Method and device for testing dynamic installation parameters of interference bushing based on Hopkinson pressure bar

Through Hopkinson's pressing rod technology, the mechanical parameters during the dynamic installation process of composite bushings are collected and processed in real time, and the lack of mechanical response analysis of dynamic installation methods in the existing technology is solved, and the structure of composite bushings is realized The precise installation and data collection improve the accuracy and control of the detection results.

CN119124890APending Publication Date: 2024-12-13NORTHWESTERN POLYTECHNICAL UNIV +1
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Patent Information

Application Number
CN202411227871.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-03
Publication Date
2024-12-13

AI Technical Summary

Technical Problem

The existing dynamic installation method study lacks quantitative analysis of installation rate, and it is impossible to accurately record the various mechanical responses of composite bushings during installation.

Method used

Using the dynamic installation parameter test method and device of the interference bushing based on Hopkinson's press rod, kinetic energy is provided through the discharge drive module, and the incident rod and the transmission rod are used to collect and process reflected waves, transmitted waves and wave speeds to detect the displacement and speed of the core rod in real time. and resistance, combined with electromagnetic stress generator and acquisition and processing system, realize precise control and data acquisition of the dynamic installation process of composite material bushings.

Benefits of technology

It improves the accuracy of the installation process and the reliability of the detection results, provides quantitative analysis data on the impact of installation rate, guides the optimization of process parameters of the composite bushing structure, avoids inertial forces, and has high control and repeatability.

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Abstract

The invention relates to the technical field of composite material hole strengthening, in particular to an interference lining dynamic installation parameter testing method and device based on a Hopkinson pressure bar, and the device comprises a discharge driving module, an incident bar, a transmission bar, a lining and an acquisition processing system, the other end of the incident rod is coaxially connected with a core rod, one end of the transmission rod is coaxially provided with a mounting hole, the end, deviating from the incident rod, of the core rod is sequentially provided with a perforated plate and a slotted gasket in a penetrating manner, and the incident rod penetrates out of the slotted gasket and then is connected into the mounting hole of the transmission rod; the bushing is sleeved on the core rod in the hole of the perforated plate; the collecting and processing system is used for collecting the reflected wave of the incident rod, the transmitted wave of the transmission rod and the wave speed at each moment in the dynamic installation process of the bushing so as to obtain the displacement, the speed and the resistance of the core rod at each moment in the dynamic installation process of the bushing. According to the invention, the inertia force in the installation process is avoided, and the accuracy of the detection result is improved.
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Description

Technical Field

[0001] The invention relates to the technical field of composite material hole strengthening, and in particular to a method and a device for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar. Background Art

[0002] For the installation of composite interference bushings, existing methods use presses or pneumatic pullers. These methods can be defined as a static installation method from the perspective of installation speed, that is, the stress state of all force-bearing structures is kept balanced at all times during the installation process. For example, a tool and method for installing a bushing for a multi-ear hole part. This technology solves the problem that the installation operation of a bushing for a multi-ear hole part is inconvenient and it is difficult to ensure the installation coaxiality. There is also an installation device that reduces the deformation of the bushing during shrinkage assembly. This technology can improve the coaxiality of the bushing with the base during installation and reduce the shrinkage of the inner diameter of the bushing after shrinkage assembly, thereby effectively improving the assembly accuracy.

[0003] Research on existing interference fit installation methods has shown that, whether for metal or composite materials. Dynamic installation methods can complete the installation at a higher installation speed. While being able to install fasteners with large interference amounts, the installation resistance can be effectively reduced, thereby reducing installation damage. Based on this, the prior art provides a composite material structure bushing reinforcement method based on electromagnetic loading. This method uses electromagnetic loading to complete the bushing reinforcement of the composite material structure, and has achieved significant beneficial effects compared to traditional methods. At the same time, the invention can realize the calculation of reinforcement process parameters for composite material bushings of different structures and sizes, which is used to guide the reinforcement of dynamic cold-extruded composite material bushing structures. That is, the existing research on dynamic installation methods still lacks quantitative analysis of the installation rate, and cannot accurately record various mechanical responses during the installation process.

[0004] Therefore, it is necessary to provide a method and device for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar to solve the above problems. Summary of the invention

[0005] The present invention provides a method and device for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar, so as to solve the problem that the existing research on dynamic installation methods still lacks quantitative analysis of installation rate and cannot accurately record various mechanical responses during the installation process.

[0006] The present invention discloses a dynamic installation parameter testing device for interference bushing based on Hopkinson pressure bar, which adopts the following technical scheme, including: Discharge drive module; An incident rod, one end of which is connected to the output end of the discharge driving module, and the other end of which is coaxially connected to a core rod; The transmission rod has a mounting hole coaxially opened at one end thereof, wherein an opening plate and a seam washer are sequentially penetrated at the end of the core rod away from the incident rod, and the incident rod passes through the seam washer and is connected to the mounting hole of the transmission rod; A bushing is sleeved on the core rod in the hole of the perforated plate; And a collection and processing system is used to collect the reflected wave of the incident rod, the transmitted wave of the transmission rod and the wave velocity at each moment during the dynamic installation of the bushing, and obtain the displacement, speed and resistance of the core rod at each moment during the dynamic installation of the bushing based on the reflected wave, transmitted wave and wave velocity at each moment.

[0007] Preferably, the discharge driving module comprises: an electromagnetic stress generator, which forms a discharge loop by connecting a discharge thyristor, a resistor and a capacitor in series, wherein the electromagnetic stress generator is coaxially connected to the end of the incident rod.

[0008] Preferably, the acquisition and processing system includes: A Wheatstone bridge, whose input end is electrically connected to the incident rod strain gauge provided on the incident rod and the transmission rod strain gauge provided on the transmission rod, respectively, for eliminating noise in the strain signal collected by the strain gauge and outputting a target strain signal; An ultra-dynamic resistance strain gauge, which is electrically connected to the output end of the Wheatstone bridge and is used to convert the target strain signal into a high-frequency dynamic strain signal; And a processing module is used to process the high-frequency dynamic strain signal to output the incident wave, the transmitted wave, the reflected wave and the wave velocity.

[0009] Preferably, the core rod is a spindle with thin ends and thick middle, the small diameter section of the core rod is the same as the inner diameter of the bushing, and the large diameter section of the core rod is the interference size after the bushing is installed, wherein the bushing is sleeved on the small diameter section of the core rod facing the transmission rod.

[0010] Preferably, the inner diameter of the slotted gasket is equal to the diameter of the large diameter section of the mandrel.

[0011] Preferably, the diameter of the mounting hole of the transmission rod is larger than the diameter of the large diameter section of the core rod.

[0012] Preferably, the length of the mounting hole of the transmissive rod is greater than twice the length of the core rod.

[0013] A method for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar, comprising: Install the test mandrel according to the dynamic installation parameter testing device of the interference bushing based on the Hopkinson pressure bar of the present invention; Data collection: Turn on the power supply for the data collection and processing system, and the incident rod strain gauge collects the reflected wave, the transmitted wave and the corresponding wave velocity of each wave; Data processing: The displacement, speed and resistance of the mandrel during the installation process are obtained based on the reflected wave, the transmitted wave and the corresponding wave speeds of each wave.

[0014] Preferably, the expressions for the displacement, velocity and resistance of the mandrel during the installation process are:

[0015]

[0016]

[0017] In the formula, represents the displacement of the mandrel at time t during the installation process; It represents the speed of the mandrel at time t during the installation process; The resistance of the mandrel at time t during installation; represents the elastic modulus of the material selected for the incident rod and the transmission rod; represents the reflected wave of the incident rod collected at time t during the installation process; It represents the transmitted wave at time t during the installation process; represents the wave speed of the incident and transmitted rods, represents the cross-sectional area of ​​the incident and transmitted rods.

[0018] The beneficial effects of the present invention are: 1. The present invention provides kinetic energy for the incident rod through a discharge drive module, so that dynamic installation of the interference bushing can be achieved during the movement of the incident rod, and the mechanical parameters of the core rod during the dynamic installation of the bushing are detected in real time through the acquisition and processing system. The present invention can complete the installation of the bushing and can also collect dynamic mechanical and kinematic responses during the installation process, providing a data basis for the quantitative analysis of the rate effect, guiding the process parameter optimization and mechanism research of the composite bushing structure, avoiding the inertial force during the installation process, and improving the accuracy of the detection results.

[0019] 2. Secondly, the present invention forms a discharge circuit by connecting a discharge thyristor, a resistor and a capacitor in series through an electromagnetic stress generator. The discharge circuit, the incident rod and the transmission rod constitute an electromagnetic Hopkinson pressure bar. The electromagnetic Hopkinson pressure bar is subsequently used to test the mechanical parameters during the dynamic installation of the bushing. That is, compared with the traditional bullet impact type, the electromagnetic type of the present invention can accurately control the bushing installation rate and energy, and has good controllability and high repeatability. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention 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 invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0021] Figure 1 It is a schematic diagram of the overall structure of a dynamic installation parameter testing device for an interference bushing based on a Hopkinson pressure bar of the present invention; Figure 2 It is a parameter schematic diagram of a dynamic installation parameter testing device for an interference bushing based on a Hopkinson pressure bar during bushing installation of the present invention; Figure 3 It is a flow chart of a method for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar of the present invention; Figure 4 This is a comparison chart between the parameter testing method of the present invention and the actual high-speed camera detection results.

[0022] In the figure: 1. discharge thyristor; 2. resistor; 3. capacitor; 4. incident rod; 5. core rod; 6. bushing; 7. perforated plate; 8. gasket with seam; 9. transmission rod; 10. incident rod strain gauge; 11. transmission rod strain gauge; 12. electromagnetic stress generator; 13. Wheatstone bridge; 14. ultra-dynamic resistance strain gauge; 15. processing module. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0024] An embodiment of a dynamic installation parameter testing device for an interference bushing based on a Hopkinson pressure bar of the present invention is as follows: Figure 1 As shown, it includes: a discharge driving module, an incident rod 4, a transmission rod 9, a bushing 6 and an acquisition and processing system, one end of the incident rod 4 is connected to the output end of the discharge driving module, the other end of the incident rod 4 is coaxially connected to a core rod 5, and an incident rod strain gauge 11 is arranged on the incident rod 4; a mounting hole is coaxially opened at one end of the transmission rod 9, and a transmission rod strain gauge 10 is arranged on the transmission rod 9, wherein an end of the core rod 5 away from the incident rod 4 is successively penetrated by an opening plate 7 and a seam washer 8, and the incident rod 4 is connected to the mounting hole of the transmission rod 9 after passing through the seam washer 8; the bushing 6 is sleeved on the core rod 5 in the hole of the opening plate 7; the acquisition and processing system is used to collect the reflected wave of the incident rod 4, the transmitted wave of the transmission rod 9 and the wave velocity at each moment during the dynamic installation of the bushing 6, and obtain the displacement, speed and resistance of the core rod 5 at each moment during the dynamic installation of the bushing 6 according to the reflected wave, transmitted wave and wave velocity at each moment.

[0025] Among them, the discharge driving module in this embodiment includes: an electromagnetic stress generator 12, the electromagnetic stress generator 12 forms a discharge circuit by connecting a discharge thyristor 1, a resistor 2, and a capacitor 3 in series, wherein the electromagnetic stress generator 12 is coaxially connected to the end of the incident rod 4. When working, the electrical energy stored in the capacitor 3 is converted into a stress pulse through the electromagnetic stress generator 12, thereby providing kinetic energy for the subsequent dynamic installation process of the bushing 6.

[0026] Specifically, the acquisition and processing system includes: a Wheatstone bridge 13, an ultra-dynamic resistance strain gauge 14 and a processing module 15. The input end of the Wheatstone bridge 13 is electrically connected to the incident rod strain gauge 11 set on the incident rod 4 and the transmission rod strain gauge 10 set on the transmission rod 9. The Wheatstone bridge 13 is used to eliminate the noise in the strain signal collected by the strain gauge and output the target strain signal; the ultra-dynamic resistance strain gauge 14 is electrically connected to the output end of the Wheatstone bridge 13, and the ultra-dynamic resistance strain gauge 14 is used to convert the target strain signal into a high-frequency dynamic strain signal; the processing module 15 is used to process the high-frequency dynamic strain signal to output the incident wave, the transmitted wave, the reflected wave and the wave velocity, and the processing module 15 adopts a computer.

[0027] Specifically, the mandrel 5 is a spindle with thin ends and thick in the middle. The small diameter section of the mandrel 5 is the same as the inner diameter of the bushing 6, and the large diameter section of the mandrel 5 is the interference size after the bushing 6 is installed. The bushing 6 is sleeved on the small diameter section of the mandrel 5 facing the transmission rod 9. The inner diameter of the seamed gasket 8 is equal to the diameter of the large diameter section of the mandrel 5. The diameter of the installation hole of the transmission rod 9 is larger than the diameter of the large diameter section of the mandrel 5. The bushing 6 is sleeved on the mandrel 5, and then the bushing 6 and the hole of the perforated plate 7 are sleeved to ensure that the two end faces of the bushing 6 are coplanar with the two planes of the perforated plate 7. The part of the mandrel 5 extending out of the bushing 6 is coaxially installed with the seamed gasket 8. The function of the seamed gasket 8 is to support the bushing 6 and the perforated plate 7, while reducing unnecessary damage to the core rod 5 after passing through the bushing hole of the bushing 6, thereby increasing the service life of the core rod 5. The mounting hole opened on the end face of the transmission rod 9 has a diameter larger than the maximum diameter of the core rod 5, and a length larger than twice the length of the core rod 5, to ensure that only installation resistance is generated during the installation of the bushing 6, while not affecting the collection of the transmitted wave.

[0028] A method for testing dynamic installation parameters of an interference bushing based on a Hopkinson pressure bar, comprising: S1. Installing the test mandrel: installing the test mandrel according to the dynamic installation parameter testing device for interference bushing based on the Hopkinson pressure bar of the present invention; S2, data collection: the data collection and processing system is powered on, and the incident rod strain gauge collects reflected waves, transmitted waves and the corresponding wave velocities of each wave; S3. Data processing: Based on the stress wave theory and the Hopkinson bar test principle, the mechanical parameter calculation formula is derived, and the displacement, speed and resistance of the core rod during the installation process are obtained according to the reflected wave, transmitted wave and the corresponding wave speed of each wave.

[0029] In this embodiment, the calculation method of the displacement, speed and resistance of the mandrel is derived as follows: Model simplification: The principle of the dynamic installation parameter test device of the interference bushing based on the Hopkinson pressure bar is as follows Figure 2 The actual installation includes an incident rod 4, a core rod 5, a bushing 6, a perforated plate 7, a seam washer 8 and a transmission rod 9. Figure 2 middle represents the incident wave, represents the reflected wave, Represents the transmitted wave. represents the length of the large diameter section of the mandrel 5, represents the thickness of the perforated plate 7. During the installation process, the core rod 5 is in direct contact with the inner wall of the bushing 6. The resistance that hinders its passage includes friction resistance and elastic-plastic deformation shear resistance caused by the deformation of the bushing 6. The total displacement size of the bushing 6 with resistance during installation is and The installation interface composed of the mandrel 5, the bushing 6 and the perforated plate 7 can be equivalently simplified as an object that produces finite deformation. The deformation resistance of the object is the same as the resistance of the mandrel 5 and the bushing 6 during the finite deformation process, and the deformation displacement of the object is , The simplified model is the same as the principle of the Hopkinson bar test of the dynamic compression performance of materials, which is mainly based on two basic assumptions: the one-dimensional stress assumption in the bar and the uniform distribution of stress and strain along the length of the core rod. First, according to the first basic assumption, the cross section of the bar remains flat when it is deformed, and there is only uniformly distributed axial stress along the cross section. Therefore, all motion parameters are x and t The whole problem is simplified to a one-dimensional problem. x represents the position of a particle in space, t represents the core rod, and the wave propagation speed in the incident rod and the transmission rod is constant, that is, the wave speed is The whole problem is simplified to a one-dimensional problem, and the displacement of the incident wave can be obtained , displacement of reflected wave and the displacement of the transmitted wave for:

[0030]

[0031]

[0032] because , then the velocity is the time derivative of the displacement:

[0033]

[0034]

[0035] At the same time, the two interfaces where the incident rod 4 and the transmission rod 9 contact the core rod are called interface 1 and interface 2 respectively, then the strain at interface 1 is and the strain at interface 2 It can be expressed as:

[0036]

[0037] Figure 2 The velocities of interface 1 and interface 2 are also the velocity of the incident rod. and the speed of the transmission rod They are:

[0038]

[0039] Then the displacement at interface 1 is and the displacement at interface 2 It can be expressed as:

[0040]

[0041] The relative motion speed between interface 1 and interface 2 can be expressed as:

[0042] The relative displacement between interface 1 and interface 2 can be expressed as:

[0043] set up is the elastic modulus of the rod material, and the cross-sectional areas of the incident rod 4 and the transmission rod 9 are , then the load at interface 1 is and the load at interface 2 It can be expressed as:

[0044]

[0045] Then the average load on the mandrel is It can be expressed as:

[0046] In the actual installation process, the strain gauge acquisition parameters are functions of the strain and the core rod, that is, the incident wave, reflected wave and transmitted wave can be expressed as , and Then the displacement, velocity and resistance of the mandrel 5 during the installation of the bushing 6 can be expressed as:

[0047]

[0048]

[0049] Considering the second assumption of the Hopkinson bar, namely the uniform deformation assumption, in this model, the displacement during installation is small compared to the long slender bar, and the stress and strain are uniformly distributed along its length. Then we have , can be obtained . It is simplified to:

[0050]

[0051]

[0052] In the formula, represents the displacement of the mandrel 5 at time t during the installation process; represents the speed of the mandrel (5) at time t during the installation process; The resistance of the mandrel 5 at time t during the installation process; represents the elastic modulus of the material selected for the incident rod and the transmission rod; represents the reflected wave of the incident rod collected at time t during the installation process; It represents the transmitted wave at time t during the installation process; It represents the wave velocity of the incident rod and the transmitted rod. Since the wave velocity is only related to the material, and in this embodiment, the two rods are made of the same material, the wave velocity is assumed to be the same. represents the cross-sectional area of ​​the incident and transmitted rods.

[0053] Also includes, verification of test results: Mark the experimental area: spray the extended section of the mandrel 5 with speckle and use it as the target area. Aim the high-speed camera at the target area and set and correct the dark field. Set the test acquisition frame rate and duration. Press the trigger to verify that the high-speed camera is collecting normally. Then set the high-speed camera to the high-speed acquisition waiting trigger mode. After the photos collected by the high-speed camera are processed by the computer, the displacement and speed of the mandrel 5 are output.

[0054] Result comparison: The displacement and velocity calculation results of the core rod 5 of this embodiment are compared and verified with the displacement and velocity of the core rod 5 output after being collected by a high-speed camera and processed by a computer.

[0055] Figure 4 The theoretical calculation of the method provided by the present invention is compared with the actual high-speed camera detection results. Figure 4 a is the stress signal diagram collected by the transmission rod strain gauge 10 and the incident rod strain gauge 11 during the actual installation of the bushing. After data processing, it can be obtained Figure 4 b Installation displacement time curve, Figure 4 c Installation speed time curve, Figure 4 d Installation resistance time curve. The above theoretical calculation values ​​are consistent with the direct detection data obtained by the high-speed camera. This further illustrates the feasibility of the dynamic installation parameter test method of the interference bushing based on the Hopkinson pressure bar proposed in the present invention.

[0056] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A dynamic installation parameter testing device for interference bushing based on Hopkinson pressure bar, characterized in that: include: Discharge drive module; An incident rod (4), one end of which is connected to the output end of the discharge driving module, and the other end of which is coaxially connected to a core rod (5); A transmission rod (9) has a mounting hole coaxially formed at one end thereof, wherein an opening plate (7) and a seam washer (8) are sequentially penetrated at the end of the core rod (5) away from the incident rod (4), and the incident rod (4) passes through the seam washer (8) and is connected to the mounting hole of the transmission rod (9); A bushing (6) is sleeved on the core rod (5) in the hole of the perforated plate (7); and a collection and processing system for collecting the reflected wave of the incident rod (4), the transmitted wave of the transmission rod (9) and the wave velocity at each moment during the dynamic installation of the bushing (6), and obtaining the displacement, speed and resistance of the core rod (5) at each moment during the dynamic installation of the bushing (6) based on the reflected wave, the transmitted wave and the wave velocity at each moment.

2. The dynamic installation parameter testing device of interference bushing based on Hopkinson pressure bar according to claim 1 is characterized in that: The discharge driving module comprises: an electromagnetic stress generator (12), which forms a discharge circuit by connecting a discharge thyristor (1), a resistor (2) and a capacitor (3) in series, wherein the electromagnetic stress generator (12) is coaxially connected to the end of the incident rod (4).

3. The dynamic installation parameter testing device of interference bushing based on Hopkinson pressure bar according to claim 1 is characterized in that: The acquisition and processing system includes: A Wheatstone bridge (13), the input end of which is electrically connected to an incident rod strain gauge (11) provided on the incident rod (4) and a transmission rod strain gauge (10) provided on the transmission rod (9), and is used to eliminate noise in the strain signal collected by the strain gauge and output a target strain signal; An ultra-dynamic resistance strain gauge (14), which is electrically connected to the output end of the Wheatstone bridge (13) and is used to convert the target strain signal into a high-frequency dynamic strain signal; And a processing module (15) is used to process the high-frequency dynamic strain signal to output an incident wave, a transmitted wave, a reflected wave and a wave velocity.

4. The dynamic installation parameter testing device of interference bushing based on Hopkinson pressure bar according to claim 1 is characterized in that: The core rod (5) is a spindle with thin ends and a thick middle. The small diameter section of the core rod (5) is the same as the inner diameter of the bushing (6), and the large diameter section of the core rod (5) is the interference size after the bushing (6) is installed. The bushing (6) is sleeved on the small diameter section of the core rod (5) facing the transmission rod (9).

5. The dynamic installation parameter testing device of interference bushing based on Hopkinson pressure bar according to claim 4 is characterized in that: The inner diameter of the slotted gasket (8) is equal to the diameter of the large diameter section of the mandrel (5).

6. The device for testing dynamic installation parameters of interference bushings based on Hopkinson bar according to claim 4, characterized in that: The diameter of the mounting hole of the transmission rod (9) is larger than the diameter of the large diameter section of the core rod (5).

7. The dynamic installation parameter testing device of interference bushing based on Hopkinson pressure bar according to claim 1 is characterized in that: The length of the mounting hole of the transmission rod (9) is greater than twice the length of the core rod (5).

8. A method for testing dynamic installation parameters of interference bushings based on Hopkinson pressure bars, characterized in that: include: Install the test mandrel according to the dynamic installation parameter test device of the interference bushing based on the Hopkinson pressure bar according to any one of claims 1 to 7; Data collection: the data collection and processing system is powered on, and the incident rod strain gauge (11) collects reflected waves, transmitted waves and the wave velocities corresponding to each wave; Data processing: The displacement, speed and resistance of the core rod (5) during the installation process are obtained based on the reflected wave, the transmitted wave and the wave speeds corresponding to each wave.

9. The method for testing dynamic installation parameters of interference bushings based on Hopkinson bar according to claim 8, characterized in that: The expressions for the displacement, velocity and resistance of the mandrel (5) during the installation process are: In the formula, represents the displacement of the core rod (5) at time t during the installation process; represents the speed of the mandrel (5) at time t during the installation process; The resistance of the mandrel (5) at time t during the installation process; represents the elastic modulus of the material selected for the incident rod and the transmission rod; represents the reflected wave of the incident rod collected at time t during the installation process; It represents the transmitted wave at time t during the installation process; represents the wave speed of the incident and transmitted rods, represents the cross-sectional area of ​​the incident and transmitted rods.

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