Torsional pendulum type rotational inertia experimental instrument for determining mass center shaft through multi-point weighing

Abstract

The utility model discloses a torsional pendulum type rotational inertia experimental instrument for determining a mass center shaft through multi-point weighing, which comprises a rotating shaft bracket, a central rotating shaft is rotationally arranged on the rotating shaft bracket, a volute spiral spring is arranged on the central rotating shaft, the inner end of the volute spiral spring is fixed on the central rotating shaft, and the outer end of the volute spiral spring is fixed on the rotating shaft bracket. A dial coaxial with the central rotating shaft is fixed on the rotating shaft support, a pointer extending outwards in the radial direction is arranged on the central rotating shaft, and the pointer is used in cooperation with the dial. A first tray is fixed at the top of the central rotating shaft, a plurality of pressure sensors are uniformly distributed at the top of the first tray along the circumferential direction, a second tray for placing an object to be measured is fixed at the tops of the plurality of pressure sensors, and the first tray and the second tray are coaxially arranged with the central rotating shaft. Compared with the prior art, the mass distribution of the object to be measured is measured by adopting the plurality of pressure sensors, and the position of the mass center shaft of the object to be measured can be accurately determined, so that the accurate measurement of the rotational inertia of the object in a complex shape is realized.

Description

TECHNICAL FIELD

[0001] The utility model relates to physical experiment instrument, especially, is a kind of torsional pendulum type rotational inertia experimental instrument of multiple point weighing determination mass center axis. BACKGROUND

[0002] Rotational inertia is the physical quantity describing the inertia size of object to rotational motion, and is important parameter in classical mechanics, engineering, aerospace, robot technology and other fields.For example, in the design and optimization of key components such as engine blade, flywheel, motor rotor, aircraft, artificial satellite and robot end effector, the accurate measurement and calculation of rotational inertia have decisive role.The size of rigid body rotational inertia mainly depends on the shape of rigid body, mass distribution and rotation shaft position.For the object with regular shape and uniform mass distribution, its rotational inertia can be directly calculated by theoretical formula;however, for the object with complex shape and irregular mass distribution, its rotational inertia can only be obtained by experimental measurement.The measurement of rigid body rotational inertia is also an important project of mechanics experiment in university physics experiment.Currently, common measurement methods include three-line pendulum method, torsional pendulum method and falling body method.Among them, the torsional pendulum method is widely applied due to its high measurement accuracy, simple operation and good repeatability.In measuring the rotational inertia of object around its mass center axis, ensuring that the mass center axis of the object to be measured is strictly coaxial with the central rotation shaft is the key to reduce experimental error and improve measurement accuracy.

[0003] However, the traditional torsional pendulum type rigid body rotational inertia teaching device has a significant technical limitation: lacking accurate mass center positioning function.This defect leads to that in measuring the object with irregular geometric shape or non-uniform mass distribution, only relying on visual estimation can not realize accurate alignment of mass center and rotation shaft, thereby introducing significant systematic error, which seriously affects the accuracy and reliability of measurement result. UTILITY MODEL CONTENT

[0004] The utility model aims at overcoming the insufficient of prior art, provides a torsional pendulum type rotational inertia experimental instrument of multiple point weighing determination mass center axis, to accurately determine the mass center axis position of the object to be measured, thereby ensuring the accuracy of rotational inertia measurement result.

[0005] The utility model is realized through the following technical schemes:

[0006] The torsional pendulum type rotational inertia experimental instrument of multiple point weighing determination mass center axis, including rotation shaft support, the vertical extension center rotation shaft is rotationally installed on rotation shaft support, the center rotation shaft is installed with volute spring, volute spring inner end is fixed on center rotation shaft, and outer end is fixed on rotation shaft support, the rotation shaft support is fixed with the scale disc coaxial with the center rotation shaft, the center rotation shaft is equipped with the pointer extending radially outward, and the pointer is used in cooperation with the scale disc;

[0007] The first tray is fixed on the top of the central rotating shaft, a plurality of pressure sensors are evenly distributed on the top of the first tray in the circumferential direction, a second tray for placing the object to be measured is fixed on the top of the plurality of pressure sensors, and the first tray and the second tray are coaxially arranged with the central rotating shaft.

[0008] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, the pointer is located above the scale disc, the outer end of the pointer extends beyond the edge of the scale disc and is provided with a light barrier, and the light barrier is used in cooperation with the peripheral photoelectric gate.

[0009] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, the rotating shaft support is composed of an upper end plate, a vertical plate and a lower end plate, and has a C-shaped structure as a whole; the central rotating shaft is rotatably connected with the upper end plate and the lower end plate through two bearings, and the volute spring is located between the upper end plate and the lower end plate and has an outer end fixed on the vertical plate.

[0010] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, the scale disc is fixedly installed on the top of the upper end plate.

[0011] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, the bearing is a ceramic bearing.

[0012] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, the bottom of the rotating shaft support is supported on the base.

[0013] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, three pressure sensors are evenly distributed on the top of the first tray in the circumferential direction.

[0014] As a preferred scheme of the torsion pendulum type rotational inertia experiment instrument, four pressure sensors are evenly distributed on the top of the first tray in the circumferential direction.

[0015] Compared with the prior art, the utility model has the following advantages:

[0016] The utility model provides a kind of torsional pendulum type rotational inertia experimental instrument of multiple point weighing determination centroid axis, it is uniformly distributed by being set in first tray multiple pressure sensors along circumference, and second tray for placing to be measured object is set in each pressure sensor top, by multiple point weighing technique, using multiple pressure sensors measure the mass distribution of to be measured object, the centroid axis position of to be measured object can be accurately determined, effectively solve the problem that traditional device is difficult to accurately position irregular object centroid, to realize the accurate measurement of rotational inertia of complex shape object. Meanwhile, the utility model adopts the composite measurement system of pointer-dial scale-photoelectric gate, wherein the starting angle of central rotating shaft can be accurately determined by the cooperation of pointer and dial, ensure the repeatability of each torsional pendulum experiment, reduce experimental measurement error;Light barrier is set on the outer end of pointer and cooperates with photoelectric gate, realize the measurement of torsional pendulum period, this kind of structure design is simple, ingenious and layout is reasonable, measurement precision is high and reliability is strong, with wide popularization and application value. BRIEF DESCRIPTION OF DRAWINGS

[0017] Fig. 1 It is the structural schematic diagram of the utility model.

[0018] Fig. 2 It is the schematic diagram of the utility model three point weighing determination centroid axis.

[0019] Fig. 3 It is the schematic diagram of the utility model four point weighing determination centroid axis.

[0020] Marked number in drawing:1 rotating shaft support, 2 central rotating shaft, 3 scroll spring, 4 bearing, 5 dial, 6 pointer, 7 light barrier, 8 photoelectric gate, 9 first tray, 10 pressure sensor, 11 to be measured object, 12 second tray, 13 base. DETAILED DESCRIPTION

[0021] The embodiment of the utility model is described in detail below, and the embodiment is implemented under the premise of the technical scheme of the utility model, detailed implementation mode and specific operation process are given, but the protection scope of the utility model is not limited to the following embodiment.

[0022] Reference Figs. 1 to 3The embodiment discloses a torsional pendulum type rotational inertia experimental instrument for multi-point weighing determination of a center of mass shaft, comprising a rotating shaft support 1 which is supported at the bottom on a base 13. A vertically extending center rotating shaft 2 is rotatably installed on the rotating shaft support 1, and a volute spring 3 is installed on the center rotating shaft 2, with the inner end of the volute spring 3 fixed on the center rotating shaft 2 and the outer end fixed on the rotating shaft support 1, for providing an elastic moment. The rotating shaft support 1 is composed of an upper end plate, a vertical plate and a lower end plate, and has a C-shaped structure as a whole; the center rotating shaft 2 is rotatably connected with the upper end plate and the lower end plate through two bearings 4, and the bearings 4 are ceramic bearings, which can effectively reduce the rotating friction and improve the measurement accuracy. The volute spring 3 is located between the upper end plate and the lower end plate, and the outer end of the volute spring 3 is fixed on the vertical plate.

[0023] A scale disc 5 coaxial with the center rotating shaft 2 is fixed on the rotating shaft support 1, and a pointer 6 extending radially outward is arranged on the center rotating shaft 2, which is used in cooperation with the scale disc 5 to indicate the rotation angle of the center rotating shaft 2; the scale disc 5 is fixedly installed on the top of the upper end plate of the rotating shaft support 1, and the pointer 6 is located above the scale disc 5, with the outer end of the pointer 6 extending out of the edge of the scale disc 5 and provided with a light barrier 7, which is used in cooperation with a peripheral photoelectric gate 8 to measure the oscillation period T of the to-be-measured object 11 by shielding the light of the photoelectric gate 8.

[0024] A first tray 9 is fixed on the top of the center rotating shaft 2, and a plurality of pressure sensors 10 are uniformly distributed on the top of the first tray 9 in the circumferential direction, and a second tray 12 for placing the to-be-measured object 11 is fixed on the top of the plurality of pressure sensors 10, and the first tray 9 and the second tray 12 are coaxially arranged with the center rotating shaft 2.

[0025] The number of the pressure sensors 10 can be selected according to specific conditions, and in the embodiment, three or four pressure sensors 10 are uniformly distributed on the top of the first tray 9 in the circumferential direction.

[0026] The working principle of the experimental instrument provided in the embodiment is as follows:

[0027] In the experiment of measuring the rotational inertia of a rigid body by the torsional pendulum method, the to-be-measured object 11 is first placed on the second tray 12. The center rotating shaft 2 is rotated to a predetermined initial angle and then released by observing the indication of the scale disc 5 and the pointer 6. Under the action of the elastic moment of the volute spring 3, the to-be-measured object 11 performs periodic torsional pendulum oscillation. The light barrier 7 shields the light of the photoelectric gate 8, and the oscillation period T of the to-be-measured object 11 is accurately recorded. According to the motion characteristics of the torsional pendulum system, the rotational inertia of the to-be-measured object 11 around the center rotating shaft 2 can be calculated by the following formula (1):

[0028]

[0029] In formula (1), J is the rotational inertia value of the measured object 11 around the central rotation shaft 2, K is the spring torsion constant of the spiral spring 3, and T is the measured swing period.

[0030] The spring torsion constant K value of the spiral spring 3 is obtained as follows:

[0031] A plastic cylinder with regular shape and uniform mass distribution is used as a standard object, the mass of the standard object is m0, and the diameter is D0. The theoretical value J0 of the rotational inertia of the standard object is calculated according to formula (2) as follows:

[0032]

[0033] According to the measured swing period T0 of the standard object, J0 and T0 are brought into formula (1) above, and formula (3) is obtained as follows:

[0034]

[0035] According to formula (3), the spring torsion constant K value of the spiral spring 3 can be calculated, and according to the measured swing period T, the rotational inertia J of the measured object 11 around the central rotation shaft 2 can be calculated according to formula (1).

[0036] According to the parallel axis theorem, the rotational inertia value J of the measured object 11 around the centroid axis is c which can be obtained by formula (4) as follows:

[0037] J c = J-Md 2 (4)

[0038] In formula (4), J c is the rotational inertia of the measured object 11 around the centroid axis, M is the mass of the measured object 11, and d is the distance between the centroid axis of the measured object 11 and the central rotation shaft 2.

[0039] Next, the mass M of the measured object 11 and the distance d between the centroid axis of the measured object 11 and the central rotation shaft 2 need to be measured, and the specific measurement process is as follows:

[0040] The measurement process is described by taking three-point weighing to determine the centroid axis as an example. At this time, the top of the first tray 9 is uniformly distributed with three pressure sensors 10 in the circumferential direction:

[0041] As shown in the XOY coordinate system, Fig. 2 the origin O is the center of the second tray 12, OX, OY, and OZ are the reference axes of the second tray 12. S1, S2, and S3 are the positions of the three pressure sensors 10 in the coordinate system, which are distributed in a regular triangle and the center is at the origin O. C is the position of the centroid of the measured object 11 in the plane XOY, and the horizontal coordinate of the C point is X c, the ordinate is Y c , L1, L2, L3, L4 are the vertical distances from each pressure sensor 10 to the reference axes OX, OY. Assuming that the object 11 is placed on the second tray 12, the pressure change values of the three pressure sensors 10 are ΔF1, ΔF2, ΔF3 respectively, then the mass M of the object 11 is calculated according to the following formula (5):

[0042]

[0043] Where g is the acceleration of gravity constant.

[0044] After the partial gravity of each point is measured, according to the principle of moment balance, the abscissa X of the object 11 in the plane XOY is calculated according to the following formula (6): c , the ordinate Y of the object 11 is calculated according to the following formula (7): c :

[0045]

[0046] According to the Pythagorean theorem, the straight-line distance of point C from the origin O can be calculated, which is the distance d between the centroid axis of the object 11 and the central shaft 2. The distance d between the centroid axis of the object 11 and the central shaft 2 is calculated according to the following formula (8):

[0047]

[0048] According to the mass M of the object 11 and the distance d between the centroid axis of the object 11 and the central shaft 2 obtained above, the moment of inertia J of the object 11 around the centroid axis is obtained by substituting into formula (4): c .

[0049] The measurement process is described by taking the four-point weighing to determine the centroid axis as an example. At this time, the top of the first tray 9 is uniformly distributed with four pressure sensors 10:

[0050] As shown in Fig. 3 , the origin O is the center of the second tray 12, OX, OY, OZ are the reference axes of the second tray 12. S1, S2, S3, S4 are the positions of the four pressure sensors 10 in the coordinate system, which are distributed in a square and the center is at the origin O. C point is the position of the centroid of the object 11 in the plane XOY, the abscissa of the C point is X c , the ordinate is Y c . L1, L2, L3, L4 are the vertical distances from each pressure sensor 10 to the reference axes OX, OY. Assuming that the object 11 is placed on the second tray 12, the pressure change values of the four pressure sensors 10 are ΔF1, ΔF2, ΔF3, ΔF4 respectively, then the mass M of the object 11 is calculated according to the following formula (9):

[0051]

[0052] Where g is the gravitational acceleration constant.

[0053] After the gravity at each point is measured, the abscissa X of the object to be measured 11 is calculated in the plane XOY according to the following formula (10) based on the principle of torque balance. c The ordinate Y of the test object 11 is calculated according to the following formula (11). c :

[0054]

[0055] According to the Pythagorean theorem, the straight-line distance from point C to the origin O can be calculated. This distance is the distance d between the centroidal axis of the object to be measured 11 and the central rotation axis 2. The distance d between the centroidal axis of the object to be measured 11 and the central rotation axis 2 is calculated according to the following formula (12):

[0056]

[0057] Based on the mass M of the object to be tested 11 and the distance d between its center of mass and the central axis of rotation 2 obtained above, substituting these values ​​into equation (4) yields the moment of inertia J of the object to be tested 11 about its center of mass. c .

[0058] In summary, this embodiment uses multiple pressure sensors 10 to determine the position of the centroidal axis of the object 11 to be tested, and employs a composite measurement system consisting of a pointer 6, a dial 5, and a photoelectric gate 8 to measure the initial angle and oscillation period of the central rotating shaft 2, thereby achieving precise measurement of the rotational inertia of objects with complex shapes. This experimental instrument features an ingenious structural design, high measurement accuracy, good repeatability, and wide applicability, which can greatly improve the effectiveness of experimental teaching.

[0059] The above are merely preferred embodiments of the present utility model and are not intended to limit the present utility model. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present utility model should be included within the protection scope of the present utility model.

Claims

1. A torsional pendulum moment of inertia experimental apparatus for determining the center of mass by multi-point weighing, comprising a rotating shaft support, wherein a vertically extending central rotating shaft is rotatably mounted on the rotating shaft support, characterized in that: The center rotating shaft is provided with a volute spring, the inner end of the volute spring is fixed on the center rotating shaft, the outer end of the volute spring is fixed on a rotating shaft support, the rotating shaft support is fixed with a dial coaxial with the center rotating shaft, the center rotating shaft is provided with a pointer extending radially outward, and the pointer is used in cooperation with the dial. The first tray is fixed on the top of the center rotating shaft, a plurality of pressure sensors are uniformly distributed on the top of the first tray in the circumferential direction, a second tray for placing a to-be-tested object is fixed on the top of the plurality of pressure sensors, and the first tray and the second tray are coaxially arranged with the center rotating shaft.

2. The torsion pendulum type rotational inertia tester for determining a center of mass axis of a multi-point weigher according to claim 1, characterized in that: The pointer is located above the dial, the outer end of the pointer extends out of the edge of the dial and is provided with a light barrier, and the light barrier is used in cooperation with a peripheral photoelectric gate.

3. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 1, wherein: The rotating shaft support is composed of an upper end plate, a vertical plate and a lower end plate, and has a C-shaped structure as a whole; the center rotating shaft is rotatably connected with the upper end plate and the lower end plate through two bearings respectively, and the volute spring is located between the upper end plate and the lower end plate, and the outer end of the volute spring is fixed on the vertical plate.

4. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 3, wherein: The dial is fixedly installed on the top of the upper end plate.

5. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 3, wherein: The bearing is a ceramic bearing.

6. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 3, wherein: The bottom of the rotating shaft support is supported on the base.

7. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 1, wherein: The top of the first tray is uniformly provided with three pressure sensors in the circumferential direction.

8. The torsion pendulum type rotational inertia tester for determining a center of mass axis of the multi-point weighing scale according to claim 1, wherein: The top of the first tray is uniformly provided with four pressure sensors in the circumferential direction.

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