Indirect method of measuring dynamic stiffness of a proof mass assembly design and method of use

Abstract

A design calculation and use method of a retarder mass block assembly for indirectly measuring dynamic stiffness transmitted by a multi-type flexible pipe, wherein the retarder mass block assembly is designed according to basic parameters of the flexible pipe to be measured and a required effective test frequency range (f min , f max ), the upper and lower limits of the mass of the retarder mass block are determined, and the retarder mass block assembly and the retarder mass block unit are selected. The retarder mass block assembly mainly comprises the retarder mass block unit and connecting fasteners, the retarder mass block assembly is connected with the transition element, the flexible pipe to be measured and the excitation element by the connecting fasteners respectively, and axial measurement and transverse measurement of the indirectly measured dynamic stiffness are completed. By using combinations of different retarder mass block unit assemblies, the measurement requirements of dynamic stiffness transmitted by multi-type flexible pipes can be met without changing the overall structure of the measurement rack.

Description

Technical Field

[0001] This invention relates to an indirect method for measuring dynamic stiffness, and further to the design and use of a resisting mass block in the dynamic stiffness measurement method. Background Technology

[0002] To isolate and attenuate structural vibration noise transmitted along equipment feet, pipelines, and supporting structures, vibration damping components such as flexible joints and vibration isolators are widely used in shipbuilding, automotive, and aerospace industries. Dynamic stiffness is an important indicator for evaluating the vibration isolation performance of vibration damping components, reflecting their dynamic characteristics. Dynamic stiffness refers to the dynamic excitation force required to generate a unit displacement under dynamic load. The dynamic stiffness of vibration damping components plays a decisive role in the performance of vibration isolation systems in engineering. Too much dynamic stiffness cannot achieve the ideal vibration isolation effect, while too little dynamic stiffness, although it can improve vibration isolation performance, can lead to fatigue failure and instability due to excessive structural deformation.

[0003] There are two main methods for measuring the dynamic stiffness of elastic damping components: direct and indirect. The direct method requires measuring the displacement (velocity or acceleration) at the input end of the elastic damping component and the damping force at the output end. The indirect method measures the transmissibility of vibration (displacement, velocity, or acceleration) when there is a large rigid mass at the output end of the elastic damping component. The direct method can accurately measure the dynamic stiffness at low frequencies below 10Hz, but due to the influence of the fundamental frequency of the basic test frame, the upper limit of the test frequency is usually around 300Hz, resulting in a low test frequency range that cannot reflect the dynamic characteristics of the elastic damping component in the mid-to-high frequency range. The indirect method indirectly obtains the damping force at the output end by measuring the displacement (velocity or acceleration) of the rigid body at the output end of the elastic element, and the upper limit of the test frequency can reach 5kHz.

[0004] When testing the dynamic stiffness of elastic damping elements, longitudinal excitation typically does not cause torsion in the element, while lateral excitation always couples lateral translation and torsion. Therefore, the experimental setup for measuring the axial dynamic stiffness of flexible joints differs from that for measuring lateral stiffness. Lateral dynamic stiffness testing, through a symmetrical arrangement, enhances unidirectional vibration at the input end, thereby reducing the impact of torsional vibration on test accuracy and resulting in more precise results. (Indirect method for axial dynamic stiffness measurement reference) Figure 4 Indirect method for measuring lateral dynamic stiffness reference Figure 5 .

[0005] The indirect method for measuring the transmitted dynamic stiffness of elastic damping elements theoretically assumes that the output force at the receiving end of the test bench is approximately equal to the damping force at the output end of the elastic element, i.e.:

[0006] F2≈F 2,b =k 2,1 u1 (1)

[0007] In the formula: k 2.1 F1 is the transmitted dynamic stiffness of the tested component; F2 is the excitation force at the output end of the tested elastic damping component; F 2.b x1 represents the resistance force at the output end of the elastic damping element under test; x1 represents the displacement at the input end of the elastic damping element under test. From Newton's second law, we can obtain:

[0008] F 2,b =(m2+m f )ü2 (2)

[0009]

[0010] but:

[0011]

[0012] In the formula: m2 is the mass of the output blocking mass block; m f x1 represents the mass of the transition element and the mass of the flange at the output end of the elastic damping element under test; x2 represents the displacement at the output end of the elastic damping element under test; x2 / x1 is defined as the vibration (displacement) transmissibility, which is also equal to the corresponding velocity ratio and acceleration ratio.

[0013] Therefore, the dynamic stiffness of the component under test can be obtained by measuring the vibration transmissibility between the input and output ends, combined with the frequency and the selection of the stagnation mass, and then using equation (4).

[0014] I. Frequency Application Scope

[0015] The testing device can only obtain effective measurement data within a certain frequency range, one limitation of which comes from the available bandwidth of the exciter. The frequency range limitation when using the indirect method mainly stems from the accuracy of the approximate measurement of transmissibility in formula (4). This approximate accuracy should be within 1 dB, i.e., the variation range should be within 12% of the calculated dynamic stiffness amplitude. This requirement applies only to f min ≤f≤f max This satisfies the condition within a finite frequency range. Where f is... min The lower limit frequency of the measurement, f max This is the upper limit frequency for measurement.

[0016] ① Determination of the upper frequency limit using the indirect method

[0017] When using the indirect method, determine the upper limit frequency f. max The method involves determining the upper limit frequency f by selecting a suitable resistive mass block based on the Monograph in the standard to prevent the resistive force from vibrating like a rigid body above a certain frequency. max Another newly proposed method is to use numerical calculation software to obtain the frequency f of the first-order elastic deformation of the stabilizing mass in the free state.t At this time, the upper limit frequency f max ≈f t / 3.

[0018] ② Determination of the lower limit frequency using the indirect method

[0019] First, estimate the lower natural frequency f0 and the lower limit frequency f in the test setup. min It is approximately three times the highest natural frequency of all vibration modes (including all axial vibration modes) affecting the measurement direction in a test device with a low natural frequency.

[0020] II. Method for determining the mass of the blocking mass block

[0021] Existing standards provide Monographs for selecting standard resisting mass blocks (cylinders or cubes with equal diameter and height). For non-standard resisting mass blocks, methods are provided for experimentally measuring the effective mass and thus determining the upper limit of the effective test frequency.

[0022] The standard provides a post-test method, which requires first determining the blocking mass block and then experimentally determining the effective test frequency. This is not conducive to the design of the test bench and does not provide a design method suitable for measuring the dynamic stiffness of various types of flexible pipes.

[0023] To address the technical challenge of determining the mass of a stabilizing mass block, a design method for a stabilizing mass block assembly based on an indirect method for measuring the dynamic stiffness transmitted by a general-purpose flexible conduit is proposed.

[0024] Based on the basic parameters of the flexible connector under test and the required effective test frequency range (f) min f max The design of the stabilizing mass block assembly mainly includes stabilizing mass block units and connecting fasteners. The stabilizing mass block assembly is connected in pairs to the transition element, the flexible tube under test, and the excitation element via connecting fasteners, enabling axial and lateral measurements of dynamic stiffness. By combining different stabilizing mass block assemblies, the measurement requirements for dynamic stiffness transmission through various types of flexible tubes can be met without altering the overall structure of the measuring platform. Summary of the Invention

[0025] To address the aforementioned technical issues, a method for designing, calculating, and conducting combined experiments on a resistive mass block assembly for measuring the dynamic stiffness transmitted by various types of flexible nozzles is proposed.

[0026] ① The method for determining the mass of the resistive mass block is based on the basic parameters of the flexible connector under test and the required effective test frequency range (f). min f max Design the stabilizing mass block assembly. Determine the upper and lower limits of the stabilizing mass block's mass, as well as its shape and dimensions.

[0027] ② Combined application of stabilizing mass blocks: The stabilizing mass block assembly mainly includes stabilizing mass block units and their connecting fasteners. The stabilizing mass block assembly is connected to the transition element, the flexible tube under test, and the excitation element in pairs through connecting fasteners. By using combinations of different stabilizing mass block assemblies, the axial and lateral measurements of dynamic stiffness can be performed without changing the overall structure of the measuring platform, thus meeting the measurement requirements for the transmission of dynamic stiffness by various types of flexible tubes.

[0028] I. Determining the mass of the axially resisting mass includes the lower and upper limits of the mass of the axially resisting mass, and the lower and upper limits of the mass of the transversely resisting mass.

[0029] First, determine the lowest resonant frequency f of the flexible connector to be tested. e Predict the hysteresis quality, and then calculate the minimum hysteresis quality required to meet the test accuracy in each frequency range based on the constraints. The former must meet the quality range of the latter, otherwise the test accuracy will not be met.

[0030] 1. Determining the minimum axially hindering mass, i.e., determining the lower limit of the axially hindering mass, includes the following methods:

[0031] 1) Lowest resonant frequency selection method

[0032] Based on the lowest resonant frequency f of the flexible connector under test ez Select the impeding mass m 2z The shape and size. The selection steps are as follows:

[0033] ① First, estimate the lowest resonant frequency of the flexible nozzle under test according to equation (5).

[0034]

[0035] In the formula: k oz The axial low-frequency dynamic stiffness of the flexible nozzle under test; m el For the quality of the flexible pipe elastic component

[0036] ② Determine f oz —by m 2z The mass of the flexible hose under test (including auxiliary vibration isolation springs) / the natural frequency of the spring system. When the mass of the flexible hose under test is considered non-negligible, the entire system can be simplified to a two-degree-of-freedom system, and the required f... oz When the frequency f can be considered to be the first-order axial natural frequency of the system; when the mass of the flexible nozzle under test is considered negligible, the entire system is simplified to a single-degree-of-freedom system, and the required f... oz This can be considered as the system's first-order axial natural frequency:

[0037]

[0038] To ensure the validity of the test, 0.1f is required. ez ≥f oz .

[0039] When considering a single degree of freedom:

[0040]

[0041] ③f oz Take 0.1f ez Estimate m 2z Quality:

[0042] When considering two degrees of freedom:

[0043]

[0044] In the formula: k a To decouple the spring stiffness; m1 and m 2z These are the masses of the excitation element and the retardation mass block, respectively.

[0045] When considering a single degree of freedom:

[0046]

[0047] 2) Method for selecting constraints

[0048] The lower limit of the mass of the stabilizing mass block for both axial and lateral measurements can be determined using the constraint selection method. The difference between the input (vibration acceleration level in the test direction of the excitation element) and the output (vibration acceleration level in the test direction of the stabilizing mass block) obtained from the experiment must satisfy the inequality ΔL. 1,2 =L a1 -L a2 Given the constraint of ≥20dB, we can obtain...

[0049]

[0050] Then, based on equations (4) and (10), it can be deduced that...

[0051]

[0052] Where: m 2z With m 2h These are the masses of the axial and lateral resistance mass blocks, respectively.

[0053] Furthermore, the determination of the lower limit of the mass of the axially measuring hindering mass block assembly is jointly determined by the minimum resonant frequency selection method and the constraint condition selection method, that is, the lower limit of the axial hindering mass is determined by... Sure.

[0054] 2. Determining the minimum lateral resistance mass, i.e., determining the lower limit of the lateral resistance mass, includes the following methods:

[0055] 1) The method for selecting the lowest resonant frequency includes the following steps:

[0056] ① Determine the natural frequency of the bending vibration of the flexible joint with fixed ends according to mechanical vibration theory.

[0057]

[0058] In the formula: L is the length of the flexible nozzle; E is the elastic modulus of the material; I is the moment of inertia of the bending section; m′ is the mass of the elastic part of the flexible nozzle.

[0059] According to mechanics of materials, the low-frequency bending stiffness (without rotation at the free end) of a flexible joint is:

[0060]

[0061] k w The low-frequency bending stiffness of the flexible nozzle can be approximated as the static stiffness of the flexible nozzle at low frequencies. Using equation (13), the unknowns E and I in equation (12) are replaced with known quantities k. w Therefore, the natural frequency of the flexible connector can be calculated, i.e.:

[0062] ② Determine f oh -by m 2h The natural frequency of the mass / spring system of the flexible conduit under test (including auxiliary vibration isolation springs)

[0063] Because the lateral dynamic stiffness testing device is arranged symmetrically, and the elastic part of the tested flexible nozzle and the blind plate have relatively small masses that contribute little to the system's natural frequency, the testing system can be simplified to the energy method when analyzing the natural frequency of the entire system. Figure 7 As shown:

[0064] Where L1 and L2 are the lengths of the springs arranged axially and vertically, respectively, δ st For maximum deflection, an axially arranged spring can be considered as a cantilever beam fixed at one end, hereinafter referred to as a beam. Assume the mass of the axially arranged spring is m. 1.1 The mass of the vertically arranged spring is m. 1.2 The mass of the block is m, and the density of the two springs is ρ. i =m 1.i / L i According to mechanics of materials, the static deflection at a distance l from point o is:

[0065]

[0066] The equation for the dynamic deflection curve can then be written as:

[0067]

[0068] x(t) is the vibration displacement at the end of the cantilever beam, and its vibration mode can be written as:

[0069]

[0070] Then, according to the law of conservation of energy, the natural frequency of the system can be derived as:

[0071]

[0072] In the formula m 1.1 For the axial spring mass, m 1.2 For the mass of the vertical spring, m 2h Let k1 be the mass of the lateral blocking mass block, and k2 be the axial bending stiffness of the spring and the vertical axial stiffness of the spring, respectively.

[0073] Furthermore, to verify the correctness of the derivation method of the above natural frequency, i.e., formula (18), the results calculated by numerical simulation software are compared with the theoretical calculation results. As a preferred choice, k1 is 1×10⁵ N / m, k2 is 1×10⁶ N / m, and m is 1000 kg. Then, the fundamental frequency of the system is calculated to be 5.278 Hz by formula (18). Substituting the parameters into the numerical simulation software, the first three rigid body modes of the steel cube are obtained as shown in Table 1. The results show that the relative error between the theoretical result and the first natural frequency obtained by numerical simulation is only 5.03%, which is consistent with engineering practice.

[0074] Table 1. Natural Frequency Analysis of the Simplified Model System

[0075]

[0076] ③ Estimate the resistance mass m 2h

[0077] The minimum mass of the transversely hindering mass block can be obtained from equations (14) and (18).

[0078]

[0079] Furthermore, the determination of the lower limit of the mass of the lateral measurement hindrance mass block assembly is jointly determined by the minimum resonant frequency selection method and the constraint condition selection method, namely... 3. Determining the upper limit of the blocking mass, i.e., based on the upper limit frequency f of the test. max Determining the upper limit of the mass of the hindrance mass block involves the following steps.

[0080] ① After establishing a standard steel cube or steel cylinder impeding mass block using 3D modeling software, calculate its natural frequencies in the free state using numerical simulation software to obtain its first-order elastic modal frequency f. t Furthermore, the upper limit frequency f of the test of the impeded mass block is obtained. max That is, f max ≈f t / 3. The upper limit frequency obtained using the described method is approximately 100 Hz lower than the upper limit frequency in the standard Monotonic diagram, and the trend shows a good match. This indicates that the upper limit frequency obtained using the described method is a conservative value and can be used to obtain the relationship between the size of irregularly shaped hindrance mass blocks and the upper limit frequency.

[0081] ② Using numerical simulation software, the relationship between the upper limit frequency of the selected steel cube or equal-height cylinder resisting mass test and the upper limit of the resisting mass block is calculated. Figure 6 .

[0082] Furthermore, the upper limit of the obtained stabilizing mass block is combined with the lower limit principle of the stabilizing mass block to determine the lower limit mass of the stabilizing mass block m2, thereby finally selecting the upper and lower limits of the mass of the stabilizing mass block m2.

[0083] II. Design and application of the stabilizing mass assembly: The stabilizing mass assembly includes stabilizing mass block units and connecting fasteners. The stabilizing mass block assembly is connected to the transition element, the flexible tube under test, and the excitation element in pairs through connecting fasteners. By using combinations of different stabilizing mass block assemblies, the measurement requirements for transmitting dynamic stiffness of various types of flexible tubes can be met without changing the overall structure of the measuring platform.

[0084] The steps involved in designing the assembly of the impeding mass block are as follows:

[0085] 1) Given that the axial and lateral static stiffness ranges of a certain series of flexible nozzles are k a1 ~k a2 The mass range of the elastomer portion is m. n1 ~m n2 The measurement frequency range is f 1.1 ~f 1.2 The sum of the axial stiffnesses of the vertical decoupling springs of the measuring platform is k. b1 The sum of the axial bending stiffnesses of the springs is k. b2 .

[0086] 2) According to the theoretical formula for the lower limit of axial resisting mass, the mass range of the resisting mass block required for measuring the axial dynamic stiffness of the flexible nozzle on the test bench is m. 2z.1 ~m 2z.2 .

[0087] According to the theoretical formula for the lower limit of lateral resisting mass, the mass range of a single resisting mass block required for measuring the lateral dynamic stiffness of a flexible nozzle on a test bench is m. 2h.1 ~m 2h.2 .

[0088] 3) Using a combination of numerical simulation and experimental methods, the upper limit frequency achievable by non-standard stabilizing mass blocks was studied. The results show that standard stabilizing mass blocks, after reasonable division, can meet testing requirements when used individually or in combination. This allows for the measurement of dynamic stiffness transmission in multiple series and types of flexible conduits without altering the overall structure of the measuring platform. The mass of the combined stabilizing elements should be m ZH ≥max(m 2z.2 m 2h.2 After disassembly, the blocking element should be m CF ≈min(m 2z.1 m 2h.1 ).

[0089] 4) Since each flexible connector has a different mounting flange (e.g., the flanges and mounting bolts corresponding to DN50 and DN100 flexible connectors are different), matching transition elements are designed. If each transition element is designed properly, multiple flexible connectors can be connected to the resisting mass block using a single transition element, thus meeting the measurement requirements for transmitting dynamic stiffness of various types and series of flexible connectors. The example transition element described can meet the measurement requirements under different pressure conditions, such as water pressure and air pressure.

[0090] Compared with the prior art, the present invention solves the following problems:

[0091] Based on the basic parameters of the flexible connector under test and the required effective test frequency range (f) min f max Design a resistive mass block assembly.

[0092] The stabilizing mass block assembly mainly consists of stabilizing mass block units and connecting fasteners. By combining different stabilizing mass block assemblies, the measurement requirements for the dynamic stiffness of various types of flexible pipes can be met without changing the overall structure of the measuring platform. The disassembly form and shape combination of the stabilizing mass blocks should be selected according to the actual situation. Theoretically, the stabilizing mass block can be disassembled into n (n≥2) parts while meeting the testing requirements. Attached Figure Description

[0093] Figure 1 Cylindrical resisting mass block units and assemblies, including (a) a 341.92 kg cylindrical resisting mass block unit, (b) a 683.84 kg cylindrical resisting mass block unit, and (c) a 1025.76 kg cylindrical resisting mass block assembly. Figure 2Cube-shaped stabilizing mass block units and assemblies, including (a) a 367.92 kg cube-shaped stabilizing mass block unit, (b) a 735.85 kg cube-shaped stabilizing mass block unit, and (c) a 1103.77 kg cube-shaped stabilizing mass block assembly. Figure 3 Transition element

[0094] Figure 4 3D rendering of the axial measurement bench

[0095] Figure 5 3D rendering of the transverse measurement platform

[0096] Figure 6 (a) Relationship between upper limit frequency and steel cube size; (b) Relationship between upper limit frequency and steel cylinder size.

[0097] Figure 7 Radial excitation physical model

[0098] The diagram is labeled as follows: 1-Excitation element; 2-Fastener connecting the excitation element and the flexible conduit under test; 3-Flexible conduit under test; 4-Fastener connecting the flexible conduit under test and the transition element; 5-Transition element; 6-Fastener connecting the transition element and the stabilizing mass block assembly; 7-341.92kg cylindrical stabilizing mass block unit; 8-Fastener connecting stabilizing mass block units 7 and 9; 9-735.85kg cubic stabilizing mass block unit; 10-Pressure control valve; 11-367.92kg cubic stabilizing mass block unit. 12 - Fasteners connecting units 11 and 13 of the resisting mass block unit; 13 - 735.85kg cubic resisting mass block unit; 14 - Flexible connecting pipe mounting hole on the transition element; 15 - Water inlet / air inlet port; 16 - Valve mounting hole; 17 - Transition element mounting hole on the resisting mass block unit; 18 - Connection hole of the resisting mass block unit; 19 - 10 25.76kg cylindrical resisting mass block assembly; 20 - 11 03.77kg cubic resisting mass block assembly; 21 - Restricting mass block connection hole on the transition element. Detailed Implementation

[0099] A method for measuring dynamic stiffness using a resistive mass block assembly is disclosed. This assembly is applied to a device for measuring dynamic stiffness using an indirect method. The device includes: an excitation element 1, a resistive mass block assembly 19, a flexible tube under test 3, and a transition element 5. One end of the transition element 5 is connected to the resistive mass block assembly 19 via a fastening nut 6 that passes through a resistive mass block connection hole 21 on the transition element and a transition element mounting hole 17 on the resistive mass block unit. The other end is connected to the flexible tube under test 3 via a fastener 4 that passes through a flexible tube mounting hole 14 on the transition element. The flexible tube 3 is connected to the excitation element 1 via a fastener 2 that connects the flexible tube under test to the excitation element. The design of the indirect method dynamic stiffness measurement stand, excitation element, resistive mass block unit, and transition element is based on CN 214149737 U. The stabilizing mass block assembly mainly includes multiple stabilizing mass block units and connecting fasteners. The stabilizing mass block units are connected by connecting fasteners. For example, cylindrical stabilizing mass block units 7 and 9 are connected by connecting fasteners 8 through mounting connection holes 18 to form cylindrical stabilizing mass block assembly 19; cubic stabilizing mass block units 11 and 13 are connected by connecting fasteners 12 through mounting connection holes 18 to form cubic stabilizing mass block assembly 20.

[0100] Example 1:

[0101] The axial static stiffness of a certain series of flexible joints (DN32~DN250) is known to be 2×10. 5 ~1.6×10 6 N / m, lateral static stiffness is 0.5×10 5 ~5×10 5 The mass of its elastic component ranges from 5 to 60 kg, with a strength of N / m. The frequency range of the predicted quantity is 20 to 500 Hz. The sum of the axial stiffnesses of the vertical decoupling springs on the measuring platform is 5 × 10⁻⁶. 5 N / m, the sum of the axial spring bending stiffness is 5×10 5 N / m.

[0102] (1) Design of the impeding mass block assembly

[0103] After analyzing each flexible connector in the series according to the design method of the resisting mass block assembly described in the invention, the minimum mass of the assembled resisting mass block assembly is found to be 1013.21 kg, and the mass of the disassembled unit is 316.63 kg. Ignoring additional components (mounting rings, bolts, etc.) and transition elements of the resisting mass block assembly, and considering the measured upper limit frequency and the effective stiffness range of the decoupling spring, the following selections are made:

[0104] When using cylindrical blocks of equal height as components of the stabilizing mass block, the cylindrical stabilizing mass block assembly 19 is selected with a mass of 1025.76 kg (0.55 × 0.55 m). After disassembly, it consists of cylindrical stabilizing mass block unit 1 (7) with a mass of 341.92 kg (0.55 × 0.18 m) and cylindrical stabilizing mass block unit 2 (9) with a mass of 683.84 kg (0.55 × 0.37 m).

[0105] The cylindrical resisting mass block unit 7 and the cylindrical resisting mass block unit 9 can be used for both axial and radial measurements.

[0106] When using a cube of equal height as the retardation element, a cube retardation mass block assembly 20 with a mass of 1103.77 kg (0.52 × 0.52 m) is selected. This is further divided into cube retardation mass block unit 11 with a mass of 367.92 kg (0.52 × 0.17 m) and cube retardation mass block unit 13 with a mass of 735.85 kg (0.52 × 0.35 m). Retardation mass block units 11 and 13 are connected by fastening bolts 12 to form the cube retardation mass block assembly 20.

[0107] (2) Design of transition elements

[0108] Since the flanges and mounting bolts for each flexible nozzle are different (e.g., the flanges and mounting bolts for DN50 and DN100 flexible nozzles are different), a matching transition element 5 is designed. If each transition element 5 is designed properly, multiple flexible nozzles can share a single transition element. The transition element 5 has flexible nozzle mounting holes 14, water and air inlet holes 15, valve mounting holes 16, and hindrance mass unit connection holes 21. The flexible nozzle mounting holes 14 and hindrance mass unit connection holes 21 are arranged in a ring.

[0109] Different flexible connectors 3 can be installed through the flexible connector mounting holes 14 to achieve various types and series of flexible connectors. The flexible connectors are connected to the resistive mass assembly 19 through the resistive mass unit connection holes 21 on the transition element 5 using connecting fasteners to achieve the measurement requirements of transmitting dynamic stiffness. The water inlet and air inlet holes 15 can meet the measurement requirements under different pressure conditions, including both water pressure and air pressure.

[0110] The cubic blocking element 20 and the cylindrical blocking element 19 are connected in the same way.

[0111] (3) Select the flexible connector with the required resistance mass.

[0112] A flexible conduit with a resisting mass of 341.92 kg is required to transmit dynamic stiffness for axial and lateral measurements. Specifically, for axial measurements, a cylindrical resisting mass block unit 7 with a mass of 341.92 kg (dimensions 0.55 × 0.18 m) is selected.

[0113] (4) Axial measuring device

[0114] The connecting hole 21 of the resisting mass block on the transition element 5 is connected to the suitable transition element mounting hole 17 on the resisting mass block element 7 using bolts 6, thereby achieving the connection between the resisting mass block element 7 and the transition element 5. The mounting flange at one end of the flexible pipe 3 is connected to the flexible pipe mounting hole 15 on the transition element 5, thereby achieving the installation of the flexible pipe 3 and the resisting mass block element 7.

[0115] The pressure-bearing surface of the excitation element 1 is the surface that bears the vertical pressure of the fluid (in direct contact with the pressurized fluid). The excitation element 1 is mounted to the other end of the flexible connecting pipe 3 by bolts 2, which ensures that the excitation element 1 receives the excitation force generated by the vibrator or vibration platform evenly. The pressure control valve 10 is installed in the valve mounting hole 16 on the transition element 5.

[0116] (5) Lateral measurement

[0117] The excitation element 1 is positioned in the middle and connected to the flexible conduits 3 on both sides via fastening bolts 2. The flexible conduits 3 are connected to the transition element 5 via fastening bolts 4, and the transition element 5 is connected to the retardation mass block unit 7 via bolts 6. The retardation mass block elements used on both sides for lateral measurement are cylindrical, and the mass of the retardation mass block unit 7 is 341.92 kg (dimensions 0.55 × 0.18 m). The final implementation scheme of the retardation element for lateral measurement is shown in Figure 5.

[0118] Example 2

[0119] The only difference from Example 1 is the use of a flexible conduit with a resisting mass of 683.84 kg. Theoretical calculations indicate that a resisting element with a mass of 1025.76 kg should be used for axial measurement. This involves assembling and connecting resisting mass elements 7 and 9 using fasteners 8 to form the resisting mass block assembly 19 required for the axial test stand. The resisting mass elements at both ends of the lateral measurement section are also 683.84 kg each. The final implementation scheme for the resisting element during axial measurement is shown in Figure 4.

[0120] Example 3

[0121] The only difference from Example 1 is the use of a flexible connecting pipe with a resisting mass of 1025.76 kg. Theoretical calculations indicate that a resisting element with a mass of 1025.76 kg should be used for axial measurement. This means that resisting mass elements 7 and 9 are assembled and connected using fasteners 8 to form the resisting mass block assembly 19 required for the axial test stand. For lateral measurement, the resisting mass elements 9 at both ends each weigh 683.84 kg.

[0122] This invention utilizes a combination of different resistive mass block components to meet the measurement requirements for dynamic stiffness transmission in various types of flexible conduits without altering the overall structure of the measuring platform. The disassembly form and shape combination of the resistive mass blocks should be selected based on the actual situation. Theoretically, the resistive mass block can be disassembled into n (n≥2) parts while meeting the testing requirements.

Claims

1. A design method for indirectly measuring the dynamic stiffness of a resistive mass assembly, comprising determining the basic parameters of the flexible guide tube to be tested and the required effective test frequency range ( ). f min , f max The design sets the upper and lower limits of the mass of the impeding mass block assembly, characterized by: The lowest resonance frequency method is used to determine the lowest resonance frequency of the flexible connector under test. f e Determine its first natural frequency f 0; then, using the constraint selection method, determine the lower limit mass of the axial and lateral measuring resistive mass block assembly; use numerical simulation software to calculate the natural frequencies of the resistive mass block assembly in the free state, and obtain its first-order elastic modal frequencies. f t The relationship between the upper limit frequency of the stabilizing mass block assembly test and the upper limit mass and size of the stabilizing mass block assembly, calculated using numerical simulation software, is used to determine the upper limit mass and size of the stabilizing mass block assembly. The determination of the lower limit of the axial measurement mass of the stabilizing mass block assembly adopts the lowest resonant frequency selection method, including the following steps: ① First, estimate the lowest resonant frequency of the flexible nozzle under test according to formula (5). （5） In the formula: The axial low-frequency dynamic stiffness of the flexible nozzle to be tested; For the quality of the elastic components of the flexible conduit; ② Determine -Depend on m 2z The mass of the flexible conduit under test, including the auxiliary vibration isolation spring, is considered to be non-negligible when the natural frequency of the spring system is considered to be non-negligible. Therefore, the entire system can be simplified to a two-degree-of-freedom system. It can be considered as the first-order axial natural frequency of the system, using formula (6): Calculations are required to ensure the validity of the test. ; When the mass of the flexible nozzle under test is considered negligible, the entire system simplifies to a single-degree-of-freedom system, and the required... It can be considered as the first-order axial natural frequency of the system, using formula (7). calculate; ③ Pick Estimate m 2z Quality: When considering two degrees of freedom, use formula (8). calculate, In the formula: To decouple the spring stiffness; and These are the masses of the excitation element and the axially hindering mass block, respectively. When considering a single degree of freedom, use formula (9). calculate; The determination of the lower limit of the mass of the lateral measurement hindrance mass block assembly adopts the lowest resonant frequency selection method, including the following steps: ①According to mechanical vibration, the natural frequency of the bending vibration of the flexible pipe with fixed ends is determined by formula (12). In the formula For the length of the flexible connector, The elastic modulus of the material. For the moment of inertia of the bending section, The mass of the elastic part of the flexible connector; The low-frequency bending stiffness of the flexible nozzle is given by formula (13). Calculate, where The low-frequency bending stiffness of the flexible nozzle can be approximated as the static stiffness of the flexible nozzle at low frequencies. Equation (13) is used to convert the unknown quantity in equation (12). and Replace with known quantities Thus, the natural frequency of the flexible nozzle can be calculated, i.e., formula (14). ; ② Determine -Depend on m 2h The mass of the flexible conduit under test, including the auxiliary vibration isolation spring, is related to the natural frequency of the spring system, i.e., formula (18). In the formula The mass of the axial decoupling spring. Let the mass of the vertical decoupling spring be . m 2h The mass of the lateral resistance mass block. These are the bending stiffness of the axial decoupling spring and the axial stiffness of the vertical decoupling spring, respectively. ③ Estimate the resistance mass block m 2h From equations (14) and (18), the minimum mass of the transversely hindering mass block can be obtained, i.e., equation (19). .

2. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: The determination of the lower limit of the mass of the axial and lateral measuring impediment mass block assembly adopts the constraint condition selection method, including the following steps: When using the indirect method, the difference between the input and output values ​​obtained from the experimental measurements must satisfy the inequality. Given the dB constraint, we can obtain equation (10). Then, according to equation (4) From equation (10), formula (11) can be derived. , In formulas (4), (10), (11) and These are the masses of the axial and lateral resistance mass blocks, respectively. The transmitted dynamic stiffness of the measured component. m 2 represents the mass of the output-end blocking mass block; m f For the mass of the transition element and the mass of the output flange of the tested elastic damping element, x 1 represents the displacement at the input end of the elastic damping element being measured. x 2. Displacement at the output end of the tested elastic damping element f min This is the lower limit frequency for measurement.

3. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: The determination of the lower limit of the axial measurement hindering mass block assembly's mass is jointly determined by the minimum resonance frequency selection method and the constraint condition selection method, that is, the lower limit of the axial hindering mass is determined by... Sure.

4. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: The determination of the lower limit of the mass of the lateral measurement hindrance mass block assembly is jointly determined by the minimum resonant frequency selection method and the constraint condition selection method, that is, by... Sure.

5. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: The lower limit of the mass of the transverse measurement hindrance mass block assembly is determined by the natural frequency formula (18), and the theoretical calculation result of formula (18) is verified by the result of the numerical simulation software.

6. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: Based on the upper limit frequency of the test Determining the upper limit of the mass of the hindrance mass block includes the following steps: ① After establishing a standard steel cube or steel cylinder impeding mass block using 3D modeling software, calculate its natural frequencies in the free state using numerical simulation software to obtain its first-order elastic modal frequencies. Furthermore, the upper limit frequency of the test for the retardation mass block is obtained. ,Right now ; ② The relationship between the upper limit frequency of the selected steel cube or equal-height cylinder resisting mass block test and the upper limit of the resisting mass block is obtained by using numerical simulation software.

7. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: Based on the aforementioned method for determining the lower limit of axial resisting mass, the mass range of the resisting mass block assembly required for measuring the axial dynamic stiffness of the flexible nozzle on the test bench can be obtained as follows: m 2z.1 ~ m 2z.2 Based on the aforementioned method for determining the lower limit of lateral resistance mass, the mass range of a single resistance mass block required for measuring the lateral dynamic stiffness of the flexible connector on the test bench can be obtained as follows: m 2h.1 ~ m 2h.2 The mass of the combined blocking elements m ZH ≥max( m 2z.2 , m 2h.2 ); the mass of the blocking element after disassembly m CF ≈min( m 2z.1 , m 2h.1 Theoretically, the resisting mass block can be broken down into n parts, where n≥2.

8. The design method for an indirect method of measuring the dynamic stiffness of a resistive mass block assembly according to claim 1, characterized in that: Applied to the field of indirect method for measuring dynamic stiffness, the retardation mass block assembly is connected to the transition element, the flexible tube under test, and the excitation element in pairs by connecting fasteners to perform axial and lateral measurements of dynamic stiffness. The retardation mass block assembly includes multiple retardation mass block units and connecting fasteners, and the retardation mass block units are connected by connecting fasteners.

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