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Abstract

The ride comfort is a key research area for the quality improvement of railway vehicles. Several control methods have been developed to improve the ride comfort, in which the semi-active control approach inherits the advantages of passive and active control approaches. However, the semi-active control may perform ineffectively in vibration attenuation when the carbody load changes. To address this issue, we proposed a novel hybrid control method that combines the skyhook (SH) and displacement velocity (DV) control methods to reduce vibrations of the carbody in the lateral direction under carbody load changes. First, a hybrid control model built in Matlab software was applied to a quarter railway vehicle model for a preliminary assessment of the ride comfort. Second, to provide a more comprehensive evaluation, the proposed model was applied to a whole railway vehicle model using co-simulation (Matlab-Simpack). In the quarter model, under the sinusoidal excitation, the hybrid control showed a lower acceleration by 48.5% and 42.8% when the carbody load reduced to a half and a quarter, respectively, compared to the passive control. This finding was confirmed with the whole model. Moreover, in the whole model, under the track irregular excitation, the hybrid control showed a lower acceleration by 26.6% and 17.4% when the carbody load reduced to a half and a quarter, respectively. Further, the proposed method showed an acceptable safety level, measured by the derailment coefficient (0.0743 at a half load and 0.089 at a quarter load). In conclusions, the proposed hybrid SH-DV control exhibits high robustness, adaptability, effectiveness, and acceptable safety level in response to variations in body load.

Keywords

Hybrid control railway vehicle ride comfort semi-active control vibration control

Introduction

Railway vehicles form the backbone of efficient transportation systems, serving to drive economic development, alleviate urban mobility challenges, and foster social connectivity.¹ The continuous expansion in operation speed and carbody’s load of the railway vehicle warrants the enhancement of the ride comfort and safety level. As a conventional approach, the passive control of the suspension system has been commonly used because of its robustness, simplicity, reliability, and cost-effectiveness in suppressing vibrations of the carbody derived from the rail track irregularities. However, this approach mainly utilizes a fixed damping coefficient, which might be ineffective when working within a wide range of vibration frequencies.² The drawbacks of passive control can be addressed with the active control approach,^3–5 which has an excellent control performance and robustness in improving the ride comfort of the railway vehicle. However, this advanced approach also exists several limitations, such as high costs, high energy consumption, structural complexity, demanding maintenance requirements, and weight and space constraints.⁶ As a potential alternative for the two methods mentioned above, the semi-active control suspension approach offers several advantages over passive suspension systems while mitigating some of the drawbacks of active suspension systems, including high cost-effectiveness, simple structures, high reliability, low energy consumption, and easy integration into existing infrastructure.⁷ In previous studies, the semi-active control method has been applied in various suspension system of railway vehicles, such as electrorheological (ER) damper equipment by Hoseinzadeh et al.,⁸ hydraulic damper equipment by Ripamonti et al.,⁹ and magnetorheological (MR) damper equipment by Kim et al.⁷ and Sharma et al.¹⁰ Among the semi-active suspension systems, the magnetorheological damper (MRD) stands out as the most effective semi-active damper due to their ability to rapidly adjust damping force in response to changeable track conditions. In addition, the MRD provides a wide range of damping coefficients from soft to stiff damping under the change of external magnetic field.¹¹

Many semi-active control algorithms have been deployed to MR damper of railway vehicle suspension system to suppress undesirable vibrations, which can be divided into two main approaches. The first approach referred to as the singular control approach includes conventional control methods (e.g., skyhook (SH),¹² acceleration-driven-damper (ADD),¹³ and displacement velocity (DV)¹⁴ controls) and intelligent control methods (e.g., fuzzy logic control¹⁵ and neural network^16,17 controls). The conventional methods of singular control approach may work ineffectively in a wide range of vibration excitation frequencies. For instance, SH control is effective only at low frequencies, whereas ADD or DV can work well only at high frequencies. On the other hand, the intelligent control methods of singular control approach offer higher effectiveness in vibration isolation; however, they have several limitations, including high costs, and a requirement of extensive experimental data collection. The second approach involves the combination of various singular control methods, such as SH-DV,¹⁴ SH-ADD,¹⁸ and self-adjusting hybrid damping (SAHDC) control.¹⁹ This approach not only inherits the strengths of singular control methods but also mitigates their individual weaknesses, that is, ability to work effectively in a wide range of vibration excitation frequency. However, the mixed control approach may show limited performance in vibration isolation under the carbody’s load changes. In this study, we pointed out this issue through simulation results of a mixed SH-DV control theory¹⁴ applying into a quarter railway vehicle model when the carbody load reduces to a quarter of the full load as shown in Figure 1. Therein, the ride comfort of the carbody was evaluated using the transmissibility of carbody acceleration. Specifically, at low frequencies, the mixed SH-DV control method only reached approximately 70% of the asymptotic effectiveness that could be achieved with the SH control. In contrast, at high frequencies, this method achieved approximately 90% of the asymptotic effectiveness of DV control. The ineffectiveness of the mixed SH-DV control might be attributable to inaccurate transition point of control states under the carbody load changes.

Figure 1.

Transmissibility characteristic curves for several commonly used control methods at a quarter of the full carbody load.

To overcome this limitation, we proposed a hybrid SH-DV control with two transition points of control states, corresponding to three control regions: SH for low frequencies, DV for high frequencies, and mixed SH + DV control for frequencies in response to the carbody load changes. This approach can adapt to a wide range of the carbody load changes while inheriting the advantages of individual control methods. The effectiveness of this proposed control in improving the ride comfort was verified using a whole railway vehicle model in Simpack in conjunction with a hybrid control model in Simulink (i.e., co-simulation).

Analysis railway vehicle model

Modeling

Two numerical models that represent real railway vehicles were employed to verify our proposed hybrid control theory at different carbody loads: (1) a quarter railway vehicle model and (2) a whole railway vehicle model. The ride comfort was evaluated preliminarily in the quarter model and more precisely in the whole model under the vibration excitation following a sinusoidal function. To be close to the real-world application, the track irregularity was also applied to the whole model and provided a more comprehensive evaluation of the ride comfort and the running safety level.

Quarter railway vehicle model

For ease of implementation, a quarter railway vehicle model was used to provide a primary evaluation of the proposed hybrid control method on the ability of vibration isolation, using Simulink/Matlab. A quarter model (often referred to as a static model) is a simple model that has been widely used in numerical simulation in transportable vehicle research. It includes primary and secondary lateral suspension systems, in which the former contains a spring and the latter consists of a spring and a damper. Yang et al.¹⁴ built a simplified quarter railway vehicle model (as shown in Figure 2) that ignores the node stiffness in the design of the control strategy due to the large value of the node stiffness and derived the model’s dynamic equations¹⁴ to form equation (1). This paper used this simplified quarter model, given that it focused on impacting the damping coefficient only rather than the stiffness. The ride comfort was thus assumed to behave similarly for different values of suitable stiffness under the change of the damping coefficient. The proposed control method was then applied to the whole model to provide a more comprehensive and precise evaluation in terms of vibration attenuation ability and running safety level. The basic parameters of the passive lateral suspension system for the railway vehicle used in this study of equation (1) are provided in Table 1.

{\begin{cases} m_{c} {\ddot{y}}_{1} + k_{1} (y_{1} - y_{2}) + c_{1} ({\dot{y}}_{1} - {\dot{y}}_{2}) = 0 \\ m_{t} {\ddot{y}}_{2} - k_{1} (y_{1} - y_{2}) - c_{1} ({\dot{y}}_{1} - {\dot{y}}_{2}) + k_{2} (y_{2} - y_{w}) = 0 \end{cases}

(1)where y₁, y₂, and y_w are lateral displacements of the carbody, bogie, and track, respectively.

Figure 2.

Simplified quarter model of railway vehicle.

Table 1.

Parameters of the quarter railway vehicle model.

Parameters	Value	Unit
Mass of quarter carbody, m_c	9308	kg
Mass of half bogie, m_t	1981	kg
Lateral stiffness of the secondary suspension, k₁	9 × 10⁵	N·m⁻¹
Lateral damping of the secondary suspension, c₁	2 × 10⁴	Ns·m⁻¹
Lateral stiffness of the primary suspension, k₂	15.69 × 10⁶	N·m⁻¹

Whole railway vehicle model

Based on the preliminary results from the simplified quarter model, the hybrid control method was further evaluated in the whole railway vehicle model, which can reflect the impacts of vertical and longitude suspension systems, the running speed, and excitations in different directions (e.g., vertical, gauge, and roll excitations). This model (often referred to as a dynamic model) built in Simpack software has been used in many studies to replace the real railway vehicle, given that the simulation results from the whole railway vehicle are shown to be close to experimental results. Figure 3 shows the whole railway vehicle model, including one carbody, two bogies, and four wheelsets. They are connected by primary and secondary suspension systems, which consist of springs, air springs, rubbers, torsion bars, and dampers in the vertical, lateral, and longitude directions. Note that there are two lateral dampers: one connected between the front carbody and the front bogie, and the other connected between the back carbody and the back bogie. Each carbody, bogie frame, and wheelset in this model have six degrees of freedom (DOF) (surge, heave, sway, yaw, pitch, and roll motions), while each axle box rotating arm has one DOF (pitch), which are clearly explained in Ref. 18.

Figure 3.

The railway vehicle model on Simpack (a) full and (b) bogie.

This dynamic model employed the UIC510-2 standard²⁰ to define the shape of the wheels, the UIC60 standard²¹ to define the shape of the rails, and the UIC519 standard²² as the basis for the connection between these two parts. In addition, the speed of the railway vehicle model was set at 80 km/h, based on the allowed speed at which it can be operated,²³ and the track was chosen as 5 km in length, which is the goal of this study, and it was assumed to be flat and straight.

Simulation condition setting

Sinusoidal function excitation

In this paper, a straight track line was used to evaluate the dynamic simulation of the train. Firstly, the sinusoidal function vibration excitation is used as the input signal for the simplified quarter and whole railway vehicle models, in which, the amplitude of vibration excitation is 0.005 m, the frequency range of the simulation is from 0.1 to 20 Hz, the simulation time is 50 s, and the step size is 0.001 s.²⁴

Track irregularity

Secondly, the track irregularity is also used as the input signal for the whole railway vehicle to comprehensively evaluate the vibration attenuation effectiveness of the hybrid control, which is represented by the German low-interference track irregularity. The track irregularities are featured by their power spectral densities (PSDs), which are defined using the measured data and thus reflect real-world conditions of the vibration excitation source. There are four main types of irregularities, including vertical irregularity, lateral alignment irregularity, cross-level irregularity, and gauge irregularity, which are referred to as track geometry irregularities and estimated by equations (2)–(5), respectively¹⁸:

P_{v} = \frac{C_{v} \cdot ω_{c}^{2}}{(ω^{2} + ω_{r}^{2}) \cdot (ω^{2} + ω_{c}^{2})}

(2)

P_{l} = \frac{C_{l} {\cdot ω}_{c}^{2}}{(ω^{2} + ω_{r}^{2}) \cdot (ω^{2} + ω_{c}^{2})}

(3)

P_{c r} = \frac{C_{v} \cdot ω_{c}^{2} {\cdot ω}^{2}}{d^{2} \cdot (ω^{2} + ω_{r}^{2}) \cdot (ω^{2} + ω_{c}^{2}) \cdot (ω^{2} + ω_{s}^{2})}

(4)

P_{g} = \frac{C_{g} \cdot ω_{c}^{2} {\cdot ω}^{2}}{(ω^{2} + ω_{r}^{2}) \cdot (ω^{2} + ω_{c}^{2}) \cdot (ω^{2} + ω_{s}^{2})}

(5)where

P_{v}

P_{l}

P_{c r}

, and

P_{g}

are the power spectral density of vertical, lateral, cross-level, and gauge track irregularity, respectively;

C_{v}

, and

C_{l}

are the roughness constants;

C_{g}

is the reference coefficient based on vibration amplitude of the gauge irregularity; d is half of the wheel rolling circle distance;

ω

is the spatial wave number, while

ω_{c}

ω_{r}

, and

ω_{s}

are the truncated wave numbers, respectively.

Based on the standard of German low-interference track irregularities,¹⁴ the lateral irregularities are presented in Figure 4 for the input signal of the numerical simulation problem.

Figure 4.

Track lateral irregularity with German low-interference track irregularity.

Evaluation of railway vehicle model

For the quarter model, a preliminary result of the ride comfort evaluation was measured in the acceleration index, whereas for the whole model, a more comprehensive evaluation of the proposed control theory was made with three indicators: acceleration, Sperling, and derailment.

Ride comfort

The evaluation of the ride comfort through the acceleration of the carbody is a simple well-known method; however, to evaluate more accurately the ride comfort, not only the acceleration value but also the acceleration frequency (i.e., Sperling index) of the carbody should be considered. Therefore, in this paper, the amplitude of the carbody’s acceleration and the Sperling index of the passenger for railway vehicle were measured in the whole model.

The Sperling index was determined based on the standard of the China Railway GB/T5599-2019,¹⁴ which is shown in equation (6).

W_{y} = 0.896 \sqrt[10]{\frac{{a_{c}}^{3}}{f_{c}} F_{c} (f)}

(6)where W_y is the Sperling index of the railway vehicle, a_c is the acceleration of the carbody (cm/s²), f_c is the vibration frequency of the carbody (Hz), and F_c(f) is the correction coefficient of vibration frequency, which can be calculated through equation (7).

F_{c} (f) = {\begin{cases} 0.8 f_{c}^{2}, f_{c} = 0.5 \sim 5.4 H z \\ \frac{650}{f_{c}^{2}}, f_{c} = 5.4 \sim 26 H z \\ 1, f_{c} > 26 H z \end{cases}

(7)

According to Ref. 14, a Sperling index of less than 2.5 is considered a standard for the ride comfort of the carbody in train operation.

Running safety

The derailment phenomenon is a serious issue in railway safety, possibly caused by various factors, such as the curve radius, track irregularities, the friction coefficient between the wheel and rail, the train speed, and so on. In this paper, the derailment coefficient is considered to evaluate the train safety level when applying the proposed hybrid control theory. This index has been described and analyzed carefully in previous studies, especially in Japan, for example, Takai et al.²⁵ and Ishida et al.²⁶ The derailment coefficient can be determined using “Nadal’s equation” (equation (8)), which is commonly used to calculate the margin against the flange-climb derailment quantitatively.²⁶

D_{y} = \frac{Y_{l}}{Q_{w}} = \frac{\tan α_{w} - μ_{e}}{1 + μ_{e} \tan α_{w}}

(8)where

D_{y}

is derailment coefficient,

Y_{l}

is lateral force,

Q_{w}

is wheel force,

α_{w}

is wheel flange angle (rad),

μ_{e}

is equivalent friction coefficient, it is defined in equation (9),

F_{y}

is lateral creep force,

N_{n}

is normal force,

μ

is friction at wheel flange,

γ

is index expressing saturation characteristic of creep force,

θ

is wheel angle of attack,

k_{22}

is lateral creep coefficient.

μ_{e} = \frac{F_{y}}{N_{n}} = μ \times \frac{θ ∙ k_{22}}{N_{n} {(μ^{γ} + {(\frac{θ ∙ k_{22}}{N_{n}})}^{γ})}^{\frac{1}{γ}}}

(9)

A derailment coefficient of 1.0 or less was chosen as the standard running safety level, following Ref. 25.

New hybrid control strategy

Defining natural frequency range of carbody as changing carbody weight

The carbody weight is defined as a total of the carbody self-load (i.e., idle) and passenger load, which is undoubtedly changeable between idle and the full load due to changes in the number of passengers at different stop stations. According to Ref. 27, the weight ratio of the full carbody load to the idle load $ε$ ranges between 1.75 and 2 times. In this study, to examine the flexibility of our method, we selected a higher value of $ε = 4$ , corresponding to a change in the carbody weight from a full load to a quarter load. That means the carbody mass changes within a range of $[0.25 m, m]$ .

Equation (10) was used to determine the carbody’s natural angular frequency $ω_{n}$ and natural frequency $f_{n}$ , which depends only on the carbody mass $m$ and the stiffness $k$ of the secondary suspension system. When the carbody mass changes within the range of [ $0.25 m, m]$ , the natural frequency of the body ranged between $f_{n}$ and ${2 f}_{n}$ , equivalent to a range of $1.5 - 3.0 Hz$ , referring to Table 1.

{\begin{cases} ω_{n} = \sqrt{\frac{k}{m}} \\ f_{n} = \frac{1}{2 π} \sqrt{\frac{k}{m}} \end{cases}

(10)

During operation, the frequency of the carbody’s vibration excitation changes from low to high under the track irregularities. Besides, the carbody’s natural frequency also changes from $f_{n}$ to ${2 f}_{n}$ , as proved above. Thus, the carbody’s resonance may occur not only at a fixed frequency point but within a frequency range of $[f_{n}, {2 f}_{n}]$ , instead, requiring a control method that covers this frequency range—the ineffective region for the conventional mixed control methods. For ease of understanding, the carbody’s vibration excitation frequency was grouped into three specific frequency regions: (I) low frequency: from 0 to $f_{f}$ ; (II) ineffective frequency: from $f_{f}$ to $f_{q}$ ; and (III) high frequency: $f_{q}$ to extremely. In which, $f_{f} = f_{n}, f_{q} = 2 f_{n}$ are the natural frequencies of the carbody at full and quarter load states, respectively. As a result, as the carbody load changes from full to half or quarter load, the conventional singular control approach is effective only at a specific frequency region ((I) or (III)), while the conventional mixed control approach may perform ineffectively at frequency region (II).

Analysis of mixed SH-DV control

To demonstrate the ineffectiveness of the conventional mixed control approaches under a change in the carbody load, an example analyzing for the mixed SH-DV control is presented. In the mixed SH-DV control strategy, the excitation vibration frequency of the carbody is estimated by the acceleration and velocity function (equation (11)) and compared with the conversion coefficient c to determine the conversion status to SH or DV control.¹⁴ Therein, c is the intersection point between SH control and DV control, defined as $c = 2 π f_{c}$ , depending on a constant $f_{c}$ , referred to as the crossover frequency. $f_{c}$ is determined at the full load of the carbody and thus only suitable for that load condition.

{\begin{cases} S H, {\ddot{y}}_{1}^{2} - c^{2} \cdot {\dot{y}}_{1}^{2} < 0 \\ D V, {\ddot{y}}_{1}^{2} - c^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \end{cases}

(11)

The SH and DV control strategy are implemented through determining the damping coefficients $c_{S H}$ and $c_{D V}$ by equation (12)²⁸ and (13),¹⁴ respectively. In which, $y_{1}$ , ${\dot{y}}_{1}, {\ddot{y}}_{1}$ , and $y_{2}$ , ${\dot{y}}_{2}, {\ddot{y}}_{2}$ are lateral displacements, velocities, accelerations of the body and the bogie, respectively, the maximum and minimum damping coefficients of semi-active MR damper were selected (c_max = 50,000 Ns·m⁻¹) and (c_min = c_max/12 = 4167 Ns·m⁻¹):

c_{S H} = {\begin{cases} \max (c_{\min}, \min (c_{\max}, | c_{\max} \frac{{\dot{y}}_{1}}{{\dot{y}}_{1} - {\dot{y}}_{2}} |)), {\dot{y}}_{1} ({\dot{y}}_{1} - {\dot{y}}_{2}) \geq 0 \\ c_{\min}, {\dot{y}}_{1} ({\dot{y}}_{1} - {\dot{y}}_{2}) < 0 \end{cases}

(12)

c_{D V} = {\begin{cases} \max (c_{\min}, \min (c_{\max}, | \frac{k_{1} (y_{1} - y_{2})}{{\dot{y}}_{1} - {\dot{y}}_{2}} |)), (y_{1} - y_{2}) ({\dot{y}}_{1} - {\dot{y}}_{2}) < 0 \\ c_{\min}, (y_{1} - y_{2}) ({\dot{y}}_{1} - {\dot{y}}_{2}) \geq 0 \end{cases}

(13)

Figure 5 compares the carbody acceleration transmissibility at the full and quarter carbody loads. Figure 5(a) shows the improvement of the ride comfort at full load of the carbody load. The mixed SH-DV control method obtained 90% of the asymptotic effectiveness of SH and DV control. As the carbody load changed to a quarter load (Figure 5(b)), the mixed SH-DV control seemed to be less effective, approximated by 70% of the asymptotic effectiveness of SH control at low frequency and 90% of asymptotic effectiveness of DV control at high frequency. That might be due to incorrect transition point of the control state $f_{c}$ ; instead, this point should be $f_{r c}$ , which is illustrated in Figure 5(b). Therefore, the mixed SH-DV control may perform less effectively in the actual operation where the carbody load is changeable.

Figure 5.

Performance of SH-DV control with fixed conversion coefficient c at two conditions of the carbody load: (a) full (b) a quarter.

Proposed hybrid control

To overcome the drawbacks of the conventional mixed control approaches under the carbody load changes, a new hybrid SH-DV control strategy was proposed, adaptable to three specific regions of vibration excitation frequency by corresponding controls: (I) low frequency, using the SH control; (II) ineffective frequency, using the SH and DV control simultaneously; and (III) high frequency, using the DV control.

This hybrid approach ensures each control reaching its effective point in the suitable frequency region (I) and (III), while the use of the two control methods simultaneously can improve the performance under the carbody load changes (region (II)). The separation of different control areas with linear transition of control states helps to reduce the sensitivity at the control state transition points. The hybrid control strategy is clearly explained in Figure 6.

Figure 6.

Contribution coefficients under the body’s vibration frequency.

Figure 6 presents the contributions of each control type across the excitation frequency range, in which α and β are the contribution coefficients of the SH and DV control methods, respectively. The control state is converted to the SH control system when α = 1 (or β = 0) and to the DV control system when β = 1 (or α = 0). When the vibration frequency region of the carbody coincides with the natural frequency region of the body, that is, 0 < α < 1 (or 1 > β > 0), the SH and DV control systems are simultaneously active, in which the influence intensity of each control method depends on the contribution coefficients (α, β). In Figure 6, the contribution of each control type appears linear across the vibration frequency band ( $f_{f}$ to $f_{q}$ ). Specifically, when the vibration frequency ranged from $f_{f}$ to ${1.5 f}_{f}$ , α reduced from 1 to 0.75, corresponding to β increasing from 0 to 0.25. We chose a larger contribution coefficient for the SH control than that for the DV control because, in this phase, the SH control showed higher effectiveness than that of the SH-DV control (Figure 5(b)), where only the DV control is active. When the vibration frequency continued increasing to $f_{q}$ , α reduced from 0.75 to 0, corresponding to β increasing to 1. Since the contribution coefficients of the two control types varied linearly, the proposed control strategy reduced the sensitivity of the state transition point and increased the ability of this proposed control to adapt to the carbody’s natural frequency range.

Equation (14) explains the contributions made by either the SH or DV control individually or the dual SH + DV control. Therein, $c_{f}, c_{m}, {and c}_{q}$ are conversion coefficients at a full, medium, and quarter carbody load, respectively, where $c_{f} = 2 π f_{f}$ , $c_{m} = 1.5 c_{f} = 3 π f_{f}$ , and $c_{q} = 2 c_{f} = 4 π f_{f}$ .

{\begin{cases} S H, {\ddot{y}}_{1}^{2} - c_{f}^{2} \cdot {\dot{y}}_{1}^{2} < 0 \\ α \cdot S H + β \cdot D V, {\begin{cases} {\ddot{y}}_{1}^{2} - c_{f}^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \\ {\ddot{y}}_{1}^{2} - c_{q}^{2} \cdot {\dot{y}}_{1}^{2} < 0 \end{cases} \\ D V, {\ddot{y}}_{1}^{2} - c_{q}^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \end{cases}

(14)

Furthermore, equation (15) defines the influence intensity of each control type by establishing values α and β. α and β are constant when the carbody’s vibration frequency is outside of the range [ $f_{f}, f_{q}$ ]. In contrast, when the carbody’s vibration frequency is within the range [ $f_{f}, f_{q}$ ], the influence intensity of each control type is linearly dependent on the carbody’s estimated angular vibration frequency $| {\ddot{y}}_{1} / {\dot{y}}_{1} |$ , that is, the absolute ratio of its acceleration to its velocity.¹⁴ The conditions for each control type to be active were mentioned in equations (12) and (13), that is, ${\dot{y}}_{1} ({\dot{y}}_{1} - {\dot{y}}_{2})$ for the SH control and $(y_{1} - y_{2}) ({\dot{y}}_{1} - {\dot{y}}_{2})$ for the DV control.

{\begin{cases} α = 1; β = 0, {\ddot{y}}_{1}^{2} - c_{f}^{2} \cdot {\dot{y}}_{1}^{2} < 0 \\ {\begin{cases} α = \frac{- 1}{2 f_{f}} | \frac{{\ddot{y}}_{1}}{{\dot{y}}_{1}} | \frac{1}{2 π} + 1.5 \\ β = \frac{1}{2 f_{f}} | \frac{{\ddot{y}}_{1}}{{\dot{y}}_{1}} | \frac{1}{2 π} - 0.5 \end{cases}, {\begin{cases} {\ddot{y}}_{1}^{2} - c_{f}^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \\ {\ddot{y}}_{1}^{2} - c_{m}^{2} \cdot {\dot{y}}_{1}^{2} < 0 \end{cases} \\ {\begin{cases} α = \frac{- 3}{2 f_{f}} | \frac{{\ddot{y}}_{1}}{{\dot{y}}_{1}} | \frac{1}{2 π} + 3 \\ β = \frac{3}{2 f_{f}} | \frac{{\ddot{y}}_{1}}{{\dot{y}}_{1}} | \frac{1}{2 π} - 2 \end{cases}, {\begin{cases} {\ddot{y}}_{1}^{2} - c_{m}^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \\ {\ddot{y}}_{1}^{2} - c_{q}^{2} \cdot {\dot{y}}_{1}^{2} < 0 \end{cases} \\ α = 0; β = 1, {\ddot{y}}_{1}^{2} - c_{q}^{2} \cdot {\dot{y}}_{1}^{2} \geq 0 \end{cases}

(15)

Co-simulation model

Simpack can generate a complex railway vehicle model; however, it is not a tool for control design. To overcome this limitation, Simpack and Simulink nonlinear models can be simultaneously simulated using the SIMAT (abbreviation by Simpack and Matlab) co-simulation interface, in which Simpack solves the mechanical system while Matlab/Simulink solves the control loop. For instance, Chen et al.²⁹ established a combination of a vehicle model on Simpack and a control model on Matlab/Simulink. In addition, other co-simulation methods have also been developed, such as VI-Rail and Matlab/Simulink¹⁸ and UM and Matlab/Simulink.²⁴

In this study, a co-simulation SIMAT model was constructed (Figure 7), merging the railway vehicle model on Simpack with the hybrid control model on Simulink/Matlab. This co-simulation interface used the IPC (interface for coupling Simpack and Simulink) with a sampling period of 0.001 s and a simulation time of 50 s. The input for Simpack (i.e., the output of Simulink) was the control force for the front and back lateral dampers, whereas the output of Simpack (i.e., the input for Simulink) included the model’s displacement, velocity, and acceleration. The hybrid control model contained the SH and DV controls. It utilized the control signal (the acceleration and velocity of the body) to enable the control type, and then used the displacement, velocity, and acceleration magnitudes of the body and bogie to establish values for the front and back lateral damper forces.

Figure 7.

The co-simulation of the whole railway vehicle model.

Results and discussion

We assessed the performance of the proposed hybrid control theory in comparison with two other relevant control methods: passive and mixed SH-DV controls, as follows:

Quarter railway vehicle model

Figure 8 shows preliminary results of the proposed control theory for the ride comfort measured by acceleration in the quarter railway vehicle model at different carbody loads (full, a half, and a quarter loads). Overall, the three control methods degraded the performance of the vibration attenuation as the carbody load decreased. However, in all examined scenarios of the carbody load, the hybrid control presented the highest performance compared with the passive and mixed SH-DV controls. Specifically, at full load (Figure 8(a)), the hybrid control had the same effectiveness as the SH-DV control and was better than the passive control. Specifically, the acceleration of the hybrid control was 52.2% lower than that observed in the passive control at the resonant frequency of 1.55 Hz. At half the full body load (Figure 8(b)), the hybrid control showed better performance than the two other control types. Specifically, the acceleration of the hybrid control was 4% lower than that of the SH-DV control and 48.5% lower than that of the passive control at the resonance frequency of 2.2 Hz. Especially at a quarter of full body load (Figure 8(c)), the hybrid control showed significantly higher effectiveness with a 10.3% lower acceleration than the SH-DV control at the frequency of 2.9 Hz and a 42.8% lower acceleration than the passive control at the resonance frequency of 3.25 Hz.

Figure 8.

The acceleration of the carbody with the passive, SH-DV, and hybrid controls at (a) a full load, (b) a half of full load, and (c) a quarter of full load of the carbody.

Whole railway vehicle model under a sinusoidally-formulated track excitation

The ride comfort was assessed using acceleration index under a sinusoidally-formulated excitation track in the whole railway vehicle model at different carbody loads, as shown in Figures 9–11. Table 2 summarizes the peak and root mean squares (RMS) of the acceleration of the carbody for those scenarios of carbody loads. The acceleration of the carbody produced by the three methods in the whole model showed similar characteristics to those in the quarter model. The hybrid control presented the best ability in vibration isolation as the carbody load decreased from the full to a quarter condition. Specifically, based on the peak value of the acceleration index, the hybrid method significantly reduced the acceleration of the carbody by 38.89% and 33.07% at the full and a half of the carbody load, respectively, and slightly reduced the acceleration by 1.76% at a quarter of the carbody load, compared with the passive control. These reductions were relatively higher than those of the mixed SH-DV control (35.76%, 27.61%, and −8.11%, respectively). Given that the peak point of acceleration index might be affected by the jerk phenomenon, the RMS was also provided to compare the acceleration of the three methods in terms of overall performance over time. Those findings were also observed in the results based on the RMS of acceleration. Especially, the hybrid method significantly reduced the acceleration of the carbody by 12.30% of the acceleration at a quarter carbody load, suggesting that the hybrid control showed the best overall performance over time.

Figure 9.

The acceleration of the carbody at a full load with (a) root mean square of acceleration in frequency domain and (b) absolute of acceleration at 1.6 Hz in time domain.

Figure 10.

Acceleration of carbody at a half of full load with (a) RMS of acceleration in frequency domain and (b) absolute acceleration at 2.2 Hz in time domain.

Figure 11.

Acceleration of carbody at quarter load with (a) RMS acceleration in frequency domain and (b) absolute acceleration at 3.5 Hz in time domain.

Table 2.

The ride comfort of the passive, SH-DV control, and hybrid control types at different carbody loads.

Load of carbody	Types of control	Peak value (m·s⁻²)	Decline rate (%)	RMS (m·s⁻²)	Decline rate (%)
Full load	Passive	2.129	Reference	1.497	Reference
	SH-DV	1.3677	35.76	0.9627	35.69
	Hybrid	1.301	38.89	0.9355	37.51
Half load	Passive	2.4294	Reference	1.781	Reference
	SH-DV	1.7586	27.61	1.268	28.80
	Hybrid	1.6261	33.07	1.165	34.59
Quarter load	Passive	2.6275	Reference	2.081	Reference
	SH-DV	2.8407	−8.11	1.95	6.30
	Hybrid	2.5814	1.76	1.825	12.30

Whole railway vehicle model under the track irregularities

Finally, the performance of the proposed control method was evaluated more comprehensively with regard to the ride comfort of the carbody and the running safety of the train in the whole railway vehicle model under the track irregularity condition. The ride comfort of the carbody was assessed with the acceleration and Sperling indices, as shown in Figure 12 and Table 3. The results for the ride comfort of the carbody under the track irregularity condition were consistent with those under the sine-formulated vibration excitation of the track. For instance, with a quarter of the full carbody load, the hybrid control showed a lower peak value of acceleration by 17.43% relative to the passive control, which was higher than the decline rate of the SH-DV control (13.82%). The decline rates based on RMS were relatively close to those based on the peak value in all scenarios of the carbody load. Regarding the Sperling index, all three methods generated an acceptable value of Sperling index (<2.5). In particular, the mixed SH-DV and hybrid methods showed a lower Sperling index, which is favorable, than that of the passive method.

Figure 12.

The acceleration of carbody of three control types at different load conditions: (a) full, (b) half, and (c) quarter.

Table 3.

The ride comfort of the passive, SH-DV control, and hybrid control types at different carbody loads.

Load of carbody	Types of control	Peak value (m·s⁻²)	Decline rate (%)	RMS (m·s⁻²)	Decline rate (%)	Sperling index (W_y)	Decline rate (%)
Full	Passive	0.6195	Reference	0.2334	Reference	2.221	Reference
	SH-DV	0.4110	33.66	0.1468	37.10	1.891	14.85
	Hybrid	0.3938	36.43	0.1427	38.86	1.871	15.76
Half	Passive	0.4770	Reference	0.2140	Reference	2.143	Reference
	SH-DV	0.3840	19.50	0.1679	21.54	1.971	8.03
	Hybrid	0.3503	26.56	0.1609	24.81	1.940	9.47
Quarter	Passive	0.3742	Reference	0.1890	Reference	2.006	Reference
	SH-DV	0.3225	13.82	0.1540	18.52	1.865	7.02
	Hybrid	0.3090	17.43	0.1505	20.37	1.855	7.53

In addition to ride comfort, we also evaluated railway vehicle safety with the derailment coefficient, given its critical importance for passenger transportation.²⁶ The derailment coefficient was determined at the resonance frequency at different carbody loads, as presented in Table 4. As shown in Figure 13 and Table 4, when the carbody load decreased from a full load to a half or a quarter, the derailment coefficient was remarkably lower than 1.0 based on the peak value in all three control methods, indicating a high safety level. In summary, our proposed hybrid method effectively and robustly reduced the vibration as the carbody load declined to a half or a quarter load while maintaining a high safety level.

Table 4.

The running safety of passive, SH-DV, and hybrid control types at different carbody loads.

Load of carbody	Types of control	Derailment coefficient
Load of carbody	Types of control	Peak value	RMS
Full load	Passive	0.0598	0.0186
	SH-DV	0.0593	0.0191
	Hybrid	0.0572	0.0191
Half load	Passive	0.0691	0.0254
	SH-DV	0.0735	0.0258
	Hybrid	0.0743	0.0260
Quarter load	Passive	0.1035	0.0332
	SH-DV	0.0907	0.0332
	Hybrid	0.0890	0.0331

Figure 13.

The derailment coefficients of different control types at (a) full, (b) half, and (c) quarter load of the carbody load.

The outperformance of the hybrid control over the passive and SH-DV control methods might be explained as follows: The proposed control method uses two crossover frequency points where the control algorithm converts between SH and DV control methods. As a result, it forms three regions for converting the control methods: SH, SH + DV, and DV controls, in which the SH control takes the role at a full carbody load, the DV control works most effectively at a quarter or less than a quarter load, and the SH + DV control is responsible for the case of the carbody load changes (e.g., reduce from the full to a half or a quarter load as shown in this study). Therefore, the proposed hybrid control method can adapt in response to carbody load changes and take advantage of individual control methods in their optimal conditions.

Conclusion

In this paper, we proposed a hybrid control, including SH and DV control with two transition points of control states. This control is applied to MR damper of the secondary lateral suspension system of the train. This control is demonstrated for its effectiveness in suppressing the vibration of the train body under the wide change of the car body load through numerical simulation analysis. Firstly, under the track irregularity condition, the proposed method significantly improved ride comfort with a reduction in the acceleration and Sperling indices of the carbody. In particular, the hybrid control reduced the acceleration of the carbody by 36.43%, 26.56%, and 17.43% with the carbody at full, half, and quarter loads, respectively, compared to the passive control. In terms of the Sperling index, the relative decline rate was 15.76%, 9.47%, and 7.53%, respectively. Secondly, in the whole dynamic model, the hybrid control not only has good ride comfort but also ensures the running safety of the train, similar to the mixed SH-DV control and much better than passive control. This study allows for the expansion of the running train load, which promotes economic effectiveness in the transportation field. However, as a limitation, our results have yet been verified in an experiment. Although simulative results demonstrated the effectiveness of the hybrid control, this study has yet covered some important scenarios in the real world, such as slope and curve tracks, time delay of the control system, the impacts of bad weather conditions, and wheel-rail pair wear. Those scenarios will be considered in our future research.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by Ministry of Science and Technology, Taiwan (Project Number: MOST 111-2221-E-027-125).

ORCID iD

Tan-Linh Huynh

References

Alotaibi

Quddus

Morton

, et al. Transport investment, railway accessibility and their dynamic impacts on regional economic growth. Research in Transportation Business & Management 2022; 43: 100702. DOI: 10.1016/j.rtbm.2021.100702.

Jiang

Matamoros-Sanchez

Goodall

, et al. Passive suspensions incorporating inerters for railway vehicles. Veh Syst Dyn 2012; 50: 263–276. DOI: 10.1080/00423114.2012.665166.

Tian

Luo

Ren

, et al. Active radial system of railway vehicles based on secondary suspension rotation angle sensing. Veh Syst Dyn 2020; 59: 765–784. DOI: 10.1080/00423114.2020.1722183.

Zeng

Zhang

Song

. Lateral-vertical coupled active suspension on railway vehicle and optimal control methods. Veh Syst Dyn 2020; 60: 258–280. DOI: 10.1080/00423114.2020.1814358.

Zheng

Zolotas

Goodall

. Combined active suspension and structural damping control for suppression of flexible bodied railway vehicle vibration. Veh Syst Dyn 2019; 58: 198–228. DOI: 10.1080/00423114.2019.1572902.

Giossi

Persson

, et al. Active suspension in railway vehicles: a literature survey. Railway Engineering Science 2020; 28: 3–35. DOI: 10.1007/s40534-020-00207-w.

Kim

H-C

Shin

Y-J

You

, et al. A ride quality evaluation of a semi-active railway vehicle suspension system with MR damper: railway field tests. Proc Inst Mech Eng F J Rail Rapid Transit 2016; 231: 306–316. DOI: 10.1177/0954409716629706.

Hoseinzadeh

Rezaeepazhand

. Vibration suppression of composite plates using smart electrorheological dampers. Int J Mech Sci 2014; 84: 31–40, DOI: 10.1016/j.ijmecsci.2014.03.033.

Ripamonti

Chiarabaglio

. A smart solution for improving ride comfort in high-speed railway vehicles. J Vib Control 2019; 25: 1958–1973. DOI: 10.1177/1077546319843377.

10.

Sharma

Kumar

. Ride performance of a high speed rail vehicle using controlled semi active suspension system. Smart Mater Struct 2017; 26(5): 055026. DOI: 10.1088/1361-665X/aa68f7.

11.

Wei

Zhu

Jia

. A semi-active control suspension system for railway vehicles with magnetorheological fluid dampers. Veh Syst Dyn 2016; 54: 982–1003. DOI: 10.1080/00423114.2016.1177189.

12.

J-S

Shin

Y-J

Koo

H-W

, et al. Vibration control of a semi-active railway vehicle suspension with magneto-rheological dampers. Adv Mech Eng 2016; 8: 1687814016643638. DOI: 10.1177/1687814016643638.

13.

Savaresi

Silani

Bittanti

. Acceleration-driven-damper (ADD): an optimal control algorithm for comfort-oriented semiactive suspensions. J Dyn Syst Meas Control 2004; 127: 218–229. DOI: 10.1115/1.1898241.

14.

Yang

Zhao

Liu

, et al. A new semi-active control strategy on lateral suspension systems of high-speed trains and its application in HIL test rig. Veh Syst Dyn 2022; 61: 1317–1344. DOI: 10.1080/00423114.2022.2081221.

15.

Bhardawaj

Sharma

. Development of multibody dynamical using MR damper based semi-active bio-inspired chaotic fruit fly and fuzzy logic hybrid suspension control for rail vehicle system. Proc Inst Mech Eng - Part K J Multi-body Dyn 2020; 234: 723–744. DOI: 10.1177/1464419320953685.

16.

Metered

Bonello

Oyadiji

. An investigation into the use of neural networks for the semi-active control of a magnetorheologically damped vehicle suspension. Proc Inst Mech Eng - Part D J Automob Eng 2010; 224: 829–848. DOI: 10.1243/09544070jauto1481.

17.

Ghoniem

Awad

Mokhiamar

. Control of a new low-cost semi-active vehicle suspension system using artificial neural networks. Alex Eng J 2020; 59: 4013–4025. DOI: 10.1016/j.aej.2020.07.007.

18.

Liao

Liu

Yang

. Semiactive control of high-speed railway vehicle suspension systems with magnetorheological dampers. Shock Vib 2019; 2019: 1–17. DOI: 10.1155/2019/5279380.

19.

Zeng

Shi

, et al. A hybrid damping control strategy for high-speed trains running on existing tracks. J Low Freq Noise Vib Act Control. 2022; 41: 1258–1271. DOI:10.1177/14613484221087513.

20.

UIC CODE 510-2 . Trailing stock: wheels and wheelsets. Conditions concerning the use of wheels of various diameters. 4th ed. Paris, France: International Union of Railways, 2004.

21.

Pombo

Ambrósio

Pereira

, et al. A study on wear evaluation of railway wheels based on multibody dynamics and wear computation. Multibody Syst Dyn 2010; 24: 347–366. DOI: 10.1007/s11044-010-9217-8.

22.

Attivissimo

Danese

Giaquinto

, et al. A railway measurement system to evaluate the wheel–rail interaction quality. IEEE Trans Instrum Meas 2007; 56: 1583–1589. DOI: 10.1109/tim.2007.903583.

23.

Jin

Liu

Sun

, et al. Theoretical and experimental investigation of a stiffness-controllable suspension for railway vehicles to avoid resonance. Int J Mech Sci 2020; 187: 105901. DOI: 10.1016/j.ijmecsci.2020.105901.

24.

Yiwei

Shaopu

Yongqiang

, et al. A new semi-active control strategy and its application in railway vehicles. Advances in Applied Nonlinear Dynamics, Vibration and Control-2021: The proceedings of 2021 International Conference on Applied Nonlinear Dynamics, Vibration and Control (ICANDVC2021) 1. Berlin: Springer, 2022, pp. 240–252.

25.

Takai

Uchida

Muramatsu

, et al. Derailment safety evaluation by analytic equations. Quarterly Report of RTRI 2002; 43: 119–124. DOI: 10.2219/rtriqr.43.119.

26.

Ishida

Miyamoto

Maebashi

, et al. Safety assessment for flange climb derailment of trains running at low speeds on sharp curves. Quarterly Report of RTRI 2006; 47: 65–71.

27.

Tomioka

Takigami

. Experimental and numerical study on the effect due to passengers on flexural vibrations in railway vehicle carbodies. J Sound Vib 2015; 343: 1–19. DOI: 10.1016/j.jsv.2015.01.001.

28.

Shiao

Huynh

T-L

. Suspension control and characterization of a variable damping magneto-rheological mount for a micro autonomous railway inspection car. Appl Sci 2022; 12: 7336. DOI: 10.3390/app12147336.

29.

Chen

Long

Yuan

C-C

, et al. Non-linear modelling and control of semi-active suspensions with variable damping. Veh Syst Dyn 2013; 51: 1568–1587. DOI: 10.1080/00423114.2013.814799.

A new hybrid control strategy for improving ride comfort on lateral suspension system of railway vehicle

Abstract

Keywords

Introduction

Analysis railway vehicle model

Modeling

Quarter railway vehicle model

Whole railway vehicle model

Simulation condition setting

Sinusoidal function excitation

Track irregularity

Evaluation of railway vehicle model

Ride comfort

Running safety

New hybrid control strategy

Defining natural frequency range of carbody as changing carbody weight

Analysis of mixed SH-DV control

Proposed hybrid control

Co-simulation model

Results and discussion

Quarter railway vehicle model

Whole railway vehicle model under a sinusoidally-formulated track excitation

Whole railway vehicle model under the track irregularities

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References