of lower disc cycle turnover.When the moment of inertia of lower disc changes (as jobbie additional on lower disc), its torsional cyclic will change.Three-line pendulum is exactly the moment of inertia drawing any mass objects by measuring its torsional cyclic.
The principle of three-line pendulum test moment of inertia derives many devices.As Authorization Notice No. be CN200996883Y patent document discloses a kind of three line Inertia Based on Torsion Pendulum Method rotational inertia test apparatus, comprise the support that has upper cross plate and lower cross plate, a upper disk, a lower swinging disc, three wire rope, three wire rope adjusting mechanisms being fixed on adjustable steel wire rope length on disk, be arranged on fixture lower swinging disc can being fixed tested article, upper disk and lower swinging disc central coaxial are arranged, 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, upper cross plate is fixedly connected with output shaft free end downwards and the reducing gear of the precision drive vertically arranged, the central horizontal of upper disk is fixedly connected on the free end of output shaft, side lower cross plate being positioned at lower swinging disc is fixedly connected with the detent mechanism with scalable thimble, and lower swinging disc edge offers the recess corresponding to thimble head, and the thimble state of stretching out can snap in this recess.Utilize this patent to test 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, have a strong impact on test result.Special in the aerocraft system etc. with fuel oil, the state of the apparatus for vertical placing of three-line pendulum and the usual nearly tangential movement of aircraft is not inconsistent.For Large Scale Space Vehicle system, as fighter plane and airline carriers of passengers, the pendulum length of three-line pendulum requires, greatly to being difficult to realize, to reach 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.Easily rotate with solving three-line pendulum method of testing 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 moment is arranged on corresponding fulcrum, and namely the line of two fulcrums is the turning axle of tested object.
2) provide two elastic supports in order to the tested object of supplemental support by spring, the position of two elastic supports is about the axisymmetry of tested object;
3) side to tested object exerts a force, and tested object is rotated, release force, makes tested object do twisting vibration around the turning axle of self;
4) natural frequency of tested system is obtained;
Tested system refers to tested object and spring, if added additional standard mass, tested system is then tested object, spring and additional standard mass.
5) successively place additional standard mass in the side of tested object, after each placement, all repeat step 3) to 4), the natural frequency of tested system after acquisition each placement additional standard mass;
6) natural frequency of the some groups of tested systems obtained according to step 4) and step 5) and the additional standard mass corresponding to this frequency are around the moment of inertia of the turning axle of tested object, again by carrying out linear regression analysis to these data, obtain the moment of inertia of tested object.
When not placing additional standard mass, the natural frequency f of tested system:
f = 1 2 π nkD J = 1 2 π K 0 J - - - ( 1 )
Wherein k is the elasticity coefficient of spring; When tested object bilateral all has spring, n is 2, and when tested object only has side to have a spring, n is 1; D is the distance of spring center line to the turning axle of tested object; K 0for coefficient of colligation, its value is the product of nkD; J is the moment of inertia of tested object around turning axle;
When placing additional standard mass, the natural frequency f of tested system i:
f i = 1 2 π nkD J + m i D i = 1 2 π K 0 J + m i D i = 1 2 π K 0 J + J i - - - ( 2 )
Wherein m ifor the quality of additional standard mass; D ifor additional standard mass center of gravity is to the distance of the turning axle of tested object; J ifor additional standard mass is around the moment of inertia of turning axle;
Formula (2) transition form can obtain formula (2.1):
J i=K 0/(2πf i) 2-J(2.1)
Linear fit equation (3) is determined according to formula (2.1):
J i = K o _ / ( 2 π f i ) 2 - J - - - ( 3 )
Wherein for equivalent stiffness, it is the slope of linear fit equation; Often organize 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.Least square linear fit is carried out to several points, obtains the moment of inertia J of tested object.
As preferably, step 2) in the spring at two elastic support places all by compression 15% ~ 30%.Spring keeps a suitable initial compression amount can promote the precision of test, makes tested object have the rotary motion of better quality.
As preferably, step 3) angle that rotates of tested object 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 record the vibration signal of tested object by installing some vibration transducers be connected with data acquisition system (DAS) in the structure of tested object, and process by the vibration signal of data acquisition system (DAS) to record the natural frequency obtaining tested system.
The kind of vibration transducer has multiple, and the type selected is determined according to test request, and as preferably, described vibration transducer is laser displacement sensor or acceleration transducer.Laser sensor is more accurate, be applicable to the accurate measurement that structural vibration displacement is less, and laser sensor does not produce additional mass, is used for gathering displacement signal; Acceleration transducer, use extensively, service band is wider, gathers acceleration signal.
As preferably, the described data acquisition system sampling time is 10 ~ 20s.Sampling time is determined according to the frequency of tested object, and the frequency low then sampling time is long, frequency height then 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 the problem adopting the device of three-line pendulum principle to affect test result because easily rotating and rock two kinds of aggregate motions, and to inapplicable problems such as aircraft.
A kind of proving installation of moment of inertia, comprise for being arranged on additional standard mass on tested object and vibration transducer, and the data acquisition system (DAS) to be connected with described vibration transducer, also comprise the supporting mechanism for supporting tested object, this supporting mechanism comprises:
Bearing;
Be arranged on two bearings on described bearing;
Be fixed on two springs on described bearing, the both sides being 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.Inclinometer is in order to the angle of test pressing; The telemeter rod pre compressed magnitude measuring spring, spring center line, additional standard mass center of gravity are to the distance of the turning axle of tested object.
The invention has the beneficial effects as follows: by tested object moment being arranged on two fulcrums, coordinate the spring of two supplemental support, make tested object can carry out rotating freely vibration, due to the attenuation of 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 be obtained the moment of inertia of measurand fast accurately 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 utilizes 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 controls, now measures the moment of inertia of model plane around 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 namely 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 namely this method can test unsymmetric structure.
2) provide two elastic supports in order to supplemental support model plane by spring; 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; spring initial length is 20cm; the elastic coefficient is 200N/cm, and the rear spring of installation is compressed 20%.
3) side to model plane exerts a force, and makes model plane rotate 10 °, release force, makes model plane do twisting vibration around the turning axle of self.
4) on model plane, 3 acceleration transducers are installed, be arranged on port wing, fuselage (position aligns turning axle), starboard wing successively, and acceleration transducer is connected with data acquisition system (DAS), by the vibration signal of data acquisition system (DAS) record model plane, the sampling time of acquisition system is 13s, sample frequency is 100Hz, carries out digital signal processing again, obtain the natural frequency of tested system after having gathered the vibration signal of unmanned plane to gathered vibration signal.
Tested system refers to tested object and spring, if added additional standard mass, tested system is then model plane, spring and additional standard mass.
5) additional standard mass is successively placed in the side of model plane wing; all step 3) to 4 is repeated) after each placement; the natural frequency of tested system after acquisition each placement additional standard mass; as shown in table 1; for the parameter list corresponding to each test sequence number, comprise the distance of additional standard mass quality, additional standard mass center of gravity and model plane turning axle, the moment of inertia of additional standard mass around turning axle and the natural frequency of tested system.
Table 1
6) four groups of data in table 1 are obtained according to step 4) and step 5), often organize data and comprise the natural frequency of tested system and the additional standard mass corresponding to this frequency moment of inertia around turning axle, again by carrying out linear regression analysis to these data, obtain the moment of inertia of model plane.
When not placing additional standard mass, the natural frequency f of tested system is shown in formula (1):
f = 1 2 π nkD J = 1 2 π K 0 J - - - ( 1 )
Wherein k is the elasticity coefficient of spring; When model plane bilateral all has spring, n is 2, and when model plane only have side to have a spring, n is 1; D is the distance of spring center line to the turning axle of model plane; K 0for coefficient of colligation, its value is the product of nkD; J is the moment of inertia of model plane around turning axle;
When placing additional standard mass, the natural frequency f of tested system isee formula (2):
f i = 1 2 π nkD J + m i D i = 1 2 π K 0 J + m i D i = 1 2 π K 0 J + J i - - - ( 2 )
Wherein m ifor the quality of additional standard mass; D ifor additional standard mass center of gravity is to the distance of the turning axle of model plane; J ifor the moment of inertia of 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)
Linear fit equation (3) is determined according to formula (2.1):
J i = K 0 _ / ( 2 π f i ) 2 - J - - - ( 3 )
Wherein for equivalent stiffness, it is the slope of linear fit equation; Often organize 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.
Least square linear fit is carried out to four points, as shown in Figure 2, obtains 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 the problem adopting the device of three-line pendulum principle to affect test result because easily rotating and rock two kinds of aggregate motions, 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 on tested object and vibration transducer 4, and the data acquisition system (DAS) be connected with vibration transducer, also comprise the supporting mechanism for supporting tested object, this supporting mechanism comprises:
Bearing 2;
Be arranged on the bearing 1 that on bearing two are coaxially arranged;
Be fixed on the both sides being arranged in bearing axis of two springs, 3, the two spring symmetries 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 be regulated the position of bearing, improve the applicability of the proving installation of moment of inertia with this by liftable mechanism.
The proving installation of moment of inertia also comprises an inclinometer and telemeter rod.Inclinometer is in order to the angle of test pressing; The telemeter rod pre compressed magnitude measuring spring, spring center line, additional standard mass center of gravity are to the distance of the turning axle of tested object.

Claims (6)

1. a method of testing for moment of inertia, is characterized in that, comprises the following steps:
1) provide two fulcrums, tested object moment is arranged on corresponding fulcrum, and namely the line of two fulcrums is the turning axle of tested object;
2) provide two elastic supports in order to the tested object of supplemental support by spring, the position of two elastic supports is about the axisymmetry of tested object;
3) side to tested object exerts a force, and tested object is rotated, release force, makes tested object do twisting vibration around the turning axle of self;
4) natural frequency of tested system is obtained;
5) successively place additional standard mass in the side of tested object, after each placement, all repeat step 3) to 4), the natural frequency of tested system after acquisition each placement additional standard mass;
6) according to step 4) and step 5) natural frequency of some groups of tested systems that obtains and the additional standard mass corresponding to this frequency be around the moment of inertia of the turning axle of tested object, again by carrying out linear regression analysis to these data, obtain the moment of inertia of tested object.
2. the method for testing of moment of inertia according to claim 1, is characterized in that, step 2) in the spring at two elastic support places all by compression 15% ~ 30%.
3. the method for testing of moment of inertia according to claim 1, is characterized in that, step 3) exert a force to the side of tested object, tested object is rotated, and the angle that tested object rotates is 5 ° ~ 15 °.
4. the method for testing of moment of inertia according to claim 1, it is characterized in that, step 4) in record the vibration signal of tested object by installing some vibration transducers be connected with data acquisition system (DAS) in the structure of tested object, and process by the vibration signal of data acquisition system (DAS) to record the natural frequency obtaining tested system.
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.
CN201310600962.6A 2013-11-22 2013-11-22 A kind of method of testing of moment of inertia and device Expired - Fee Related CN103674425B (en)

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