Development of CDC Shock Absorber Design Software

Abstract

In response to the low design efficiency caused by the numerous design parameters of existing shock absorbers, this research presents the design of an efficient software tool for obtaining the external characteristics of Continuous Damping Control (CDC) shock absorbers. Firstly, a mathematical model for the damping force of the shock absorber was established based on principles from fluid dynamics, elasticity mechanics, and throttle orifice models in the rebound and compression valve systems. Secondly, a Graphical User Interface (GUI) was developed to visualize the external characteristics and conduct simulation studies of the CDC shock absorber. Finally, experiments were performed on a shock absorber test bench to validate the external characteristics of the CDC shock absorber using initial structural parameters. The GUI software interface enables direct adjustment of the shock absorber's structural parameters and signal excitation, thereby enhancing the practical efficiency of the shock absorber. A comparison between simulation and experimental results reveals that the relative error rate is generally high when the velocity amplitude is 0.052m/s, with a maximum relative error rate of 24.44%. For other excitation velocity amplitudes, the relative error rate remains within 10%. This demonstrates the high accuracy and reliability of the established mathematical model for the CDC shock absorber, providing a solid theoretical foundation for studying the shock absorber's external characteristics.

1 Introduction

In recent years, with the progress of science and technology and the improvement in living standards, the demand for vehicles has gradually improved, and the automotive industry has also witnessed rapid development. Due to these factors, the smoothness of driving as an important investigation index for automotive performance has received extensive attention from people [1]. Research results show that strong vibration will not only lead to fatigue damage of important parts of the vehicle, reduce the service life, reliability, and driving safety of the vehicle, but also seriously damage human organs [2,3,4]. Therefore, vibration shock absorbers are widely used in the design of various types of vehicles to provide good smoothness in various complex dynamic environments. Passive shock absorbers are still widely used because of their low cost and simple structure [5]. However, this type of shock absorber has the obvious disadvantage that its external characteristics (damping characteristics) are fixed and cannot be adapted to different road conditions [6]. Active shock absorbers need to be equipped with high-precision servo devices, sensors, complex control systems, and additional power sources, which are costly and consume a lot of energy, therefore reducing the performance of the whole vehicle [7]. The viscosity of the “current fluid” and “magnetorheological fluid” of the electrodynamic and magnetorheological shock absorbers, which are adjustable, can be changed according to the strength of the physical field, and therefore the damping force can be continuously adjusted [8,9,10]. Continuous Damping Control (CDC), as a kind of semi-active shock absorber, can theoretically realize any damping force within the working interval formed by the maximum and minimum damping force and can achieve continuous adjustment, which is a more advanced kind of shock absorber in semi-active shock absorber. In recent years, some domestic enterprises and scientific research institutes have conducted research on CDC shock absorber, but due to the late start and weak technology, many of them are still in the initial stage of research, and the research literature is relatively small. A lot of key technologies have not yet been solved, nor have reliable products been launched for the market [11]. The external characteristic curve, also known as the damping characteristics curve, is the most important indicator of the shock absorber performance, which can judge the shock absorber performance comprehensively, and is also an important part of the characteristic parameters of the vehicle suspension system [12]. Therefore, in this paper, a graphical user interface (GUI) with MATLAB/Simulink simulation tool and visualization function is used to visualize the external characteristics of the CDC shock absorber, which can help shock absorber developers to design and analyze the CDC shock absorber. It is of great significance to improve the design efficiency of the shock absorber and to reduce the research and development time and cost.

2 Establishment of Mathematical Model of CDC Shock Absorber Damping Force

2.1 CDC Shock Absorber

The CDC shock absorber studied in this paper is shown in Fig. 1. The normal working process of the shock absorber is to switch back and forth between the recovery stroke and the compression stroke, while the oil is circulated inside the shock absorber. During the circulating work, the fluid is throttled by the valve holes to form the damping force of the shock absorber, which cuts down the excitation from the road surface to the frame or body, and improves the smoothness, stability, and comfort of the vehicle, and then through the control valve to change the throttling effect of the valve holes according to the size of the different control currents to control the shock absorber's work performance to achieve the desired effect.

Fig. 1

CDC shock absorber structure diagram

1-plastic cover; 2-guide oil seal assembly; 3-inner cylinder barrel normally open throttle hole; 4-intermediate chamber; 5-reservoir chamber; 6-outer cylinder barrel; 7-Limit ring; 8-Piston; 9-Extension valve; 10-CDC control valve assembly; 11-Bottom valve assembly; 12-Piston rod; 13-Working cylinder rod chamber; 14-Intermediate cylinder; 15-Inner cylinder (working cylinder); 16-Flow valve support; 17-Flow valve plate and flow valve adjusting spring; 18-Extension valve adjusting spring; 19-Extension valve adjusting nut; 20-Rodless chamber of working cylinder; 21-Fixed lugs.

2.2 CDC Shock Absorber Working Stroke Oil Flow Modelli

The CDC shock absorber in the recovery stroke of the working process of the oil flow through the piston assembly, the bottom valve assembly and the CDC control valve assembly and other structures as a series–parallel connection of different valves and throttle orifices, to facilitate the analysis and understanding of the problem, and then build a mathematical model of the CDC shock absorber damping force, such as Fig. 2 for the recovery stroke of the oil circulation diagram.

Fig. 2

CDC shock absorber recovery stroke oil circulation path diagram

S1-working cylinder rodless chamber; S2-working cylinder rodded chamber; S3-intermediate cylinder inner chamber; S4-oil reservoir chamber; a-compensation valve; b-extension valve; c-Rod chamber of the working cylinder; d-Stacked valve disc; d1-Stacked valve disc constant throttling orifice; d2-Stacked valve disc variable flow throttling orifice; e-Valve disc constant throttling orifice (through-hole I); f-Valve spool adjustable flow orifice; g-pilot valve constant flow throttling orifice (through hole II); h-equivalent relief valve; k-CDC shock absorber control valve; y-equivalent adjustable relief valve.

Similarly, through the compression stroke working process of the oil through the piston assembly, bottom valve assembly and CDC control valve assembly, and other structures such as different valves and throttle orifice series–parallel connection, you can get the compression stroke oil circulation path.

2.3 CDC Shock Absorber Damping Force Modelling

Since the recovery stroke of the CDC shock absorber is modeled along roughly the same lines as the compression stroke, only the recovery stroke will be analyzed later.

Since the shock absorber will have multiple valves and throttle ports during a single operating cycle under normal operating conditions, forming a series–parallel oil circuit, assuming that the total pressure loss in series and parallel is $\Delta p_{c,z}$, $\Delta p_{b,z}$, and the total flow rate is $Q_{c,z}$, $Q_{b,z}$, respectively, and if there are n series-connected throttle ports, with the same flow rate through each of them, then the total pressure loss is the sum of the pressure loss of each throttle port, i.e.

$$\left\{ \begin{gathered} Q_{{c,z}} = Q_{{c,1}} = Q_{{c,2}} = \cdots = Q_{{c,n}} \hfill \\ \Delta p_{{c,z}} = \Delta p_{{c,1}} + \Delta p_{{c,2}} + \cdots + \Delta p_{{c,n}} \hfill \\ \end{gathered} \right.$$

(1)

With n throttle ports in parallel, the pressure difference between the two sides of each throttle is equal and the total flow rate is equal to the sum of the flow rates of the individual throttles, i.e.:

$$\left\{ \begin{gathered} Q_{b,z} = Q_{b,1} + Q_{b,2} + \cdots + Q_{b,n} \hfill \\ \Delta p_{b,z} = \Delta p_{b,1} = \Delta p_{b,2} = \cdots = \Delta p_{b,n} \hfill \\ \end{gathered} \right.$$

(2)

The modeling of the throttle orifices in each valve system for the shock absorber recovery and compression stroke is too lengthy and can be accomplished by combining fluid and elastic mechanics, so it will not be repeated here.

When the piston rod is given a speed of movement, it will drive the piston and the internal oil flow of the shock absorber, the oil through the various valve groups and holes for throttling the formation of damping force, according to the law of conservation of flow, the total amount of oil inflow and outflow from the various chambers remains unchanged, which is the basic idea for the establishment of the mathematical model of damping force of CDC shock absorber.

• 1. When $\Delta p_{h} \le \Delta p_{h\max }$ in the equivalent relief valve

At this time, the equivalent relief valve is not open, assuming that the damping fluid is incompressible, the fluid density is uniformly distributed, ignoring the effect of temperature on the viscosity of the fluid, etc., so the shock absorber in the work of the tandem oil circuit in the oil through each throttle hole, in turn, is equal to the flow rate, and the total amount of fluid in the shock absorber is unchanged, and the flow rate of $Q_{c}$ is due to the piston and rod to do the restoration of the movement when squeezing the rod cavity fluid due to the result of the so that it can be obtained:

$$Q_{c} = (A_{piston} - A_{rod} )v_{f} = \frac{{\uppi (d_{piston}^{2} - d_{rod}^{2} )}}{4}v_{f}$$

(3)

where: $Q_{c}$- the flow rate through the normally open throttle orifice of the rod chamber of the working cylinder; $A_{piton}, A_{rod}$-Area of piston and piston rod; $v_{f}$-Velocity of the piston when it is in recovery motion; $d_{piton} d_{rod}$-Diameter of piston and piston rod.

Since $\Delta p_{h} \le \Delta p_{h\max }$ when the flow $Q_{h} = 0$, at this time in the shock absorber internal oil circulation path in the overall general direction can be regarded as a series oil circuit.

so $Q_{c} = Q_{d} = Q_{d1} + Q_{d2} = Q_{y} = Q_{e} = Q_{f} = Q_{g} = \frac{{\uppi (d_{piston}^{2} - d_{rod}^{2} )}}{4}v_{f}$, the following relationship can be obtained by associating $\Delta p_{c}$, $\Delta p_{d}$, $\Delta p_{e}$, $\Delta p_{f}$, $\Delta p_{g}$, and stacking the differential pressure $\Delta p_{c}$, $\Delta p_{d}$, $\Delta p_{e}$, $\Delta p_{f}$, $\Delta p_{g}$ to get the differential pressure between the rod chamber and the oil storage chamber $\Delta p_{24}$. In the recovery stroke of the shock absorber, due to the existence of the rod, the oil in the rodless chamber increases more than the oil in the rod chamber decreases more than $\frac{{\uppi d_{rod}^{2} }}{4}x_{f}$, while the total oil inside the shock absorber remains unchanged, to prevent the occurrence of air travel distortion phenomenon and excessive differential pressure during the working process, the internal part of the shock absorber has to be filled with a certain amount of nitrogen, and the volume of nitrogen increases. Therefore, the volume of nitrogen increases during the recovery stroke $\frac{{\uppi d_{rod}^{2} }}{4}x_{f}$, which can be obtained from the following equation:

$$P_{{N_{2} }} V_{{N_{2} }}^{n} = P_{4} \left(V_{{N_{2} }} + \frac{{\uppi d_{rod}^{2} }}{4}x_{f} \right)^{n}$$

(4)

Due to the smaller throttling effect of the compensating valve, it is known that the rodless cavity pressure $P_{1} = P_{4}$, viz.

$$P_{1} = \left( {\frac{{V_{{N_{2} }} }}{{V_{{N_{2} }} + \frac{{\uppi d_{rod}^{2} }}{4}x_{f} }}} \right)^{n} P_{{N_{2} }}$$

(5)

where: $P_{1}$-Pressure in rodless cavity; $V_{{N_{2} }}$-Initial volume of nitrogen inside the shock absorber; $P_{{N_{2} }}$-Initial pressure of nitrogen inside the shock absorber; $n$-Multivariate index; $x_{f}$-Displacement of the piston rod movement during the recovery stroke.

In summary, an expression for the damping force of the shock absorber during the recovery stroke can be established as:

$$\begin{gathered} F_{fuyuan} = \Delta p_{21} A_{piston} - P_{2} A_{rod} \hfill \\ \;\;\;\;\;\;\;\;\; = \Delta p_{21} A_{piston} - (P_{2} - P_{1} + P_{1} )A_{rod} \hfill \\ \;\;\;\;\;\;\;\;\; = \Delta p_{21} A_{piston} - (\Delta p_{21} + P_{1} )A_{rod} \hfill \\ \end{gathered}$$

(6)

Since it is known that $\Delta p_{24}$, and $\Delta p_{24} \approx \Delta p_{21}$. .(2.58) Substituting (2.59) the mathematical model of the damping force at the recovery stroke when $\Delta p_{h} \le \Delta p_{h\max }$ in the equivalent relief valve can be obtained.

2. When $\Delta p_{h} { > }\Delta p_{h\max }$ in the equivalent relief valve.

When the pressure reaches the equivalent relief valve opening threshold $\Delta p_{h\max }$, the valve disc opens a certain amount of $f_{h}$, and the oil begins to overflow.

so $Q_{c} = Q_{d} = Q_{d1} + Q_{d2} = Q_{y} = Q_{e} + Q_{h} = Q_{f} + Q_{h} = Q_{g} + Q_{h} = \frac{{\uppi (d_{piston}^{2} - d_{rod}^{2} )}}{4}v_{f}$, solving the joint equation for $\Delta p_{c}$, $\Delta p_{d}$, $\Delta p_{e}$, $\Delta p_{f}$, $\Delta p_{g}$, and the same will be the pressure difference $\Delta p_{c}$, $\Delta p_{d}$, $\Delta p_{e}$, $\Delta p_{f}$, $\Delta p_{g}$ superposition of the differential pressure between the rod chamber and the oil storage chamber can be obtained $\Delta p_{24}$, and then use the same method of calculating the recovery stroke damping force model in the equivalent relief valve at $\Delta p_{h} \le \Delta p_{h\max }$, to derive a mathematical model of the recovery stroke damping force when the equivalent relief valve at $\Delta p_{h} { > }\Delta p_{h\max }$.

3 Visualisation of the External Characteristics of the Shock Absorber

3.1 Implementation of Simulation Flow and Operation Interface

Based on the mathematical model of shock absorber recovery and compression stroke established above, its damping force simulation model can be constructed using MATLAB/Simulink software.

As shown in Fig. 3, the flow chart of the simulation of the external characteristics of the CDC shock absorber is shown. Firstly, the geometrical (structural) parameters of the shock absorber structure and the fluid parameters are given and the excitation motion parameters are also given, the speed of the piston rod ($v$) is used to judge whether the shock absorber is in the recovery stroke or the compression stroke; secondly, according to the magnitude of the relationship between $\Delta p_{h}$ and $\Delta p_{h\max }$(whether the equivalent relief valve is open or not), the damping force solution is carried out for the four cases, and the data are obtained to draw the external characteristic diagrams.

Fig. 3

Simulation flow chart of external characteristics of CDC shock absorber

Due to the complex structure of the CDC shock absorber model and a large number of design parameters, the actual tuning process is cumbersome and prone to errors, and the simulation output results are not intuitive, so it is necessary to process and plot the obtained simulation data to obtain the external characteristic curve diagram. For this reason, the next section will deal with this problem.

As shown in Fig. 4, the flowchart of the visualisation of the external characteristics is implemented, and the design of the manipulation interface and the writing of the callback functions are carried out with the Simulink simulation model of the shock absorber built out.

Fig. 4

Flow chart for visualisation of external characteristics

As shown in Fig. 5, a layout editor view of the visual control interface for the external characteristics of the shock absorber was created using GUIDE. The following five types of controls are used in the design of the control interface:

Fig. 5

GUI control interface design

Static text controls (Text): such as “Continuous Adjustment of Current”, “Piston Diameter”, “Piston Rod Diameter”, etc. in the interface; Edit box controls (Edit): here, the callback function is used to write the initial geometric structure parameters, the excitation signal and the oil parameters of such shock absorber as the default values. The Edit Box control (Edit): In the Edit Box, the callback function is used to write the initial geometrical structure of the shock absorber, the excitation signal under normal conditions, and the oil parameter values as the default values, so that when running the program, all the editable textboxes will have the values, which is convenient for adjusting the parameters and prompting for the initial structural parameters of the shock absorber; Push Button Controls (Push Button): For example, the Push Button Controls (Push Button) can be used to adjust the parameters of the shock absorber. Push Button: Push buttons such as “Start Simulation”, “Save Diagram”, “Exit”, etc.; Panel: A panel such as “Menu Bar”, which is used to illustrate that different functions in the menu can be selected for the application. Axes: The Axes control is used to visualise the external characteristics of the vibration shock absorber by plotting the power diagrams and the velocity characteristic curves respectively.

Finally, after the control interface is designed, it needs to be supported by corresponding callback functions, i.e., a callback function is associated with a process in advance, so that when the process is running, it can be called on the preset callback function and used to activate other processes, and the callback functions are different for different controls.

3.2 Visual Simulation of External Characteristics

Click Run in the designed GUI interface to enter the execution page of the program, at this time, the blank editable text box is automatically embedded in the initial default value of the callback function compilation, and then click the “Choosefile” button to select the Simulink simulation model that needs to be simulated, and then enter the size of the signal value that needs to be simulated, and then click the “Start Simulation” to simulate. After that, click the “Choosefile” button to select the Simulink simulation model to be simulated, and then input the size of the signal value to be simulated as needed, and then click the “Start Simulation” button to start the simulation. The external characteristic curve will be drawn automatically and displayed in the graphic plotting area, thus realising the visualisation of the external characteristics of the CDC shock absorber. If the oscilloscope corresponding to the damping force of the Simulink shock absorber is opened while the programme is running, the effect of some parameter adjustments on the damping force can be observed in real time. As shown in Fig. 6, the maximum speed is $0.524{\text{m/s}}$, the working stroke is ${ - 0}{{.05m\sim + 0}}{\text{.05m}}$, and the input current values are 0A, 0.3A, 0.6A, 0.9A, 1.2A, and 1.5A, respectively, for the visualisation of the external characteristics of the simulation.

Fig. 6

GUI simulation diagram for visualisation of external characteristics

From the velocity characteristic curve in Fig. 6, it can be seen that the recovery and compression stroke is mainly divided into two stages, the first stage is: when $\Delta p_{h} \le \Delta p_{h\max }$, that is, the equivalent relief valve did not carry out the overflow effect, the oil pressure rises more steeply; when $\Delta p_{h} { > }\Delta p_{h\max }$, the equivalent relief valve opens, and begins to overflow part of the oil resulting in the slowing down of the rate of rise of the damping force, this is the second stage.

4 CDC Shock Absorber External Characteristics Experiment

In this paper, the experimental rig for the external characteristics of the CDC shock absorber mainly includes mechanical structure, hydraulic system and electrical control system. The mechanical structure is mainly used to fix the shock absorber, actuator and sensors; the hydraulic system is mainly used to make the actuator produce excitation with different frequencies and amplitudes; and the electrical control system is mainly responsible for the processing of the signals.

According to the cartridge shock absorber bench test requirements, before the test, the CDC shock absorber to be tested needs to stand for at least 6 h at a temperature of 20 ± 3 °C, and five exhaust processes are completed under the test conditions of a stroke of ± 50 mm and an excitation frequency of 1.67 Hz (0.524 m/s). Afterwards, in the recovery of the maximum stroke of 0.05 m, i.e., the excitation amplitude is limited to ± 50 mm, the frequency is 0.166 Hz, 0.417 Hz, 0.815 Hz, 1.67 Hz, respectively, and the corresponding excitation of the speed amplitude of 0.052 m/s, 0.131 m/s, 0.256 m/s, 0.524 m/s respectively under the conditions of the control valve, the measured drive current of each drive current ( 0A, 0.3A–1.2A, 1.5A) under the corresponding damping force and piston rod speed experimental data, as shown in Fig. 7.

Fig. 7

The relationship between current-piston rod speed-damping force

From the figure can be obtained, at the same speed, the damping force with the increase in the value of the current and reduce;damping force and piston rod speed of the relationship have a common feature, that is, the control valve under the drive current of the damping force and the corresponding piston rod speed have a clear turning point, turning point after the damping force increase rate decreases, here the turning point for the equivalent relief valve relief pressure due to unloading. However, in general, the damping force increases with the increase of piston rod speed for the same drive current. Based on the experimental data measured in Fig. 7, the relative error rates are calculated as shown in Tables 1, 2, 3, 4, compared with the simulation data of the relationship between piston rod speed and damping force under different control current conditions in Fig. 6.

Table 1 Comparison of experimental and simulated damping forces when the velocity amplitude is 0.052 m/s

Table 2 Comparison of experimental and simulated damping forces when the velocity amplitude is 0.131 m/s

Table 3 Comparison of experimental and simulated damping forces when the velocity amplitude is 0.256 m/s

Table 4 Comparison of experimental and simulated damping forces when the velocity amplitude is 0.524 m/s

From the above table, it can be seen that the relative error rates between the experimental data and the simulation data are generally large when the excitation velocity amplitude is 0.052 m/s, and the largest relative error rate reaches 24.44%. At other excitation speed amplitudes, the relative error rate is below 10%, and the relative error rates of the simulation and experimental results are within the acceptable range, so it can be shown that the mathematical model of the vibration shock absorber has a high accuracy and reliability. From the above table, it can be seen that, due to the neglect of some influencing factors during the mathematical modeling of the damper damping force, the peak values of the recovery and compression damping forces obtained from the simulation are smaller than those obtained from the experiments, e.g., the friction force between the piston and the working cylinder inside the damper. In addition, the gap between the piston rod guiding fixture and the piston rod on the experimental bench is small, which is easy to cause the eccentricity of the piston rod when the actuator vibrates up and down, resulting in the friction force, especially when the velocity amplitude is 0.052 m/s, the denominator is very small, the numerator is unstable, and the friction force is stronger, which is very easy to cause a large relative error, and the friction force increases as the velocity increases and the control current decreases, the friction force increases, and the friction force increases as the control current decreases. As the speed increases and the control current decreases, the damping force increases and the relative role of friction is weakened, so most of the relative error rate values in the table tend to decrease as the speed increases and the current decreases.

5 Summary

• (1) Based on the structure and working principle of the CDC shock absorber, the oil flow model during the recovery and compression strokes is established. The mathematical model of the damping force of the CDC shock absorber based on the structural parameters is derived according to the opening and closing states of the equivalent relief valve during the working process of the shock absorber, and then the simulation model of the CDC shock absorber is finally constructed.

• (2) Based on the established Simulink model, the design and implementation of the Graphical User Interface (GUI) of the external characteristics are completed, in which the external characteristic curves corresponding to any structural parameter values of the damper under different operating conditions can be obtained directly through the adjustment of the parameters. At the same time, it is also possible to use the GUI to analyze the influence of structural parameters such as the diameter of the pilot valve constant hole and the diameter of the regulating valve plate on the external characteristics of the CDC shock absorber, which is conducive to the design and analysis of the CDC shock absorber by the damper developers, and it improves the efficiency of the design of the damper and reduces the cost of the R&D time, which is important for the research and development of the damper.

• (3) In order to verify the accuracy of the mathematical model of shock absorber damping force and the reliability of the visualisation software design, the initial structural parameters of this type of CDC shock absorber were tested using the shock absorber experimental rig, and the experimental results showed that the relative error rates between the simulation and the experimental results were within the acceptable range, which demonstrated that the visualisation of the external characteristics can be used for the design and analysis of CDC shock absorber, thus improving the design efficiency. The results show that the visualisation of external characteristics can be used for the design and analysis of CDC shock absorber, thus improving the design efficiency.