CN106092442A - KK bearing method rotation inerttia instrument and measuring method thereof - Google Patents

KK bearing method rotation inerttia instrument and measuring method thereof Download PDF

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Publication number
CN106092442A
CN106092442A CN201610538168.7A CN201610538168A CN106092442A CN 106092442 A CN106092442 A CN 106092442A CN 201610538168 A CN201610538168 A CN 201610538168A CN 106092442 A CN106092442 A CN 106092442A
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Prior art keywords
photogate
rotary head
light barrier
bearing
rotary
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CN106092442B (en
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陈水桥
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Zhejiang University ZJU
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Zhejiang University ZJU
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00Testing static or dynamic balance of machines or structures
    • G01M1/10Determining the moment of inertia

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Length Measuring Devices By Optical Means (AREA)
  • Force Measurement Appropriate To Specific Purposes (AREA)

Abstract

The invention discloses a kind of KK bearing method rotation inerttia instrument and measuring method thereof.Support is vertically installed on base, and rotary head is enclosed within one end of rotating shaft in friction free mode by bearing assembly, and rotating shaft is hingedly mounted on cantilever tip;Rotary head is provided with balanced component and hangs restructuring part, is provided with photogate to the base lateral symmetry immediately below rotary head, and photogate realizes the detection of rotary head angular velocity of rotation for coordinating with balanced component, and photogate is connected with measuring instrument;Suspending end hangs weight, discharge after rotary head multi-turn that bracing wire is rewound, rotary head and balanced component thereon are rotated under the rotary inertia of weight drives, rotary course gathers rotating angular acceleration by photogate and light barrier, calculates and obtain rotary inertia.Instrument of the present invention is a kind of new instrument, and its design principle complies fully with the theory on textbook, can accomplish that experiment is without departing from books, it is possible to easy to understand and displaying.

Description

KK bearing method rotation inerttia instrument and measuring method thereof
Technical field
The present invention relates to a kind of experiment survey meter device, especially relate to a kind of KK bearing method rotation inerttia instrument And measuring method.
Background technology
What rotation inerttia reflected is the attribute of object rotation.Law of rotation is the most fixed of description object fixed-axis rotation Rule.In order to reduce the frictional resistance impact on experiment, this instrument uses high accuracy KK bearing to be used as rotary shaft.
The rotation inerttia experiment content that always university physics laboratory must be opened.Present each colleges and universities overwhelming majority rotates Inertia instrument is all three-line pendulum measuring instrument or torsional pendulum type measuring instrument.But tell about in the ultimate principle of this two instrument and theoretical book Principle has the biggest discrepancy, and it simply achieves the approximate measure of rotary inertia amount, can not with say on theoretical book synchronization and Linking, student's ratio is more difficult.These experimental apparatus have actually detached books, the maximum puzzlement of these the most numerous experimental apparatus, Also it is the biggest problem perplexing University Laboratory Construction now.Instrument gets more and more, and the instrument met is fewer and feweri.
Summary of the invention
In order to solve problem present in background technology, a kind of KK bearing method rotation inerttia instrument provided by the present invention Device and measuring method thereof, use mode based on KK bearing method to measure rotary inertia.
The technical solution used in the present invention is:
One, a kind of KK bearing method rotation inerttia instrument:
The photogate including base and being arranged on base and support, support is vertically installed on base, and rotary head leads to Crossing bearing assembly to be enclosed within one end of rotating shaft in friction free mode, the other end of rotating shaft is hingedly mounted on cantilever tip, rotating shaft It is horizontally mounted;Being provided with balanced component and hanging restructuring part of rotary head side face, pacifies to the base lateral symmetry immediately below rotary head Equipped with photogate, photogate realizes the detection of rotary head angular velocity of rotation for coordinating with balanced component, and photogate is with measuring instrument even Connect.
Described balanced component includes the Liang Gen gimbal lever, two column, regulating nut and light barrier, the Liang Gen gimbal lever pair Claim ground to be radially inserted into the both sides of rotary head side face, the gimbal lever of side is cased with column and regulating nut, opposite side Being cased with column and light barrier in the gimbal lever, described photogate is positioned at the circumference that light barrier rotates in a circumferential direction around rotary head central shaft On path.
Described extension restructuring part includes that bracing wire and suspending end bracing wire upper end are fixing with the side face of rotary head and is connected, bracing wire lower end Being connected with suspending end, suspending end is provided for providing the weight of rotary inertia.
Described column is fixed in the gimbal lever, and regulating nut is for the moment of adjustment bar so that rotary head peace The center of gravity of the system that weighing apparatus assembly is formed is positioned at rotary head center.
Described light barrier is U-shaped structure.
Described photogate includes that power supply E, resistance R, electric capacity C and diode D, resistance R and diode D are connected on power supply E Two ends, electric capacity C is connected in parallel on resistance R two ends, the two ends of electric capacity C connect respectively single-chip microcomputer CLK, single-chip microcomputer CLK respectively with display Connect with controller.
Described rotary head includes foundation, KK bearing, bearing fixing sleeve, central shaft and turning set, and the two ends of central shaft lead to Crossing KK bearing to be respectively fitted in two bearing fixing sleeves, two bearing fixing sleeves are socketed in turning set two ends respectively, central shaft Wherein one section is sleeved in one end of foundation, and the other end of foundation is coaxially connected with rotating shaft, and the sidewall of turning set is provided with for putting down The hole of weighing apparatus bar plug-in mounting.By the connection of the KK bearing of minimal drag and the transition socket of intermediate bearing fixed cover, rotary head is led to Cross bearing assembly to be enclosed within one end of rotating shaft in friction free mode.
Axle sleeve is contained on bearing, and whole system of can ining succession is the most freely rotatable.Length mark it is carved with on cursor, in order to Regulation cylinder is to the distance in axle center.Knots modification cylinder just can change mass of system distribution to the distance in axle center, i.e. changes The rotary inertia of system.Light barrier is contained in one end of cursor, and when system rotates, photogate is in the light by light barrier, often It is in the light and once produces an electric impulse signal, to quit work after pilot angle acceleration analysis instrument starts.
Two, a kind of KK bearing method method for measuring rotary inertia:
1) use described measuring instrument, described suspending end hang weight, discharges after rotary head multi-turn that bracing wire is rewound, Rotary head and balanced component thereon are rotated, by photogate and gear in rotary course under the rotary inertia of weight drives Mating plate gathers rotating angular acceleration β;
2) so use formula below equation calculate obtain rotary inertia:
M=J β
M=TR=m/(g-a) R=m/gR-m/βR2
Wherein, T be bonding force away from the pulling force corresponding to M, be the gravity of weight;m/Being weight quality, R is outside rotary head Diameter, g is acceleration of gravity.
If rotary inertia J is constant for system, in system and measure corresponding angular acceleration β with different moment loadings, Making the available highly desirable straight line of M β figure, the slope of straight line is exactly the size of the rotary inertia of system.
The most further, described step 2) replace with: by hanging the weight of Different Weight on suspending end, calculating obtains Obtaining angular acceleration β corresponding under different weights, draw M β figure and be fitted each point, the slope of the straight line obtained after matching is made For rotary inertia.Can verify that explanation law of rotation, it is thus achieved that more accurate measurement result.
Described step 1) in rotary course gathers rotating angular acceleration β by photogate and light barrier particularly as follows:
1.1) two photogate utilizing measuring instrument to pass through on light barrier rotation round path gather acquisition respectively and are in the light Sheet is in the light before and after passing time interval, and then uses below equation to calculate the average angle speed obtaining light barrier through photogate Degree:
ω1=△ S/ △ t1
ω2=△ S/ △ t2
Wherein, △ S represents the distance parameter between two frequency modulated light sheets, ω1The average of first photogate is passed for light barrier Angular velocity, ω2The mean angular velocity of second photogate, △ t is passed for light barrier1During for light barrier by first photogate First time be in the light and the time interval that is in the light of second time, △ t2It is in the light by first time during second photogate for light barrier The time interval being in the light with second time;
1.2) use below equation to calculate to obtain:
β=(ω21)/△t
Wherein, △ t/Represent the light barrier time between two photogate;
Light barrier time △ t between two photogate/Employing below equation calculates:
△ t=(△ t/-△t1/2+△t2/2)
Wherein, △ t/Represent that light barrier is from leaving first photogate to entering second photogate elapsed time Every.
The principle of the present invention is as follows:
Rotary inertia is the tolerance of object inertia size in rotation.Being m to quality, radius is r, and a length of L's is uniform Cylinder, when rotating shaft is passed through barycenter and is perpendicular to geometrical axis, the cylinder rotary inertia J to this axleCSize be:
J C = 1 4 mr 2 + 1 12 mL 2
If rotating shaft with by the shaft parallel of above-mentioned barycenter but by barycenter, and between distance be D, see Fig. 1, then Can use below equation obtain cylinder to the rotary inertia of this axle be:
JCylinder=JC+mD2
Pivot structure as shown in Figure 2, is J without rotary inertia during two cylinders0, then two cylinders are loaded onto After, rotary inertia J is:
IfThen
From above formula it can be seen that, the rotary inertia of rotation system is relevant relative to the distribution situation of rotating shaft with its quality, although Total system mass is constant, but owing to cylinder m leaves the distance D change of rotating shaft, J also changes.When measuring different D by experiment Corresponding J value, and make J D2Figure, can obtain straight line, and the slope of straight line is exactly the two cylindrical quality sum, Straight line intercept on J axle is exactly constant J/
Object bonding force away from M act under, the angular acceleration obtained and bonding force be big Theravada's direct ratio away from ground, with rotation Inertia is inversely proportional to, i.e. M=J β.
Therefore the method that the present invention uses such scheme to pass through experiment measures bonding force away from M and β, then directly according to rotation Law records the size of rotary inertia J indirectly.
The invention has the beneficial effects as follows:
Instrument of the present invention is a kind of new instrument, and its design principle complies fully with the theory on textbook, can accomplish reality Test without departing from books, it is possible to easy to understand and displaying.
Accompanying drawing explanation
Fig. 1 is the principle schematic of cylinder rotary inertia.
Fig. 2 is the apparatus structure schematic diagram of simple rotating shaft experiment.
Fig. 3 is apparatus structure schematic diagram of the present invention.
Fig. 4 is resultant moment effect lower rotary shaft moment schematic diagram of the present invention.
Fig. 5 is light barrier fundamental diagram of the present invention.
Fig. 6 is the circuit structure diagram of light barrier of the present invention.
Fig. 7 is the structural blast figure of rotary head.
In figure: 1, rotary head, 2, the gimbal lever, 3, column, 4, regulating nut, 5, light barrier, 6, photogate, 7, support, 8, rotating shaft, 9, measuring instrument, 10, bracing wire, 11, suspending end, 12, base;101, foundation, 102, KK bearing, 103, bearing fixing sleeve, 104, central shaft, 105, turning set.
Detailed description of the invention
Below in conjunction with the accompanying drawings and the present invention is described in further detail by specific embodiment.
As it is shown on figure 3, the present invention includes base 12 and the photogate 6 being arranged on base and support 7, support 7 is vertical Being arranged on base 12, rotary head 1 is enclosed within one end of rotating shaft 8 in friction free mode by bearing assembly, another of rotating shaft 8 End is hingedly mounted on support 7 top, and rotating shaft 8 is horizontally mounted;Being provided with balanced component and hanging restructuring part of rotary head 1 side face, turns Being provided with photogate 6 to base 12 lateral symmetry immediately below dynamic 1, photogate 6 rotates for coordinating realization with balanced component 1 angular velocity of rotation detection, photogate 6 is connected with measuring instrument 9.
Balanced component includes 2, two column 3 of the Liang Gen gimbal lever, regulating nut 4 and light barrier 5, and the Liang Gen gimbal lever 2 is right Claim ground to be radially inserted into the both sides of rotary head 1 side face, the gimbal lever 2 of side is cased with column 3 and regulating nut 4, another Being cased with column 3 and light barrier 5 in the gimbal lever 2 of side, light barrier 5 is U-shaped structure, and photogate 6 is positioned at light barrier 5 around rotary head In the circular path that 1 central shaft rotates in a circumferential direction.Column 3 is fixed in the gimbal lever 2, and regulating nut 4 is for adjustment bar 2 Moment so that the center of gravity of the system that rotary head 1 and balanced component are formed is positioned at rotary head 1 center.
Extension restructuring part includes that bracing wire 10 and suspending end 11 bracing wire 10 upper end are fixing with the side face of rotary head 1 and is connected, bracing wire 10 Lower end is connected with suspending end 11, and suspending end 11 is provided for providing the weight of rotary inertia.
As shown in Figure 6, photogate 6 includes that power supply E, resistance R, electric capacity C and diode D, resistance R and diode D are connected on Power supply E two ends, electric capacity C is connected in parallel on resistance R two ends, and the two ends of electric capacity C connect single-chip microcomputer CLK, single-chip microcomputer CLK respectively respectively with aobvious Show that device and controller connect.
As it is shown in fig. 7, rotary head 1 includes foundation 101, KK bearing 102, bearing fixing sleeve 103, central shaft 104 and rotates Set 105, the two ends of central shaft 104 are respectively fitted in two bearing fixing sleeves 103 by KK bearing 102, two bearing fixing sleeves 103 are socketed in turning set 105 two ends respectively, central shaft 104 wherein one section be sleeved in one end of foundation 101, foundation 101 The other end is coaxially connected with rotating shaft 8, and the sidewall of turning set 105 is provided with the hole for the gimbal lever 2 plug-in mounting.
Embodiments of the invention and implementation process thereof are as follows:
1) axle sleeve is contained on bearing, and whole system of can ining succession is the most freely rotatable.Length mark it is carved with on cursor, in order to Regulation cylinder is to the distance in axle center.
Cylinder 3 is fixed in the gimbal lever 2, and light barrier is also secured in the gimbal lever 2, regulates by rotating regulating nut 4 Regulating nut 4 is arranged on the radial position in the gimbal lever 2, and then regulation makes the gimbal lever 2 of both sides balance each other, i.e. make to turn The center of gravity of the whole system that dynamic 1 and the gimbal lever 2 are formed is at the center of rotary head 1.
Photogate is set, each photogate of embodiment has a light-emitting tube and light receiving tube, light-emitting tube optically focused Pearl big gun (has lens before 2.2V/0.25A pearl big gun), and the model of light receiving tube is 3DU52 (also can receive pipe by infrared emission).Photoelectricity Door be equivalent to a switch, for control and the sampling time, its circuit operation principle as shown in Figure 6: when have light impinge upon reception manage Time upper, circuit does not constitutes loop, no signal output on resistance R;When light is kept off, receiving pipe conducting, circuit constitutes loop, resistance R On have signal to export.So photogate is equivalent to a time sampling device.
Connecting test instrument and photogate, tester is mainly constituted with single-chip microcomputer, and it can be deposited the various data of experiment Enter interior storehouse, in order to take out one by one after having tested, many experiments can be carried out at identical conditions, and each speed can be calculated Degree, acceleration and the average acceleration of repetitive measurement, average acceleration absolute error.
2) hanging weight on suspending end 11, after rotary head 1 multi-turn of bracing wire 10 being rewound, release starts to rotate, light barrier pair Photogate is in the light, and is often in the light and once produces an electric impulse signal, to stop after pilot angle acceleration analysis instrument starts Work.
3) as it is shown in figure 5, there are two photogate in measuring instrument, photoelectricity test instrument can measure and store motion light-blocking block On two light barriers be in the light and the time interval △ t that is in the light of second time by first time during the first photoelectricity I1With pass through First time during the second photogate II is in the light and the time interval △ t being in the light for the second time2,
The time interval △ t that light barrier is experienced from the first photogate to the second photogate/.Between two frequency modulated light sheets Distance parameter △ S can on computing light-blocking block two light barriers by mean angular velocity ω during the first photogate1=△ S/ △ t1With By mean angular velocity ω during the second photogate2=△ S/ △ t2
Due to △ t1With △ t2The least, think that object makees uniformly accelerated motion within this time, therefore △ t approx1Time Interior mean angular velocity is as △ t1Instantaneous angular velocity ω in/2 these moment1;△ t2Mean angular velocity in time is as △ t2Instantaneous angular velocity ω in/2 these moment2.And from ω1Increase to ω2Required time is modified to △ t=(△ t/-△t1/2+△ t2/ 2), therefore defining according to acceleration, the average angular acceleration using below equation calculating to obtain within the △ t time is:
β=(ω21)/△t
According to the △ t recorded1, △ t2, the light barrier interval △ S value of △ t and key entry, after tested instrument record, display union It, obtain ω1, ω2With β it is.
It is constant that embodiment arranges D=3cm, R=2cm, and respectively with 15g, 25g, 35g, 45g, 55g link code is tested.Measure 5 Group, the data of 10 times, such as following table:
Then the average obtaining each angular acceleration improves degree of accuracy, such as following table after summary:
Substituting into formula asks final rotary inertia to be J:
Embodiment utilizes Inertia Based on Torsion Pendulum Method measuring instrument as reference, and recording its rotary inertia is: JRock=6043.6g.cm2, two Person's error is:
Wherein, δ represents error, JRockRepresenting the rotary inertia that Inertia Based on Torsion Pendulum Method measurement obtains, J represents that the inventive method is measured The rotary inertia arrived.
Cylinder 3 in the gimbal lever of knots modification both sides just can change System Nature to the distance between rotary head 1 axial line Amount distribution, thus change the rotary inertia of whole institute examining system.
Embodiment then passes through the weight hanging Different Weight on suspending end 11, takes multiple measurements and calculates, and draws M β schemes, and checking illustrates law of rotation, it is thus achieved that more accurate measurement result.
As can be seen here, the accuracy of the present invention and effectiveness, there is prominent significant technique effect.Experimental apparatus uses KK high-precision bearing can guarantee that resistance is the least, f drag effects be less than 8%.And photodiode response time is 1 3us, low The photodiode of response time can guarantee that experimental data quickly obtains.

Claims (10)

1. a KK bearing method rotation inerttia instrument, it is characterised in that: include base (12) and be arranged on base Photogate (6) and support (7), support (7) is vertically installed on base (12), and rotary head (1) is rubbed with nothing by bearing assembly Mode be enclosed within one end of rotating shaft (8), the other end of rotating shaft (8) is hingedly mounted on support (7) top, and rotating shaft (8) level is pacified Dress;Being provided with balanced component and hang restructuring part, base (12) lateral symmetry immediately below rotary head (1) of rotary head (1) side face Photogate (6) is installed, photogate (6) realizes rotary head (1) angular velocity of rotation detect for coordinating with balanced component, photoelectricity Door (6) is connected with measuring instrument (9).
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described balance group Part includes the Liang Gen gimbal lever (2), two column (3), regulating nut (4) and light barrier (5), and the Liang Gen gimbal lever (2) is symmetrically Radially it is inserted into the both sides of rotary head (1) side face, the gimbal lever (2) of side is cased with column (3) and regulating nut (4), Being cased with column (3) and light barrier (5) in the gimbal lever (2) of opposite side, described photogate (6) is positioned at light barrier (5) and rotates In the circular path that dynamic head (1) central shaft rotates in a circumferential direction.
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described extension restructuring Part includes that bracing wire (10) and suspending end (11) bracing wire (10) upper end are fixing with the side face of rotary head (1) and is connected, bracing wire (10) lower end Being connected with suspending end (11), suspending end (11) is provided for providing the weight of rotary inertia.
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described regulating nut (4) for the moment of adjustment bar (2) so that the center of gravity of the system that rotary head (1) and balanced component are formed is positioned at rotary head (1) center.
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described light barrier (5) it is U-shaped structure.
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described photogate (6) including that power supply E, resistance R, electric capacity C and diode D, resistance R and diode D are connected on power supply E two ends, electric capacity C is connected in parallel on electricity Resistance R two ends, the two ends of electric capacity C connect single-chip microcomputer CLK respectively.
A kind of KK bearing method rotation inerttia instrument the most according to claim 1, it is characterised in that: described rotary head (1) foundation (101), KK bearing (102), bearing fixing sleeve (103), central shaft (104) and turning set (105), central shaft are included (104) two ends are respectively fitted in two bearing fixing sleeves (103) by KK bearing (102), two bearing fixing sleeves (103) point Be not socketed in turning set (105) two ends, central shaft (104) wherein one section be sleeved in one end of foundation (101), foundation (101) the other end is coaxially connected with rotating shaft (8), and the sidewall of turning set (105) is provided with the hole for the gimbal lever (2) plug-in mounting.
8. a KK bearing method method for measuring rotary inertia, it is characterised in that:
1) use the arbitrary described measuring instrument of claim 1~7, described suspending end (11) hangs weight, by bracing wire (10) Discharge after back-roll rotary head (1) multi-turn so that rotary head (1) and balanced component thereon drive backspin at the rotary inertia of weight Turn, rotary course gathers rotating angular acceleration β by photogate (6) and light barrier (5);
2) so use formula below equation calculate obtain rotary inertia:
M=J β
M=TR=m/(g-a) R=m/gR-m/βR2
Wherein, T be bonding force away from the pulling force corresponding to M, be the gravity of weight;m/Being weight quality, R is that rotary head (1) is the most straight Footpath, g is acceleration of gravity.
A kind of KK bearing method method for measuring rotary inertia the most according to claim 8, it is characterised in that: described step 2) replace It is changed to: by the upper weight hanging Different Weight of suspending end (11), calculating and obtain angular acceleration β corresponding under different weight, Drawing M β figure to be fitted each point, the slope of the straight line obtained after matching is as rotary inertia.
A kind of KK bearing method method for measuring rotary inertia the most according to claim 8, it is characterised in that: described step 1) In middle rotary course by photogate (6) and light barrier (5) collection rotating angular acceleration β particularly as follows:
1.1) gather acquisition light barrier (5) respectively by two photogate (6) on light barrier (5) rotation round path to pass Before and after be in the light time interval, and then use below equation to calculate the average angle speed obtaining light barrier (5) through photogate (6) Degree:
ω1=△ S/ △ t1
ω2=△ S/ △ t2
Wherein, △ S represents the distance parameter between two frequency modulated light sheets, ω1The average of first photogate (6) is passed for light barrier (5) Angular velocity, ω2The mean angular velocity of second photogate (6), △ t is passed for light barrier (5)1For light barrier (5) by first First time during photogate (6) is in the light and the time interval being in the light for the second time, △ t2For light barrier (5) by second photogate (6) first time time is in the light and the time interval being in the light for the second time;
1.2) use below equation to calculate to obtain:
β=(ω21)/△t
Wherein, △ t/Represent the light barrier (5) time between two photogate (6);
The light barrier (5) time △ t between two photogate (6)/Employing below equation calculates:
△ t=(△ t/-△t1/2+△t2/2)
Wherein, △ t/Represent that light barrier (5) is from leaving first photogate (6) to entering second photogate (6) elapsed time Interval.
CN201610538168.7A 2016-07-06 2016-07-06 KK bearings method rotation inerttia instrument and its measuring method Expired - Fee Related CN106092442B (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106940944A (en) * 2017-04-27 2017-07-11 公安海警学院 Adjustable wide type photoelectricity door physical synthesis experiment instrument
CN112697344A (en) * 2020-11-24 2021-04-23 潍柴动力股份有限公司 Rotational inertia measuring device and measuring method

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106940944A (en) * 2017-04-27 2017-07-11 公安海警学院 Adjustable wide type photoelectricity door physical synthesis experiment instrument
CN112697344A (en) * 2020-11-24 2021-04-23 潍柴动力股份有限公司 Rotational inertia measuring device and measuring method
CN112697344B (en) * 2020-11-24 2022-07-19 潍柴动力股份有限公司 Rotational inertia measuring device and measuring method

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