Characteristic analysis method for integrated multi-parameter hydro-viscous speed control system | Scientific Reports

Scientific Reports volume 14, Article number: 27346 (2024) Cite this article

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Hydro-viscous clutch has become an inevitable choice for special vehicle transmissions. As a nonlinear dynamic system with large lagging link, its timing performance is affected by input rotational speed, lubricating oil temperature and pressure and other factors. However, from the control perspective, the speed regulation law, formation mechanism control characteristics, global model of hydro-viscous speed control system (HSCS) are unclear. To solve these problems, this paper presents a comprehensive analysis of the Hydro-viscous Speed Control System (HSCS), focusing on its steady-state and dynamic speed control characteristics. A data-driven model is established to describe the relationship between input rotational speed, output speed, control oil pressure, and lubricating oil temperature. The findings provide a foundation for optimizing HSCS structure and parameters, enhancing the performance and reliability of such systems in special vehicle transmissions and establishing a temperature-speed control system for special vehicle transmissions.

The Hydro-viscous clutch is a new type of mechanical speed regulating device that uses the viscosity of liquid and the shear action of oil film to transmit power. Its basic working principle is based on Newton’s law of internal friction. It transmits power through the oil film shear force between the main and driven parts, realizes stepless speed regulation and synchronous operation, and can protect the transmission system from overload. So, it is widely used in special vehicle transmissions due to its compact structure1, high efficiency, and capability for stepless speed control. However, the speed regulation performance of the Hydro-viscous Speed Control System (HSCS) is affected by various factors such as input rotational speed, lubricating oil temperature, and pressure. In addition, the proportional valve also has certain nonlinear factors2,3. The HSCS is reflected as a multi-parameter, strong coupling and strong nonlinear hydraulic transmission system. But in the actual application process, the actual impact of factors on system performance is often judged by engineering experience. From the control point of view, the law and formation mechanism of HSCS are not clear4,5,6,7, and there is no guiding significance for the design of control method of HSCS. Therefore, the hydro-viscous clutch often appears overheating, warping deformation and serious damage problems when working8,9,10,11. This study aims to analyze these factors and develop a comprehensive model to improve the control characteristics of HSCS.

Nowadays, with the development and progress of sensor technology, the parameters affecting the performance of hydro-viscous clutch, such as lubricating oil temperature and lubricating pressure, which are difficult to be quantitatively collected, can be accurately measured12,13. Based on that, to improve the control performance of HSCS, the characteristics of HSCS have been explored. Researchers have made some progress in the mathematical model and flow field test of viscous torque14,15. Pär Marklund et al. studied the torque transmission characteristics of clutches operating at low speed and heavy load under boundary lubrication5. Cui et al. studied the mathematical model of fluid torque caused by shear stress under the influence of fluid temperature in a HSCS16. Steven W. Shaw et al. proposed a hybrid averaging method and harmonic balance method to determine the steady-state response of nonlinear hydraulic systems, including stability information17. Yousong Shi et al. used the Hopf bifurcation theory to test the stability of the nonlinear hydraulic system18. Based on the nonlinear mathematical model, the stability and sensitivity of the governor control parameters were obtained. Yanhe Song, Kaixian Ba et al. studied the nonlinear dynamic behavior of the pressure servo valve control cylinder system, and obtained the influence of key parameters on the nonlinear self-excited behavior19,20.

From the mechanical and fluid point of view, the mechanism analysis of HSCS has been relatively perfect, but from the control point of view, the speed regulation law and formation mechanism of HSCS are not clear, and the control characteristics and global model are not clear.

To fully leverage the advantages of HSCS, further reveal and obtain HSCS characteristics and parameters, and provide a basis for optimizing the structure and parameters, evaluating and analyzing the performance of HSCS. The article analyzes the characteristics of the liquid viscosity speed control system. The analysis of HSCS characteristics includes three parts: Disturbance factor analysis of HSCS, test method design of speed regulation characteristics and analysis of HSCS characteristics. The specific description is as follows:

Firstly, the comprehensive modeling of HSCS is carried out. Through scientific and reasonable test methods, accurate and sufficient test data of HSCS performance are obtained. Based on this, the analysis of disturbance factors of HSCS is completed, and the static and dynamic speed control characteristic indexes are obtained to reveal the influence of disturbance factors on the system.

Secondly, the test method of HSCS is designed, and the evaluation index is selected to analyze the disturbance factors of the hydro-viscous speed regulation. On this basis, the test software of the hydro-viscous speed regulation performance test is compiled to realize the full automation of the test process and data processing.

Finally, the linear force driving characteristics of the hydro-viscous control mechanism which means proportional valve-controlled cylinder (PVC) are analyzed. And then the steady-state and dynamic speed regulation characteristics and laws of hydro-viscous are analyzed in turn, and the steady-state and dynamic speed control characteristics under different working conditions are obtained respectively. The characteristics of HSCS are analyzed through experiments, and the characteristics and parameters of the hydro-viscous speed regulation control are revealed and obtained. It helps to reveal and obtain the control characteristics of HSCS, providing a basis for the structure and parameter optimization, performance evaluation and analysis of HSCS machinery and hydraulic system.

This paper provides the basis for integrated modeling and control method design. It helps to reveal and obtain the control characteristics and parameters of HSCS, providing a basis for the structure and parameter optimization, performance evaluation and analysis of HSCS machinery and hydraulic system.

The first step in analyzing the characteristics of an HSCS is to develop an integrated model. It is the key basis for studying the characteristics of the HSCS. This model needs to capture the key relationships between friction plate surface roughness R, oil film thickness \(\delta\), and the resulting torque transmission. By applying the Stribeck curve14, we classify the friction state of the main and driven friction plates during the working process into fluid lubrication, mixed friction, boundary friction, and static friction. The model is then used to predict the dynamic behavior of the system under various operating conditions.

As shown in Fig. 1, this paper will tested the friction of rolling bearing and sliding bearing, and established the relationship between speed ν, normal load G, dynamic viscosity of lubricating oil \(\mu\)and friction coefficient f, it will explain the change of friction state of HSCS in working process.

Stribeck friction state of HSCS in working process.

Comprehensive value of surface roughness of friction pair.

Where \({R_1}\) and \({R_2}\)are the maximum height \({R_y}\) of the surface profile of the two dual friction plates.

Liquid lubrication: the ratio \(\lambda\) of oil film thickness to surface roughness is about [3,5], and the surface of the two friction plates is completely separated by the continuous oil film. The high-speed difference operation condition of HSCS belongs to this mode, and the output torque is small under this condition.

Mixed friction: the ratio of oil film thickness to the comprehensive value of surface roughness \(\lambda\) is small (about 3 or less), part of the surface of the two dual friction plates is separated by the oil film, and part of the contact between the asperities occurs, and the friction plate under the speed difference operation condition of HSCS is in this mode.

Boundary friction: the ratio of oil film thickness to surface roughness \(\lambda\) is small (about 0.4–1), the contact between the asperities on the friction surface increases, and the friction surface has only a thin boundary oil film (about 0.1\(\mu m\) below). The friction coefficient increases sharply. The HSCS belongs to this working condition when the speed difference is small, and the output speed fluctuates greatly, which is an unstable working area.

Static friction: the oil film thickness is zero, the active and passive friction plate is pressed into one, the relative motion speed is zero, which is the synchronous transmission condition of the hydro-viscous speed control clutch.

The friction state of the hydro-viscous clutch is closely related to the oil film thickness. The relationship between the oil film thickness and the force is shown as Fig. 2.

Simplified schematic diagram of modeling mechanism.

The HSCS adopts the mechanical structure of oil cylinder driving piston to realize the control of oil film thickness. The force of oil film in the clearance of piston extrusion friction pair is as follows.

(1) Force of cylinder pressure on piston \({F_1}\). (2) Force generated by the disc spring between each pair of friction pairs \({F_{i2}}\). (3) Friction force produced by the sealing ring when the piston moves \({F_3}\), its direction is opposite to the direction of piston movement. (4) Friction force produced by the external spline when the piston moves \({F_{i4}}\), the direction of which is opposite to the direction of piston movement.

When the piston squeezes the oil film in the clearance of the friction pair, the oil film will have a reaction force on the piston, which is called the oil film bearing capacity, as follows:

(1) The oil groove on the friction plate produces a dynamic pressure \({F_{i5}}\) bearing capacity when it moves relative to the piston, and its value is positive. (2) The static pressure \({F_{i6}}\) carrying capacity generated when the lubricating oil passes through the gap between the stationary friction plates is positive.

When the HSCS is in a fluid friction state, the dynamic equation of the first friction plate is as follows

The dynamic equation of the second friction plate is as follows

The dynamic equation of the third friction plate is as follows

The dynamic equation of the (i-2) th friction plate is as follows

The dynamic equation of the (i-1) th friction plate is as follows

For the above expression, \({F_1}\) is the input, \({F_{i2}}\) and spring compression linear relationship (\(i=1,2,3 \ldots \ldots ,28\)), \({F_3}\) and \({F_{i4}}\) can be estimated from relevant test data. Therefore, in the digital test modeling, it is necessary to obtain the relationship between \({F_{i5}}\), \({F_{i6}}\) and parameters such as speed, oil film thickness and fluid static pressure. The specific treatment method will be described in detail in Sect. 3.2.

After solving the above mathematical model, theoretically, the displacement of each friction plate \({\delta _1},{\delta _2},{\delta _3}\)……, according to the friction pair clearance initial value \({\delta _1},{\delta _2},{\delta _3}\)……, so that each pair of friction oil film thickness \({\delta _{sj}}\). The oil film transmission torque of each pair of friction pairs can be expressed as

Where \({M_j}\) is the torque transmitted by the j-th pair of oil film (\(j=1,2,3 \cdots \cdots ,28\)), \(f( \cdot )\) represents the function, \(\mu\) is the fluid viscosity, \({\omega _1}\) is the input rotational speed, \({\omega _2}\) is the output speed, and \(\delta\) is the oil film thickness.

The total output torque of the HSC clutch can be expressed as

Where M is the total output torque.

In this report, the external load of the HSC clutch is the fan, and the fan torque is proportional to the square of the fan speed.

Where \(f( \cdot )\) denotes the function.

Ignoring the elastic effect of the coupling, the dynamic equation of the HSC clutch driving fan system is

Where J is the total moment of inertia of the system, and B is the system damping.

Under stable or constant speed conditions, the following relationship exists in the HSCS driving fan system.

Where \(\Delta M\) is the torque loss.

When the external control pressure is the larger, the local area of the friction pair begins to contact, and the friction plate is in a mixed friction or boundary friction state. Because the friction disc surface is processed with oil groove, the transmission torque of the friction pair can be decomposed into two parts, one part is the transmission torque of the friction plate contact part, and the other part is the oil film shear transmission torque. The i-th pair mechanical contact part of the friction pair transmits torque as follows

Where f is the contact friction coefficient of the friction pair, k is the proportion of the area without oil groove on the surface of the friction pair, and \({p_{wi}}\) is the contact pressure of the i-th pair friction pair.

Where \({F_i}\) represents the external normal force on each pair of friction pairs, which is related to the output pressure of the proportional pressure reducing valve and the area of the control cylinder.

Substitution Eq. (13) into Eq. (12).

The oil film shear transmission torque of the oil groove part in the i-th pair of the friction pair is

Where h represents the depth of the oil groove of the friction plate.

The total torque that can be transmitted by the i-th pair friction pair of HSCS in the contact state is

The total output torque \({M_c}\) of the hydro-viscous clutch under contact condition is

The transient acceleration process of the fan driven by the HSCS can be obtained by joint solution. In Eq. (16), Fi, f and k are input variables, \({F_i}\) is related to the output of the proportional pressure reducing valve, f is related to the contact surface material, surface condition and relative motion speed of the friction pair, and k is related to the structure of the friction plate.

The modeling process of the entire digital test model is shown in Fig. 3.

Modeling flow diagram.

By controlling the piston to form the input drive of the axial position of the friction plate, the axial position of the friction plate is input into the axial dynamic calculation function and the rotational dynamic calculation function at the same time.

Calculate the torque to obtain the output speed and transfer the speed value to the axial dynamic calculation function, combined with the axial position to obtain the real-time axial force, and feedback to the axial force calculation input to obtain the real-time position balance value.

The calculated real-time position balance value is input into the rotational force calculation function and the axial force calculation function again until the stable output value of the balance is calculated by the model.

The model of HSCS mainly includes five modules: control system, power input, rotary transmission, linear transmission and load simulation. The main modeling work is in three parts: control system, rotary transmission and linear transmission. This article will discuss whether there are some working points in which the procedure finds some possible singularity and the output is not available in modules.

The control system includes the compression piston and hydraulic system characteristics, in which the hydraulic system characteristics are calculated by an independent hydraulic system model and imported into the overall model of the hydro-viscous clutch in the form of a data table. Since the external characteristics of the hydraulic system are imported through the data table, this means that its behavior is predefined and smooth, and there are no discontinuous points or singular points. Therefore, in the control system module, the model will not appear singularity.

The rotary drive and linear drive hydro-viscous clutch are simplified into a 28-degree-of-freedom mass spring damping series system to realize the quantitative description of the dynamic characteristics of the friction plate. The rotating transmission part calculates the relationship between clutch torque and speed. For each set of friction pairs, the relationship between torque and speed is calculated by physical model or empirical formula. These formulas are usually based on the principle of viscosity and friction mechanics and are continuous within the operating range. And the rotating transmission module is constructed by connecting multiple smooth sub-models in series, so the whole module will not have a singularity. The linear transmission module calculates the axial movement, power transmission and oil film force transmission of the friction plate. Similarly, these calculations are based on physical models and empirical formulas, reflecting continuous changes in friction, oil film thickness, and pressure. These formulas and models are stable and continuous in the normal operating range, so no singularity is introduced.

Finally, according to the above methods and processes, this article establishes a multi-parameter integrated simulation model including pressure control, friction pair-oil film and fan load.

Although we have previously analyzed that the model is smooth and continuous in the normal operating range, there are some extreme or special situations. For example, the pressure of the hydraulic system may exceed the physical limit of the equipment, resulting in system failure; when the speed of the rotating transmission module approaches zero, the torque calculation of the friction pair may be singular. The clearance between the friction plates in the linear transmission module is too large or too small, and the oil film force may lose its effectiveness. In these cases, the calculation results may be unstable, the accuracy may be reduced, and even the singularity may occur, resulting in the output being unavailable. In order to avoid these problems, we introduce boundary checking and exception handling mechanisms into the program to ensure that reasonable output can still be provided under extreme working conditions and avoid unusable results. Through reasonable boundary check and exception handling mechanism, the system can still ensure stable operation in these extreme cases, and ensure that there is no singularity or singularity in the whole model.

The technical implementation roadmap for the analysis of hydro-viscous speed regulation characteristics includes the disturbance factor analysis of HSCS, test method design of speed regulation characteristics and speed control characteristic analysis of HSCS:

Through scientific and reasonable test methods, accurate and sufficient test data of HSCS performance are obtained. Based on this, the analysis of disturbance factors of HSCS is completed, and the static and dynamic speed control characteristic indexes are obtained to reveal the influence of disturbance factors on the system.

The test method of speed control performance is to obtain accurate and sufficient test data of HSCS performance, including four parts: steady-state speed control test, dynamic speed control test and speed regulation characteristic index. steady-state and dynamic speed control test correspond to two different test conditions. The speed control characteristic index is used to evaluate the performance of HSCS. It can also be divided into static characteristic index and dynamic characteristic index. On this basis, the test software of HSCS performance to realize the full automation of the test process and data processing.

The speed control characteristics analysis includes valve-controlled cylinder transmission characteristic analysis, hydro-viscous steady-state speed modulation characteristic, hydro-viscous dynamic speed modulation characteristic, data actuation modeling four parts. Firstly, the linear force driving characteristics of the hydro-viscous control mechanism which means proportional valve-controlled cylinder (PVC) are analyzed. Then, the steady-state and dynamic speed control characteristics and laws of hydro-viscous are analyzed in turn, and the steady-state and dynamic speed control characteristics under different working conditions are obtained respectively. Finally, based on the speed control law and characteristic index, a data-driven model describing input/output rotational speed, control oil pressure and lubricating oil temperature is established.

The main factors affecting the output speed stability of hydro-viscous drive system are engine speed fluctuation, lubricating oil temperature change and load change.

The statistical analysis of multiple sets of real vehicle road spectrum data is carried out to obtain the dynamic change law of engine speed under typical working conditions, which is divided into steady state and dynamic state. The input and output rotational speed running-in curve are shown in Fig. 4.

Input and output rotational speed running-in curve.

In Fig. 4, the abscissa time is 8000s, comprehensive analysis of the two figures it can be concluded that the change rule of the engine is basically similar. As shown in Fig. 4(a), select the representative of the five sections, covering the engine speed amplitude and frequency changes, it is enlarged to draw. In Fig. 4(b), it takes 6s for the engine from the speed of 2400 rpm to the maximum speed of 1060 rpm, the speed change of about 1340 rpm. In Fig. 4(c), it is concluded that the engine takes 4s from 746 rpm to 1300 rpm, and the speed changes about 554 rpm. Engine speed from 1100 rpm to 840 rpm in 2s, the speed change of about 260 rpm. From Fig. 4(d), it is concluded that the engine changes from 1600 rpm to 700 rpm in 5s, and the speed changes about 900 rpm. Engine speed from 1250 rpm to 900 rpm in 1s, speed change of about 350 rpm. Engine speed from 839 rpm to 759 rpm in 2s, the speed change of about 80 rpm. From Fig. 4(e), the engine changes from 2436 rpm to 1315 rpm in 8s, and the speed changes about 1121 rpm. Engine speed from 2424 rpm to 1723 rpm in 7s, the speed change of about 700 rpm. From Fig. 4(f), it is concluded that the engine takes 3s from 0 rpm to 950 rpm, and the speed changes about 950 rpm. Engine speed from 1937 rpm to 0 rpm, take 16s, speed change of about 1900 rpm.

At this point, the steady state analysis is shown in Fig. 5.

Steady-state condition analysis.

The spectrum analysis of engine and fan speed shows that the fluctuation frequency band of engine speed is about 1.2 Hz and the fluctuation range is about 150 rpm.

The dynamic condition of engine input rotational speed is analyzed and shown in Fig. 6.

The running-in curve and speed change rate fluctuation curve.

The spectrum characteristics are analyzed according to the curve. The spectrum analysis of the engine and fan speed in the whole domain shows that the dynamic change rate (acceleration) of the engine speed is concentrated in 0-200 rpm/s.

The following analysis of the changes in lubricating oil temperature on the performance of HSCS disturbance. The change of lubricating oil temperature causes the change of oil viscosity, which mainly affects the strip phenomenon of HSCS. Let the lubricating oil temperature increase from 70℃ to 100℃, the steady-state curves of HSC at different oil temperatures are obtained, as shown in Fig. 7.

The steady-state curves of HSC at different oil temperatures.

As the oil temperature ascending, the shape of the curve does not change significantly, but the drag rotational speed is significantly reduced. This is because the oil viscosity is reduced, and the drag torque is also reduced.

Through the above analysis, the following conclusions can be obtained.

Lubricating oil temperature affects the discharge phenomenon, oil temperature increases with drag rotational speed and torque decreases, the rate of change − 10 rpm/℃. The lubricating oil temperature will locally change the range of oil pressure, and the working point of oil temperature ascending will move down. The lubricating oil temperature has little effect on the shape of the speed control characteristic curve and the closed loop control effect.

According to the above analysis of the disturbance factors of HSCS, it is determined that the main factors affecting the stability of the output speed of the HSCS are the fluctuation of the engine speed and the change of the lubricating oil temperature. Therefore, the following performance test methods are designed to test the force control performance of the proportional valve controlled cylinder, the speed control performance of HSCS and the fluctuation of the input rotational speed in HSCS. The evaluation index is refined to further study the actual influence of factors such as engine speed fluctuation and lubricating oil temperature change on HSCS.

The test method of timing performance is to obtain accurate and sufficient test data of hydro-viscous speed control performance, including four parts: steady-state speed control test, dynamic speed control test, speed control characteristic index and test software design. Aiming at the comprehensive model of HSCS established above, from the perspective of control performance analysis, the comprehensive test method and performance evaluation index of HSCS and components are reasonably designed.

Steady-state force control performance: under the input rotational speed of zero and high speed, the control signal changes slowly from zero to maximum, and the variation characteristics between the control signal and the control pressure/force are tested.

Step response characteristics: respectively, at the input rotational speed of zero and high speed, the control signal step change, test control pressure/ force step response characteristics.

Dynamic tracking characteristics: respectively, at the input rotational speed of zero and high speed, the control signal to do sinusoidal law between zero and maximum cycle change, test the output speed change curve, using sinusoidal point by point scanning, drawing frequency characteristics.

Pressure closed loop test: Closed loop control method is used to realize pressure closed loop control, eliminate pressure hysteresis, complete the above three tests, and compare the performance differences between open loop and closed loop.

Steady-state speed control test: From 1000 rpm to the maximum speed at different input rotational speeds, with an interval of 200 rpm, the steady-state relationship (large hysteresis curve) of control signal, control oil pressure and output speed was tested at different input rotational speeds.

Control step test: under different input rotational speeds, fast step change of control signal, and the step response curve of the output speed is tested.

Closed loop speed control test: in different input rotational speed, the implementation of speed closed loop control, eliminate nonlinear link, test the desired speed and output speed change relationship, calculate the effective speed range and control index.

Input rotational speed step test: In the speed open loop and closed loop mode, the input rotational speed step change, the control signal (open loop) or the desired speed (closed loop) remains unchanged, test the output speed and load torque curve under the disturbance, calculate the output speed and load torque fluctuation process.

Input rotational speed cycle fluctuation: Respectively in the speed of open loop and closed loop mode, the input rotational speed does cycle change (sinusoidal or constant speed), control signal (open loop) or the desired speed (closed loop) remain unchanged, test the output speed and load torque under the disturbance of the curve, calculate the output speed and load torque fluctuation process.

To accurately describe the static and dynamic performance indicators of the HSCS, and to facilitate the comparative analysis of the performance of the open loop speed control and the closed loop speed control process, the following performance evaluation indicators are proposed in combination with Fig. 8.

Speed regulation performance evaluation index diagram.

The effective speed control domain: used to characterize the quality of the output speed N of the speed control system. It is the effective speed control range of the system and does not contain the unstable area where the output speed changes dramatically. The speed control domain of the ascending phase and the speed control domain of the descending phase can be decomposed. The speed control domain of the ascending phase is [\({N_1},{N_2}\)], and the percentage form is \(\left( {{N_2}-{N_1}} \right)/\left( {{N_3}-{N_1}} \right) \times 100\%\). The speed range of the descending phase is [\({N_5},{N_0}\)], and the percentage form is \(\left( {{N_5}-{N_0}} \right)/\left( {{N_4}-{N_0}} \right) \times 100\%\).

Effective control region: used to characterize the effective range of speed control system input control signal U, does not contain the control dead zone and saturation zone. The control domain of the ascending phase and the descending phase can be decomposed. The speed control domain of the ascending phase is [\({U_1},{U_2}\)], and the percentage form is \(\left( {{U_2}-{U_1}} \right)/\left( {{U_3}-{U_0}} \right) \times 100\%\). The speed range of the descending phase is [\({U_5},{U_0}\)], and the percentage form is \(\left( {{U_5}-{U_0}} \right)/\left( {{U_3}-{U_0}} \right) \times 100\%\).

Control dead zone: used to characterize the range where the control signal does not play the role of speed control. It can be decomposed into the ascending dead zone and the descending dead zone. The ascending dead zone is [\({U_0},{U_1}\)], and the percentage form is. the descending dead zone is [\({U_3},{U_4}\)], and the percentage form is \(\left( {{U_1}-{U_0}} \right)/\left( {{N_3}-{N_0}} \right) \times 100\%\).

Hysteresis loop: the maximum width used to describe the hysteresis curve is expressed as the maximum difference between the two control signals corresponding to the output speed.

Nonlinearity: used to characterize the maximum deviation of the characteristic curve from its fitted line in the effective speed range, which can be decomposed into the nonlinearity of the ascending phase and the nonlinearity of the descending phase.

Rotational speed fluctuation rate: When engine input rotational speed fluctuates, the change of the output speed of HSCS, the percentage form is \(({{\Delta v} \mathord{\left/ {\vphantom {{\Delta v} {{v_{ave}}}}} \right. \kern-0pt} {{v_{ave}}}}) \times 100\%\).

Dynamic load change rate: Due to the fluctuation of the output speed of HSCS, the dynamic change of the load torque is caused. The percentage form is \(({{\Delta \tau } \mathord{\left/ {\vphantom {{\Delta \tau } {{\tau _{ave}}}}} \right. \kern-0pt} {{\tau _{ave}}}}) \times 100\%\).

After determining the test method of HSCS and speed regulation performance evaluation index, it is necessary to conduct Speed Control Characteristic Analysis of HSCS through experiments.

The analysis of speed control characteristics includes three aspects: analysis of valve-controlled cylinder transmission characteristics, steady-state speed control characteristics of hydro-viscous, and dynamic speed control characteristics of hydro-viscous. Firstly, the linear force driving characteristics of PVC are analyzed. Then, the steady-state and dynamic speed control characteristics and laws of hydro-viscous are analyzed in turn, and the steady-state and dynamic speed control characteristics under different working conditions are obtained respectively. Finally, based on the speed control law and characteristic index, a data-driven model describing input/output rotational speed, control oil pressure and lubricating oil temperature is established.

In this paper, the experimental research is carried out by the experimental platform of the hydro-viscous speed control system, which is composed of the hydro-viscous clutch and the proportional valve-controlled cylinder system. The input of the hydro-viscous speed control system is directly connected to the engine, and the output drives the fan to rotate for heat dissipation. By controlling the oil film thickness and adjusting the input and output speed ratio, the fan speed and torque are adjusted to complete the temperature control.

The working principle and control principle of the hydro-viscous speed control system experimental platform for special vehicles are shown in Fig. 9(a) and (b) respectively. The engine directly drives the friction pair of the hydro-viscous clutch to rotate. By controlling the output force of the proportional valve-controlled cylinder system, the friction pair gap is controlled, and then the adjustment of the fan drive speed and torque is completed.

Hydro-viscous speed control system from working principle to control principle. (a) Working principle. (b) control principle.

The experimental platform is composed of ZLMH-73 liquid-viscous clutch test platform shown in Fig. 10(a) and IP-PRZ-59-MP150 proportional valve test platform shown in Fig. 10(b).

Experimental platform of hydro-viscous speed control system for special vehicles.

The proportional valve-controlled cylinder system is composed of a proportional pressure reducing valve and a hydraulic cylinder, which generates the motion force of the friction plate of the hydro-viscous clutch. It is the oil film thickness control unit in the hydro-viscous clutch. The basic parameters of PVC currently used are shown in Table 1 below.

When the input rotational speed of the hydro-viscous clutch is zero and the clutch speed is adjusted, the force control curve of the proportional valve controlled cylinder is shown in Figs. 11 and 12, and the laws are basically the same.

Force control curve of PVC with zero input rotational speed.

Force control curve PVC in speed regulation process.

As it can be seen in Fig. 12: firstly, the control curve of pressure and force is a hysteresis loop curve with certain nonlinearity, but its nonlinearity is much smaller than that of the hydro-viscous clutch, which can be used as a linear element. Subsequently, the change of input rotational speed basically does not affect the force control characteristics of proportional valve controlled cylinder. Finally, pressure control range is 0–16 Bar, the actual effective control range is 0-6.2 Bar. Force control range is 0–10 KN, the actual effective control range is 0–4 KN.

When the hydro-viscous clutch is not fully combined (control less than 40%), the output pressure/force fluctuation is small. When the clutch is fully fitted, the output pressure/force fluctuation is large.

The steady-state speed control performance test and dynamic speed control characteristic test of the HSCS were carried out on the bench. The basic parameters are shown in Table 2 below.

The input rotational speed range is 1500 rpm-4500 rpm, according to the input rotational speed: 1500 rpm, 2000 rpm, 2500 rpm, 3000 rpm, 3500 rpm, 4000 rpm, 4500 rpm. At each speed gear, open loop steady-state speed control performance test and step response test are carried out, respectively.

When the input rotational speed is 4500 rpm, the control signal changes slowly from 0 to 38%, and the change period is 80s. The steady-state speed curve under open loop conditions is shown in Fig. 13.

Steady-state speed regulation curve at 4500 rpm input rotational speed.

Table 3 summarizes the control performance indices for an input rotational speed of 4500 rpm. The large hysteresis observed in the control domain, particularly during the descending phase, highlights the non-linear behavior of the system. This suggests that improvements in the control algorithm could significantly enhance system performance by reducing these non-linear effects.

Figure 14 shows the steady speed curves at other input rotational speeds. It shows that the open loop speed control performance of the HSCS is reflected as a large hysteresis nonlinear system. Its speed control characteristics are greatly affected by the input rotational speed and oil temperature. The specific speed control law is characterized as follows.

Steady-state speed regulation curve at different rotational speeds.

Firstly, the steady-state relationship between the control signal and the output speed is characterized by a large hysteresis curve with a saturated dead zone, and there is a large hysteresis loop.

Secondly, there is an obvious dead zone in the ascending process of speed control, accounting for about 38%. The characteristic curve is seriously nonlinear. When it is close to the saturation zone, the speed change is extremely severe, and the stability is poor, so it is difficult to implement closed loop control.

Thirdly, there is an obvious dead zone in the process of speed control decline, accounting for about 43%. The characteristic curve is seriously nonlinear. When it is just out of the saturation zone, the speed change is extremely severe, and the stability is poor, so it is difficult to implement closed loop control.

Fourthly, there is a large hysteresis loop in the characteristic curve, and the hysteresis loop in the middle of the curve is small. The closer to the dead zone of the ascending and descending phases, the larger the hysteresis loop will be. The maximum hysteresis loop in the high-speed section appears near the dead zone of the descending phase.

Finally, the characteristic curve is greatly affected by the input rotational speed. The specific performance is as follows. With the increase of the input rotational speed, the drag rotational speed and control domain increase significantly, the effective control domain increases, the control dead zone decreases, and the hysteresis increases first and then decreases.

The input rotational speed is kept at 4500 rpm so that the control signal changes step by step, the open loop dynamic response process is observed and recorded, and the corresponding dynamic performance indicators are analyzed.

To analyze the dynamic response characteristics of HSCS, the oil pressure control signal is changed step by step when the engine input rotational speed is constant, and the response characteristics of the hydro-viscous output speed are tested.

Oil pressure control signal step 0–15% response curve is shown in Fig. 15.

Step response curve of different control signals.

The control signal step 0–15% response curve is shown in Fig. 15(a). In Fig. 15(a), the ascending time is 9.8s and the descending time is 14.1s.

The response curve of the control signal step 0–20% is shown in Fig. 15(b). According to Fig. 15(b), the ascending time is 4.6s and the descending time is 15.3s.

The control signal step 0–50% response curve is shown in Fig. 15(c), According to Fig. 15(c), the ascending time is 3.1s and the descending time is 20.9s.

Through the step response test of the above control signal, the following conclusions can be obtained:

Firstly, there is a significant difference between the upper step and the lower step of the control signal in the response process of the output speed of the hydro-viscous clutch. The ascending time of the speed is obviously faster than the descending time of the speed, that is, the combination process of the hydro-viscous clutch is obviously faster than its detachment process.

Secondly, the valve-controlled cylinder drive is a single-acting process. The friction plate of the hydro-viscous clutch can be combined quickly by the valve-controlled cylinder drive, but the detachment process depends on the lubricating oil pressure, and the friction plate is separated slowly due to the low oil pressure.

Finally, affected by load inertia, the dynamic response of HSCS is slow, not high dynamic fast response process, the fastest response time is greater than 3s, so the closed loop control cycle should not be too fast.

The experimental analysis of HSCS revealed significant differences between the steady-state and dynamic speed control characteristics. In steady-state conditions, the system exhibited a large hysteresis loop, particularly during the descending phase, indicating a non-linear response to control inputs. In dynamic conditions, the response time varied significantly depending on the control signal, with faster engagement times compared to disengagement. These findings suggest that the system’s control strategy needs to be optimized to reduce hysteresis and improve response times, particularly under varying load conditions.

This study has successfully modeled and analyzed the speed control characteristics of HSCS, providing insights that can be used to optimize its design. In this paper, to analyze the speed regulation control characteristics of HCSC (including the steady-state speed control characteristics and the dynamic speed control characteristics) and obtain the specific characteristic parameters, the friction states of the active friction plate and driven friction plate in the working process are divided into four types: fluid lubrication, mixed friction, boundary friction and static friction. Therefore, the comprehensive model of HSCS is established. According to the system model, the multi-region formation mechanism of HSCS is analyzed, which provides a basis for the comprehensive modeling and control method design. After the evaluation index of speed control performance is determined, through the characteristic analysis experiment of HSCS, the characteristics and laws of steady-state and dynamic speed control of HSCS are analyzed in turn. Moreover, the characteristics of steady-state and dynamic speed control under different working conditions are obtained, respectively. Then according to the speed control law and characteristic index, a data-driven model is established, which describes input/output rotational speed, control of pressure and temperature of oil. Finally, the effective pressure control range of HSCS is 0-6.2 Bar. The effective control range of force control is 0–4 KN. The fastest response time is more than 3s. The above conclusions are helpful to further reveal and obtain the control characteristics and parameters of HSCS, to provide a basis for the structure and parameter optimization, which provides a basis for the structure and parameter optimization, performance evaluation and analysis of HSCS machinery and hydraulic system. However, the findings also highlight several areas that require further investigation. For example, the large hysteresis observed in steady-state speed control suggests that the current control strategy may not be optimal for all operating conditions. Future work should explore alternative control strategies, such as building a temperature speed dual loop speed control system, that minimize hysteresis and improve the system’s responsiveness under dynamic conditions.”

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request author on reasonable request.

Meng, Q. R. & Hou, Y. F. Mechanism of hydro-viscous soft start of belt conveyor. J. China Univ. Min. Technol. 18, 459–465 (2008).

Article Google Scholar

Mercorelli, P. & Werner, N. Integrating a piezoelectric actuator with mechanical and hydraulic devices to control camless engines. Mech. Syst. Signal Process. 78, 55–70 (2016).

Article ADS Google Scholar

Qu, S., He, T. & Zhu, G. G. Engine EGR valve modeling and switched LPV control considering nonlinear dry friction. IEEE/ASME Trans. Mechatron. 25, 1668–1678 (2020).

Article Google Scholar

Liao, X., Yang, S., Hu, D. & Gong, G. Analysis and revision of torque formula for hydro-viscous clutch. Energies. 14, 7884 (2021).

Article CAS Google Scholar

Cui, H., Lian, Z., Li, L. & Wang, Q. Analysis of influencing factors on oil film shear torque of hydro-viscous drive. Industrial Lubrication Tribology. 70, 1169–1175 (2018).

Article Google Scholar

Bullough, W. A., Johnson, A. R., Hosseini-Sianaki, A., Makin, J. & Firoozian, R. The electro-rheological clutch: design, performance characteristics and operation. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering. 207, 87–95 (1993).

Wang, Y., Qian, Q., Chen, G., Jin, S. & Chen, Y. Multi-objective optimization design of cycloid pin gear planetary reducer. Adv. Mech. Eng. 9, 1–10 (2017).

Google Scholar

Qin, Y., Gong, G., Wang, F. & Sun, C. Research on pressure control strategy of hydraulic system of hydro-viscous variable speed clutch. J. Harbin Eng. Univ. 41, 1377–1383 (2020).

Google Scholar

Qin, Y. F., Gong, G. G., Wang, F. & Sun, C. C. Displacement controller design for piston of hydro-viscous clutch based on RBF neural network. Chin. J. Eng. 26, 603–610 (2019).

Google Scholar

Su, Y., Zheng, C. & Mercorelli, P. Velocity-free friction compensation for motion systems with actuator constraint. Mech. Syst. Signal Process. 148, 107132 (2021).

Article Google Scholar

Zheng, C., Su, Y. & Mercorelli, P. Simple saturated relay non-linear PD control for uncertain motion systems with friction and actuator constraint. IET Control Theory Appl. 13, 1920–1928 (2019).

Article MathSciNet Google Scholar

Ba, K. et al. Bionic perception and transmission neural device based on a self-powered concept. Cell. Rep. Phys. Sci. 5, 102048 (2024).

Article Google Scholar

Ma, G. et al. Bioinspired, fiber-based, flexible self-powered sensor for wearable applications. Device 100508 (2024).

Xie, F. et al. Dynamic transmission of oil film in soft-start process of HVD considering surface roughness. Industrial Lubrication Tribology. 70, 463–473 (2018).

Article Google Scholar

Berglund, K., Marklund, P., Lundh, H. & Larsson, R. Prediction of driveline vibrations caused by ageing the limited slip coupling. Proc. Institution Mech. Eng. Part. D: J. Automobile Eng. 230, 1687–1698 (2016).

Article Google Scholar

Huang, J., Wei, J. & Qiu, M. Laminar flow in the gap between two rotating parallel frictional plates in hydro-viscous drive. Chin. J. Mech. Eng. 25, 144–152 (2012).

Article Google Scholar

Shaw, S. W., Rosenberg, S. & Shoshani, O. A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators. Nonlinear Dyn. 111, 3969–3979 (2023).

Article Google Scholar

Shi, Y. & Zhou, J. Stability and sensitivity analyses and multi-objective optimization control of the hydro-turbine generator unit. Nonlinear Dyn. 107, 2245–2273 (2022).

Article Google Scholar

Song, Y. H. et al. Study on nonlinear dynamic behavior and stability of aviation pressure servo valve-controlled cylinder system. Nonlinear Dyn. 108, 3077–3103 (2022).

Article Google Scholar

Ba, K. et al. A compensation strategy of end-effector pose precision based on the virtual constraints for serial robots with RDOFs. Fundamental Res. https://doi.org/10.1016/j.fmre (2024).

Article Google Scholar

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This research was supported the by the National Natural Science Foundation of China (52475072 and 52475071), the National Natural Science Foundation of China (51975506 and 52122503), and the Natural Science Foundation of Hebei Province (E2022203002 and E2024203244).

School of Mechanical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei, China

Yuan Wang, Kaixian Ba, Bin Yu, Xiang Feng, Wenpeng Zou & Feiyue Gao

Propulsion System Technology Department, Beijing Institute of Technology, Beijing, 100081, China

Kai Zhao, Shoukun Wang, Lin Zhang & Liang Wang

China North Vehicle Research Institute, Beijing, 100081, China

Kai Zhao

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Y.W., K.B., and K.Z. conceived the idea, designed the experiments, and analyzed the data. S.W., B.Y., W.Z., F.G., Y.W., and K.B. helped with the experiments and provided some advice. L.Z., K.B., and L.W. wrote and revised the manuscript, Y.W. and X.F. supplemented the contents and experiments in the manuscript. All authors contributed to the paper.

Correspondence to Kaixian Ba or Kai Zhao.

The authors declare no competing interests.

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Wang, Y., Ba, K., Zhao, K. et al. Characteristic analysis method for integrated multi-parameter hydro-viscous speed control system. Sci Rep 14, 27346 (2024). https://doi.org/10.1038/s41598-024-77274-0

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Received: 03 January 2024

Accepted: 21 October 2024

Published: 09 November 2024

DOI: https://doi.org/10.1038/s41598-024-77274-0

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