A rotating platform friction signal excitation device
By designing a combination of bumper head, lead screw, drive mechanism and buffer mechanism on the rotating platform, fine control of bumper signal strength is achieved using stepper motor and controller, and the uncontrollable bumper signal output in the prior art is solved. The issue of strength ensures the safety of the experiment and the integrity of the equipment.
Patent Information
- Application Number
- CN202111209212.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-10-18
- Publication Date
- 2025-01-10
- Estimated Expiration
- 2041-10-18
AI Technical Summary
Existing rotary mechanical impact excitation devices cannot control the output strength of the impact signal, and may cause the excitation member to break during high rotation speed or long-term contact, affecting the experimental safety and damage to the measurement equipment.
A rotating platform collision signal excitation device including a bumper head, a screw, a drive mechanism and a buffer mechanism is designed. The movement of the screw is controlled by the drive mechanism to contact or separate the bumper head from the rotation mechanism, and the buffer mechanism is used to control the movement of the screw. Retraction is achieved after collision, and fine control of the intensity of the collision signal is achieved using stepper motors and controllers.
It realizes flexible control of the friction signal strength, avoids excessive collision damage to the rotating mechanism and lead screw, and ensures the safety of the experiment and the integrity of the equipment.
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Figure CN113848051B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical field of rotating machinery fault simulation devices, and in particular to a rotating platform friction signal excitation device. Background Art
[0002] Rubbing refers to collision and friction. In existing rotating machinery, as the requirements for production efficiency increase, rotating machinery is developing towards high performance, high efficiency and high parameters. The gap between moving and static parts is constantly decreasing, which makes the possibility of rubbing increasing. Rubbing causes severe vibration, wear and even damage to the machine. Among them, the rubbing between the rotor and the stator of the rotating machinery is a common fault in operation. In order to effectively monitor the occurrence of rubbing faults, it is necessary to analyze the rubbing signal. In order to conduct experiments, it is necessary to design an excitation device for the rubbing signal. According to the different parts of the rubbing, it can be divided into radial and axial rubbing. The radial rubbing of the rotating shaft is a typical fault in high-speed rotating machinery. Chinese patent CN201811145724.X discloses a pneumatic rubbing device that can measure the rubbing force, which includes a pneumatic system and a rubbing system. The rubbing of different materials can be simulated by replacing the rubbing head. Chinese patent CN201610625416.1 discloses a dual-rotor test bench rubbing test method using a flexibly detachable rubbing block for local rubbing.
[0003] For the existing friction excitation devices, the friction signal is stimulated by manually shortening the distance between the friction screw and the shaft to be contacted, and the output intensity of the friction signal cannot be controlled. During the experiment, if the rotating mechanism rotates too fast or the friction screw is in contact with the rotating mechanism for too long, the friction screw and other excitation parts may break, which may affect the safety of the test personnel and cause certain damage to the measuring machine. Summary of the invention
[0004] The embodiment of the present application provides a rotating platform rubbing signal excitation device, which solves the problem that the rubbing signal is excited by manually shortening the distance between the rubbing head and the output shaft of the rotating mechanism to be contacted in the prior art, but the output intensity of the rubbing signal cannot be controlled and the experimental safety is not guaranteed. The technical solution is as follows:
[0005] According to an embodiment, a rotating platform rubbing signal excitation device is provided, comprising a rubbing head, a lead screw, a driving mechanism and a buffer mechanism, wherein the free end of the rubbing head contacts the output shaft of the rotating mechanism placed on the rotating platform to generate a rubbing signal; the lead screw is connected to the rubbing head, and the axial directions of the lead screw and the rubbing head are consistent; the driving mechanism is connected to the lead screw, and the lead screw drives the rubbing head to move in the axial direction of the lead screw under the driving mechanism, so that the rubbing head contacts or separates from the output shaft of the rotating mechanism; the buffer mechanism is located between the rubbing head and the lead screw, and the buffer mechanism causes the rubbing head to retract after contacting the output shaft of the rotating mechanism.
[0006] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, it also includes: a conversion joint, one end of the conversion joint is connected to the lead screw, and the other end of the conversion joint is connected to the rubbing head, so that the rubbing head and the lead screw are coaxially connected; wherein the buffer mechanism is fixed in the conversion joint, and the end of the rubbing head away from the free end is in contact with the buffer mechanism, so that there is a distance between the rubbing head and the lead screw.
[0007] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, the buffer mechanism is a shock-absorbing spring, and the end of the rubbing head away from the free end abuts against the shock-absorbing spring, so that the rubbing head retracts along the axial direction from the rubbing head to the lead screw after contacting the output shaft of the rotating mechanism.
[0008] For example, in a rotating platform friction signal excitation device provided in one embodiment, the driving mechanism is a stepping motor, the lead screw is passed through the stepping motor, and a lead screw nut matching the lead screw is provided in the stepping motor to drive the lead screw to move.
[0009] For example, in a rotating platform friction signal excitation device provided in one embodiment, it also includes: a driver and a controller, wherein the driver is electrically connected to the stepper motor, and is used to drive and control the rotation of the stepper motor to achieve control of the speed and direction of the stepper motor; the controller is electrically connected to the driver, and is used to send a control signal to the driver.
[0010] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, after the rubbing head contacts the output shaft of the rotating mechanism placed on the rotating platform to generate a rubbing signal, the controller sends a control signal to the driver, and the driver drives the stepper motor to reverse, and the stepper motor drives the lead screw to move in a direction away from the rotating platform to separate the rubbing head from the output shaft of the rotating mechanism.
[0011] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, it also includes a sliding mechanism, which includes a base, a sliding part and a connecting head: the base includes a bottom plate and a side plate vertically connected to the bottom plate, the stepper motor is arranged on the bottom plate, the lead screw passes through the bottom plate, and a slide rail parallel to the lead screw is provided on the side plate; the sliding part is located on the slide rail and slidably cooperates with the slide rail; one end of the connecting head is connected to the sliding part so that the connecting head moves along the slide rail, and the other end is connected to one end of the lead screw away from the rubbing head, so that the lead screw moves in the axial direction of the lead screw under the drive of the stepper motor.
[0012] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, a threaded hole is provided at one end of the connecting head away from the sliding portion, and one end of the lead screw away from the rubbing head is fixedly connected to the threaded hole by a screw.
[0013] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, it also includes a supporting structure, which includes a supporting base and a supporting plate, wherein the supporting base is located on both sides of the rotating platform and is fixedly connected to the rotating platform; the supporting plate connects the two supporting bases, and the supporting plate is located directly above the rotating platform; wherein the base is fixed on the supporting plate, and the lead screw passes through the support plate so that the rubbing head connected to the lead screw contacts the output shaft of the rotating mechanism placed on the rotating platform to generate a rubbing signal.
[0014] For example, in a rotating platform rubbing signal excitation device provided in one embodiment, the stiffness of the support plate is smaller than the stiffness of the support base.
[0015] The beneficial effects brought about by a rotating platform rubbing signal excitation device provided in some embodiments of the present application are as follows: the present application realizes the output of rubbing signals of different intensities by changing the rotation speed of the driving mechanism, thereby solving the problem that the existing rubbing excitation device excites the rubbing signal by manually shortening the distance between the rubbing head, rubbing screw and other excitation objects and the output shaft of the rotating mechanism to be contacted, and cannot control the output intensity of the rubbing signal. During the experiment, the buffer mechanism is used to ensure that the rubbing head can retract within a short period of time after the collision occurs, thereby avoiding damage to the output shaft of the rotating mechanism caused by excessive collision and breaking of the lead screw, thereby ensuring safety during the experiment. BRIEF DESCRIPTION OF THE DRAWINGS
[0016] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0017] Figure 1 This is a front view of the rotating platform friction signal excitation device of the present application;
[0018] Figure 2 It is a side view of the rotating platform friction signal excitation device of the present application;
[0019] Figure 3 It is a top view of the rotating platform friction signal excitation device of the present application;
[0020] Figure 4 It is a front view of the friction signal excitation device of the present application;
[0021] Figure 5 is a side view of the rubbing signal excitation device of the present application;
[0022] Figure 6 is a stereoscopic diagram of the friction signal excitation device of the present application;
[0023] Figure 7 It is a schematic diagram of the internal structure of the conversion head of the present application;
[0024] Figure 8 It is a schematic diagram of the rotating platform friction signal excitation device of the present application.
[0025] Figure markings: 100-rotating platform, 110-rotating mechanism, 200-friction head, 300-screw, 400-driving mechanism, 410-stepping motor, 500-buffer mechanism, 600-conversion joint, 700-sliding mechanism, 710-base, 711-bottom plate, 712-side plate, 713-slide rail, 720-sliding part, 730-connecting head, 731-threaded hole, 800-support structure, 810-support base, 820-support plate. DETAILED DESCRIPTION
[0026] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.
[0027] Unless otherwise defined, the technical terms or scientific terms used in the present disclosure should be understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.
[0028] According to a rotating platform friction signal excitation device provided in an embodiment, Figure 1-6 As shown, it includes a rubbing head 200, a lead screw 300, a driving mechanism 400 and a buffer mechanism 500. The free end of the rubbing head 200 contacts the output shaft of the rotating mechanism 110 placed on the rotating platform 100 to generate a rubbing signal; the lead screw 300 is connected to the rubbing head 200, and the axial directions of the lead screw 300 and the rubbing head 200 are consistent; the driving mechanism 400 is connected to the lead screw 300, and the lead screw 300 drives the rubbing head 200 to move in the axial direction of the lead screw 300 under the driving of the driving mechanism 400, so that the rubbing head 200 contacts or separates from the output shaft of the rotating mechanism 110; the buffer mechanism 500 is located between the rubbing head 200 and the lead screw 300, and the rubbing head 200 retracts after contacting the output shaft of the rotating mechanism 110 through the buffer mechanism 500. According to the above embodiment, the present application drives the lead screw 300 to perform linear reciprocating motion along the axial direction of the lead screw 300 through the driving mechanism 400. When the rubbing head 200 at the end of the lead screw 300 collides with the surface of the rotating mechanism 110 at a certain speed, a rubbing signal will be generated on its surface. According to the installation position of the driving mechanism 400 relative to the rotating mechanism 110, the downward movement distance and speed of the driving mechanism 400 are reasonably designed. The present application can achieve the output of rubbing signals of different intensities by changing the rotation speed of the driving mechanism 400, reduce the damage of the rubbing head 200 to the rotating mechanism 100 in the rubbing experiment, and ensure that the rubbing head 200 can retract within a short period of time after the collision occurs through the buffer mechanism 500, so as to avoid excessive movement of the rubbing head 200 to damage the output shaft of the rotating mechanism 100 and the lead screw 300.
[0029] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 7As shown, it also includes: a conversion joint 600, one end of which is connected to the lead screw 300, and the other end of which is connected to the rubbing head 200, so that the rubbing head 200 and the lead screw 300 are coaxially connected; wherein the buffer mechanism 500 is fixed in the conversion joint 600, and one end of the rubbing head 200 away from the free end is in contact with the buffer mechanism 500, so that there is a distance between the rubbing head 200 and the lead screw 300. Among them, one end of the conversion joint 600 is threadedly connected to the lead screw 300. According to the above embodiment, the coaxial connection between the rubbing head 200 and the lead screw 300 is realized by the conversion joint 600, so that the lead screw 300 and the rubbing head 200 can realize synchronous axial movement. The buffer mechanism 500 is used to maintain a certain distance between the rubbing head 200 and the lead screw 300, that is, the rubbing head 200 and the lead screw 300 are not in contact with each other, thereby avoiding the impact force generated by the collision between the rubbing head 200 and the output shaft of the rotating mechanism 100 being directly transmitted to the lead screw 300, thereby causing the lead screw 300 to break. In this application, by setting a buffer mechanism 500 between the rubbing head 200 and the lead screw 300, it is ensured that the rubbing head 200 can retract within a short period of time after the collision occurs, thereby avoiding excessive movement of the rubbing head 200 to damage the output shaft of the rotating mechanism 100 and the lead screw 300.
[0030] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 7 As shown, the buffer mechanism 500 is a shock-absorbing spring, and the end of the rubbing head 200 away from the free end abuts against the shock-absorbing spring, so that the rubbing head 200 retracts along the axial direction from the rubbing head 200 to the lead screw 300 after contacting the output shaft of the rotating mechanism 110. According to the above embodiment, the upper part of the conversion joint 600 is connected to the lead screw 300 through a thread, and the lower part abuts against the rubbing head 200 through a shock-absorbing spring. When the lead screw 300 moves axially toward the rotating platform 100, the rubbing head 200 contacts the output shaft of the rotating mechanism 110 to generate a signal of rubbing and friction. The existence of the shock-absorbing spring enables the rubbing head 200 to rebound upward for a period after the collision, thereby avoiding the driving mechanism 400 from being stuck, and at the same time avoiding the damage to the output shaft of the rotating mechanism 110 caused by the collision being too intense, and also avoiding the breakage of the lead screw 300, thereby ensuring the safety during the experiment.
[0031] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 1-6As shown, the driving mechanism 400 is a stepper motor 410, the lead screw 300 is passed through the stepper motor 410, and a lead screw nut matched with the lead screw 300 is provided in the stepper motor 410 to drive the lead screw 300 to move. According to the above embodiment, the present application selects the stepper motor 410 as the driving mechanism 400, and utilizes the good data control characteristics of the stepper motor, so as to facilitate the use of a computer as the driving source of the stepper motor, and generate control pulses through a program to drive and control the stepper motor 410.
[0032] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 8 As shown, it also includes: a driver and a controller, the driver is electrically connected to the stepper motor 410, and is used to drive and control the rotation of the stepper motor 410 to achieve control of the speed and direction of the stepper motor 410; the controller is electrically connected to the driver, and is used to send a control signal to the driver.
[0033] Specifically, after the rubbing head 200 contacts the output shaft of the rotating mechanism 110 placed on the rotating platform 100 and generates a rubbing signal, the controller sends a control signal to the driver, and the driver drives the stepper motor 410 to reverse, and the stepper motor 410 drives the lead screw 300 to move in a direction away from the rotating platform 100 so that the rubbing head 200 is separated from the output shaft of the rotating mechanism 110. According to the above embodiment, the present application ensures that the stepper motor 410 can reverse quickly within a short period of time after the collision between the rubbing head 200 and the output shaft of the rotating mechanism 110 occurs through program control, so that the rubbing head 200 immediately rises after contacting the output shaft of the rotating mechanism 110, driving the lead screw 300 and the rubbing head 200 to leave the surface of the rotating structure 110, avoiding damage to the output shaft of the rotating mechanism 110 caused by excessive collision, and also avoiding the breakage of the lead screw 300, thereby ensuring safety during the experiment.
[0034] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 4-6As shown, it also includes a sliding mechanism 700, and the sliding mechanism 700 includes a base 710, a sliding part 720 and a connecting head 730: the base 710 includes a bottom plate 711 and a side plate 712 vertically connected to the bottom plate 711, the stepping motor 410 is arranged on the bottom plate 711, the lead screw 300 passes through the bottom plate 711, and a slide rail 713 parallel to the lead screw 300 is provided on the side plate 712; the sliding part 720 is located on the slide rail 713 and slidably cooperates with the slide rail 713; one end of the connecting head 730 is connected to the sliding part 720 so that the connecting head 730 moves along the slide rail 713, and the other end is connected to one end of the lead screw 300 away from the friction head 200, so that the lead screw 300 moves in the axial direction of the lead screw 300 under the drive of the stepping motor 410. Among them, the slide rail 713 is installed on the side plate 712 by bolt connection, one end of the connecting head 730 is installed on the sliding part 720 by screws, the slide rail 713 is parallel to the axial direction of the lead screw 300, according to the above embodiment, the lead screw 300 is connected to the sliding part 720 on the slide rail 713 through the connecting head 730, and the sliding part 720 can move up and down on the slide rail 713, so that the lead screw 300 can make a linear motion along the axial direction of the lead screw 300 under the drive of the stepper motor 410.
[0035] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 4-6 As shown, a threaded hole 731 is provided at one end of the connector 730 away from the sliding part 720, and one end of the lead screw 300 away from the rubbing head 200 is fixedly connected to the threaded hole 731 by a screw. Specifically, two threaded holes 731 are provided at one end of the connector 730 away from the sliding part 720, one of which is matched with the lead screw 300, and the other threaded hole 731 is screwed by a screw matched therewith to achieve a screwing effect, further ensuring that the lead screw 300 is fixed and does not rotate. According to the above embodiment, by providing a threaded hole 731 at one end of the connector 730 away from the sliding part 720, a screw is passed through the threaded hole 731 so that one end of the lead screw 300 is fixedly connected to one end of the connector 730, ensuring that the lead screw 300 does not rotate under the drive of the stepping motor 410 but moves linearly in the vertical direction, thereby driving the rubbing head 200 to rub against the output shaft of the rotating mechanism 110.
[0036] For example, in a rotating platform friction signal excitation device provided in one embodiment, Figure 1-3As shown, it also includes a support structure 800, which includes a support base 810 and a support plate 820. The support base 810 is located on both sides of the rotating platform 100 and is fixedly connected to the rotating platform 100; the support plate 820 connects the two support bases 810, and the support plate 820 is located directly above the rotating platform 100; wherein the base 710 is fixedly arranged on the support plate 820, and the lead screw 300 passes through the support plate 820 so that the rubbing head 200 connected to the lead screw 300 contacts the output shaft of the rotating mechanism 110 placed on the rotating platform 100 to generate a rubbing signal. wherein the base 710 is installed on the support plate 820 by bolt connection, the support base 810 is connected to the rotating platform 100 by T-block bolts, and the two support bases 810 on the left and right sides of the rotating platform 100 are connected to the horizontal support plate 2 by screws.
[0037] For example, in the rotating platform rubbing signal excitation device provided in one embodiment, the rigidity of the support plate 820 is less than the rigidity of the support base 810. According to the above embodiment, by selecting a material with a rigidity smaller than that of the support base 810 as the support plate 820, it is possible to reduce excessive damage to the rotating platform 100 caused by the rubbing process, and avoid motion jamming during the collision process.
[0038] The rotating platform rubbing signal exciting device of the present application realizes the output of rubbing signals of different intensities by changing the rotation speed of the stepper motor 410, and solves the problem that the output intensity of the rubbing signal cannot be controlled by the existing rubbing exciting device, which stimulates the rubbing signal by manually shortening the distance between the exciting objects such as the rubbing head and the rubbing screw and the output shaft of the rotating mechanism to be contacted. During the experiment, a double layer of insurance is formed by the buffer mechanism 500 and the controller to ensure that the rubbing head 200 can retract within a short period of time after the collision occurs, and the controller can control the stepper motor 410 to reverse, to ensure that the rubbing head 200 immediately rises after contacting the output shaft of the rotating mechanism 110, and drives the lead screw 300 and the rubbing head 200 to leave the surface of the rotating structure 110, to avoid damage to the output shaft of the rotating mechanism 110 caused by excessively intense collision, and to avoid breakage of the lead screw 300, thereby ensuring safety during the experiment.
[0039] Although the embodiments of the present application have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims.
Claims
1. A rotating platform friction signal excitation device, characterized in that: include: a rubbing head, wherein a free end of the rubbing head contacts an output shaft of a rotating mechanism placed on the rotating platform to generate a rubbing signal; A lead screw connected to the friction head, wherein the lead screw and the friction head have the same axial direction; A driving mechanism connected to the lead screw, wherein the lead screw drives the rubbing head to move in the axial direction of the lead screw under the driving mechanism, so that the rubbing head contacts or separates from the output shaft of the rotating mechanism; and A buffer mechanism is located between the friction head and the lead screw, and the friction head is caused to retract after contacting the output shaft of the rotating mechanism through the buffer mechanism; Also includes: A conversion joint, one end of which is connected to the lead screw, and the other end of which is connected to the rubbing head, so that the rubbing head and the lead screw are coaxially connected; Wherein, the buffer mechanism is fixed in the conversion joint, and one end of the friction head away from the free end abuts against the buffer mechanism, so that there is a distance between the friction head and the lead screw; The buffer mechanism is a shock absorbing spring, and one end of the friction head away from the free end abuts against the shock absorbing spring, so that the friction head retracts along the axial direction from the friction head to the lead screw after contacting the output shaft of the rotating mechanism; The driving mechanism is a stepping motor, the lead screw is passed through the stepping motor, and a lead screw nut matched with the lead screw is arranged inside the stepping motor to drive the lead screw to move.
2. The rotating platform friction signal excitation device according to claim 1, characterized in that: Also includes: A driver is electrically connected to the stepper motor and is used to drive and control the stepper motor to rotate. Controlling the speed and direction of the stepper motor; The controller is electrically connected to the driver and is used to send a control signal to the driver.
3. The rotating platform friction signal excitation device according to claim 2, characterized in that: After the rubbing head contacts the output shaft of the rotating mechanism placed on the rotating platform and generates a rubbing signal, the controller sends a control signal to the driver, and the driver drives the stepper motor to reverse, and the stepper motor drives the lead screw to move in a direction away from the rotating platform to separate the rubbing head from the output shaft of the rotating mechanism.
4. The rotating platform rubbing signal excitation device according to claim 1, characterized in that: Also included is a sliding mechanism, the sliding mechanism comprising: The base comprises a bottom plate and a side plate vertically connected to the bottom plate, the stepping motor is arranged on the bottom plate, the lead screw passes through the bottom plate, and a slide rail parallel to the lead screw is arranged on the side plate; A sliding portion, located on the slide rail and slidably matched with the slide rail; and A connecting head, one end of which is connected to the sliding part so that the connecting head moves along the slide rail, and the other end is connected to an end of the lead screw away from the friction head so that the lead screw moves in the axial direction of the lead screw under the drive of the stepping motor.
5. The rotating platform friction signal excitation device according to claim 4, characterized in that: A threaded hole is provided at one end of the connecting head away from the sliding part, and one end of the lead screw away from the rubbing head is fixedly connected to the threaded hole through a screw.
6. The rotating platform rubbing signal excitation device according to claim 4, characterized in that: Also included is a support structure, the support structure comprising: A supporting base, located on both sides of the rotating platform and fixedly connected to the rotating platform; and A support plate, connecting the two support bases, and the support plate is located directly above the rotating platform; Wherein, the base is fixed on the support plate, and the lead screw passes through the support plate so that the rubbing head connected to the lead screw contacts the output shaft of the rotating mechanism placed on the rotating platform to generate a rubbing signal.
7. The rotating platform rubbing signal excitation device according to claim 6, characterized in that: The rigidity of the support plate is smaller than the rigidity of the support base.
Citation Information
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