CN209028918U - Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device - Google Patents

Abstract

The utility model provides a kind of measurement of Coriolis acceleration and acceleration composite theorem examines experimental provision, which includes transport motion component, relative motion component and test sensor；Transport motion component includes rack, first motor, first rotating shaft and the first turntable；For first rotating shaft perpendicular to the first turntable, the top of first rotating shaft is located at the center location of the first turntable；Relative motion component includes the first support frame, the second support frame, the second motor, the second shaft and the second turntable；Second flange is provided in second shaft, the second turntable is mounted in the second shaft by second flange；Measurement sensor includes speed probe and acceleration transducer.It is the utility model compact, low cost, easy to use, intuitive, it can be applied to classroom instruction, show phenomenon and Experimental Research.The presence that can be not only used for visually demonstrating Coriolis acceleration, also can accurately measure Coriolis acceleration size, while can also examine acceleration composite theorem.

Description

Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device

technical field

The utility model belongs to the technical field of experimental teaching devices for kinematics and dynamics, in particular to an experimental device for Coriolis acceleration demonstration measurement and acceleration synthesis theorem testing.

Background technique

When analyzing the synthetic motion of an object, when the motion system rotates on a fixed axis, the absolute acceleration of the moving point at a certain instant is equal to the vector sum of its implicated acceleration, relative acceleration and Coriolis acceleration at that instant. Coriolis acceleration is caused by the interaction between the implicated motion and the relative motion when the dynamic system is rotating. The force corresponding to the Coriolis acceleration is called the Coriolis force. Coriolis acceleration widely exists in our real life, such as different scours on both sides of the riverbed, and opposite directions of cyclones in the northern and southern hemispheres. Coriolis acceleration is a difficult point in courses such as "Theoretical Mechanics" and "Mechanical Principles", mainly because Coriolis acceleration is relatively abstract, and its causes and direction judgments are difficult to understand. The generation of Coriolis acceleration is usually not easy to observe because of the accompanying rotation. Therefore, it is necessary to intuitively display the phenomenon of Coriolis acceleration through the experimental device and measure its size. The acceleration synthesis theorem involves space vector operations and is also relatively complex. It is necessary to further test the resultant acceleration components on the basis of measuring the Coriolis acceleration.

To demonstrate or measure Coriolis acceleration, some experimental setups exist.

The patent number is ZL201420694536.3, the authorization announcement number CN 204257073 U, the authorization announcement date is 2015.04.08, the applicant is: Zhejiang Normal University, the patent application: a Coriolis acceleration demonstrator, the variable frequency motor of the demonstrator drives the large turntable to rotate, On the large turntable, the DC motor drives the belt to move, and the belt is subjected to the Coriolis force perpendicular to the direction of the belt in the horizontal plane, and the belt moves closer to the middle or separates to both sides. As the rotational speed and belt inclination change, the Coriolis force changes and the corresponding belts move closer or apart. The turntable water pump demonstration platform developed by Hohai University is similar. This kind of experimental device can demonstrate the phenomenon of Coriolis acceleration, but it is bulky and cannot measure the magnitude of Coriolis force or Coriolis acceleration.

Patent No. ZL201410209679.5, Authorization Announcement No. CN 104021708 B, Authorization Announcement Date 2016.06.08, Applicant: Shanghai University of Science and Technology, Applied Patent: Coriolis acceleration demonstrator and Coriolis inertial force measurement method, the Coriolis acceleration demonstrator Added Coriolis force measurement section. Start the motor, make the inner cylinder and the belt rotate in the opposite direction, make the two straight sides of the belt close together, and record the minimum distance between the two straight sides with an infrared laser range finder. Turn off the motor, push the two push rods, respectively drive the two pressure sensors, push the two sliders to slide on the guide rails, squeeze the two straight edges of the belt to make the distance equal to the above minimum distance, and read the pressure gauge on the pressure sensor Multiply by the area of the sensor piston, you can get the size of the Coriolis force. Although this experimental device can measure the Coriolis force, it is measured by an indirect method. The shape of the belt after deformation under the action of the Coriolis force is different from the shape after the deformation under the action of the slider; the actual force of the belt also includes the occurrence of implicated The centripetal force of the acceleration, so the measurement error is large.

In addition, Hu Rui of Wuhan University of Technology installed a pointer on the slider subjected to Coriolis force, and the brush on the pointer recorded the trajectory of the pointer for quantitative analysis; Wang Songsong of Nanjing University of Aeronautics and Astronautics used a steel ball subjected to Coriolis force to compress the spring, and the spring was deformed , using the transmission mechanism composed of pulley, lead wire and displacement compensation screw to transmit the spring deformation to the display device, so as to display the existence of Coriolis acceleration. The measurement methods of these devices are all indirect methods, which have large measurement errors, complex structures and high costs.

However, there is no report on the experimental device for testing the acceleration synthesis theorem.

SUMMARY OF THE INVENTION

The purpose of the utility model is to provide a Coriolis acceleration demonstration measurement and acceleration synthesis theorem testing experimental device, which can not only demonstrate the Coriolis acceleration phenomenon, but also test the Coriolis acceleration, analyze the factors affecting the Coriolis acceleration, and also pass The experimental setup tests the acceleration synthesis theorem.

In order to achieve the above purpose, the present invention adopts the following technical solutions to achieve.

Coriolis acceleration measurement and acceleration synthesis theorem test experimental device, the experimental device includes an implicated motion component, a relative motion component and a measurement sensor;

The implicated movement component includes a frame, a first motor, a first rotating shaft and a first turntable; the frame is composed of an upper support plate, a bottom plate and a side plate; the first motor is arranged inside the frame, and an output shaft of the first motor is arranged with a a first gear; the bottom of the first rotating shaft is arranged on the bottom plate, and a first bearing is arranged between the first rotating shaft and the bottom plate; a second gear is sleeved in the middle of the first rotating shaft, and the first gear is meshed with the second gear; Passing over the upper support plate, a second bearing is arranged between the first shaft and the upper support plate; the top of the first shaft is provided with a first flange, and the top of the first shaft supports the first turntable through the first flange; the first shaft is vertical On the first turntable, the top of the first shaft is located at the center of the first turntable;

The relative motion assembly includes a first support frame, a second support frame, a second motor, a second rotating shaft and a second turntable; the first support frame and the second support frame are arranged on the first turntable, and the second motor is arranged on the first support The second turntable is vertically arranged, and the second shaft passes through the center of the second turntable; the output shaft of the second motor is connected to one end of the second shaft through a coupling, and the other end of the second shaft is supported on the second shaft. On the support frame, a third bearing is arranged between the second shaft and the second support frame; a second flange is also arranged on the second shaft, and the second turntable is mounted on the second shaft through the second flange;

The measurement sensor includes a rotational speed sensor and an acceleration sensor; the rotational speed sensor is used to measure the rotational speed and direction of the first turntable and the second turntable; the acceleration sensor is used to measure the acceleration of a certain point on the second turntable in three orthogonal directions.

Wherein, the first turntable is provided with a first guide groove and a second guide groove, the bottom of the first support frame is embedded in the first guide groove, and the bottom of the second support frame is embedded in the second guide groove; the first support frame The installation position on the first guide groove is adjustable, and the installation position of the second support frame on the second guide groove is adjustable.

When the experimental device of the utility model performs the Coriolis acceleration phenomenon demonstration, the second turntable adopts a soft disk; when the experimental device performs the Coriolis acceleration formula test and the acceleration synthesis theorem test, the second turntable uses a hard disk. When the second turntable is a hard disk, a third guide groove and a fourth guide groove are arranged on the disk surface of the second turntable, and the third guide groove and the fourth guide groove are symmetrically distributed with the center O of the _second turntable, and the The symmetry line L 1 of the three guide grooves, the symmetry line L ₂ of the fourth guide groove and the circle center O ₂ of the _second turntable are located on the same straight line; The installation position of the acceleration sensor on the third guide groove is adjustable; the fourth guide groove is provided with a second three-way acceleration sensor, and the installation position of the second three-way acceleration sensor on the fourth guide groove is adjustable.

In addition, a current collecting ring is arranged on the first rotating shaft between the first turntable and the frame, the outer ring of the collecting ring is fixed on the frame, and the inner ring of the collecting ring is sleeved and fixed on the first rotating shaft.

Furthermore, the first motor is a stepping motor, a variable frequency motor or a servo motor, and the second motor is a stepping motor, a variable frequency motor or a servo motor; the first motor is connected to the controller through the first driver, and the second motor is connected through the second driver. Connected with the controller; the controller controls the rotational speed magnitude and rotational speed direction of the first motor through the first driver, and the controller controls the rotational speed magnitude and rotational speed direction of the second motor via the second driver.

The beneficial effects of the utility model are: small size, low cost, convenient and intuitive use, and can be applied to classroom teaching, displaying phenomena and experimental research. It can be used to visually demonstrate the existence of Coriolis acceleration, which is easy to understand the principle of Coriolis acceleration; it can also accurately measure the magnitude of Coriolis acceleration to help students understand the influencing factors of Coriolis acceleration in an all-round way; at the same time, it can also test the acceleration synthesis theorem. It plays an important role in improving the teaching effect of courses such as "Theoretical Mechanics" and "Mechanical Principles".

Description of drawings

1 is a schematic structural diagram of the Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device of the present invention;

2 is another structural schematic diagram of the Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device of the present invention;

3 is a schematic structural diagram of the third guide groove and the fourth guide groove of the present invention being arranged on the second turntable;

4 is a schematic structural diagram of the first motor and the second motor connected to the controller respectively of the present invention;

5 is a schematic diagram of the movement of the first turntable and the second turntable of the present invention;

Fig. 6 is the coordinate direction diagram of the first three-direction acceleration sensor of the present invention;

7 is a calculation and analysis diagram of the Coriolis acceleration tested by the first three-direction acceleration sensor of the present invention;

FIG. 8 is a calculation and analysis diagram of the first three-direction acceleration sensor of the present invention to verify the acceleration synthesis theorem.

In the figure, 1. the frame; 2. the first motor; 3. the collector ring; 4. the first flange; 5. the first support frame; 6. the second motor; 7. the first three-way acceleration sensor; 8 .Coupling; 9. Second shaft; 10. Second three-way acceleration sensor; 11. Second gear; 12. First gear; 13. Second turntable; 14. Second flange; 15. First turntable ; 16. The first shaft; 17. The second support frame; 18. The upper support plate; 19. The bottom plate; a driver; 25. a second driver; 26. a second guide slot; 27. a third guide slot; 28. a fourth guide slot.

Detailed ways

As shown in FIG. 1 and FIG. 2 , the present invention provides an experimental device for Coriolis acceleration measurement and acceleration synthesis theorem test, including an implicated motion component, a relative motion component and a measurement sensor.

The implicated movement assembly includes a frame 1, a first motor 2, a first rotating shaft 16 and a first turntable 15; the frame 1 is composed of an upper support plate 18, a bottom plate 19 and a side plate 20; the first motor 2 is arranged inside the frame 1 , the output shaft of the first motor 2 is provided with a first gear 12; the bottom of the first rotating shaft 16 is set on the bottom plate 19, and a first bearing is provided between the first rotating shaft 16 and the bottom plate 19; Two gears 11, the first gear 12 meshes with the second gear 11; the upper part of the first shaft 16 passes through the upper support plate 18, and a second bearing is arranged between the first shaft 16 and the upper support plate 18; the top of the first shaft 16 is provided There is a first flange 4, and the top of the first shaft 16 supports the first turntable 15 through the first flange 4; the first shaft 16 is perpendicular to the first turntable 15, and the top of the first shaft 16 is located at the center of the first turntable 15 . When the first motor 2 is working, the output shaft of the first motor 2 rotates, which drives the first gear 12 to rotate, the first gear 12 drives the second gear 11 to rotate, and the second gear 11 drives the first shaft 16 to rotate. 16 drives the first turntable 15 to rotate to realize the implicated movement.

The relative motion assembly includes a first support frame 5, a second support frame 17, a second motor 6, a second rotating shaft 9 and a second turntable 13; the first support frame 5 and the second support frame 17 are arranged on the first turntable 15, The second motor 6 is arranged on the first support frame 5; the second turntable 13 is arranged vertically, the second shaft 9 passes through the center of the second turntable 13; the output shaft of the second motor 6 is connected to the second turntable 6 through the coupling 8 One end of the rotating shaft 9 is connected, and the other end of the second rotating shaft 9 is supported on the second supporting frame 17 , and a third bearing 22 is arranged between the second rotating shaft 9 and the second supporting frame 17 ; Two flanges 14 , the second turntable 13 is mounted on the second shaft 9 through the second flange 14 . When the second motor 6 is working, the output shaft of the second motor 6 rotates to drive the second shaft 9 to rotate, and the second shaft 9 drives the second turntable 13 to rotate to achieve relative movement.

As shown in FIG. 4 , the first motor 2 is a stepping motor, a variable frequency motor or a servo motor, and the second motor 6 is a stepping motor, a variable frequency motor or a servo motor; the first motor 2 is connected to the controller 23 through the first driver 24 , the second motor 6 is connected to the controller 23 through the second driver 25; the controller 23 controls the speed and direction of the first motor 2 through the first driver 24, and the controller 23 controls the Speed size and speed direction.

In addition, as shown in FIG. 2 , the first turntable 15 is provided with a first guide groove 21 and a second guide groove 26 , the bottom of the first support frame 5 is embedded in the first guide groove 21 , and the bottom of the second support frame 17 is embedded in the first guide groove 21 . Embedded in the second guide groove 26 . The installation position of the first support frame 5 on the first guide groove 21 is adjustable, and the installation position of the second support frame 17 on the second guide groove 26 is adjustable. By adjusting the installation position of the first support frame 5 on the first guide groove 21 and the installation position of the second support frame 17 on the second guide groove 26, the position of the second turntable 13 on the first turntable 15 is adjusted so that The relative positions of the first turntable 15 and the second turntable 13 change.

Further, the inclination angle of the second rotating shaft 9 can be changed by lowering or raising the height of the first support frame 5, so that the relative angle of the first rotating disk 15 and the second rotating disk 13 can be changed.

Furthermore, the first rotating shaft 16 between the first turntable 15 and the frame 1 is provided with a collector ring 3 , the outer ring of the collector ring 3 is fixed on the frame 1 , and the inner ring of the collector ring 3 is sleeved in parallel. Fixed on the first shaft 16 . Since the second motor 6 rotates with the first turntable 15, the cable will be entangled when the cable is used to supply power to it, and it cannot continue to work. Therefore, a collector ring 3 is provided on the first rotating shaft 16 between the first turntable 15 and the frame 1 , and the current of the second driver 25 is transmitted to the upper second motor 6 through the collector ring 3 .

The measuring sensor of the present invention includes a rotational speed sensor and an acceleration sensor; the rotational speed sensor is used to measure the rotational speed and direction of the first turntable 15 and the second turntable 13 ; the acceleration sensor is used to measure a certain point on the second turntable 13 at three positive acceleration in the cross direction. The rotational speed sensor can use a contact sensor or a non-contact sensor. The present invention preferably uses a non-contact sensor. A reflective label is attached to the first turntable 15 or the second turntable 13, and the non-contact sensor can be used to measure the rotational speed. The acceleration sensor adopts a three-direction acceleration sensor, which is used to measure the acceleration of a certain point on the second turntable 13 in three orthogonal directions.

When demonstrating the Coriolis acceleration phenomenon in the experimental device of the present invention, the second turntable 13 adopts a soft disk, and the optional material is rubber. When the second turntable 13 is a soft disk, there is no Guide groove and acceleration sensor.

When testing the Coriolis acceleration formula and the acceleration synthesis theorem in the experimental device of the present invention, the second turntable 13 adopts a hard disk, and the optional material is acrylic glass. As shown in FIG. 1 , when the second turntable 13 is a hard disk, a third guide groove 27 and a fourth guide groove 28 , and a third guide groove 27 and a fourth guide groove 28 are provided on the disk surface of the second turntable 13 . It is symmetrically distributed with the center O ₂ of the second turntable 13, and the line of symmetry L 1 of the third guide groove 27, the line of symmetry L ₂ of the fourth guide groove 28 and the center O ₂ of the _second turntable 13 are located on the same straight line, such as As shown in FIG. 3; the third guide groove 27 is provided with a first three-way acceleration sensor 7, and the installation position of the first three-way acceleration sensor 7 on the third guide groove 27 is adjustable; the fourth guide groove 28 is provided with a third Two and three-way acceleration sensors 10, and the installation positions of the second and three-way acceleration sensors 10 on the fourth guide groove 28 are adjustable.

The data test terminal of the utility model is used for displaying and recording test data. The data tested by the tachometer is directly displayed on the display screen on the tachometer, while the data tested by the accelerometer is transmitted to the mobile phone or computer through wired or wireless means, and the mobile phone or computer can display various data tested by the accelerometer in real time. , through data processing and calculation, the calculation expression of Coriolis acceleration and the acceleration synthesis theorem are tested. Specifically, the wired method is to transmit the data tested by the acceleration sensor on the second turntable 13 to the mobile phone or computer through the collector ring 3; the wireless method is to integrate the acceleration sensor, the battery and the wireless signal transmitter into a small module, The transmission and reception of the signal transmits the data tested by the acceleration sensor to the mobile phone or computer, such as the Bluetooth wireless transmission method.

1. The method for demonstrating the Coriolis acceleration phenomenon based on the Coriolis acceleration measurement and the acceleration synthesis theorem test device of the present utility model is as follows:

step 1,

Preparation: Adjust the frame 1 so that the first turntable 15 is in a horizontal state, the second turntable 13 is a soft disk, install the second turntable 13 on the second shaft 9, adjust the first support frame 5 and the second support frame 17, so that the second turntable 13 is perpendicular to the first turntable 15, and the vertical projection of the center of the second turntable 13 coincides with the center of the first turntable 15; the second turntable 13 does not need to install an acceleration sensor;

Step 2,

Check the rotation speed of the first motor 2: start the first motor 2, close the second motor 6, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the first turntable 15 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the first turntable 15; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Check the rotation speed of the second motor 6: start the second motor 6, close the first motor 2, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the second turntable 13 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the second turntable 13; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Step 3,

3.1 When the first turntable 15 rotates at a constant speed according to the set rotation speed, and the second turntable 13 does not rotate, although there is rotation of the moving coordinate system without relative motion, no Coriolis force is generated. The turntable 13 is not deformed;

3.2 When the first turntable 15 does not rotate, the second turntable 13 rotates at a constant speed according to the set rotation speed, only relative motion without the rotation of the moving coordinate system, and no Coriolis force is generated. At this time, the second turntable 13 of soft material does not rotate. deformed;

3.3 When the first turntable 15 rotates at a constant speed according to the set rotation speed, while the second turntable 13 rotates at a constant speed according to the set rotation speed, due to the rotation of the moving coordinate system and the relative movement of the moving point on the moving coordinate system, a Coriolis force, the Coriolis force causes the upper and lower parts of the second turntable 13 of soft material to deflect in opposite directions along the axial direction of the second shaft 9, thereby visually demonstrating the Coriolis acceleration effect; then changing the first The magnitude and direction of the rotational speed of a turntable 15 or the second turntable 13, and the changes in the magnitude and direction of the deformation of the second turntable 13 are observed, thereby showing the influence of the magnitude and direction of the rotational speed on the Coriolis force;

3.4 Adjust the position of the second turntable 13 on the first turntable 15 by adjusting the installation position of the first support frame 5 on the first guide groove 21 and the installation position of the second support frame 17 on the second guide groove 26. Then, make the first turntable 15 rotate at a constant speed according to the set rotation speed, and at the same time, when the second turntable 13 rotates at a constant speed according to the set rotation speed, observe the change of the deformation of the second turntable 13 of soft material, and show the first turntable 15 and the second turntable 13. The influence of the relative position change of the second turntable 13 on the Coriolis force;

3.5 Restore the experimental device of the present utility model to the initial state of step 1; then lower or raise the height of the first support frame 5 to change the inclination angle of the second rotating shaft 9; then make the first turntable 15 according to the set rotating speed Rotate at a constant speed, while the second turntable 13 rotates at a constant speed according to the set rotation speed, observe the change of the deformation of the second turntable 13 of soft material, and show the influence of the relative angle change of the first turntable 15 and the second turntable 13 on the Coriolis force.

2. The method for testing the Coriolis acceleration formula based on the Coriolis acceleration measurement and the acceleration synthesis theorem test device of the present utility model is as follows:

step 1,

Preparation: Adjust the rack 1 so that the first turntable 15 is in a horizontal state, the second turntable 13 is a hard disk, install the second turntable 13 on the second shaft 9, adjust the first support frame 5 and the second support frame 17, so that the second turntable 13 is perpendicular to the first turntable 15, and the vertical projection of the center of the second turntable 13 coincides with the center of the first turntable 15; The first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 are installed on the groove 28, and the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 are symmetrically distributed around the center O ₂ of the second turntable 13; The second turntable 13 makes the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 lie in the same horizontal plane, then keep the first turntable 15 and the second turntable 13 stationary, turn on the first three-way acceleration sensor 7 and the second turntable 13 The two-three-way acceleration sensor 10 is zero-adjusted;

Step 2,

Check the rotation speed of the first motor 2: start the first motor 2, close the second motor 6, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the first turntable 15 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the first turntable 15; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Check the rotation speed of the second motor 6: start the second motor 6, close the first motor 2, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the second motor 6 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the second motor 6; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Step 3,

3.1 When the first turntable 15 rotates at a constant speed according to the set rotation speed, and the second turntable 13 does not rotate, although there is rotation of the moving coordinate system without relative motion, no Coriolis acceleration is generated. At this time, the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 simultaneously measure zero acceleration in the direction perpendicular to the second turntable 13;

3.2 When the first turntable 15 does not rotate and the second turntable 13 rotates at a constant speed according to the set rotational speed, there is only relative motion without the rotation of the moving coordinate system, and no Coriolis acceleration is generated. At this time, the first three-way acceleration sensor 7 and The second three-way acceleration sensor 10 simultaneously measures that the acceleration in the direction perpendicular to the second turntable 13 is zero;

3.3 When the first turntable 15 rotates at a constant speed according to the set speed, and the second turntable 13 rotates at a constant speed according to the set speed, the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 measure the vertical The acceleration in the direction of the second turntable 13 changes with a sinusoidal law; the magnitude and direction of the rotational speed of the first turntable 15 and the second turntable 13, and the magnitude and direction of the Coriolis acceleration are recorded;

Then change the size and direction of the rotation speed of the first turntable 15 or the second turntable 13, or adjust the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 along the third guide groove 27 and the fourth guide groove 28. The position on the second turntable 13 from the center of the circle O ₂ , at this time, the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 measure the acceleration in the direction perpendicular to the second turntable 13. The magnitude or direction changes; record the first three The position of the directional acceleration sensor 7 and the second three-directional acceleration sensor 10 on the second turntable 13 from the center of the circle _O2 changes, and the magnitude and direction of the rotational speed of the first turntable 15 and the second turntable 13 and the magnitude and direction of the Coriolis acceleration are recorded. ;

3.4 Restore the experimental device of the present utility model to the initial state of step 1; then adjust the installation position of the first support frame 5 on the first guide groove 21 and the installation position of the second support frame 17 on the second guide groove 26, to adjust the position of the second turntable 13 on the first turntable 15, and then make the first turntable 15 rotate at a constant speed according to the set rotation speed, while the second turntable 13 rotates at a constant speed according to the set rotation speed. The acceleration sensor 7 and the second three-way acceleration sensor 10 measure that the acceleration variation law in the direction perpendicular to the second turntable 13 changes; record the position change of the second turntable 13 on the first turntable 15, and record the first turntable 15 and The magnitude and direction of the rotational speed of the second turntable 13, and the magnitude and direction of the Coriolis acceleration;

3.5 Restore the experimental device of the present utility model to the initial state of step 1; then by lowering or raising the height of the first support frame 5, the inclination angle of the second rotating shaft 9 is changed, so that the first turntable 15 and the second turntable 13 are opposite to each other. The angle changes, and then the first turntable 15 rotates at a constant speed according to the set rotation speed, while the second turntable 13 rotates at a constant speed according to the set rotation speed. At this time, the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 It is measured that the acceleration variation law in the direction perpendicular to the second turntable 13 changes; the height change of the first support frame 5 is recorded, and the magnitude and direction of the rotational speed of the first turntable 15 and the second turntable 13, the magnitude of the Coriolis acceleration and the direction;

Step 4,

Arrange and calculate the recorded data and test the Coriolis acceleration formula.

In the process of Coriolis acceleration measurement performed by the above-mentioned device of the present invention: (Note: the following analysis and calculation are based on the first three-direction acceleration sensor 7 as an example, and the position point M of the first three-direction acceleration sensor 7 is used as the detection point. , the second three-direction acceleration sensor 10 is used as a symmetry and supplement, and the analysis and calculation of the second three-direction acceleration sensor 10 is exactly the same as that of the first three-direction acceleration sensor 7, and will not be repeated here.)

As shown in FIG. 5 , the center of the first turntable 15 is O ₁ , and the center of the second turntable 13 is O ₂ . The first turntable 15 rotates on a fixed axis with an angular velocity ω _e , and its motion is an implicated motion. A moving reference frame O ₂ xyz is set on the second turntable 13, the x-axis is parallel to the second turntable 13 along the horizontal direction, the y-axis is parallel to the second turntable 13 along the vertical direction, and the z-axis is perpendicular to the second turntable 13 along the horizontal direction . The second turntable 13 rotates around the z-axis with an angular velocity ω _r , and its motion is a relative motion.

A first triaxial acceleration sensor 7 and a second triaxial acceleration sensor 10 are arranged on the second turntable 13; as shown in FIG. 6, the first triaxial acceleration sensor 7 or the second triaxial acceleration sensor 10 can simultaneously measure x′ , y′, and z′ three directions of acceleration, wherein the z′ axis is parallel to the z axis, the y′ axis is along the circumferential direction of the second turntable 13 , and the x′ axis is along the radial direction of the second turntable 13 .

The Coriolis acceleration is caused by the interaction between the implicated motion and the relative motion when the dynamic system is rotating. The Coriolis acceleration vector The expression is

in, represents the involved angular velocity vector of the rotation of the coordinate system O ₂ xyz, It represents the relative motion velocity vector of the moving point relative to the moving coordinate system O ₂ xyz. Taking the position point M of the first three-way acceleration sensor 7 as an example, its relative motion speed is

v _r =rω _r (2)

Among them, r is the distance from the point M to the center O ₂ , as shown in FIG. 7 , the angle between the line connecting the point M and the center O ₂ and the x-axis is α; the direction of the Coriolis acceleration is perpendicular to the second turntable 13 ; according to the vector Cross-product relationship, the Coriolis acceleration a _c can be obtained:

a _c = 2ω _e v _rx = 2ω _e v _r sinθ (3)

Among them, θ is the angle between the angular velocity vector direction of the implicated motion and the velocity direction of the relative motion. It can be seen from Fig. 7

θ=α (4)

When the second turntable 13 rotates at a constant speed,

α=ω _r t (5)

t is the time when the first three-way acceleration sensor 7 starts to rotate from the horizontal position;

By formula (2)(3)(4)(5), we can get

a _c =2ω _e rω _r sinω _r t (6)

It can be seen from formula (6) that the Coriolis acceleration of the measured point M changes in a cosine law. When the measured point M turns to the horizontal angle α=0° or 180°, the Coriolis acceleration is zero; when the measured point M turns to the horizontal angle α=90° or -90°, the Coriolis acceleration is zero. The acceleration takes the maximum value or the minimum value (determined by the rotation direction of the second turntable 13 )

a _cmax =-a _cmin =2ω _e rω _r (7)

By testing the acceleration values of the first triaxial acceleration sensor 7 and the second triaxial acceleration sensor 10 in the z' direction, and comparing with the calculation result of the above formula, the Coriolis acceleration formula can be verified.

3. The method for testing the acceleration synthesis theorem based on the Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device of the present utility model is as follows:

step 1,

Preparation: Adjust the rack 1 so that the first turntable 15 is in a horizontal state, the second turntable 13 is a hard disk, install the second turntable 13 on the second shaft 9, adjust the first support frame 5 and the second support frame 17, so that the second turntable 13 is perpendicular to the first turntable 15, and the vertical projection of the center of the second turntable 13 coincides with the center of the first turntable 15; The first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 are installed on the groove 28, and the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 are symmetrically distributed around the center O ₂ of the second turntable 13; The second turntable 13 makes the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 lie in the same horizontal plane, then keep the first turntable 15 and the second turntable 13 stationary, turn on the first three-way acceleration sensor 7 and the second turntable 13 The two-three-way acceleration sensor 10 is zero-adjusted;

Step 2,

Check the rotation speed of the first motor 2: start the first motor 2, close the second motor 6, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the first turntable 15 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the first turntable 15; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Check the rotation speed of the second motor 6: start the second motor 6, close the first motor 2, input parameters to the controller 23, and calculate the theoretical value of the rotation speed of the second turntable 13 according to the input parameters; in order to ensure accuracy, Use a non-contact rotational speed sensor to measure the actual value of the rotational speed of the second turntable 13; record the actual rotational speed value corresponding to different input parameters of the controller 23 for use in experiments;

Step 3,

3.1 When the first turntable 15 rotates at a constant speed according to the set rotation speed, and the second turntable 13 does not rotate, although there is a rotation of the moving coordinate system without relative motion, the implicated acceleration is not zero at this time, and the relative acceleration and Coriolis acceleration zero; record the magnitude and direction of the rotational speed of the first turntable 15, and record the magnitude and direction of the accelerations of the first three-direction acceleration sensor 7 and the second three-direction acceleration sensor 10 in the three directions of x', y', and z';

3.2 When the first turntable 15 does not rotate and the second turntable 13 rotates at a constant speed according to the set rotation speed, there is only relative motion without the rotation of the moving coordinate system. At this time, the relative acceleration is not zero, and the implicated acceleration and Coriolis acceleration are zero. ; Record the magnitude and direction of the rotational speed of the second turntable 13, and record the magnitude and direction of the accelerations of the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 in the three directions of x', y', and z';

3.3 When the first turntable 15 rotates at a constant speed according to the set rotation speed, and the second turntable 13 rotates at a constant speed according to the set rotation speed, at this time, there are simultaneously involved acceleration, relative acceleration and Coriolis acceleration; record the first turntable. 15 and the magnitude and direction of the rotational speed of the second turntable 13, and record the magnitude and direction of the acceleration of the first three-direction acceleration sensor 7 and the second three-direction acceleration sensor 10 in the three directions of x', y', and z';

Then change the size and direction of the rotation speed of the first turntable 15 or the second turntable 13, or adjust the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 along the third guide groove 27 and the fourth guide groove 28. The position on the _second turntable 13 from the center O ; Record the size and direction of the rotation speed of the first turntable 15 and the second turntable 13, record the position change of the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 on the second turntable 13 from the center of the circle O ₂ , and record the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 The magnitude and direction of the acceleration of the three-direction acceleration sensor 7 and the second three-direction acceleration sensor 10 in the three directions of x', y', and z';

3.4 Restore the experimental device of the present utility model to the initial state of step 1; then adjust the installation position of the first support frame 5 on the first guide groove 21 and the installation position of the second support frame 17 on the second guide groove 26, to adjust the position of the second turntable 13 on the first turntable 15; then make the first turntable 15 rotate at a constant speed according to the set rotational speed, and at the same time the second turntable 13 rotates at a constant speed according to the set rotational speed. The acceleration sensor 7 and the second three-direction acceleration sensor 10 measure the acceleration change law in the three directions of x', y', z' to change; record the position change of the second turntable 13 on the first turntable 15, and record the first turntable 15. The magnitude and direction of the rotational speed of the first turntable 15 and the second turntable 13, and the magnitude and direction of the accelerations of the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 in the three directions of x', y', and z';

3.5 Restore the experimental device of the present utility model to the initial state of step 1; then by lowering or raising the height of the first support frame 5, the inclination angle of the second rotating shaft 9 is changed, so that the first turntable 15 and the second turntable 13 are opposite to each other. The angle changes; then make the first turntable 15 rotate at a uniform speed according to the set rotational speed, while the second turntable 13 rotates at a uniform speed according to the set rotational speed, at this time the first three-way acceleration sensor 7 and the second three-way acceleration sensor 10 The magnitude and direction of the acceleration in the three directions of x', y' and z' are measured to change; the height change of the first support frame 5 is recorded, and the magnitude and direction of the rotational speed of the first turntable 15 and the second turntable 13 are recorded, Record the acceleration magnitude and direction of the first triaxial acceleration sensor 7 and the second triaxial acceleration sensor 10 in the three directions of x', y', and z';

Step 4,

Arrange and calculate the recorded data to test the acceleration synthesis theorem.

In the process of the above-mentioned device of the present invention carrying out the acceleration synthesis theorem test: (Note: the following analysis and calculation are based on the first three-direction acceleration sensor 7 as an example, and the position point M of the first three-direction acceleration sensor 7 is used as the detection point. , the second three-direction acceleration sensor 10 is used as a symmetry and supplement, and the analysis and calculation of the second three-direction acceleration sensor 10 is exactly the same as that of the first three-direction acceleration sensor 7, and will not be repeated here.)

The vector according to the acceleration synthesis theorem of rotation with a fixed axis expression

in, For the implicated acceleration vector, is the relative acceleration vector, is the Coriolis acceleration vector. As an example, here the second turntable 13 is perpendicular to the first turntable 15, and the vertical projection of the center _O2 of the second turntable ₁₃ coincides with the center O1 of the first turntable 15; when the first turntable 15 rotates at a constant speed, the magnitude of the acceleration involved is

a _e =rcosαω _e ² (9)

implicated in acceleration The direction is parallel to the second turntable 13 in the horizontal direction, as shown in FIG. 8 .

When the second turntable 13 rotates at a constant speed, the magnitude of the relative acceleration is

a _r =rω _r ² (10)

relative acceleration The direction is directed to the center O ₂ along the radius of the second turntable 13 , as shown in FIG. 8 .

According to the coordinate conversion relationship, the magnitude of the acceleration measured by the first three-way acceleration sensor 7 in the y' direction is:

a _y′ = a _e sinα (11)

Simultaneously Equation (5), Equation (9) and Equation (11) can be obtained

That is, the acceleration measured by the first three-direction acceleration sensor 7 in the y' direction changes in a sinusoidal pattern, and the period is half of the period of the second turntable 13. When the measured point M turns to the horizontal angle α=-45° or 135° ° to take the maximum value as When the measured point turns to the angle α=45° or -135° with the horizontal direction, take the minimum value as

The magnitude of the acceleration measured by the first three-direction acceleration sensor 7 in the x' direction is:

a _x′ = -a _r -a _e cosα (13)

Simultaneously Equation (5), Equation (9), Equation (10) and Equation (13) can be obtained

That is, the acceleration measured by the first three-direction acceleration sensor 7 in the x′ direction changes in a cosine law, and the period is half of the period of the second turntable 13 . When the measured point turns to the horizontal angle α=0° or 180°, the minimum value is -rω _r ² -rω _e ² ; when the measured point M turns to the horizontal angle α=90° or At -90°, take the maximum value as -rω _r ² .

The acceleration measured by the first three-direction acceleration sensor 7 in the z' direction is the previous Coriolis acceleration. Through the measurement, if the data measured by the acceleration sensor in the three directions are within the error range, the acceleration synthesis theorem is tested.

Claims (6)

1. Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device, is characterized in that: this experimental device comprises implicated motion component, relative motion component and measurement sensor; The implicated movement assembly includes a frame (1), a first motor (2), a first rotating shaft (16) and a first turntable (15); the frame (1) is composed of an upper support plate (18), a bottom plate ( 19) and a side plate (20); the first motor (2) is arranged inside the frame (1), and a first gear (12) is arranged on the output shaft of the first motor (2); the first rotating shaft ( 16) The bottom is arranged on the bottom plate (19), and a first bearing is arranged between the first rotating shaft (16) and the bottom plate (19); 12) meshing with the second gear (11); the upper part of the first rotating shaft (16) passes through the upper support plate (18), and a second bearing is arranged between the first rotating shaft (16) and the upper support plate (18); the first The top of the rotating shaft (16) is provided with a first flange (4), and the top of the first rotating shaft (16) supports the first turntable (15) through the first flange (4); the first rotating shaft (16) is perpendicular to the first turntable (15), the top of the first rotating shaft (16) is located at the center of the first turntable (15); The relative motion assembly includes a first support frame (5), a second support frame (17), a second motor (6), a second rotation shaft (9) and a second turntable (13); the first support frame (17) 5) and the second support frame (17) are arranged on the first turntable (15), the second motor (6) is arranged on the first support frame (5); the second turntable (13) is arranged vertically, The second rotating shaft (9) passes through the center of the second rotating disk (13); the output shaft of the second motor (6) is connected to one end of the second rotating shaft (9) through the coupling (8), and the second rotating shaft ( The other end of 9) is supported on the second support frame (17), and a third bearing (22) is provided between the second shaft (9) and the second support frame (17); the second shaft (9) is also provided with a third bearing (22). There is a second flange (14), and the second turntable (13) is mounted on the second shaft (9) through the second flange (14); The measurement sensor includes a rotational speed sensor and an acceleration sensor; the rotational speed sensor is used to measure the rotational speed size and direction of the first turntable (15) and the second turntable (13); the acceleration sensor is used to measure a certain point on the second turntable (13) acceleration in three orthogonal directions. 2 . The Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device according to claim 1 , wherein the first turntable ( 15 ) is provided with a first guide groove ( 21 ) and a second guide groove ( 26 ). 3 . ), the bottom of the first support frame (5) is embedded in the first guide groove (21), the bottom of the second support frame (17) is embedded in the second guide groove (26); The installation position on the first guide groove (21) is adjustable, and the installation position of the second support bracket (17) on the second guide groove (26) is adjustable. 3. Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device according to claim 1, is characterized in that: when this experimental device performs Coriolis acceleration phenomenon demonstration, the second turntable (13) adopts a soft disk; the When the experimental device performs the test of the Coriolis acceleration formula and the test of the acceleration synthesis theorem, the second turntable (13) adopts a hard disk. 4. Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device according to claim 3, characterized in that: when the second turntable (13) is a hard disk, the disk surface of the second turntable (13) is provided with There are a third guide groove (27) and a fourth guide groove (28), the third guide groove (27) and the fourth guide groove (28) are symmetrically distributed with the center O ₂ of the second turntable (13), and the third guide groove (27) and the fourth guide groove (28) are symmetrically distributed with The line of symmetry L 1 of the groove (27), the line of symmetry L ₂ of the fourth guide groove (28) and the center O ₂ of the _second turntable (13) are located on the same straight line; the third guide groove (27) is provided with a A three-way acceleration sensor (7), the installation position of the first three-way acceleration sensor (7) on the third guide groove (27) is adjustable; the fourth guide groove (28) is provided with a second three-way acceleration sensor ( 10), the installation position of the second three-way acceleration sensor (10) on the fourth guide groove (28) is adjustable. 5 . The Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device according to claim 1 , wherein: the first rotating shaft ( 16 ) between the first turntable ( 15 ) and the frame ( 1 ) is provided with There is a collector ring (3), the outer ring of the collector ring (3) is fixed on the frame (1), and the inner ring of the collector ring (3) is sleeved and fixed on the first rotating shaft (16). 6. Coriolis acceleration measurement and acceleration synthesis theorem testing experimental device according to claim 1, wherein the first motor (2) is a stepping motor, a frequency conversion motor or a servo motor, and the second motor (2) 6) It is a stepping motor, a variable frequency motor or a servo motor; the first motor (2) is connected to the controller (23) through the first driver (24), and the second motor (6) is connected to the controller through the second driver (25) (23) Connection; the controller (23) controls the speed and direction of the first motor (2) through the first driver (24), and the controller (23) controls the second motor (6) through the second driver (25) speed and direction of rotation.