Experimental device for measuring object coupling pendulum by using unbalanced bridge and resistance strain gauge method

Abstract

The invention discloses an experimental device for measuring an object coupling pendulum by using an unbalanced bridge and a resistance strain gauge method, the experimental device comprises a cross rod and pendulum rods hinged to two ends of the cross rod, the lower ends of the two groups of the pendulum rods are also connected with pendulum bobs, and a coupling spring assembly is also adjustably connected between the two groups of the pendulum rods; an angular displacement sensor signal output device is further connected to the middle of the cross rod, and angular displacement measurement sensing assemblies are connected between the two sides of the angular displacement sensor signal output device and the two swing rods respectively. The angular displacement measurement sensing assembly comprises a tension sensing unit and a signal amplification conditioning module, and an angular displacement sensor signal output device is connected to an oscilloscope. Compared with the prior art, the experimental device for measuring the object coupling pendulums through the unbalanced bridge and the resistance strain gauge method has the advantages that the experimental device is based on the strain gauge sensor, the evolution curve of the vibration angular displacement and the time of the two coupling pendulums can be measured in real time, and the coupling process can be better studied.

Description

Technical Field

[0001] This invention relates to the field of experimental research in physics and mechanics, specifically to an experimental apparatus for measuring coupled pendulums of objects using an unbalanced bridge and resistance strain gauge method. Background Technology

[0002] In physical mechanics research experiments, the main focus is on the experimental phenomena and operational laws of coupled systems. Coupled systems are found in many fields such as mechanics, electricity, and optics, and problems in these different fields can be analyzed and studied using coupled mode theory.

[0003] Most current experimental devices are complex in structure, making it difficult for trainees to understand how to operate them and to learn about the motion and energy exchange laws of such systems. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the above-mentioned technical defects and provide an experimental device based on strain gauge sensors that can measure the evolution curves of the vibration angular displacement and time of two coupled pendulums in real time, and can better study the coupling process of the unbalanced bridge and the resistance strain gauge method for measuring the coupled pendulum of an object.

[0005] To solve the above-mentioned technical problems, the technical solution provided by the present invention is: an experimental device for measuring the coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method, comprising a crossbar and pendulum rods hinged at both ends of the crossbar, with a pendulum bob connected to the lower end of the two sets of pendulum rods, and a coupling spring assembly adjustablely connected between the two sets of pendulum rods;

[0006] An angular displacement sensor signal output device is also connected to the middle of the crossbar, and angular displacement measurement sensing components are connected to both sides of the angular displacement sensor signal output device and the two sets of swing arms respectively.

[0007] The angular displacement measurement sensing component includes a tension sensing unit and a signal amplification and conditioning module, and the angular displacement sensor signal output unit is connected to an oscilloscope.

[0008] Preferably, it also includes a leveling base connected to the crossbar.

[0009] Preferably, the tension sensing unit forms a symmetrical DC bridge with resistors R1-R4, wherein:

[0010] Resistor R1 is a resistance strain gauge, resistors R2-R4 are fixed resistors, and resistors R1-R4 form the four arms of the bridge.

[0011] The resistors R1 and R2 are connected in series to form one arm of the bridge, and the resistors R3 and R4 are connected in series to form the other arm of the bridge. The output of the bridge is connected between the connection point of resistors R1 and R2 and the connection point of resistors R3 and R4.

[0012] Preferably, the initial resistance value of resistor R1 is equal to the resistance value of resistor R2, which is R, and the resistance value of resistor R3 is equal to the resistance value of resistor R4, which is R'.

[0013] R≠R'.

[0014] Preferably, the tension sensing unit further includes a spring body connected to a resistance strain gauge, and the free end of the spring body is connected to a pendulum rod via a kit.

[0015] Preferably, the coupling spring assembly includes a position adjustment block connected to the rocker arm and a spring plate connecting the two sets of position adjustment blocks.

[0016] Preferably, the horizontal adjustment base includes a device base, columns connected to the device base, and multiple sets of partitions connected between the columns;

[0017] The device base is provided with adjustable feet between itself and the ground, the crossbar is connected to the bottom partition, and the angular displacement sensor signal output device is connected to the next partition.

[0018] The advantages of this invention compared to the prior art are as follows: Based on the content of this invention, the working mechanism and characteristics of a conveniently coupled system, such as an oscilloscope, are explained through an initial balanced and unbalanced output symmetrical DC bridge (horizontal bridge) operating in an unbalanced state.

[0019] The two pendulums are coupled together by a spring plate. When the two pendulums move in the vertical plane, they form a double-oscillator coupled pendulum mechanical model. The coupling degree of the system can be changed by changing the position of the coupling spring plate on the pendulum rod, making it highly adaptable to different application needs. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the three-dimensional structure of an experimental setup for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method.

[0021] Figure 2 This is a schematic diagram of the front view of an experimental setup for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method.

[0022] Figure 3 This is a side view of the experimental setup for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method.

[0023] Figure 4 This is a partial structural schematic diagram of the enlarged view of this device.

[0024] Figure 5 This is a schematic diagram of in-phase motion.

[0025] Figure 6This is a schematic diagram of the reverse phase motion.

[0026] Figure 7 This is a schematic diagram of normal vibration.

[0027] Figure 8 This is a schematic diagram showing the usage status when connecting an oscilloscope.

[0028] Figure 9 This is a schematic diagram illustrating the working principle.

[0029] Figure 10 This is a schematic diagram of a coupled pendulum model.

[0030] Figure 11 This is a diagram illustrating the cycle.

[0031] As shown in the figure: 1. Horizontal bar, 2. Pendulum bar, 3. Pendulum, 4. Angular displacement sensor signal output device, 5. Tension sensing unit, 6. Spring body, 7. Kit, 8. Position adjustment block, 9. Spring plate, 10. Device base, 11. Column, 12. Partition, 13. Adjustable foot. Detailed Implementation

[0032] The present invention will now be described in further detail with reference to the accompanying drawings.

[0033] Combined with appendix Figure 1-11 As shown:

[0034] An experimental apparatus for measuring the coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method includes a crossbar 1 and pendulum rods 2 hinged at both ends of the crossbar 1. A pendulum bob 3 is connected to the lower end of each set of pendulum rods 2, and a coupling spring assembly is adjustablely connected between the two sets of pendulum rods 2. An angular displacement sensor signal output device 4 is also connected to the middle of the crossbar 1. Angular displacement measurement sensing components are connected to both sides of the angular displacement sensor signal output device 4 and respectively between the two sets of pendulum rods 2. The angular displacement measurement sensing components include a tension sensing unit 5 and a signal amplification and conditioning module. The angular displacement sensor signal output device 4 is connected to an oscilloscope.

[0035] The tension sensing unit 5 contains a symmetrical DC bridge with resistors R1-R4, wherein:

[0036] Resistor R1 is a resistance strain gauge, resistors R2-R4 are fixed resistors, and resistors R1-R4 form the four arms of the bridge.

[0037] The resistors R1 and R2 are connected in series to form one arm of the bridge, and the resistors R3 and R4 are connected in series to form the other arm of the bridge. The output of the bridge is connected between the connection point of resistors R1 and R2 and the connection point of resistors R3 and R4.

[0038] The initial resistance of resistor R1 is equal to that of resistor R2, which is R; the resistance of resistor R3 is equal to that of resistor R4, which is R'.

[0039] When R≠R', and the resistance increment ΔR < R of arm R1, the output voltage ΔU of the bridge is: ΔU = U0xΔR / 4R;

[0040] In operation, the tension sensing unit 5 also includes a spring body 6 connected to the resistance strain gauge. The free end of the spring body 6 is connected to the swing rod 2 via a kit 7. The coupling spring assembly includes a position adjustment block 8 connected to the swing rod 2 and a spring plate 9 connected between the two sets of position adjustment blocks 8.

[0041] To ensure the equipment can be adapted for use,

[0042] It also includes a leveling base connected to the crossbar 1. The leveling base includes a device base 10, a column 11 connected to the device base 10, and multiple sets of partitions 12 connected between the columns 11.

[0043] The device base 10 is provided with adjustable feet 13 between itself and the ground. The crossbar 1 is connected to the bottom partition 12, and the angular displacement sensor signal output device 4 is connected to the next partition 12.

[0044] For the adjustment of kit 7 and position adjustment block 8, they are connected to the rocker arm 2 and secured with bolts tightened into the slots on their outer walls. Figure 4 As shown.

[0045] When using it, you can first teach the user the experimental principle of measuring the swing angle, that is, by using an unbalanced bridge and a resistance strain gauge to measure the voltage output of the unbalanced bridge, a voltage signal proportional to the swing angle can be obtained.

[0046] To understand the conditions for the formation of a "beat," an object participates in two movements with a very small difference in frequency, and their vibrations form a beat phenomenon, as well as the magnitude of the beat frequency (the difference between the two frequencies).

[0047] The equation of the pendulum is:

[0048]

[0049] The first factor in the formula changes slowly over time relative to the latter; it can be considered as a slow change in amplitude. Since only the absolute value of this factor represents the change in amplitude, the angular frequency of the amplitude change is twice the angular frequency of this factor, i.e., the beat frequency is...

[0050] ω 拍 =ω1-ω0

[0051] Master the method of measuring the period of a pendulum using a memory oscilloscope and how to adjust the oscilloscope, taking a conventional oscilloscope as an example:

[0052] X-axis timeline, scan parameters set to 10s / division;

[0053] Y-channel 1 and Y-channel 2 are set to: direct coupling mode, sensitivity 100mV / division;

[0054] Trigger settings: Trigger source CH1, DC coupled.

[0055] In use, each pendulum in this application experiences two torques: one from gravity, and the pendulum angle φ is often very small, so the gravitational torque can be written as...

[0056] M=mgLsinφ≈Dφ,

[0057] In the formula, D = mgL, where L is the pendulum length; the other torque comes from the spring plate, M′ = kΔxl, where k is the stiffness coefficient of the spring plate; l is the distance from the pendulum axis to the fixed point of the spring plate; Δx is the change in length of the spring plate relative to its original length, because Δx = lφ, therefore...

[0058] M′=kl 2 φ=D′φ

[0059] Where D′=kl 2 If pendulum P1 remains stationary at its equilibrium position, and pendulum P2 is deviated to the right by an angle φ2 from its equilibrium position, the total torque acting on pendulum P2 is (with pendulum P2 being to the right of its equilibrium position as positive).

[0060] like Figure 10 As shown:

[0061] When pendulum P2 deviates from φ2, if pendulum P1 deviates to the left by an angle of φ1, the total torque acting on pendulum P2 is...

[0062]

[0063] In the formula, J is the moment of inertia of pendulum P2. Similarly, the total torque acting on pendulum P1 is:

[0064]

[0065] Equations (2-8-1) and (2-8-2) are the system of differential equations for the coupled pendulum, which can be rewritten as follows:

[0066]

[0067] In the formula: Solving the system of differential equations (3) and (4) yields the following results:

[0068]

[0069] In the formula: ω1 is related to coupling, a1, a2, b1, b2 are parameters related to the initial states of the two pendulums. Taking the derivatives of equations (2-8-5) and (2-8-6), we can obtain the expressions for the angular velocities of the two pendulums.

[0070]

[0071] Discuss the motion under three initial states:

[0072] In-phase motion, such as Figure 5

[0073] The initial conditions are t = 0, φ1 = φ2 = φ a ; The two pendulums will deflect in the same direction by the same angle φ. a Simultaneously released, the two pendulums move in the same phase. Substituting the initial conditions into formulas (2-8-5) to (2-8-8), we obtain the equations of motion for the two pendulums.

[0074] φ1(t)=φ2(t)=φ a cosω0t (2-8-9)

[0075] At this time, the frequency ω of the in-phase vibration 同 =ω0, coupling has no effect, and the oscillation periods of the two pendulums are the same.

[0076] Reverse phase motion, such as Figure 6

[0077] The initial conditions are: t = 0, -φ1 = φ2 = φ a ; That is, the two pendulums are deflected from their equilibrium positions by φ1 = -φ. a ,φ2=φ a Then they are released simultaneously. Afterward, the spring plates will continuously extend and retract, significantly affecting the coupled vibration of the pendulums. Substituting the initial conditions into formulas (5) to (8), we can obtain the equations of motion for the two pendulums as follows:

[0078] φ1(t)=φ a cosω1t (2-8-10)

[0079] φ2(t)=-φ a cosω1t (2-8-11)

[0080] It can be seen that the frequencies of the two pendulums The coupling works, and the oscillation periods of the two pendulums are the same. Since ω1 > ω0, therefore we should have

[0081] Normal vibrations such as Figure 7

[0082] The initial conditions are: t = 0, φ1 = 0, φ2 = φ a ; With pendulum P1 fixed, pendulum P2 deviates from its equilibrium position by an angle φ. a That is, φ1=0, φ2=φ a Then, both pendulums are released simultaneously. Initially, only pendulum P2 oscillates. As time increases, the oscillation of pendulum P2 gradually decreases, while the oscillation of pendulum P1 gradually increases, until pendulum P2 stops oscillating, while pendulum P1 reaches its maximum oscillation, completing all energy transfer. Then, the reverse process begins. Substituting the initial conditions into formulas (2-8-5) to (2-8-8), we can obtain the equations of motion for the two pendulums as follows:

[0083]

[0084] At this point, a distinct "beating" phenomenon can be observed. φ1(t) and φ2(t) undergo normal vibrations with slowly changing amplitudes, also known as beat vibrations. The frequency of the beat vibration is ω. 拍 =ω1-ω0, the oscillation frequency of each pendulum is The period is The oscilloscope display of the pendulum vibrations shows that after the impact between pendulums P1 and P2, the amplitude of pendulum P1 gradually increases due to coupling, while the amplitude of pendulum P2 gradually decreases, indicating energy conservation between the two. After half a beat, the energy of pendulum P2 is completely converted into the energy of pendulum P1, and then the reverse occurs, with the energy of pendulum P1 being converted back into the energy of pendulum P2, and so on. In this way, both pendulums undergo "beat" vibrations, and the beat period can be measured from the vibration diagram.

[0085] Ratio The coupling degree of the pendulum can be written in the following form.

[0086]

[0087] because ω 同 =ω0, so the coupling degree of the pendulum can be expressed as

[0088]

[0089] When using the system, the motion characteristics of the coupled pendulum system under different initial conditions should be studied. To reduce errors when measuring each motion cycle of the system, 10 to 20 complete waveforms should be selected from the vibration waveform and the time intervals should be measured to obtain the required cycle value.

[0090] 1. Measure the natural frequency of a single pendulum and adjust it so that the vibration frequencies (or periods) of the two pendulums are the same, that is, the two systems have the same vibration mode (the experimental setup has been set, and the natural frequency can be obtained from the in-phase vibration frequency).

[0091] 2. Connect the pendulum at different positions using spring coupling, and measure the in-phase motion frequency ω of the coupled system. 同 and the frequency table of anti-phase motion ω 反 The normal frequencies of the coupled pendulum were measured; the linear relationship between the square of the coupling length and the square of its antiphase oscillation frequency was verified.

[0092] 3. Measurements showed that the square of the coupling length l was linearly related to the beat frequency at different coupling lengths. 2 ~ω 拍 .

[0093] As shown in the table below:

[0094]

[0095]

[0096] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0097] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0098] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the invention, such designs should fall within the protection scope of the present invention.

Claims

1. An experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method, characterized in that: It includes a crossbar (1) and a swing arm (2) hinged at both ends of the crossbar (1). The lower ends of the two sets of swing arms (2) are also connected to a pendulum (3). A coupling spring assembly can also be adjusted between the two sets of swing arms (2). An angular displacement sensor signal output device (4) is also connected to the middle of the crossbar (1), and angular displacement measurement sensing components are connected to both sides of the angular displacement sensor signal output device (4) and to the two sets of swing arms (2) respectively. The angular displacement measurement sensing component includes a tension sensing unit (5) and a signal amplification and conditioning module, and the angular displacement sensor signal output unit (4) is connected to an oscilloscope.

2. The experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 1, characterized in that: It also includes a leveling base connected to the crossbar (1).

3. The experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 1, characterized in that: The tension sensing unit (5) contains a symmetrical DC bridge with resistors R1-R4, wherein: Resistor R1 is a resistance strain gauge, resistors R2-R4 are fixed resistors, and resistors R1-R4 form the four arms of the bridge. The resistors R1 and R2 are connected in series to form one arm of the bridge, and the resistors R3 and R4 are connected in series to form the other arm of the bridge. The output of the bridge is connected between the connection point of resistors R1 and R2 and the connection point of resistors R3 and R4.

4. The experimental apparatus for measuring the coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 3, characterized in that: The initial resistance value of resistor R1 is equal to that of resistor R2, which is R; the resistance value of resistor R3 is equal to that of resistor R4, which is R'. R≠R'.

5. The experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 4, characterized in that: The tension sensing unit (5) also includes a spring body (6) connected to a resistance strain gauge, and the free end of the spring body (6) is connected to the pendulum (2) via a kit (7).

6. The experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 1 or 4, characterized in that: The coupling spring assembly includes a position adjustment block (8) connected to the rocker arm (2) and a spring plate (9) connected between the two sets of position adjustment blocks (8).

7. The experimental apparatus for measuring a coupled pendulum of an object using an unbalanced bridge and resistance strain gauge method according to claim 2, characterized in that: The horizontal adjustment base includes a device base (10), a column (11) connected to the device base (10), and multiple sets of partitions (12) connected between the columns (11); The device base (10) is provided with adjustable feet (13) between itself and the ground. The crossbar (1) is connected to the bottom partition (12), and the angular displacement sensor signal output device (4) is connected to the next partition (12).

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