Study on the influence of pipe effect on the vibration characteristics of electro-hydraulic exciter | Scientific Reports

Scientific Reports volume 14, Article number: 26491 (2024) Cite this article

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In this paper, an electro-hydraulic exciter controlled by an alternating current distribution valve is proposed, and a systematic analysis of the influence of pipe effect on the vibration characteristics of the electro-hydraulic exciter is investigated by simulation and experiments. The vibration characteristics curves for different pipe parameters are obtained, and the relative errors between simulation and experiment are evaluated. Moreover, a significant regression model of pipe parameters and vibration characteristics of the electro-hydraulic exciter is established by using the quadratic regression analysis method and the Box-Behnken experiment design method. Significant differences in the influence of pipe parameters on vibration characteristics are obtained by ANOVA (Analysis of Variance), and the influence of pipe parameter interaction on vibration characteristics is discussed. The results show that the relative importance of pipe parameters on the vibration characteristics of electro-hydraulic exciter, from high to low, is as follows: pipe diameter, elastic modulus, and pipe length. Notably, there is also an interaction between the pipe parameters, and the significance of these interactions is ranked from high to low as the interaction between the layers of steel wire and diameter, the interaction between diameter and length, and the interaction between the layers of steel wire and length.

Vibration testing is crucial to modern industry’s basic research and product development. It is widely used in equipment manufacturing, energy power, aerospace, offshore vessels, and coal mining, among other engineering fields. Vibration test equipment plays a crucial role in engineering research and development, quality control, and process optimization1. Vibration and vibration resistance tests on hydraulic components is an important part for improving equipment reliability, especially important in aviation. Hydraulic systems and hydraulic lines play a key role in aircraft. Karpenko M2obtained the fluid pressure and vibration spectrum of the hydraulic flexible high-pressure hose through experimental test, study the dynamic characteristics and damage of aircraft hydraulic system lines. According to the vibration excitation principle, vibration test equipment can be divided into three categories: mechanical, electrical, and electro-hydraulic. Electro-hydraulic excitation equipment relies on the fluid medium for power transmission and energy conversion and has greater dynamic stress, higher power density, and load-adaptive characteristics than other excitation methods3. Electro-hydraulic excitation can be divided into two types based on the presence or absence of control valves in the electro-hydraulic excitation apparatus hydraulic circuit: valveless direct current excitation and valve-controlled alternating current excitation.

The valveless direct current excitation system is characterized by low energy loss, high efficiency and easy control. The valve-controlled alternating current electro-hydraulic excitation system has a simple structure, is small, and is lightweight, but it can also output high-frequency low-amplitude or low-frequency high-amplitude vibration characteristics4,5. Therefore, the valve-controlled alternating current electro-hydraulic excitation system is widely used in the field of construction machinery.

The investigation of the dynamic characteristics of a valve-controlled alternating current electro-hydraulic excitation system is crucial to the evolution of electro-hydraulic excitation technology and apparatus6. For this reason, many academics have designed a variety of rotary valves for alternating current vibration excitation and researched valve-controlled alternating current electro-hydraulic excitation systems. Liu et al7. designed an electro-hydraulic vibrator controlled by a multi-shoulder rotary valve and analyzed the spool structure of the electro-hydraulic exciter on the vibration waveform of the vibration pattern. Wang et al8. proposed the use of a double rotary valve to control the vibration waveform of an electro-hydraulic exciter and studied the influence of double rotary valve control on the vibration characteristics of electro-hydraulic exciter by simulation and experiment. Yan et al9. design a high-frequency inertial electro-hydraulic excitation system employing a 2-degree-of-freedom rotary valve, derive an analytical model of the system waveform, operating frequency, and boundary conditions, and discuss the distortion characteristics of the excitation system’s vibration waveform. Wu et al10. designed a two-stage rotary excitation valve that can improve the vibration frequency and amplitude of the electro-hydraulic excitation system, analyzed the working principle of the excitation valve and obtained the influence of the structural parameters of the two-stage rotary excitation valve on the amplitude and frequency of the electro-hydraulic excitation system through simulation and experiment. Xu et al11. proposed a novel high frequency two-dimensional (2D) rotary valve variable mechanism, which is used to generate discrete fluid by the fluid pulse-width-modulation to control and distribute the flow. Xu et al12. designed a new structure of a rotary valve, analyzed the rotary valve port flow characteristics and throttling loss using the CFD (Computational Fluid Dynamics) method, and summarized the advantages of this rotary valve applied in an electro-hydraulic excitation system. Wang et al13. designed an electro-hydraulic single-axis excitation system under the control of rotary valves. Wang et al14. proposed a seismic wave generation and control method based on double rotary valves to meet the needs of large-scale tests for seismic simulation shaking table waveform adjustment, analyzed the static and dynamic characteristics of the system, and improved the technical level of waveform control of seismic test bench. Wang et al15. designed an electro-hydraulic exciter composed of a four-way rotary valve and a micro-range double-acting hydraulic cylinder, deduced the mapping formula of the shape of the valve port and the area of the through-flow, established a mathematical model of the electro-hydraulic exciter, and analyzed the vibration waveform of the electro-hydraulic exciter by using simulation and experimental testing. Liu et al16,17. provided a comprehensive summary of the research advancements related to wave-making devices for wave structure impact experiments. Their work identified significant technical challenges associated with maintaining amplitude and waveform control in existing wave-making machines. To address these issues, they conceived a novel pusher-plate wave-making machine controlled by rotary valves, introducing an innovative utilization of electro-hydraulic exciters. Jia et al18. proposed a 2D electro-hydraulic fatigue testing machine program with a single rod piston cylinder controlled by an excitation valve, investigated the matching relationship between the resonance frequency of the testing machine and the excitation frequency, and found that fatigue testing on the load resulted in the “energy back-up” phenomenon at the resonance frequency. Cai et al19. designed a new structure of rotary valve-controlled electro-hydraulic exciter, using AMESim simulation and the central combination of design of experiments to establish the vibration amplitude of the exciter process parameters and vibration amplitude of the mapping response model to determine the interactive relationship between the process parameters and the electro-hydraulic exciter vibration characteristics.

The above mentioned literature demonstrated the practicality of rotary valve matched-flow excitation technology as well as the validity of associated research methodologies through numerical analysis, modeling, and experimental verification. The hydraulic shock and water hammer in the pipe of the electro-hydraulic exciter will be caused by the fast switching speed of the rotary valve port state. These phenomena are the fluid pipe effect, which will have a certain impact on the vibration characteristics of the electro-hydraulic exciter20,21. Ren et al22. discovered a piped effect in electro-hydraulic excitation systems controlled by rotary valves, which may be connected to a pipe structure. Dai et al23. proposed a novel 2D electric feedback flow control valve to solve the problem of low integration and control accuracy of flow control valves, which overcomes the influence of the valve port’s load change on the flow.

In our previous study, an electro-hydraulic excitation system controlled by a rotary valve was established, and the influence laws of the main structural parameters of the rotary valve and the excitation hydraulic cylinder on the vibration characteristics of the electrohydraulic excitation system were analyzed, but the pipe effect was not investigated24. Motivated by the above observations, the present study mainly concentrates on the influence of the pipe effect on the vibration characteristics of an electro-hydraulic excitation system. Taking into account the fluid pipe effect derived from pipe parameters, a mathematical model and experimental bench of the electro-hydraulic exciter are established. Model simulation, experimental test, quadratic regression analysis, and Box-Behnken test design are used to study the influence of pipe parameters and their interactions on the vibration characteristics of the electro-hydraulic exciter. This study paves the way for improving vibration performance and structural optimization of electro-hydraulic exciter.

The alternating distribution electro-hydraulic exciter is mainly composed of a pumping station, supply/return pipe, alternating distribution valve, working pipe, excitation hydraulic cylinder, and other auxiliary mechanisms, as shown in Fig. 1. The hydraulic principle is shown in Fig. 2.

Structure diagram of the electro-hydraulic exciter.

Hydraulic principle of the electro-hydraulic exciter. (1) Tank; (2) Electromagnetic relief valve; (3) Filter; (4) Cooler; (5) Motor; (6) Excitation hydraulic cylinder; (7) Alternating distribution valve; (8) Hydraulic pump; (9) Check valve; 10 Accumulator; 11. Pressure gauge; 12. Flow meter; 13. Computer; 14. Acquisition system; 15. Displacement sensor.

During the operation of the alternating current electro-hydraulic exciter, the pumping station supplies a specific pressure and flow of hydraulic oil to the alternating distribution valve through the liquid supply pipe, where the alternating distribution valve functions as a two-position four-way directional valve. The alternating distribution valve is directly driven and controlled by the frequency conversion motor. When the motor rotates the alternating current valve at a specific frequency, the hydraulic oil flows alternately through the working pipes into the upper and lower chambers of the hydraulic cylinder for excitation. The piston rod of the hydraulic cylinder reciprocates due to the pressure of oil, while the low-pressure liquid returns to the oil tank through the return pipe. The continuous rotation of the motor drives the alternating distribution valve, causing the pressure oil to alternately flow into and out of the hydraulic cylinder for excitation, enabling the realization of alternating current excitation. The vibration displacement of the hydraulic cylinder can be measured using a displacement sensor located at the end of the piston rod, and the data can be transmitted to the computer in real-time through the data acquisition system.

The alternating distribution valve is the core component of the electro-hydraulic exciter, and its structural principle is shown in Fig. 3. It mainly consists of front and rear end covers, valve bodies, valve cores, valve cores, bearings, seals, etc. During operation, the spool shoulder staggered opening of several oil grooves, the valve chest is opened on the 6 ports, of which the P-port and T-port are symmetrically distributed before and after the valve chest XZ-plane, and are connected to the supply/return pipe of the pumping station; A-port, B-port symmetrically distributed up and down the body YZ-plane, and through the working pipe with the A port and B port are symmetrically distributed above and below the valve chest YZ-plane, connected to the upper and lower chambers of the excitation hydraulic cylinder through the working pipe, and the direction of hydraulic oil flow is changed alternately through the relative rotation of the valve spool and valve body. In the position shown in the figure, the pump station input pressure oil flow from the P port to the A port, the hydraulic cylinder cavity liquid flow through the B port to the T port; due to the symmetrical distribution of the A, B two ports, the valve spool with the motor to turn through a certain angle, the P port flow to the B port, the A port flows to the T port; the two processes by the spool base body is separated and synchronized with the valve spool rotating, the pressure oil to promote the piston rod to produce vibration. The exciter can output vibration signals of different frequencies and amplitudes by adjusting the pumping station pressure, flow rate, and motor speed.

Alternating distribution valve structural principle.

Based on the structure and working principle of the alternating distribution valve, it is observed that the trend of symmetrical distribution in both ports A and B of the over flow area remains the same. Taking oil port A as an example, the mathematical analysis of the cross-section of the alternating current distribution valve overflow is carried out using analytical calculation method, as shown in Fig. 4.

Diagram of a cross-section of oil port A.

According to the principle of alternating distribution valve, we define the number of oil grooves as Z, the spool oil groove center angle is α (α = π/2Z), the oil grooves are staggered on both sides of the shoulder of the spool and the openings are of the same size. On the same side of the two adjacent oil tank center angle β = 4α, the oil tank length is x, the spool radius is R, and when the spool rotates with the motor at an angular velocity ω, the angular displacement is θ (θ = ωt), the arc length is l = Rθ. The spool is rotated to the moment of the closure of the oil port for the zero position when the spool angular displacement θ is gradually increased from 0 to α, the arc length l is gradually increased, the overflow cross-sectional area Sv gradually increases, and reaches the maximum value at θ = α. At this time, the oil port A is in the fully open state. When the spool angular displacement θ gradually increases from α to 2α, the arc length l gradually decreases and reaches a minimum value of 0 at θ = 2α, at which time the oil port A is in a fully closed state. Since the oil port is symmetrically distributed, the spool angular displacement θ increases from 2α to 4α, and the flow direction of the two oil ports A and B are interchanged. According to the above analysis, it can be obtained that the cross-sectional areas of the two oil ports A and B are:

where Sv1 is the cross-sectional area of the A port flow, and Sv2 is the cross-sectional area of the B port flow.

The equivalent bridge circuit of the electro-hydraulic exciter can be derived from the analysis of the alternating distribution valve flow, as shown in Fig. 5. Thus, the flow equations for the alternating distribution valve are calculated as:

The variables in the equation are defined as follows: Q1 denotes the flow rate at port A, Q2 denotes the flow rate at port B, Ps denotes the pressure at the pump station, and Po denotes the return pressure, Pa denotes the pressure in the upper compartment of the hydraulic cylinder, and Pb denotes the pressure in the lower chamber, ρ denotes the density of the hydraulic fluid.

Electro-hydraulic exciter equivalent bridge circuit.

The continuity equation for the flow in the upper and lower chambers of the excitation hydraulic cylinder should be established as follows:

The given parameters are defined as follows: Ap denotes the area of the piston of the excitation hydraulic cylinder, y denotes the displacement of the excitation hydraulic cylinder, Va denotes the volume of the upper chamber of the excitation hydraulic cylinder, Vb denotes the volume of the lower chamber of the excitation hydraulic cylinder, and βe denotes the modulus of elasticity of the volume of hydraulic oil.

The volume relationship between the upper and lower chambers of the excitation hydraulic cylinder can be expressed as follows:

where Vo is the initial volume, and V is the total volume of the excitation hydraulic cylinder.

The alternating valve and the excitation hydraulic cylinder are connected through the working pipe, this connection leads to the transmission of pressure waves in the pipe, resulting in pipe effect. This effect is notably observed in the distribution of liquid inductance (I), liquid resistance (R), and liquid capacitance (C) along the axis direction of the pipe25. During the motor rotation process, the changing state of the valve port causes the alternating distribution valve to generate pressure waves that induce varying degrees of shock oscillation. These pressure waves, in conjunction with the pipe effect, affect the vibration characteristics of the electro-hydraulic exciter26. To analyze the influence of the pipe effect on the vibration characteristics of the electro-hydraulic exciter, the mathematical model of the working pipe in the electro-hydraulic exciter is established by using the piece wise lumped parameter method. The pipe is divided into nsections, and the liquid inductance, liquid resistance, and liquid capacity effect of each section of the pipe are concentrated27. The physical model of the pipe and the equivalent bond graph model are obtained, as shown in Fig. 6.

Centralized model for pipe segmentation.

Figure 6 shows Igi, Rgi, and Cgi (where i varies from 1 to n) representing the liquid inductance, liquid resistance, and liquid capacitance for a specific section of the pipe. The mathematical relationships between the three and the pipe parameters are as follows28:

where Lg represents the length of the conduit and dg represents its diameter.

The hydraulic resistance of the pipe is composed of two parts: steady-state hydraulic resistance Rgsi and dynamic hydraulic resistance Rgdi. Because the alternating distribution valve outputs alternating pressure waves, the flow rate in the working pipe is pulsating, and the liquid flow state is turbulent. There are :

where Qg is the flow rate of the liquid in the pipe; vg is the kinematic viscosity of the liquid in the pipe.

where n is the number of pipe segments; δ is the pipe wall thickness; and Eg is the pipe modulus of elasticity.

Equation (8) to (10) illustrate that the liquid capacity, resistance, and sensation resulting from liquid flow in the pipe are influenced by the pipe’s length, inner diameter, wall thickness, and modulus of elasticity. In the case of the electro-hydraulic exciter, the wall thickness of its pipe remains relatively constant. Therefore, the primary pipe effect arises from the pipe’s length, inner diameter, and modulus of elasticity.

Based on the theoretical analysis of the alternating distribution valve and the mathematical model of the electro-hydraulic exciter, the simulation model of the electro-hydraulic exciter is established based on the Simcenter Amesim29, as shown in Fig. 7.

Electro-hydraulic exciter simulation model.

To verify the accuracy of the model, test samples of the alternating distribution valve and the working pipe are manufactured, in line with the principle of maintaining consistency between simulation and testing. The vibration characteristics test bench for the electro-hydraulic exciter is then established at the designated test site, including alternating current distribution valves, working pipes, an excitation system consisting of an excitation hydraulic cylinder, a pressure control system, an electrical control system, a pumping station system, and a data acquisition system. In order to obtain the vibration displacement of the electro-hydraulic exciter, a rope type displacement sensor is installed on the piston rod of the exciter hydraulic cylinder, and the sensor base is magnetically fixed on the table, as shown in Fig. 8.

Test bench for electro-hydraulic exciter.

The relevant parameters for simulation calculation and experimental testing need to be consistent, as shown in Table 1.

The study involved manufacturing different layers of steel wire braided hoses and AISI 304 steel pipes to investigate the impact of pipe parameters on the vibration characteristics of an electro-hydraulic exciter30,31. The working pipe parameters and sample numbers are shown in Fig. 9.

Pipe samples.

The experimental measurement is WXY-31 type displacement sensor with the range is 0 ~ 100 mm, the data acquisition system is NI PXI-6218, and the sampling frequency is 512 Hz. To reduce the influence of test errors on the test results, the average value of three test results under the same condition is taken as the test analysis data. Additionally, in the parameter setting stage of Simcenter Amesim, set the parameters in Table 1; Fig. 9 to the numerical simulation model of the electro-hydraulic exciter AmeSim shown in Fig. 7, and then use Simcenter Amesim to numerically simulate the vibration characteristics of the electro-hydraulic exciter.

The vibration characteristics curves of electro-hydraulic exciter with different pipe materials are obtained through model simulation and experiments, as shown in Fig. 10.

Vibration characteristics curves under different pipe materials.

From Fig. 10, it can be known that the vibration waveform of the electro-hydraulic exciter exhibits an approximate sinusoidal pattern. Due to certain fluctuations and interference in the experimental results, there is a certain degree of error between the simulation results and the experimental results. As the pipe material changes, the frequency domain peak in the simulation results decays from 31.28 dB to 23.74 dB, and the frequency domain peak in the experimental results decays from 46.06 dB to 38.71 dB. Moreover, the vibration characteristics of the electro-hydraulic exciter in both the test and model simulation results remain consistent despite variations in pipe materials. The test results exhibit larger fluctuations in the peak and trough, attributed to changes in the alternating distribution valve oil port state. These changes induce hydraulic shock due to sudden shifts in the direction of the vibration waveform32. The pipe is affected by pump pressure fluctuations, resulting in severe fluid structure interactions in the pipe system. Due to the vibration of the pipe, it also has a certain impact on the electro-hydraulic exciter. Therefore, according to the results shown in Fig. 10, the smaller the elastic modulus of the pipe, the softer the pipe, and the greater the impact of pipe vibration on electro-hydraulic exciter.

Additionally, the vibration waveform of different pipes experiences a decrease in peak value and a phase lag phenomenon, due to variations in pipe modulus of elasticity and fluid capacity during hydraulic fluid flow causing a decrease in the peak of the vibration wave and extending the time required for waveform stabilization. Statistical indicators, including the peak displacement (ymax) and the corresponding time (t) of the first wave peak, are extracted from both the test results and the model simulation. The obtained results are then compared and listed in Table 2.

The comparison results in Table 2 indicate that the ymax of pipe 1 is the highest, with experimental and simulation results of 0.716 mm and 0.711 mm, respectively, and a relative error of 0.69%. The ymax of pipe 4 is the smallest, with experimental and simulation results of 0.267 ms and 0.263 ms, and a relative error of 1.50%. The relative errors between the model simulations and experimental results of the statistical indicators for the vibration characteristics of electro-hydraulic exciters, under each pipe sample, are below 5%.

According to the theoretical analysis, in addition to the pipe material (modulus of elasticity), the pipe diameter and length are also the key factors of the derivative pipe effect (influence due to pipe structural parameters). Figure 11 shows the vibration characteristics of the electro-hydraulic exciter corresponding to different pipe diameters and lengths when the pipe material is AISI 304.

Vibration characteristics curves under different pipe parameters among: (a) different pipe diameters, and (b) different pipe lengths.

As shown in Fig. 11, the peak vibration displacements of pipe 1 corresponding to the electro-hydraulic exciter experiment and simulation are 0.716 mm and 0.711 mm, respectively, with a relative error of 0.70%. The time to the first wave peak is 103.85 ms. Similarly, for pipe 5, the peak vibration displacements are 0.374 mm and 0.386 mm, respectively, with a relative error of 3.21%. The time to the first wave peak is 104.62 ms; For pipe 6, the peak vibration displacements are 0.684 mm and 0.691 mm, respectively, with a relative error of 1.02%. The first wave peak occurs at a time of 103.92 ms. By observing the spectrum experiment curve, it can be seen that increasing the pipe diameter causes the amplitude of the electro-hydraulic exciter spectrum to decay from 46.06 dB to 41.23 dB, and increasing the pipe length causes the amplitude of the electro-hydraulic exciter spectrum to decay from 46.06 dB to 45.68 dB. Therefore, we can conclude that increasing the length and diameter of the pipe will decrease the peak vibration displacement and a lagging phase lag (time difference between the amplitudes of the two wave forms) of the electro-hydraulic exciter. Additionally, the influence of length and diameter on the peak vibration displacement of the electro-hydraulic actuator is greater than that of phase.

In summary, the numerical simulation of the vibration characteristics of the electro-hydraulic exciter has the same trend as the characteristic curve obtained from experimental testing results, and the inspection index values are close, proving that the model simulation can accurately describe the vibration characteristics of the electro-hydraulic actuator.

Theoretical modeling, model simulations, and experimental tests have been used to demonstrate that fluid pipe effects derived from pipe material (modulus of elasticity), length, and diameter do exist and have an effect on the vibration characteristics of electro-hydraulic exciter. To analyze the interaction of the piping effect, based on the quadratic regression equation, the Box-Behnken method was used to design a factor interaction analysis scheme with the number of layers of braided rubber hose steel wires (with different modulus of elasticity), piping diameter, and length as the experimental factors, and with the peak vibration displacement of electro-hydraulic exciter as the response, and the experimental factors and levels are shown in Table 3. According to the Box-Behnken method, a total of 17 sets of experimental tests need to be completed. In this study, the peak vibration displacement of the exciter is obtained by simulation based on the numerical model of the electrohydraulic exciter established by Simcenter Amesim. The results are shown in Table 4.

The least square method is used to establish the quadratic regression equation between the pipe factor and the displacement peak value of the electro-hydraulic exciter33:

where β0 is the coefficient of the constant term; βiis the coefficient of the primary term; βii is the coefficient of the secondary term; βijis the coefficient of the interaction term; and xi is the influencing factor, i, j = 1, 2, 3.

Using Eq. (12) to centralize the quadratic term coding in the regression equation:

The coefficients in the regression equation can be expressed as follows:

The multivariate fitting analysis of the regression equation is carried out by using the data in Table 4, and the regression model of the peak displacement of the electro-hydraulic exciter under the interaction of pipe factors is obtained:

The regression model underwent analysis of variance (ANOVA) to assess its level of significance, using the R2 (goodness of fit) test. The results are shown in Table 5.

The degree of significance of each item in the table is indicated by the marked degree. The assessment of the ANOVA results shows that: the F value of the quadratic regression model is 747.07, the P value is less than 0.0001, all types of R2 are greater than 0.9, and the signal-to-noise ratio is 99.625, which proves that the fitted model has a high level of significance; the model dislocation term, P = 0.2237 > 0.05, indicates that the dislocation term is not significant, and the model is a high fit to the test. Taking the peak vibration displacement test samples of the electro-hydraulic exciter and the prediction results of the regression model as the coordinates, the (X, Y) scatter plot shown in Fig. 12 is obtained, and the scatter points are approximately distributed around Y = X, indicating that the prediction results of the regression model are accurate34.

Comparison of predicted values with experiment values.

The P value is used to identify the significant degree of influence of piping factors on the response of the regression model, P < 0.0001, which shows that the influence of this factor on the regression model is highly significant; P < 0.05, which shows that the influence of this factor on the regression model is significant. According to Table 5, the significant degree of influence of piping factors on the peak vibration displacement of electro-hydraulic exciter can be obtained as follows: x2 > x1 > x3 (primary term), that is, diameter has the greatest impact, followed by the layers of steel wire, while length has the least impact on the peak vibration displacement of electro-hydraulic exciter; x1 × 2 > x2 × 3 > x1 × 3 (interaction term), that is, the interaction between the layers of steel wire and diameter has the greatest impact, followed by the interaction between diameter and length, while the interaction between the layers of steel wire and length has the least impact on the peak vibration displacement of electro-hydraulic exciter.

To analyze the interaction of factors in the pipe effect in detail, the response surface of the interaction term in the regression model is obtained, as shown in Fig. 13.

Response surface of pipe parameters interaction among (a) layers of steel wire and pipe length interaction, (b) layers of steel wire and pipe diameter interaction, and (c) pipe diameter and length interaction.

It can be observed from Fig. 13(a) that when the pipe diameter is 10 mm and the layers of steel wire ranges from (1,4), the peak displacement increases with increasing layers of steel wire. When pipe length is 230 mm, the increase was approximately 60.7%. And the pipe length ranges from (180 mm,230 mm), the peak displacement increases with decreasing pipe length. When the layers of steel wire is 4, the increase was approximately 21.3%. This indicates that when the pipe diameter is constant, the sensitivity of the layers of steel wire to the influence of the electro-hydraulic exciter is stronger than the pipe length. As is shown in Fig. 13(b), when the pipe length is 180 mm and the layers of steel wire ranges from (1,4), the peak displacement increases with increasing layers of steel wire. When the pipe diameter is 10 mm, the increase was approximately 79.1%. And the pipe diameter ranges from (10 mm, 32 mm), the peak displacement increases with decreasing pipe diameter. When layers of steel wire is 4, the increase was approximately 89.1%. This indicates that when the pipe length is constant, the sensitivity of the pipe diameter to the influence of the electro-hydraulic exciter is stronger than the layers of steel wire. Figure 13(c) reflects that when the layers of steel wire is 1 and the pipe length ranges from (180 mm, 230 mm), the peak displacement increases with decreasing pipe length. When the pipe diameter is 10 mm, the increase was approximately 15.4%. And the pipe diameter ranges from (10 mm, 32 mm), the peak displacement increases with decreasing pipe diameter. When pipe length is 180 mm, the increase was approximately 91.2%. This indicates that when the layers of steel wire is constant, the sensitivity of the pipe diameter to the influence of the electro-hydraulic exciter is stronger than the pipe length.

Comparing the curvature of the response surfaces of the three factors, it can be found that the pipe diameter is the major factor affecting the vibration characteristics of the electro-hydraulic exciter, and in its interaction with the number of layers of steel wires and the length of the pipe, the peak displacement of the electro-hydraulic exciter changes most significantly.

(1) An electro-hydraulic exciter controlled by an alternating distribution valve is proposed to mathematically model the electro-hydraulic exciter considering the fluid pipe effects derived from the pipe parameters and to build a simulation model and prototype test site based on the LMS Imagine.Lab AMESim. The results show that the vibration waveform of the electro-hydraulic exciter is similar to the sine wave, and the vibration waveform is affected by the oil port state of the alternating distribution valve, and there is a large fluctuation at the peak and trough. When the elastic modulus of the pipe changes from large to small, the peak value of the vibration waveform of the electro-hydraulic exciter decreases and the phase lag phenomenon occurs due to the influence of the liquid capacity effect.

(2) The vibration characteristics of the electro-hydraulic exciter are simulated and tested. The relative error between the simulation and the test is less than 2%. The simulation and analysis method can truly reflect the vibration characteristics of the electro-hydraulic exciter.

(3) Based on the quadratic regression equation and the Box-Behnken test design method, the prediction model of the influence of pipe parameters on the vibration characteristics of the electro-hydraulic exciter is obtained. The variance analysis shows that the model’s mismatch term P = 0.2237 > 0.05, and the mismatch term is not significant. There is no significant difference between the prediction method and the test results.

(4) The vibration characteristics of the electro-hydraulic exciter are affected by the pipe effect, which is influenced by multiple factors. Among these factors, the pipe diameter holds the most significance, followed by the elastic modulus and pipe length. The response surface analysis from the regression model reveals that the interaction involving the pipe diameter, elastic modulus, and pipe length has the most pronounced impact on the vibration characteristics of the electro-hydraulic exciter.

(5) Due to the significant impact of pipe effects on electro-hydraulic exciter, in order to improve the vibration characteristics of electro-hydraulic exciter, optimal matching of pipe parameters can be carried out in future research, and the influence of liquid flow coupling in pipe on electro-hydraulic exciter can be discussed. Alternatively, alternative current distribution valves and excitation hydraulic cylinders can be integrated to form new compact electro-hydraulic exciter.

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Lu, Z. et al. Nonlinear dissipative devices in Structural Vibration Control: a review. J. Sound Vib. 423, 18–49. https://doi.org/10.1016/j.jsv.2018.02.052 (2018).

Article ADS Google Scholar

Karpenko, M. Landing Gear failures connected with high-pressure hoses and analysis of Trends. Aircr. Tech. Problems[J] Aviat. 26 (3), 145–152. https://doi.org/10.3846/aviation.2022.17751 (2022).

Article MathSciNet Google Scholar

Ruan, L. S. et al. Electro-hydraulic vibration exciter controlled by 2D valve. J. Mech. Eng. 45 (11), 125–132. 10.1016/j (2009). electro-mechanical integrating.2015.12.006.

Article Google Scholar

Xing, T. et al. Progresses of Research on Hydraulic Vibration Technology. China Mech. Eng. 23 (03), 362–367 (2012).

Google Scholar

Zhao, G. C. et al. Electro-Hydraulic vibration method and vibration characteristic analysis of the Electro-Hydraulic Vibration System controlled by an alternating distribution valve. J. Vib. Shock. 41 (18), 143–149 (2022).

Google Scholar

Liu, Y. et al. Present Status and Prospect of high-frequency Electro-Hydraulic Vibration Control Technology[J]. Chin. J. Mech. Eng. 32 (1), 1–16. https://doi.org/10.1186/s10033-019-0406-y (2019).

Article ADS Google Scholar

Liu, Y. et al. Structure characteristics of Valve Port in the Rotation Spool Type Electro-Hydraulic Vibrator. J. Vib. Control. 23 (13), 2179–2189. https://doi.org/10.1177/1077546315612903 (2017).

Article ADS Google Scholar

Wang, T. et al. Novel Structure for Waveform Control of Twin Rotary Flowrate Valve Controlled Vibration Exciter. IEEE/ASME Transactions on Mechatronics, 26(2): 1183–1188. doi: (2020). https://doi.org/10.1109/TMECH. 2020.3025923.

Yan, R., Xian, C. J. & Jian, R. Output characteristics of a horizontal type Electro-Hydraulic Excitation System with Inertial Loading: modeling and Experimentation. J. Mech. Sci. Technol. 33, 5157–5167. https://doi.org/10.1007/s12206-019-1004-8 (2019).

Article Google Scholar

Wu, Y. P. et al. Vibration frequency characteristic study of two-stage excitation valve used in vibration experiment system. Mech. Eng. Sci. 2 (1), 30–35 (2020).

Article Google Scholar

Xu, C. et al. Investigation on a novel high frequency two-Dimensional (2D) rotary valve variable mechanism for Fluid pulse-width-modulation application. J. Mech. Sci. Technol. 37 (2), 757–765. https://doi.org/10.1007/s12206-023-0119-0 (2023).

Article Google Scholar

Xu, C. D. et al. Analysis of Flow Characteristics and Throttling Loss of a Novel High-frequency Two-dimensional Rotary Valve. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 31(5):1–9. doi: (2023). https://doi.org/10.1177/09596518231162758

Wang, H., Chen, Z. & Huang, J. A. Novel method for high-frequency non-sinusoidal vibration waveforms with Uniaxial Electro-Hydraulic shaking table based on Fourier Series. J. Vib. Control. 27 (21–22), 2466–2481. https://doi.org/10.1177/09596518231162758 (2021).

Article MathSciNet Google Scholar

Wang, T., Liu, Y. & Zhang, S. Modeling analysis of seismic Wave Generation and Control Based on Twin Rotary Valve. J. Dyn. Syst. Meas. Contr. 145 (7), 07451. https://doi.org/10.1115/1.4062616 (2023).

Article Google Scholar

Wang, H. et al. Research on Vibration Waveform of Electro-Hydraulic exciter with rotary valve based on different Valve Port shape. J. Mech. Eng. 51 (24), 146–152 (2015).

Article Google Scholar

Liu, Y., Wang, D. & Zheng, D. Pulse Wave Generation Method using Rotary Valve Control. J. Mech. Eng. 54 (20), 279–286 (2018).

Article ADS Google Scholar

Liu, Y., Cheng, S. & Zheng, D. Research Status and Prospect of High Power Wave Generation Technology. J. Mech. Eng. 52 (24), 155–163 (2016).

Article Google Scholar

Jia, W. N. & Ruan, J. Variable resonant technique for an electro-hydraulic fatigue test system. J. Vib. Shock. 35 (07), 10–14 (2016).

Google Scholar

Cai, G. P., Liu, X. & Qi, B. C. Matching process parameters of Rotary Valve Hydraulic Actuator based on AMESim. J. Hunan Univ. Sci. Technol. (Natural Sci. Edition). 34 (2), 71–79 (2019).

Google Scholar

Wang, H. et al. Analytical Solution to Orifice Design in a Rotary Valve Controlled Electro-Hydraulic Vibration Exciter for High-Frequency Sinusoidal Vibration Wavefor. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 233(5):1098–1108. doi: (2019). 10.1177/09 54408919 831123

Zhao, K. P. et al. Research on Amplitude Compensation performance of double spring electro-hydraulic vibration cylinder. Chin. J. Eng. Des. 28 (06), 737–745 (2021).

Google Scholar

Ren, Y., Tang, H. & Xiang, J. Experimental and Numerical investigations of hydraulic resonance characteristics of a high-frequency excitation system. Mech. Syst. Signal Process. 131, 617–632. https://doi.org/10.1016/j.ymssp.2019.06.002 (2019).

Dai, Q. et al. Characterization of 2D Electrical Feedback Flow Control Valve. Machines. 11 (2), 220–231. https://doi.org/10.3390/machines11020220 (2023).

Article Google Scholar

Zhao, G. et al. Study on vibration characteristics of Electro-Hydraulic Excitation System controlled by alternating Flow distribution Rotary Valve. IEEE Access. 11, 132380–132388. https://doi.org/10.1109/ACCESS.2023 (2023).

Article Google Scholar

Ren, Q. et al. Development and Parametric Analysis of Vibration System controlled by hydraulic shock rotary vibrator. Shock Vib. 1082963, 1–21. https://doi.org/10.1155/2021/1082963 (2021).

Article Google Scholar

Lubecki, M. et al. Analysis of selected dynamic properties of the Composite Hydraulic Microhos. Eng. Fail. Anal. 125, 1–9. https://doi.org/10.1016/j.engfailanal.2021.105431 (2021).

Article Google Scholar

Wu,Fan., Tang, D. I. et al. Analysis for pressure oscillations characteristics of hydraulic impact in Pipeline. Mach. Tool. Hydraulic. 45 (17), 176–179 (2017).

Google Scholar

Yan, S. M., Chen, Z. D. & Li, H. R. Study on a sectional lumped parameter model using bond graphs for turbulent pipelines. J. Mech. Eng., (07):12–14. (2001).

Wang, H., Wang, C. & Bao, Y. Y. The dynamic analysis of axle load System Pipeline[J]. Fluid Power Transmission Control, (01): 33–35. (2010).

Zhang, Q. H. et al. Research on 2D Digital Buffering Valve for Vehicle Shift. J. Mech. Eng. 54 (20), 206–212 (2018).

Article Google Scholar

Cong, H. B. et al. The Experimental Research on Equivalent elasticity coefficient of hydraulic fluid and Hos. Mach. Tool. Hydraulic. 38 (05), 81–83 (2010).

Google Scholar

Li, Z. et al. Analysis on frequency characteristics of hydraulic support’s Liquid Pipeline. J. Taiyuan Univ. Technol. 43 (02), 203–206 (2012).

ADS Google Scholar

Zhao, G. C. et al. Experimental research on interactions of slotted parameters for Rotary distributing Excitation Control Valve. China Mech. Eng. 32 (09), 1035–1042 (2021).

Google Scholar

Li, B., Xia, R. & Wang, X. W. Experimental study on Wear of Middle Plates under Multi factor interactions based on response surface method. China Mech. Eng. 30 (22), 2764–2771 (2019).

ADS Google Scholar

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We thank the anonymous reviewers for their insightful comments and suggestions for improving the paper. This research was supported by the National Natural Science Foundation of China (52204169), Liaoning Provincial Education Department Project (LJKQZ20222321 and JYTMS20230063).

School of Mechanical Engineering, Liaoning Technical University, Fuxin, 123000, China

Xin Jin, Guochao Zhao, Qiyuan Min, Dongpo Han, Nanqi Li & Hui Wang

Mining Hydraulic Technology and Equipment Engineering Research Center, Liaoning Technical University, Fuxin, 123000, China

Xin Jin, Guochao Zhao & Hui Wang

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X.J. and GC.Z. wrote the main manuscript text and QY. M. prepared Tables 1, 2, 3, 4 and 5. All authors reviewed the manuscript.

Correspondence to Guochao Zhao.

The authors declare no competing interests.

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Jin, X., Zhao, G., Min, Q. et al. Study on the influence of pipe effect on the vibration characteristics of electro-hydraulic exciter. Sci Rep 14, 26491 (2024). https://doi.org/10.1038/s41598-024-78403-5

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Received: 12 July 2024

Accepted: 30 October 2024

Published: 03 November 2024

DOI: https://doi.org/10.1038/s41598-024-78403-5

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