CN106092442B - KK bearings method rotation inerttia instrument and its measuring method - Google Patents
KK bearings method rotation inerttia instrument and its measuring method Download PDFInfo
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- CN106092442B CN106092442B CN201610538168.7A CN201610538168A CN106092442B CN 106092442 B CN106092442 B CN 106092442B CN 201610538168 A CN201610538168 A CN 201610538168A CN 106092442 B CN106092442 B CN 106092442B
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- 230000004888 barrier function Effects 0.000 claims abstract description 34
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- 230000005611 electricity Effects 0.000 claims 1
- 230000001133 acceleration Effects 0.000 abstract description 15
- 238000002474 experimental method Methods 0.000 abstract description 9
- 238000013461 design Methods 0.000 abstract description 2
- 238000010586 diagram Methods 0.000 description 6
- 238000005259 measurement Methods 0.000 description 6
- 230000008859 change Effects 0.000 description 4
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- 230000000694 effects Effects 0.000 description 3
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- 238000005516 engineering process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000004044 response Effects 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 238000005303 weighing Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M1/00—Testing static or dynamic balance of machines or structures
- G01M1/10—Determining the moment of inertia
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- Length Measuring Devices By Optical Means (AREA)
- Force Measurement Appropriate To Specific Purposes (AREA)
Abstract
The invention discloses a kind of KK bearings method rotation inerttia instrument and its measuring method.Stent is vertically installed on base, and rotary head is sleeved on one end of shaft by bearing assembly in a manner of friction free, and shaft is hingedly mounted on cantilever tip；Rotary head is provided with balanced component and hangs restructuring part, and the base both sides immediately below rotary head are symmetrically provided with photoelectric door, and photoelectric door, which is used to coordinate with balanced component, realizes that rotary head angular velocity of rotation detects, and photoelectric door is connected with measuring instrument；Weight is hung on suspending end, discharged after bracing wire is rewound rotary head multi-turn, so that rotary head and balanced component thereon are rotated in the case where the rotary inertia of weight drives, pass through photoelectric door in rotary course and light barrier gathers rotating angular acceleration, calculate and obtain rotary inertia.Instrument of the present invention is a kind of new instrument, its design principle is complied fully with the theory on textbook, can accomplish that experiment does not depart from books, be understood that and show.
Description
Technical field
The present invention relates to a kind of experiment survey meter device, more particularly, to a kind of KK bearings method rotation inerttia instrument
And its measuring method.
Background technology
What rotation inerttia reflected is the attribute that object rotates.Law of rotation is the substantially fixed of description object fixed-axis rotation
Rule.In order to reduce influence of the frictional resistance to experiment, this instrument is used as rotation axis using high accuracy KK bearings.
Rotation inerttia is always the experiment content that university physics laboratory must open.Each colleges and universities are most now rotates
Inertia instrument is all three-line pendulum measuring instrument or torsional pendulum type measuring instrument.But told about on the basic principle of this two instrument and theoretical book
Principle has very big discrepancy, it simply realizes the approximate measure of rotary inertia amount, can not it is synchronous with what is said on theoretical book and
Linking, student's ratio are more difficult.These laboratory apparatus have actually detached books, this is exactly the maximum puzzlement of numerous laboratory apparatus,
And perplex the biggest problem of University Laboratory Construction now.Instrument is more and more, and the instrument met is fewer and fewer.
The content of the invention
In order to solve the problems, such as present in background technology, a kind of KK bearings method rotation inerttia instrument provided by the present invention
Device and its measuring method, rotary inertia is measured by the way of based on KK bearing methods.
The technical solution adopted by the present invention is：
First, a kind of KK bearings method rotation inerttia instrument：
Photoelectric door and stent including base and on base, stent are vertically installed on base, and rotary head leads to
Cross bearing assembly to be sleeved on one end of shaft in a manner of friction free, the other end of shaft is hingedly mounted on cantilever tip, shaft
It is horizontally mounted；Being provided with balanced component and hanging for rotary head side face recombinates part, and the base both sides immediately below rotary head are symmetrically pacified
Equipped with photoelectric door, photoelectric door, which is used to coordinate with balanced component, realizes that rotary head angular velocity of rotation detects, and photoelectric door connects with measuring instrument
Connect.
The balanced component includes two balancing poles, two columns, regulating nut and light barrier, two balancing poles pair
Claim ground to be radially inserted into the both sides of rotary head side face, column and regulating nut are cased with the balancing pole of side, opposite side
Column and light barrier are cased with balancing pole, the photoelectric door is located at the circumference that light barrier rotates in a circumferential direction around rotary head central shaft
On path.
The extension restructuring part includes bracing wire and suspending end bracing wire upper end is fixedly connected with the side face of rotary head, bracing wire lower end
It is connected with suspending end, suspending end sets the weight for being used for providing rotary inertia.
The column is fixed on balancing pole, and regulating nut is used for the torque of adjustment bar so that rotary head peace
The center of gravity for the system that weighing apparatus component is formed is located at rotary head center.
The light barrier is U-shaped structure.
The photoelectric door includes power supply E, resistance R, capacitance C and diode D, and resistance R and diode D are connected on power supply E
Both ends, capacitance C are connected in parallel on resistance R both ends, and the both ends of capacitance C connect microcontroller CLK respectively, microcontroller CLK respectively with display
Connected with controller.
The rotary head includes foundation, KK bearings, bearing fixing sleeve, central shaft and turning set, and the both ends of central shaft lead to
Cross KK bearings to be respectively fitted in two bearing fixing sleeves, two bearing fixing sleeves are socketed in turning set both ends respectively, central shaft
Wherein one section is sleeved in one end of foundation, and the other end and shaft of foundation are coaxially connected, and the side wall of turning set, which is equipped with, to be used to put down
The hole of weighing apparatus bar inserting.Rotary head is socketed by the connection of the KK bearings of minimal drag and the transition of intermediate bearing fixing sleeve to lead to
Bearing assembly is crossed to be sleeved on one end of shaft in a manner of friction free.
On bearing, the whole system that can in succession is freely rotated axle sleeve together.Length mark is carved with cursor, so as to
Cylinder is adjusted to the distance in axle center.The distance in knots modification cylinder to axle center can change mass of system distribution, that is, change
The rotary inertia of system.Light barrier is mounted in one end of cursor, and when system rotates, light barrier is in the light photoelectric door, often
It is in the light and once produces an electric impulse signal, controls angular acceleration measuring instrument device to be stopped after starting.
2nd, a kind of KK bearings method method for measuring rotary inertia：
1) measuring instrument is used, weight is hung on the suspending end, is discharged after bracing wire is rewound rotary head multi-turn,
So that rotary head and balanced component thereon are rotated in the case where the rotary inertia of weight drives, pass through photoelectric door and gear in rotary course
Mating plate collection rotating angular acceleration β；
2) and then calculated using formula the following formula and obtain rotary inertia：
M=J β
M=TR=m/(g-a) R=m/gR-m/βR2
Wherein, T is gravity of the bonding force away from the pulling force corresponding to M, as weight；m/It is weight quality, R is outside rotary head
Diameter, g are acceleration of gravity.
If system rotary inertia J is constant, in system and corresponding angular acceleration β is measured with different moment loadings,
Make M-β figures and can obtain a highly desirable straight line, the slope of straight line is exactly the size of the rotary inertia of system.
Therefore further, the step 2) replaces with：By hanging the weight of different weight on suspending end, calculating obtains
Corresponding angular acceleration β under different weights is obtained, M-β figures is drawn and each point is fitted, the slope of the straight line obtained after fitting is made
For rotary inertia.It can verify that explanation law of rotation, obtain more accurate measurement result.
Gathering rotating angular acceleration β by photoelectric door and light barrier in rotary course in the step 1) is specially：
1.1) gathered and be in the light respectively by two photoelectric doors on light barrier rotation round path using measuring instrument
The front-and-back stop light time interval that piece passes through, and then the average angle speed for obtaining light barrier through photoelectric door is calculated using the following formula
Degree：
ω1=△ S/ △ t1
ω2=△ S/ △ t2
Wherein, △ S represent the distance between frequency modulated light piece both ends parameter, ω1It is light barrier through the flat of first photoelectric door
Equal angular speed, ω2Mean angular velocity for light barrier through second photoelectric door, △ t1Pass through first photoelectric door for light barrier
When first time be in the light and the time interval that is in the light for the second time, △ t2First time gear during for light barrier by second photoelectric door
Light and the time interval being in the light for the second time；
1.2) calculated and obtained using the following formula：
β=(ω2-ω1)/△t
Wherein, △ t represent light barrier by the time between two photoelectric doors；
Light barrier is by the time △ t between two photoelectric doors/Calculated using the following formula：
△ t=(△ t/-△t1/2+△t2/2)
Wherein, △ t/Represent light barrier from first photoelectric door is left into second photoelectric door elapsed time
Every.
The principle of the present invention is as follows：
Rotary inertia is the measurement of inertia size of the object in rotation.It is m to quality, radius r, a length of L's is uniform
Cylinder, when shaft is by barycenter and perpendicular to geometrical axis, rotary inertia J of the cylinder to the axisCSize be：
If shaft is parallel with the shaft by above-mentioned barycenter but not by barycenter, and the distance between be D, see Fig. 1, then
Can use the following formula obtain cylinder to the rotary inertia of the axis for：
JCylinder=JC+mD2
Pivot structure as shown in Figure 2, if rotary inertia is J during without two cylinders0, then two cylinders are loaded onto
Afterwards, rotary inertia J is：
IfThen
From above formula, it can be seen that, the rotary inertia of rotation system is related relative to the distribution situation of shaft with its quality, although
Total system mass is constant, but since cylinder m leaves the distance D changes of shaft, J also changes.When measuring different D by experiment
Correspondence J values, and make J-D2Figure, can obtain straight line, and the slope of straight line is exactly the quality sum of the two cylinders,
Intercept of the straight line on J axis is exactly constant J/。
Object is in the case where bonding force is acted on away from M, and the angular acceleration and bonding force obtained is away from the big Theravada's direct ratio in ground, with rotation
Inertia is inversely proportional, i.e. M=J β.
Therefore the present invention measures bonding force away from M and β by the method for experiment using the above scheme, then directly according to rotation
Law measures the size of rotary inertia J indirectly.
The beneficial effects of the invention are as follows：
Instrument of the present invention is a kind of new instrument, its design principle is complied fully with the theory on textbook, can accomplish reality
Test and do not depart from books, be understood that and show.
Brief description of the drawings
Fig. 1 is the principle schematic of cylinder rotary inertia.
Fig. 2 is the apparatus structure schematic diagram of simple shaft experiment.
Fig. 3 is apparatus structure schematic diagram of the present invention.
Fig. 4 is resultant moment effect lower rotary shaft torque 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 Structure explosion diagram of rotary head.
In figure：1st, rotary head, 2, balancing pole, 3, column, 4, regulating nut, 5, light barrier, 6, photoelectric door, 7, stent,
8th, shaft, 9, measuring instrument, 10, bracing wire, 11, suspending end, 12, base；101st, foundation, 102, KK bearings, 103, bearing fixing sleeve,
104th, central shaft, 105, turning set.
Embodiment
Below in conjunction with the accompanying drawings and specific embodiment is described in further detail the present invention.
As shown in figure 3, the present invention includes base 12 and photoelectric door 6 and stent 7 on base, stent 7 are vertical
On base 12, rotary head 1 is sleeved on one end of shaft 8 by bearing assembly in a manner of friction free, shaft 8 it is another
End is hingedly mounted on 7 top of stent, and shaft 8 is horizontally mounted；Being provided with balanced component and hanging for 1 side face of rotary head recombinates part, turns
12 both sides of base immediately below dynamic first 1 are symmetrically provided with photoelectric door 6, and photoelectric door 6 is used to coordinate realization to rotate with balanced component
First 1 angular velocity of rotation detection, photoelectric door 6 are connected with measuring instrument 9.
It is right that balanced component includes two balancing poles, 2, two columns 3, regulating nut 4 and light barrier 5, two balancing poles 2
Claim ground to be radially inserted into the both sides of 1 side face of rotary head, column 3 and regulating nut 4 are cased with the balancing pole 2 of side, it is another
Column 3 and light barrier 5 are cased with the balancing pole 2 of side, light barrier 5 is U-shaped structure, and photoelectric door 6 is located at light barrier 5 around rotary head
In the circular path that 1 central shaft rotates in a circumferential direction.Column 3 is fixed on balancing pole 2, and regulating nut 4 is used for adjustment bar 2
Torque so that the center of gravity for the system that rotary head 1 and balanced component are formed is located at 1 center of rotary head.
Hang restructuring part to be fixedly connected with the side face of rotary head 1 including bracing wire 10 and 11 bracing wire of suspending end, 10 upper end, bracing wire 10
Lower end is connected with suspending end 11, and suspending end 11 sets the weight for being used for providing rotary inertia.
As shown in fig. 6, photoelectric door 6 includes power supply E, resistance R, capacitance C and diode D, resistance R and diode D are connected on
Power supply E both ends, capacitance C are connected in parallel on resistance R both ends, and the both ends of capacitance C connect microcontroller CLK respectively, and microcontroller CLK is respectively with showing
Show that device is connected with controller.
As shown in fig. 7, rotary head 1 includes foundation 101, KK bearings 102, bearing fixing sleeve 103, central shaft 104 and rotates
Set 105, the both ends of central shaft 104 are respectively fitted in two bearing fixing sleeves 103 by KK bearings 102, two bearing fixing sleeves
103 are socketed in 105 both ends of turning set respectively, and wherein one section of central shaft 104 is sleeved in one end of foundation 101, foundation 101
The other end and shaft 8 are coaxially connected, and the side wall of turning set 105, which is equipped with, is used for the hole that balancing pole 2 inserts.
The embodiment of the present invention and its implementation process are as follows：
1) on bearing, the whole system that can in succession is freely rotated axle sleeve together.Length mark is carved with cursor, so as to
Cylinder is adjusted to the distance in axle center.
Cylinder 3 is fixed on balancing pole 2, and light barrier is also secured on balancing pole 2, is adjusted by rotating regulating nut 4
Regulating nut 4 is installed on the radial position on balancing pole 2, and then adjusts so that the balancing pole 2 of both sides balances each other, i.e. so that turning
The center of gravity of the whole system of first 1 and the formation of balancing pole 2 is moved at the center of rotary head 1.
Photoelectric door is set, has a light-emitting tube and light receiving tube, light-emitting tube optically focused in each photoelectric door of embodiment
Pearl big gun (has lens) before 2.2V/0.25A pearl big guns, and the model of light receiving tube is 3DU52 (can also use infrared emission reception pipe).Photoelectricity
Equivalent to one switch of door, it is as shown in Figure 6 for control and sampling time, its circuit operation principle：When having illumination in reception pipe
Circuit does not constitute circuit when upper, and no signal exports on resistance R；When light is kept off, reception pipe conducting, circuit forms circuit, resistance R
On have signal output.So equivalent to one time sampling device of photoelectric door.
Connecting test instrument and photoelectric door, tester are mainly to be formed with microcontroller, it can deposit the various data of experiment
Enter interior storehouse, to take out one by one after the completion of testing, many experiments can be carried out under the same conditions, and each speed can be calculated
Degree, acceleration and the average acceleration repeatedly measured, average acceleration absolute error.
2) weight is hung on suspending end 11, bracing wire 10 is rewound release after 1 multi-turn of rotary head starts to rotate, light barrier pair
Photoelectric door is in the light, and is often in the light and once produces an electric impulse signal, to control angular acceleration measuring instrument device to stop after starting
Work.
3) as shown in figure 5, there is two photoelectric doors in measuring instrument, photoelectricity test instrument can measure and store movement light-blocking block
On two light barriers by the first photoelectricity I when first time be in the light and the time interval △ t that are in the light for the second time1With pass through
The time interval △ t that first time during two photoelectric doors II is in the light and is in the light for the second time2,
The time interval △ t that light barrier is undergone from the first photoelectric door to the second photoelectric door/.According between two frequency modulated light pieces
Distance parameter △ S can be when two light barriers be by the first photoelectric door on computing light-blocking block mean angular velocity ω1=△ S/ △ t1With
Mean angular velocity ω during by the second photoelectric door2=△ S/ △ t2。
Due to △ t1With △ t2All very littles, approx think that object makees uniformly accelerated motion within the time, therefore △ t1When
Interior mean angular velocity is as △ t1The instantaneous angular velocity ω at/2 this moment1；△ t2Mean angular velocity in time is as △
t2The instantaneous angular velocity ω at/2 this moment2.And from ω1Increase to ω2Required time is modified to △ t=(△ t/-△t1/2+△
t2/ 2), therefore according to acceleration define, use the following formula calculate obtain average angular acceleration within the △ t times for：
β=(ω2-ω1)/△t
According to the △ t measured1, △ t2, △ t and key in light barrier interval △ S values, after tested instrument record, show union
It, obtains ω1, ω2It is with β.
Embodiment setting D=3cm is constant, and R=2cm, is tested with 15g, 25g, 35g, 45g, 55g weights-hoists respectively.Measurement 5
Group, such as data of 10 times, following table：
Then the average for obtaining each angular acceleration improves accuracy, such as figure following table after summary：
It is J to substitute into formula and seek final rotary inertia：
By the use of Inertia Based on Torsion Pendulum Method measuring instrument as reference, measure its rotary inertia is embodiment：JRock=6043.6g.cm2, two
Person's error is：
Wherein, δ represents error, JRockRepresent the rotary inertia that Inertia Based on Torsion Pendulum Method measurement obtains, J represents that the method for the present invention measures
The rotary inertia arrived.
Cylinder 3 on the balancing pole of knots modification both sides can change System Nature to the distance between 1 axial line of rotary head
Amount distribution, so as to change the rotary inertia of whole institute's examining system.
Embodiment then by hanging the weight of different weight on suspending end 11, takes multiple measurements and calculates, draw
M-β schemes, and verification illustrates law of rotation, obtains more accurate measurement result.
It can be seen from the above that the accuracy and validity of the present invention, have prominent significant technique effect.Used in laboratory apparatus
KK high-precision bearings can guarantee that resistance very little, f drag effects are less than 8%.It is low and the photodiode response time is 1-3us
The photodiode of response time can guarantee that experimental data quickly obtains.
Claims (5)
- A kind of 1. KK bearings method rotation inerttia instrument, it is characterised in that：Including base (12) and on base Photoelectric door (6) and stent (7), stent (7) are vertically installed on base (12), and rotary head (1) is by bearing assembly with no friction Mode be sleeved on one end of shaft (8), the other end of shaft (8) is hingedly mounted on stent (7) top, the horizontal peace of shaft (8) Dress；Rotary head (1) side face is provided with balanced component and hangs restructuring part, and base (12) both sides immediately below rotary head (1) are symmetrically Photoelectric door (6) is installed, photoelectric door (6), which is used to coordinate with balanced component, realizes that rotary head (1) angular velocity of rotation detects, photoelectric door (6) it is connected with measuring instrument (9)；The balanced component includes two balancing poles (2), two columns (3), regulating nut (4) and light barrier (5), two Balancing pole (2) is cased with column (3) symmetrically along the both sides for being radially inserted into rotary head (1) side face on the balancing pole (2) of side With regulating nut (4), column (3) and light barrier (5) are cased with the balancing pole (2) of opposite side, the photoelectric door (6) is located at Light barrier (5) is in the circular path that rotary head (1) central shaft rotates in a circumferential direction；The rotary head (1) includes foundation (101), KK bearings (102), bearing fixing sleeve (103), central shaft (104) and turns Dynamic set (105), the both ends of central shaft (104) are respectively fitted in two bearing fixing sleeves (103) by KK bearings (102), two Bearing fixing sleeve (103) is socketed in turning set (105) both ends respectively, and wherein one section of central shaft (104) is sleeved on foundation (101) One end in, the other end and shaft (8) of foundation (101) are coaxially connected, and the side wall of turning set (105), which is equipped with, is used for balancing pole (2) hole of inserting.
- A kind of 2. KK bearings method rotation inerttia instrument according to claim 1, it is characterised in that：The extension restructuring Part includes bracing wire (10) and suspending end (11), and bracing wire (10) upper end is fixedly connected with the side face of rotary head (1), bracing wire (10) lower end It is connected with suspending end (11), suspending end (11) sets the weight for being used for providing rotary inertia.
- A kind of 3. KK bearings method rotation inerttia instrument according to claim 2, it is characterised in that：The regulating nut (4) it is used for the torque of adjustment bar (2) so that the center of gravity for the system that rotary head (1) and balanced component are formed is located at rotary head (1) center.
- A kind of 4. KK bearings method rotation inerttia instrument according to claim 1, it is characterised in that：The light barrier (5) it is U-shaped structure.
- A kind of 5. KK bearings method rotation inerttia instrument according to claim 1, it is characterised in that：The photoelectric door (6) power supply E, resistance R, capacitance C and diode D are included, resistance R and diode D are connected on power supply E both ends, and capacitance C is connected in parallel on electricity R both ends are hindered, the both ends of capacitance C connect microcontroller CLK respectively.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201610538168.7A CN106092442B (en) | 2016-07-06 | 2016-07-06 | KK bearings method rotation inerttia instrument and its measuring method |
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| CN201610538168.7A CN106092442B (en) | 2016-07-06 | 2016-07-06 | KK bearings method rotation inerttia instrument and its measuring method |
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| CN106092442B true CN106092442B (en) | 2018-05-01 |
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| CN106940944A (en) * | 2017-04-27 | 2017-07-11 | 公安海警学院 | Adjustable wide type photoelectricity door physical synthesis experiment instrument |
| 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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