Micro-rotational inertia testing system and method based on adjustable double-suspension wire torsional pendulum method

Abstract

The application discloses a micro-rotational inertia testing system and method based on an adjustable double-suspension wire torsional pendulum method, which suspends and fixes an action piece on a support through two parallel suspension wires, and the rotational shaft center line of the action piece is perpendicular to the ground, the side of the action piece is in point contact with a disturbance-free release device, the disturbance-free release device is fixedly connected with a rotating table, the contact surface of the disturbance-free release device and the action piece forms a fixed angle with the suspension static plane of the action piece and the suspension wire under the rotation of the rotating table, after the disturbance-free release of the disturbance-free release device, the assembled piece obtained by assembling and fixing the action piece or a to-be-measured object and the bottom of the action piece is made to do periodic torsional pendulum along the rotational shaft center line under the constraint of the double suspension wires under the action of the friction force, the maximum rotational speed and the minimum rotational speed of the single action piece and the assembled piece in the periodic torsional pendulum process are measured and recorded, and the rotational inertia of the to-be-measured object in the periodic torsional pendulum process is calculated, so that the accurate measurement of the rotational inertia of the micro object is realized.

Description

Technical Field

[0001] This invention relates to the field of physical testing, and specifically to a system and method for testing minute rotational inertia based on the adjustable double-suspension wire torsion pendulum method. Background Technology

[0002] Moment of inertia, as a fundamental parameter for measuring the rotational inertia of rigid bodies, plays a crucial role in optical system design, precision drive control, and inertial navigation. Taking laser galvanometers as an example, the accuracy of their moment of inertia directly affects the matching of motor drives. Therefore, conducting high-precision measurements of the moment of inertia for small rotating components such as lenses is one of the key aspects of improving the overall performance of related equipment.

[0003] Among current methods for measuring moment of inertia, the double-wire method suspends the object under test with two parallel steel wires and indirectly obtains the moment of inertia information by utilizing the torsional pendulum motion around the vertical axis. While simple in structure and convenient to operate, it has the following drawbacks: its theoretical model is based on the premise that the pendulum angle is strictly less than 10°. In actual testing, this condition is easily affected by release disturbances and the nonlinearity of the wires, making it difficult to maintain and thus introducing significant errors, making it difficult to achieve the accuracy required for measuring small components such as lenses. Therefore, designing a disturbance-free release device to introduce into the measurement system to reduce the errors caused by release disturbances, and developing a small moment of inertia testing system and method based on the adjustable double-wire torsional pendulum method, has clear practical value and engineering application significance. Summary of the Invention

[0004] The purpose of this application is to address the technical problem of low actual measurement accuracy in the traditional double-suspension wire method due to the difficulty in controlling the torsion angle caused by disturbance release. It proposes a micro rotational inertia testing system and method based on the adjustable double-suspension wire torsion pendulum method. By using the friction between the object under test and the disturbance-free release device and the rotation control of the rotary table, and by introducing a tachometer, the precise measurement of the rotational inertia of micro objects can be achieved.

[0005] In a first aspect, the present invention provides a micro-rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method, comprising two suspension wires, an action element, a disturbance-free release device, a rotary table, and a support. The action element is suspended and fixed on the support by two parallel suspension wires, with the rotation axis centerline of the action element perpendicular to the ground. The side of the action element is in point contact with the disturbance-free release device, which is fixedly connected to the rotary table. Under the rotation of the rotary table, the contact surface between the disturbance-free release device and the action element forms a fixed angle with the suspension stationary plane of the action element and the suspension wires. After disturbance-free release by the disturbance-free release device, under the action of friction, the action element or the object under test, assembled and fixed to the bottom of the action element, undergoes periodic torsion pendulum along the rotation axis centerline under the constraint of the double suspension wires. The maximum and minimum rotational speeds of a single action element and assembly during the periodic torsion pendulum process are measured and recorded, and the rotational inertia of the object under test during the periodic torsion pendulum process is calculated.

[0006] Preferably, each suspension wire is fixed to the bracket by a corresponding clamping and positioning device, and the spacing and length of the two suspension wires are adjusted by the clamping and positioning device, so that the lengths of the two suspension wires are the same and remain unchanged during the periodic torsion of a single action and assembly.

[0007] Preferably, the clamping and positioning device includes a body, a fixing member, and a positioning member. The body is provided with a fixing hole and a through hole. The fixing hole accommodates the support to pass through. The fixing member fixes the body to the support and the fixing position of the suspension wire can be adjusted. The suspension wire passes through the through hole. The positioning member fixes the suspension wire to the body and the length of the suspension wire can be adjusted.

[0008] Preferably, the action is a cylinder, and the object to be measured is fixedly assembled below the round bottom surface of the cylinder.

[0009] Preferably, the undisturbed release device includes a base and two oppositely arranged contact members. The base has two parallel supporting arms and a base connecting the two supporting arms. The two contact members are fixedly installed on the two supporting arms respectively. The base is fixedly installed on a rotating platform. Each contact member has at least two contact points with the side of the cylinder, and at least four contact points constitute a contact surface. Simultaneously, the contact members are pulled out to disengage the contact members from the actuating member, so as to perform undisturbed release.

[0010] Preferably, the two arms are provided with coaxially arranged mounting holes, and the contact element passes through the mounting hole of the corresponding arm and extends to form a point contact with the side of the cylinder.

[0011] Preferably, the maximum and minimum speeds are obtained by measuring with a tachometer.

[0012] Preferably, the included angle is less than or equal to 10°.

[0013] Secondly, the present invention provides a method for testing minute rotational inertia based on the adjustable double-suspension wire torsion pendulum method, comprising the following steps:

[0014] The mass of the active component and the mass of the assembly obtained by assembling and fixing the active component and the object to be measured to the bottom of the active component are measured separately.

[0015] The actuator undergoes a disturbance-free release and measurement process, which is as follows:

[0016] Two suspension wires are fixed parallel to each other at opposite ends of the action and suspended on the bracket, so that the center line of the rotation axis of the action is perpendicular to the ground. Measure the distance and length between the two suspension wires.

[0017] The rotating table is rotated so that the contact surface between the disturbance-free release device and the action element forms a fixed angle with the stationary plane of the action element and the suspension wire. Under the action of the friction force between the disturbance-free release device and the action element, the action element makes a periodic torsional swing along the center line of the rotating shaft under the constraint of the double suspension wire.

[0018] The maximum and minimum rotational speeds of the actuator during the periodic torsional oscillation process are measured and recorded. The moment of inertia of the actuator during the periodic torsional oscillation process is calculated based on the distance and length between the two suspension wires and the maximum and minimum rotational speeds.

[0019] By fixing the lengths of the two suspension wires, the same undisturbed release and measurement process is performed on the assembly to calculate the moment of inertia of the assembly during the periodic torsional oscillation process.

[0020] The moment of inertia of the object under test during the periodic torsion process is obtained by subtracting the moment of inertia of the active component from the moment of inertia of the assembled component during the periodic torsion process.

[0021] Preferably, the included angle is less than or equal to 10°, and the formula for calculating the moment of inertia of the active component during the periodic torsional oscillation process is as follows:

[0022] ;

[0023] in, It represents the moment of inertia of the active component during a periodic torsional gyratory process. This indicates the distance between the two suspension wires of the active component during the periodic torsional oscillation process. Indicates the length of the two suspension wires. Indicates the mass of the active component. Represents gravitational acceleration. and These represent the maximum and minimum rotational speeds of the active component during the periodic oscillation process, respectively.

[0024] The formula for calculating the moment of inertia of an assembly during a periodic torsional yaw process is as follows:

[0025] ;

[0026] in, This represents the moment of inertia of the assembly during a periodic torsional process. This indicates the distance between the two suspension wires of the assembly during its periodic torsional oscillation. Indicates the mass of the assembled parts. and These represent the maximum and minimum rotational speeds of the assembly during the periodic torsional process, respectively.

[0027] The moment of inertia of the object under test during the periodic torsional oscillation is: .

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] (1) The micro rotational inertia testing system based on the adjustable double suspension wire torsion pendulum method mentioned in this invention greatly reduces the influence of external interference on the measurement results by adopting the adjustable double suspension wire torsion pendulum method combined with a disturbance-free release device, ensuring the accuracy and repeatability of periodic measurement. The system structure is stable and suitable for multiple repeated measurement scenarios. It is specifically designed for lightweight and small-sized test objects such as galvanometers and optical lenses, solving the problem that traditional three-wire pendulum method and torsion pendulum method are difficult to operate directly or have insufficient accuracy in the measurement of lightweight and small parts. It has clear targeting and practicality.

[0030] (2) In the process of formula derivation, the method for testing small rotational inertia based on the adjustable double suspension wire torsion pendulum method mentioned in this invention establishes the mathematical relationship between the actual measurement period, the spacing of the suspension wires and the rotational inertia by introducing the direct calculation relationship between the maximum rotational speed and the minimum rotational speed, thereby realizing the effective measurement of the rotational inertia of the object to be tested.

[0031] (3) The experimental device of the micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method mentioned in this invention has a simple structure, and each component is independently adjustable, which is convenient for maintenance and adaptation to small test objects such as motors and galvanometers of different specifications. The disturbance-free release device is reasonably designed, and the operation process is simple and controllable, which reduces the human influence of operators on the measurement results and has good engineering promotion value. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 This is a schematic diagram of the micro-rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method, which is an embodiment of this application.

[0034] Figure 2 This is a schematic diagram illustrating the use of a clamping and positioning device to adjust the length of the suspension wire in a micro rotational inertia testing system based on the adjustable double suspension wire torsion pendulum method, which is an embodiment of this application.

[0035] Figure 3 This is a schematic diagram illustrating the use of a clamping and positioning device to adjust the spacing of the suspension wires in a micro rotational inertia testing system based on the adjustable double suspension wire torsion pendulum method, as an embodiment of this application.

[0036] Figure 4 This is a schematic diagram of the point contact between the disturbance-free release device and the action element in a micro rotational inertia testing system based on the adjustable double suspension wire torsion pendulum method according to an embodiment of this application.

[0037] Figure 5 This is a schematic diagram of the disturbance-free release device of the micro rotational inertia testing system based on the adjustable double suspension wire torsion pendulum method, which is an embodiment of this application.

[0038] Reference numerals in the attached drawings: 1. Clamping and positioning device; 2. Suspension wire; 3. Actuating element; 4. Undisturbed release device; 5. Rotary table; 6. Tachometer; 7. Object to be measured; 8. Support; 9. Contact element; 10. Base; 11. Countersunk bolt; 12. Positioning element; 13. Fixing element. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0040] Figure 1This application illustrates an embodiment of a micro-rotational inertia testing system based on an adjustable double-suspension wire torsion pendulum method, comprising two suspension wires 2, an actuator 3, a disturbance-free release device 4, a rotary table 5, and a support 8. The rotary table 5 and the support 8 are respectively fixed on the platform. The actuator 3 is suspended and fixed to the support 8 by two parallel suspension wires 2, that is, one end of the two suspension wires 2 is suspended on the support 8, and the other end is fixedly connected to the actuator 3. The rotation axis center line of the actuator 3 is perpendicular to the ground, and the side of the actuator 3 is in point contact with the disturbance-free release device 4. The actuator 3 can be connected to the two suspension wires 2 individually, or the assembly obtained by assembling and fixing the object to be tested 7 to the bottom of the actuator 3 can be connected to the two suspension wires 2. In one example, the suspension wires 2 can be steel wire or stainless steel wire. The undisturbed release device 4 is fixedly connected to the rotary table 5. As the rotary table 5 rotates, the contact surface between the undisturbed release device 4 and the actuating element 3 forms a fixed angle with the stationary plane suspending the actuating element 3 and the suspension wire 2. In a preferred example, this angle is less than or equal to 10°. After undisturbed release via the undisturbed release device 4, the assembly obtained by fixing the actuating element 3 or the object to be measured 7 to the bottom of the actuating element 3 under frictional force undergoes periodic torsional oscillation along the center line of the rotation axis under the constraint of the double suspension wire 2. The rotary table 5 can be adjusted to rotate to a certain angle. When it is not rotated, the angle between the contact surface of the disturbance-free release device 4 and the action element 3 and the static plane of the suspension of the action element 3 and the suspension wire 2 is 0°. After the adjustment and rotation, the angle between the contact surface of the disturbance-free release device 4 and the action element 3 and the static plane of the suspension of the action element 3 and the suspension wire 2 is not 0°, but a fixed angle. At this time, the contact point of the disturbance-free release device 4 and the action element 3 will move and generate friction with the side of the action element 3. Under the action of friction, the action element 3 or the assembly will undergo periodic torsion about the center line of the rotation axis. At this time, the maximum speed and minimum speed of a single action element 3 and assembly during the periodic torsion process are measured and recorded, and the moment of inertia of the test object 7 during the periodic torsion process is calculated. The maximum speed and minimum speed are measured by the tachometer 6.

[0041] In a specific embodiment, each suspension wire 2 is fixed to the bracket 8 by a corresponding clamping and positioning device 1. The clamping and positioning device 1 is used to adjust the distance between the two suspension wires 2 and the length of the suspension wires 2. During the periodic torsional process of a single action member 3 and the assembly, the lengths of the two suspension wires 2 are the same and remain unchanged, while the distance between the two suspension wires 2 can be the same or different, and is not limited here. Specifically, refer to Figure 2 and Figure 3The clamping and positioning device 1 includes a body, a fixing member 13, and a positioning member 12. The body has a fixing hole and a through hole. The fixing hole accommodates the support 8 to pass through. The fixing member 13 fixes the body to the support 8 and allows adjustment of the fixed position of the suspension wire 2. The suspension wire 2 passes through the through hole, and the positioning member 12 fixes the suspension wire 2 to the body and allows adjustment of the length of the suspension wire 2. In one example, both the fixing member 13 and the positioning member 12 are screws. The body has a fixing hole that passes through the body, and the upper end of the body has a threaded hole. After the support 8 passes through the fixing hole, the fixing member 13 is installed on the threaded hole and tightened. The fixing member 13 abuts and fixes the support 8 to the fixing hole, thus locking the clamping and positioning device 1 to the support 8. Loosening the fixing member 13 allows the clamping and positioning device 1 to be moved left and right to adjust the distance d between the two suspension wires 2, without directly contacting the suspension wires 2. The main body also has a through hole running from top to bottom through it, through which the suspension wire 2 passes. In one example, the through hole can be in the form of a groove on the surface of the main body, while another threaded hole is provided on the side of the main body. The suspension wire 2 passes through the groove, and the positioning member 12 is fixed in the other threaded hole and tightened to fix the suspension wire 2 to the side wall of the groove to position the suspension wire 2. When it is necessary to adjust the length of the suspension wire 2, simply loosen the positioning member 12 slightly and adjust the position of the wire.

[0042] In a specific embodiment, refer to Figure 4 and Figure 5The actuator 3 is a cylinder, and the object to be measured 7 is fixedly assembled below the circular bottom surface of the cylinder. When the rotary table 5 drives the disturbance-free release device 4 to rotate to a fixed angle with the suspension stationary plane of the actuator 3 and the suspension wire 2, the side of the cylinder can make complete point contact with the disturbance-free release device 4, thereby generating friction. Under the action of friction, the actuator 3 or the assembly performs periodic torsional oscillation. In one example, the actuator 3 can be a motor with a cylindrical housing. The disturbance-free release device 4 includes a base 10 and two opposing contact elements 9. Each contact element 9 has two contact tips at its end, which form two point contacts with the cylindrical actuator 3 to stably trigger the periodic torsional oscillation of the actuator 3 or the assembly. The base 10 has two parallel supporting arms and a base connecting the two supporting arms. Two contact elements 9 are fixedly installed on the two supporting arms respectively, and the base is fixedly installed on the rotary table 5. Each contact element 9 has at least two contact points with the side of the cylinder, and at least four contact points constitute a contact surface. Simultaneously, the contact elements 9 are pulled out to disengage from the actuating element 3 for undisturbed release. A countersunk hole is provided at the bottom of the base, and the head of the countersunk bolt 11 is recessed into the countersunk hole, and fixedly connected to the rotary table 5 by the countersunk bolt 11. The two supporting arms have coaxially arranged mounting holes. The contact elements 9 pass through the mounting holes of the corresponding supporting arms and extend to form point contact with the side of the cylinder. The two contact elements 9 form a clearance fit with the mounting holes, and their front ends extend out of the supporting arms and abut against the two ends of the actuating element 3, forming a stable point contact support. If the rotary table 5 does not rotate, the angle between the contact surface and the stationary plane of the suspension of the action member 3 and the suspension wire 2 is 0°. If the rotary table 5 is rotated to less than or equal to 10°, the angle between the contact surface and the stationary plane of the suspension of the action member 3 and the suspension wire 2 will be the same as the rotation angle of the rotary table 5, which is also less than or equal to 10°.

[0043] The physical quantities to be measured in the embodiments of this application include: the mass m1 of the action 3, the mass m2 of the assembly obtained by assembling and fixing the object 7 and the action 3, the distance d1 between the two suspension wires 2 when measuring a single action 3, the distance d2 between the two suspension wires 2 when measuring the assembly, and the length l of the suspension wires 2. After adjusting the adjustable double suspension wire torsion pendulum micro-rotational inertia testing system to a testable state, the contact state between the disturbance-free release device 4 and the action 3 is adjusted to achieve point contact support. After release, the action 3 is allowed to perform periodic torsion pendulum under the constraint of the double suspension wires 2. The tachometer 6 is started to measure the maximum rotational speed n of a single action 3 within a certain time. max Minimum rotational speed n min The moment of inertia J was obtained through calculation. m After assembling and fixing the test object 7 with the action component 3 to obtain the assembly, repeat the above experimental steps and record the moment of inertia J. m+lThe moment of inertia of the object under test 7 during the periodic torsional oscillation process is J. m+l -J m .

[0044] The embodiments of this application also propose a method for testing minute rotational inertia based on the adjustable double-suspension wire torsion pendulum method. This method uses the aforementioned minute rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method and includes the following steps:

[0045] S1, measure the mass of the action 3 and the mass of the assembly obtained by assembling and fixing the action 3 and the object to be measured 7 to the bottom of the action 3 respectively;

[0046] S2, perform a disturbance-free release and measurement process on the actuator 3. The disturbance-free release and measurement process is as follows:

[0047] Two suspension wires 2 are fixed parallel to each other at opposite ends of the action member 3 and suspended on the bracket 8, so that the center line of the rotation axis of the action member 3 is perpendicular to the ground, and the distance and length between the two suspension wires 2 are measured.

[0048] Rotate the rotary table 5 so that the contact surface between the disturbance-free release device 4 and the action element 3 forms a fixed angle with the static plane of the suspension of the action element 3 and the suspension wire 2. Under the action of the friction force between the disturbance-free release device 4 and the action element 3, the action element 3 makes periodic torsional swing along the center line of the rotating shaft under the constraint of the double suspension wire 2.

[0049] The maximum and minimum rotational speeds of the actuator 3 during the periodic torsional oscillation process are measured and recorded. The moment of inertia of the actuator 3 during the periodic torsional oscillation process is calculated based on the distance and length between the two suspension wires 2 and the maximum and minimum rotational speeds.

[0050] S3, fix the length of the two suspension wires 2, and perform the same undisturbed release and measurement process on the assembly to calculate the moment of inertia of the assembly during the periodic torsional process;

[0051] S4, subtract the moment of inertia of the action 3 during the periodic torsion process from the moment of inertia of the assembly during the periodic torsion process to obtain the moment of inertia of the object under test 7 during the periodic torsion process.

[0052] In a specific embodiment, the included angle is less than or equal to 10°, and the formula for calculating the moment of inertia of the actuator 3 during the periodic torsional oscillation process is as follows:

[0053] ;

[0054] in, This represents the moment of inertia of component 3 during the periodic torsional oscillation process. This indicates the distance between the two suspension wires 2 of the active component 3 during the periodic torsional oscillation process. This represents the length of the two suspension wires 2. Indicates the mass of component 3. Represents gravitational acceleration. and These represent the maximum and minimum rotational speeds of the actuator 3 during the periodic torsional oscillation process, respectively.

[0055] The formula for calculating the moment of inertia of an assembly during a periodic torsional yaw process is as follows:

[0056] ;

[0057] in, This represents the moment of inertia of the assembly during a periodic torsional process. This indicates the distance between the two suspension wires 2 during the periodic torsional process of the assembly. Indicates the mass of the assembled parts. and These represent the maximum and minimum rotational speeds of the assembly during the periodic torsional process, respectively.

[0058] The moment of inertia of the object under test 7 during the periodic torsional pendulum process is: .

[0059] The embodiments of this application use the actuator 3 as a motor and the galvanometer lens as the object under test 7 for illustration. The specific process of the micro rotational inertia testing method based on the adjustable double suspension wire torsion pendulum method proposed in the embodiments of this application includes the following steps:

[0060] Step 1: Measure the mass of the motor. The total mass of the measuring motor and the lens motor is... .

[0061] Step 2: Fix the suspension wire 2 to both ends of the working member 3 to suspend it, and fix the other end to the bracket 8 with the clamping and positioning device 1. Measure the wire spacing. and wire length The steel wire suspension must ensure that the center line of the motor shaft is perpendicular to the ground and that the two steel wires are parallel.

[0062] Step 3: Perform a disturbance-free release and measurement process on a single motor, and measure the motor's maximum and minimum speeds, specifically including:

[0063] 1) Attach reflective strips to the motor;

[0064] 2) Press the two contact pieces 9 in the disturbance-free release device 4 against the two ends of the motor to make point contact between them;

[0065] 3) Rotate the rotary table 5 so that the contact surface of the disturbance-free release device 4 and the action element 3 forms a fixed angle of 10° with the suspension stationary plane of the action element 3 and the suspension wire 2. Since the disturbance-free release device 4 and the rotary table 5 are connected by countersunk screws, the motor rotates 10° around the center line of the rotating shaft under the action of friction.

[0066] 4) Gently pull out the contact 9 of the disturbance-free release device 4, and the motor is released, swinging freely around the center line of the rotating shaft;

[0067] 5) Turn on the tachometer 6 and ensure that the laser emitted by the tachometer 6 can illuminate the reflector strip during the motor's oscillation. At the same time, start the timer.

[0068] 6) After a certain period of time, the laser is turned off to achieve the maximum rotational speed. and minimum speed .

[0069] Step 4: Calculate the yaw period of a single motor The calculation process is as follows:

[0070] Derivation of the torsional period Functional relationship with rotational speed: During the torsional oscillation, the photoelectric tachometer 6 records a pulse signal every time the motor passes through the vertical equilibrium position. In one complete torsional oscillation cycle, the motor passes through the vertical position twice, so the laser illuminates the reflector strip twice in each cycle, meaning that every two pulses correspond to one torsional oscillation cycle.

[0071] Let the pulse frequency measured by the tachometer 6 be... (Unit: Hz), average rotational speed This represents the number of pulses recorded per minute. Defined by frequency, the number of pulses per second is:

[0072]

[0073] Since each torsional pendulum cycle contains 2 pulses, the torsional pendulum cycle is... The relationship with pulse frequency is as follows:

[0074]

[0075] That is, the torsional period With average speed The functional relationship is as follows:

[0076]

[0077] in, The unit is seconds (s). The unit is times / minute (rpm, which is the number of pulses recorded by the photoelectric tachometer per minute).

[0078] Step 5: Calculate the moment of inertia of the motor rotating about its axis. The calculation process is as follows:

[0079] 1) According to national standards, when the torsion angle of the shaft centerline is no greater than 10°, the moment of inertia is:

[0080]

[0081] in, Indicates the moment of inertia. Indicates the period of the oscillation. Indicates quality, Represents gravitational acceleration. This indicates the spacing of suspension wire 2. This indicates the length of suspension wire 2.

[0082] 2) According to the cycle The relationship between the speed and the mass of the motor , oscillation period Length of suspension wire 2 and the spacing of suspension wire 2 Substituting these values ​​into the formula for calculating the moment of inertia, we obtain the moment of inertia of the motor as follows:

[0083]

[0084] Step 6: The suspension wire 2 is fixed to both ends of the motor equipped with the galvanometer lens, suspending it. The other end is fixed to the bracket 8 with the clamping and positioning device 1, ensuring that the length of the suspension wire 2 is consistent with that in step 2. Similarly, measure the spacing of suspension wire 2. .

[0085] Step 7: Measure the maximum speed of the motor after it is equipped with the galvanometer lens. and minimum speed Specifically, this includes:

[0086] 1) Place the two contact pieces 9 in the disturbance-free release device 4 against the two ends of the motor equipped with the galvanometer lens, so that the two make point contact.

[0087] 2) Rotate the rotary table 5 so that the contact surface of the disturbance-free release device 4 and the action element 3 forms a fixed angle of 10° with the suspension stationary plane of the action element 3 and the suspension wire 2. Since the disturbance-free release device 4 and the precision rotary table 5 are connected by countersunk screws, the motor equipped with the galvanometer lens rotates 10° around the rotating shaft under the action of friction.

[0088] 3) Gently pull out the contact 9 of the disturbance-free release device 4, and the motor equipped with the galvanometer lens is released and swings freely around the axis.

[0089] 4) Turn on the tachometer 6 and ensure that the laser emitted by the tachometer 6 can illuminate the galvanometer lens during the motor's oscillation. At the same time, start the timing.

[0090] 5) After a certain period of time, the laser is turned off to achieve the maximum rotational speed. and minimum speed .

[0091] Step 8: Calculate the oscillation period of the motor equipped with the galvanometer lens using the same method as in Step 4. ;

[0092] Step 9: Calculate the moment of inertia of the motor equipped with the galvanometer lens rotating about its axis. The calculation process is as follows:

[0093] The mass of the motor equipped with galvanometer lenses , oscillation period Length of suspension wire 2 and the spacing of suspension wire 2 Substituting into the formula for calculating the moment of inertia, the moment of inertia of the motor equipped with the galvanometer lens is obtained as follows:

[0094]

[0095] Step 10: Calculate the moment of inertia of the object 7 rotating about its axis. : .

[0096] In one specific example, the mass of the motor is 0.00457 kg, the mass of the motor equipped with the galvanometer lens is 0.005309 kg, and the theoretical value of the moment of inertia of the galvanometer lens is 1.26279 × 10⁻⁶. -8 The experimentally measured spacing of the suspension wires 2 was d = 0.00796 m; the gravitational acceleration was taken as 9.80 m / s². 2 In the experiment, the length l of the suspension wire 2 was dynamically adjusted, the included angle was set to 10°, and the time t was set to 5s.

[0097] In this embodiment, the torsional oscillation period of the motor was measured at a series of different lengths of the suspension wire 2, depending on whether the motor was equipped with a galvanometer lens. The specific results are shown in Table 1. As the length of the suspension wire 2 increases, the torsional oscillation period of both the motor and the motor equipped with the galvanometer lens shows an increasing trend.

[0098] Table 1. Measured periods of the motor and the motor equipped with galvanometer lenses at different lengths of suspension wire 2.

[0099]

[0100] Table 2 presents the calculated results and percentage errors of the moment of inertia of the galvanometer lens under different lengths of the suspension wire 2. As the length of the suspension wire 2 increases, achieving parallelism of the suspension wire 2 in the adjustable double-suspension wire torsion pendulum method becomes more difficult, and the torsion angle becomes more challenging to control, leading to deviations of the measured moment of inertia from the theoretical value and an increase in measurement error. Experiments show that controlling the length of the suspension wire 2 within the range of 0.15~0.25m and precisely adjusting the spacing of the suspension wires 2 to ensure parallelism can keep the measurement error within 15%, meeting the high-precision testing requirements for minute moments of inertia. Compared with traditional methods, the percentage error of the moment of inertia of the galvanometer lens is significantly improved within the test range of the suspension wire 2 length.

[0101] Table 2 Measurement results and percentage error of the moment of inertia of the galvanometer lens

[0102]

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A micro-rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method, characterized in that, The device includes two suspension wires, an actuator, a disturbance-free release device, a rotary table, and a support. The actuator is suspended and fixed to the support by the two parallel suspension wires, with the center line of the actuator's rotation axis perpendicular to the ground. The side of the actuator is in point contact with the disturbance-free release device, which is fixedly connected to the rotary table. As the rotary table rotates, the contact surface between the disturbance-free release device and the actuator forms a fixed angle with the stationary plane of the actuator and the suspension wires. After disturbance-free release by the disturbance-free release device, the actuator or the assembly obtained by assembling and fixing the bottom of the actuator to the actuator under frictional force undergoes periodic torsional oscillation along the center line of the rotation axis under the constraint of the two suspension wires. The maximum and minimum rotational speeds of a single actuator and assembly during the periodic torsional oscillation process are measured and recorded, and the moment of inertia of the object under test during the periodic torsional oscillation process is calculated.

2. The micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 1, characterized in that, Each suspension wire is fixed to the bracket by a corresponding clamping and positioning device, and the spacing and length of the two suspension wires are adjusted by the clamping and positioning device. During the periodic torsion of a single action and assembly, the lengths of the two suspension wires are the same and remain unchanged.

3. The micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 2, characterized in that, The clamping and positioning device includes a body, a fixing member, and a positioning member. The body is provided with a fixing hole and a through hole. The fixing hole accommodates the support to pass through. The fixing member fixes the body to the support and allows adjustment of the fixing position of the suspension wire. The suspension wire passes through the through hole. The positioning member fixes the suspension wire to the body and allows adjustment of the length of the suspension wire.

4. The micro-rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 1, characterized in that, The actuator is a cylinder, and the object to be tested is fixedly assembled below the circular bottom surface of the cylinder.

5. The micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 4, characterized in that, The undisturbed release device includes a base and two opposing contact members. The base has two parallel support arms and a base connecting the two support arms. The two contact members are fixedly installed on the two support arms respectively. The base is fixedly installed on the rotating platform. Each contact member has at least two contact points with the side of the cylinder, and at least four contact points constitute the contact surface. Simultaneously, the contact members are pulled out to disengage them from the actuating element for undisturbed release.

6. The micro-rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 5, characterized in that, The two support arms are provided with coaxially arranged mounting holes, and the contact element passes through the mounting hole of the corresponding support arm and extends to form a point contact with the side of the cylinder.

7. The micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 1, characterized in that, The maximum and minimum speeds are obtained by measuring with a tachometer.

8. The micro rotational inertia testing system based on the adjustable double-suspension wire torsion pendulum method according to claim 1, characterized in that, The included angle is less than or equal to 10°.

9. A method for testing minute rotational inertia based on the adjustable double-suspension wire torsion pendulum method, characterized in that, Includes the following steps: The mass of the active component and the mass of the assembly obtained by assembling and fixing the active component and the object to be measured to the bottom of the active component are measured separately. A disturbance-free release and measurement process is performed on the actuator, which is as follows: Two suspension wires are fixed parallel to each other at opposite ends of the functional member and suspended from the bracket, so that the center line of the rotation axis of the functional member is perpendicular to the ground, and the distance and length between the two suspension wires are measured. Rotate the rotary table so that the contact surface between the disturbance-free release device and the actuating element forms a fixed angle with the static plane of the suspension of the actuating element and the suspension wire. Under the action of the friction force between the disturbance-free release device and the actuating element, the actuating element makes a periodic torsional oscillation along the center line of the rotating shaft under the constraint of the double suspension wire. The maximum and minimum rotational speeds of the active component during the periodic torsional oscillation process are measured and recorded, and the moment of inertia of the active component during the periodic torsional oscillation process is calculated based on the distance and length between the two suspension wires and the maximum and minimum rotational speeds. With the lengths of the two suspension wires fixed, the assembly is subjected to a undisturbed release and measurement process to calculate the moment of inertia of the assembly during the periodic torsional oscillation process. The moment of inertia of the object under test during the periodic torsion process is obtained by subtracting the moment of inertia of the active component from the moment of inertia of the assembly during the periodic torsion process.

10. The method for testing minute rotational inertia based on the adjustable double-suspension wire torsion pendulum method according to claim 9, characterized in that, The included angle is less than or equal to 10°, and the formula for calculating the moment of inertia of the active component during the periodic torsional oscillation process is as follows: ； in, It represents the moment of inertia of the active component during a periodic torsional gyratory process. This indicates the distance between the two suspension wires of the active component during the periodic torsional oscillation process. Indicates the length of the two suspension wires. Indicates the mass of the active component. Represents gravitational acceleration. and These represent the maximum and minimum rotational speeds of the active component during the periodic oscillation process, respectively. The formula for calculating the moment of inertia of the assembly during the periodic torsional process is as follows: ； in, This represents the moment of inertia of the assembly during a periodic torsional process. This indicates the distance between the two suspension wires of the assembly during its periodic torsional oscillation. Indicates the mass of the assembled parts. and These represent the maximum and minimum rotational speeds of the assembly during the periodic torsional process, respectively. The moment of inertia of the object under test during the periodic torsional oscillation process is: .

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