Development of control algorithm for ABS–suspension integration to reduce rotational acceleration oscillations of wheel

Abstract

In this study, we aimed to obtain smoother wheel rotational acceleration during braking with an activated anti-lock brake system (ABS). This produces effective and easily controlled rotational acceleration of a wheel by an ABS control unit. For this, the wheel load is changed by considering the interaction between the brake pressure change rates and rotational acceleration of the wheel. This is provided by means of the control strategy developed in this study. The rules of the control strategy are based on ABS test results. These tests are conducted with soft, medium-hard and hard dampers on wet and slippery road surfaces. Therefore, the control strategy changes the wheel load by setting the damper stage according to agreement between brake pressure and wheel rotational acceleration. Here, the control strategy constantly applies the damping force of the damper providing the shortest braking distance under wet or slippery road conditions. All results show that the control strategy considerably improves wheel rotational acceleration oscillations during braking with an activated ABS.

Keywords

ABS control wheel acceleration wheel load

Introduction

In an anti-lock brake system (ABS) system, slip ratio is controlled by modulating the brake pressure to prevent the wheel locking. For this, the difference between the wheel speed and vehicle speed is considered. The difference is defined as the slip ratio. The wheel speed is measured with an ABS speed sensor and the vehicle speed is estimated from the measured wheel speed changes of the four wheels for passenger cars. In order to estimate the vehicle speed, a reference speed is determined by means of the logical relationships between the measured wheel speeds. Therefore, Austin and Morrey (2000) have shown that the magnitude of the relative slip ratio is determined by comparing the measured wheel speed with the reference speed. However, if the rotational deceleration of the wheel is higher than the braking acceleration of the vehicle body, the slip control of the ABS causes the wheels to lock at the same time, because this sudden deceleration of the wheel exceeds the braking acceleration of the vehicle and it is not detected relative to the slip. This is especially true in emergency situations, where all four vehicle wheels are slipping and vehicle speed measurement becomes virtually impossible (Bruijin et al., 2010). For this reason, modified ABSs control the rotational acceleration of the wheel as well as the relative slip. This process is performed by comparing the rotational deceleration with the braking acceleration of the vehicle body. At this moment, the brake pressure control at the wheel is governed by the acceleration and deceleration of the wheel (Mastinu and Ploechl, 2014). Sugai et al. (1999) have reported that the control methods based only on relative slip are not sufficient to continue maximum braking force during braking with an activated ABS. Furthermore, Cheli et al. (2008) have noticed that the thresholds of the wheel deceleration must be considered to determine the ABS braking performance. In order to use acceleration and deceleration information of the wheel in an ABS, the oscillations at wheel rotational accelerations should be filtered and thus they should be smooth. For this, the wheel speed signals are filtered before the calculation of the angular acceleration, Zhang et al. (2004). However, the wheel acceleration is not properly filtered due to road disturbances. This makes them unstable (Savaresi et al., 2005). Watanabe and Noguchi (1990) have demonstrated that the brake pressure change points are not exactly determined due to unstable wheel decelerations. They have shown that the brake pressure, which is suitable for the actual condition of the braked wheel, is not applied by the ABS due to unstable wheel decelerations.

For this reason, some researchers have studied the factors causing the unstable oscillations of rotational wheel acceleration. They also considered the effects of these oscillations on the braking performance of an ABS. Weida et al. (1990) determined that the most important uncertainty is unidentified characteristics of the friction coefficient between the road the and tyre due to unstable wheel deceleration. Solyom et al. (2004) showed that the interaction between road and tyre is determined by means of changes in the deceleration of the wheel. Furthermore, they underlined that if the wheel deceleration deteriorates, ABS can be exposed to malfunctions. Satoh and Shiraishi (1983) have stated that sudden changes in the road surface can cause oscillations in wheel deceleration during ABS braking because of unstable wheel speed changes. Guntur (1974) detected that the deteriorations in road–tyre contact occurring with unstable oscillations of wheel deceleration cause the brake pressure not to be applied in time. Moreover, Choi et al. (2006) showed that the brake pressure oscillations occurring with unstable wheel deceleration cause braking acceleration to decrease.

In the light of these studies, it may be clearly seen that the oscillations occurring in the rotational acceleration of a wheel cause unstable brake pressure changes due to the changes at the tyre and road contact during braking with an activated ABS. The contact changes cause vertical oscillations at the wheel and thus constantly change the acceleration of the wheel. This leads to wheel acceleration oscillations under critical road conditions like rough roads. Therefore, smoother effective rolling radius changes are obtained if vertical oscillations of the wheel are decreased. This provides a smoother wheel acceleration. Thus, some researchers have studied integration systems for decreasing the vertical oscillations. For this, the impacts of active dampers on wheel load changes are considered, as continuous tyre–road contact is provided by changing damper force according to the road surface. Chou and D’Andréa-Novel (2005) stated that the new trend in braking systems is the integration of systems such as the brakes and suspensions. Soliman et al. (2009) showed that an integrated controller between the active suspension system controller and anti-lock braking system improves the braking distance and time compared with separate active suspension and ABS controllers.

In studies related to the integration, different methods are used to integrate the suspension system into the ABS. Shao et al. (2007) studied integration, provided the braking moment changed with vertical load at the same phase. Alleyne (1997) used two different controllers to hold the brake force in an optimum adhesion region by supplying coordination between the active suspension system and ABS. In this way, the loads acting on the wheel are changed by tracking the changes of brake force. Reul et al. (2009) developed a control algorithm to change the wheel load according to brake pressure changes to recover the braking performance of an ABS. Thereby, they detected that fluctuations in the relative slip can be decreased. Also, Niemz and Winner (2006) have reported that the braking distance is shortened with a semi-active suspension system integrated into the ABS. Yan and Songjun (2010) stated that the ABS–suspension integration they developed can work well to improve the braking performance. Shaomin et al. (2010) reported that the integrated controller of a semi-active suspension and ABS can not only reduce the braking time and braking distance, but also improve the ride comfort. Kaldas and Soliman (2014) designed the integration of an active suspension system into an ABS based on wheel slip control. They showed that the integration improves the braking comfort as well as braking performance. Zang and Yang (2015) demonstrated that ABS and suspension system control can improve the braking performances significantly with a shorter braking distance, larger deceleration and a faster desired slip ratio, even in extreme driving conditions.

As a result, studies indicated that integration between the adjustable damper and ABS decrease braking distance during braking with the ABS by reducing the vertical oscillations of the wheel. The control algorithm of these integrations is based on slip ratio. This shows that all integrations change the damper stage by controlling the relative slip, but any information related to rotational acceleration of the wheel is not given. However, ABS uses rotational acceleration of the wheel as reference information, to brake the wheel relative to the braking acceleration of the vehicle body, when it is higher than the braking acceleration of the vehicle body. Also, studies clearly indicate that the oscillations occurring in the rotational acceleration of the wheel cause unstable brake pressure and vertical vibrations during braking with the ABS. For this reason, the oscillations should be reduced to give accurate information associated with rotational acceleration of the wheel to the ABS.

Therefore, this study proposes a control strategy setting the damping stages from medium-hard to hard, or from hard to medium-hard according to the interaction between the wheel acceleration and brake pressure. Here, the aim is to develop a control algorithm making brake pressure changes suitable to the rotational acceleration of the wheel. The developed control strategy is based on ABS test results and this algorithm is rule based. Braking tests with an ABS are conducted on rough road that has a wet and slippery surface by using hard, medium-hard and soft dampers. It is notable that any braking test is not conducted with adjustable dampers using this control strategy.

Modelling of braking and suspension dynamics

In order to obtain the relationship between wheel acceleration, wheel load and brake pressure according to the changes in damping capacity, the quarter car braking and suspension dynamics models are used, as shown in Figure 1. This model includes two subsystems – the braking and suspension systems. In the model, the axle and vehicle body are simplified into a mass. The wheel-axle assembly and vehicle body are connected to each other by means of the damper and spring, as shown in Figure 1.

In this way, the dynamics of suspension system is connected to the braking dynamics through the spring and damper. All parameters related to this model are given in Table 1.

Table 1.

Quarter car model parameters for braking and suspension dynamics.

Model parameters	Description	Unit
m ₂	Sprung mass	kg
m ₁	Unsprung mass	kg
${\overset{\cdot}{V}}_{x}$	Braking acceleration	m/s²
V_x	Vehicle speed	m/s
R_e	Effective rolling radius of the wheel	m
F_x	Friction force	N
F_z,dyn	Dynamic wheel load	N
F_z	Total wheel load	N
F_b	Braking force	N
k ₂	Suspension spring stiffness	N/m
k ₁	Tire spring stiffness	N/m
c ₂	Damping coefficient	Ns/m
T_b	Braking torque	Nm
$\overset{\cdot}{φ}$	Wheel angular speed	rad/s
z ₂	Vertical displacement of sprung mass	m
z ₁	Vertical displacement of unsprung mass	m
z ₀	Road excitation	m

Braking dynamics

In the model, the rotational speed of the wheel and the vehicle speed acting on the wheel centre are considered degrees of freedom for the quarter car braking dynamics. Therefore, the braking dynamics for one wheel is described by two motion equations according to Newton’s second law, and the longitudinal dynamics of vehicle body are described as follows:

M {\overset{\cdot}{V}}_{x} = - μ (λ) F_{z} (t)

(1)

{\overset{\cdot}{V}}_{x} = - \frac{μ}{M} (λ) F_{z} (t)

(1a)

where M is the total mass consisting of the car body and wheel, ${\overset{\cdot}{V}}_{x}$ the braking acceleration, V_x the vehicle speed, F_z the total wheel load and µ(λ) the friction coefficient between tyre and road. In the braking dynamic for ABS, the friction coefficient is the non-linear function of slip ratio (λ). The rotational motion of the braked wheel is described as follows:

I_{w} \overset{\cdot\cdot}{φ} (t) = μ (λ) R_{e} F_{z} (t) - K_{b} P_{b} (t) R_{e}

(2)

where I_w is the inertial moment of the wheel about the rotation centre, $\overset{\cdot\cdot}{φ}$ the rotational acceleration of the wheel, R_e the effective rolling radius of the wheel, K_b the brake gain and P_b the brake pressure. The two right-hand terms of Equation (2) describe the friction and braking torques, respectively. Therefore, the rotational accelerations of the wheel and brake pressure are obtained according to these torques from Equation (2) as follows:

\overset{\cdot\cdot}{φ} (t) = \frac{R_{e}}{I_{w}} (μ (λ) F_{z} (t) - P_{b} (t) K_{b})

(3)

P_{b} (t) = \frac{μ (λ) R_{e} F_{z} (t) - I_{w} \overset{\cdot\cdot}{φ} (t)}{K_{b}}

(3a)

Similarly, the changes in wheel acceleration and brake pressure are obtained from Equations (3) and (3a) as follows:

Δ \overset{\cdot\cdot}{ϕ} (t) = \frac{1}{I_{w}} (μ (λ) R_{e} Δ F_{z} (t) - Δ P_{b} (t) K_{b})

(4)

Δ P_{b} (t) = \frac{1}{K_{b}} (μ (λ) R_{e} Δ F_{z} (t)) - I_{w} Δ \overset{\cdot\cdot}{ϕ} (t))

(4a)

Also, the changes in the friction coefficient of the wheel are described as follows:

Δ μ (λ) = \frac{I_{w}}{R_{e}} \frac{(Δ \overset{\cdot\cdot}{φ} (t) + Δ P_{b} (t) K_{b})}{Δ F_{z}}

(4b)

where $Δ P_{b} (t)$ is the brake pressure change rate, $Δ \overset{\cdot\cdot}{φ} (t)$ the change rate of wheel acceleration, $Δ F_{z} (t)$ the change rate of wheel load and the changes in friction coefficient $Δ μ (λ)$ . These change rates take positive and negative values and are thus described according to their signs as follows:

( $+ Δ P_{b}$ ) and ( $- Δ P_{b}$ ) represents the increases and decreases in brake pressure, respectively. Therefore, $Δ P_{b}$ >0 is considered when the brake pressure is increased and $+ Δ P_{b}$ is used in Equations (4), (4a) and (4b). $Δ P_{b}$ <0 is considered and $- Δ P_{b}$ is used in Equations (4), (4a) and (4b), when the brake pressure is decreased.

$(+ Δ \overset{\cdot\cdot}{φ} (t))$ and $(- Δ \overset{\cdot\cdot}{φ} (t))$ represent the rotational acceleration and deceleration of the wheel, respectively. Thus, when the wheel is accelerated, $Δ \overset{\cdot\cdot}{ϕ} (t)$ >0 is considered and $(+ Δ \overset{\cdot\cdot}{ϕ} (t))$ is used in Equations (4), (4a) and (4b). $(Δ \overset{\cdot\cdot}{ϕ} (t))$ < 0 is considered and $- Δ \overset{\cdot\cdot}{ϕ} (t)$ is used in Equations (4), (4a) and (4b), when the wheel is decelerated. Also, the acceleration and deceleration periods of the wheel are completed, if $Δ \overset{\cdot\cdot}{ϕ} (t)$ =0 is obtained. In other words, the braked wheel is stopped as soon as $Δ \overset{\cdot\cdot}{ϕ} (t)$ =0 is obtained, as shown in Equation (3). Therefore, the braking manoeuvre is completed without a locking wheel, if this continuous throughout the braking manoeuvre with an activated ABS. This enables the vehicle to stop in a shorter distance. This situation is achieved by the only brake pressure and wheel acceleration, which is suitable due to friction between the tyre and road. This result is very important in this study and it is main objective of the developed control algorithm.

$(+ Δ F_{z})$ and $(- Δ F_{z})$ represent the increases and decreases in wheel load, respectively. Therefore, $(Δ F_{z})$ >0 is considered when the wheel load is increased and $+ Δ F_{z}$ is used in Equations (4), (4a) and (4b). $(Δ F_{z})$ <0 is considered when the wheel load is decreased and $- Δ F_{z}$ is used in Equations (4), (4a) and (4b).

$(+ Δ μ (λ))$ and $(- Δ μ (λ))$ represent the increases and decreases in friction coefficient, respectively. Therefore, $Δ μ (λ)$ >0 is considered when the friction coefficient or the road contact is increased and $+ Δ μ (λ)$ is used in Equations (4), (4a) and (4b). $Δ μ (λ)$ <0 is considered when the friction coefficient or the road contact is decreased and $- Δ μ (λ)$ is used in Equations (4), (4a) and (4b).

Suspension dynamics

The suspension system between the vehicle body (sprung mass) (m₂) and axle (unsprung mass) (m₁) is modelled using a spring and viscous damper, as shown in Figure 1. In this model, the damping of the tyre is neglected, because the damping characteristic of the rubber is very low according to that of the damper. Therefore, the motion equations of this suspension model can be written as follows:

m_{2} {\overset{\cdot\cdot}{z}}_{2} + c_{2} ({\overset{\cdot}{z}}_{2} - {\overset{\cdot}{z}}_{1}) + k_{2} (z_{2} - z_{1}) = m_{2} g

(5)

m_{1} {\overset{\cdot\cdot}{z}}_{1} - c_{2} ({\overset{\cdot}{z}}_{2} - {\overset{\cdot}{z}}_{1}) - k_{2} (z_{2} - z_{1}) = - k_{1} (z_{1} - z_{0}) + m_{1} g

(6)

where z₂ and z₁ are the displacements of the vehicle body and wheel, respectively; m₁ and m₂ the wheel mass and quarter mass of vehicle body, respectively; k₂ and k₁ the spring coefficients of the suspension and tyre; c₂ the damping coefficient of damper; z₀ is road roughness and g the acceleration due to gravity. The terms m₂g and m₁g describe the static loads of the vehicle body and wheel, respectively. Therefore, the two right-hand terms of Equation (6) describe the dynamic and static wheel loads as follows:

F_{z, st} = m_{1} g

(7a)

F_{z, dyn} (t) = - k_{1} (z_{1} (t) - z_{0})

(7b)

Therefore, the vertical forces applied to vehicle body and wheel are defined as

m_{2} {\overset{\cdot\cdot}{z}}_{2} = - ({F_{c}}_{2} (v) + F_{k 2}) + m_{2} g

(8)

m_{1} {\overset{\cdot\cdot}{z}}_{1} = (F_{c 2} (v) + F_{k 2}) + (F_{z, dyn} + F_{z, st})

(9)

where F_k₂ is the body spring force, F_c₂ the body damper force and v the piston velocity of damper. Thereby, the damping force is described as follows:

(F_{c 2} (v) + F_{k 2}) = m_{1} {\overset{\cdot\cdot}{z}}_{1} - (F_{z, st} + F_{z, dyn})

(10)

The wheel load change occurring during braking is described with the following descriptions suggested by Reul et al. (2009), David and Cheng-Kuo (2010), and Niemz (2006):

Δ F_{z} (t) = F_{z} (t) - (F_{z, st} + F_{z, dyn} (t))

(11)

where F_z is the actual wheel load, F_z,st the static wheel load and F_z,dyn the dynamic wheel load. In Equation (15), the first term is the actual wheel load, depending on the vertical axle acceleration during braking. The second term is the static wheel load. The last term is the dynamic wheel load, describing the wheel load oscillations between the rim and tyre. Therefore, the wheel load change is given as follows:

Δ F_{z} (t) = m_{1} {\overset{\cdot\cdot}{z}}_{1} - (F_{z, st} + F_{z, dyn} (t))

(12)

When Equation (10) is rearranged with respect to Equation (12), the wheel load change is obtained as follows:

Δ F_{z} (t) = F_{c 2} (v) + F_{k 2}

(13)

When Equation (13) is substituted into Equations (4), (4a) and (4b), the changes in wheel acceleration, brake pressure and friction coefficient are described according to the damping force variations as follows:

Δ \overset{\cdot\cdot}{φ} (t) = \frac{R_{e}}{I_{w}} (Δ μ (λ) (F_{c 2} (v) + F_{k 2}) - Δ P_{b} (t) K_{b})

(14)

Δ P_{b} (t) = \frac{μ (λ) R_{e} (F_{c 2} (v) + F_{k 2}) - I_{w} (Δ \overset{\cdot\cdot}{ϕ} (t))}{K_{b}}

(14a)

Δ μ (λ) = \frac{I_{w}}{R_{e}} \frac{(Δ \overset{\cdot\cdot}{φ} (t) + Δ P_{b} (t) K_{b})}{(F_{c 2} (v) + F_{k 2})}

(14b)

Equations (14) (14a) and (14b) clearly show that the only variable providing brake pressure, wheel acceleration and friction coefficient change is the damping force. Hence, the all three variables interact by changing the damping forces during braking with an activated ABS.

Material and methods

In this study, the rules of the control algorithm are based on the ABS test results. For this reason, the test road should effectively excite the damper during braking with the ABS. Furthermore, it should enable the effects of the damper on the ABS braking performance to occur.

Test road

The test road used for the ABS road tests is shown in Figure 2. As seen in Figure 2(a), the rubber carpet, which has a length of 80 m and width of 6 m, covers the road. This test road contains two areas – smooth and rough areas – as shown in Figure 2(b).

The smooth area is used for initiating the braking manoeuvre with the ABS. The rough area is designed to obtain a hard environment for the vehicle tests. The smooth area has same friction coefficient as the rough area. When the rubber carpet is dry, the friction coefficient is 0.8 at the smooth and rough areas. When this carpet is wetted only by water, the friction coefficient is approximately 0.6 and the test road becomes wet. Also, when the road is wetted with soapy water, the friction coefficient of the road is decreased to 0.3 and the test road becomes slippery. In addition, wooden planks are transversely mounted onto the road surface underneath the rubber carpet to obtain a rough road area. The distance among the wooden planks is equal and this was determined to excite the suspension system with a resonance frequency at the beginning of the braking manoeuvre. This frequency is experimentally calculated as follows:

L = \frac{1}{f} V_{x}

(15)

where L is wavelength of test road, f the frequency of the road and V_x the vehicle speed. Here, the wooden planks excite the damper with the resonance frequency of wheel mass at the beginning of braking manoeuvre. Then the planks do not excite the damper with the resonance frequency as the vehicle speed decreases. As a result, when the resonance frequency and braking initial speed are substituted in Equation (15), the wavelength of the test road is calculated as shown in Table 2.

Table 2.

The wavelength and amplitude of rough test road.

The braking initial speed V=95 km/h=26.38 m/s
Suspension naturalfrequency (Hz)	The wavelength of road(m)	The amplitude of road(m)
13 Hz	2.092	0.026

The height of the planks is determined by using the static tyre deflection under static load with nominal tyre pressure (30 psi). These results are given in Table 2. Therefore, the test road exciting the damper at a resonance frequency of unsprung mass is designed. This road profile is shown in Figure 3.

The measurement system of test vehicle

In this experimental study, the angular speed of the wheel, vehicle speed, brake pressure, braking distance and effective rolling radius are measured by means of sensors, as shown in Figure 4. The measurements are performed with a 40 Hz sampling rate. This rate is selected by considering the resonance frequency of the unsprung mass, which is in the 7–20 Hz frequency range. All measurement devices and measured parameters are shown in Figure 4. The wheel speed sensor is connected to the ABS. The vehicle speed is mounted onto the test vehicle via a MicroSAT interface box with a magnetic GPS antenna, as shown in Figure 4. The brake pressure transducer is connected to the hydraulic modulator output related to the left front wheel by using a T apparatus as seen in the Figure 4. A non-contact laser height sensor is mounted to the wheel lug nuts via adjustable mounting collets. In this way, it is located exactly in the wheel centre. Also, in order to restrain the rotation of the height sensor about the wheel’s y-axis, it is mounted to the vehicle body with a rod, as shown in Figure 4.

Furthermore, the characteristics of all measurement devices and the measured parameters are shown in Table 3.

Table 3.

Sensor characteristics and measured variables.

Sensor	Measurement range and specifications – measured variable
Vehicle speed sensor (Microsat model)	0–1600 km/h with 0.1 km/h accuracy and max 100 Hz sampling rate – longitudinal speed of vehicle body
Piezo pressure transducer	1–400 Bar with 0.5 ms response time – brake pressure
Non-contact laser height sensor	100–350 mm with 0.1 mm resolution – effective rolling radius
Inductive wheel speed sensor of ABS	0–2500 Hz with 1 mm air gap – rotational speed of wheel

This ensures that the sensor remains in the vehicle body (vertical) –-direction. Also, circumferential speeds of the wheel, wheel acceleration and vehicle braking acceleration are obtained by using the measured parameters. The circumferential speed of the wheel, brake pressure change rates, rotational acceleration of the wheel and friction coefficient are obtained from the measured variables as follows.

The circumferential speed of the wheel V_w is calculated by reflecting the measured effective rolling radius onto the wheel angular speed as follows:

V_{w} = {\overset{\cdot}{φ}}_{m} R_{m, e}

(16)

where ${\overset{\cdot}{φ}}_{m}$ is the measured wheel speed and R_m,e the measured effective rolling radius. The brake pressure change rate is calculated by using measured brake pressure as in the following:

\pm Δ P_{b} = {\overset{\cdot}{P}}_{b} = \frac{d (P_{m, b})}{d (t)}

(17)

where P_m,b is the measured brake pressure and t the time taken until the vehicle speed is reduced from 95 km/h to 0. The rotational acceleration is obtained as follows:

\overset{\cdot\cdot}{φ} = \frac{d {\overset{\cdot}{φ}}_{m}}{dt}

(18)

Also, the circumferential acceleration of the wheel is obtained by using the wheel rotational speed and the measured effective rolling radius as follows:

a_{w} = \frac{d {\overset{\cdot}{ϕ}}_{m}}{dt} R_{m, e} = \overset{\cdot\cdot}{φ} R_{m, e}

(19)

The changes in friction coefficient are calculated to investigate changes at the contact between the tyre and road during braking with the ABS. The friction coefficient changes have been calculated as follows:

μ = \frac{M {\overset{\cdot}{V}}_{x}}{F_{za, st} + F_{za, dyn}}

(20)

where M is the vehicle body mass, ${\overset{\cdot}{V}}_{x}$ the vehicle braking acceleration, F_za,st the static axle load and F_za,dyn the dynamic axle load. The static axle load is obtained as follows:

F_{za, st} = m_{T} g

(21)

where m_T is the total of axle mass with one quarter of the vehicle body mass. These masses are measured by the suspension test bench shown in Figure 4a. The dynamic axle load is caused by vertical acceleration of axle and forward load transfer during braking as follows:

F_{za, dyn} = m a_{z} + \frac{Δ W}{g}

(22)

where m is the axle mass under one quarter of the vehicle body, a_z the measured vertical axle acceleration. $Δ W$ is the longitudinal load transfer during braking with the ABS as follows:

Δ W = \frac{1}{2} Mg (\frac{h_{v}}{l} \frac{{\overset{\cdot}{V}}_{x}}{g})

(23)

where h_v is the vehicle centre of gravity height and l the wheelbase. Therefore, the friction coefficient is implemented by using Equation (20) for this measured dynamic wheel load and braking acceleration. The braking acceleration is obtained by taking the derivative of measured vehicle speed with respect to the time. In this study, in order to conduct ABS tests with different damper characteristics, the damper that has valves with flat shims is used. Different damper characteristics are obtained by varying the number and thickness of the shims. Therefore, hard, medium-hard and soft damper characteristics are achieved by using same damper, as shown in Figure 5. Here, the damping force considerably increases from the soft stage to a hard damper stage. The hard damper has the highest damping force and the soft damper has the lowest.

Also, Figure 5 shows that the positive damping force is applied during the compression motion of the damper and the negative damping force is applied during the rebound motion of the damper, as shown in Figure 5.

Control strategy

The control strategy is developed depending on the results of the brake pressure and wheel acceleration measured in ABS tests, as shown in Figure 6. The control strategy aims to vary the wheel load in order to cause the wheel acceleration or deceleration to approach zero, when the vehicle is braking with an activated ABS, because the difference between friction and braking torques greatly decreases, as the acceleration or deceleration of the wheel becomes closer to zero, as shown in Equation (3). In this way, the wheel is braked without locking thanks to the balance between the friction and braking torques. This also allows the wheel speed to vary with smoother wheel acceleration. Therefore, the brake pressure changes through wheel load variations with different damping forces during braking with an activated ABS to reach these targets, as shown in Equation (14a).

Therefore, the control strategy is established as the following stages by considering Figure 6:

First stage: The increasing and decreasing rates of the brake pressure are obtained from ABS control unit.

Second stage: The changes in the wheel acceleration of the braked wheel are obtained by deriving the wheel speed measured from the ABS speed sensor.

Third stage: The changes in the brake pressure are compared with the rotational acceleration of the wheel.

Fourth stage: The direction of the piston motion is determined.

Fifth stage: The wheel loads are changed according to the interaction between the brake pressure and wheel acceleration by taking the direction of piston motion as a reference. Hence, the control rules are designed as follows.

If the wheel decelerates while the brake pressure is increasing, the braking torque is higher than the friction torque according to Equation (3). This may cause the wheel to lock. For this reason, the wheel load should be increased to make the friction torque higher than the braking torque. This increases the friction coefficient and thus the wheel deceleration is brought to closer zero in a shorter time, as shown in Equations (4) and (4b). This provides the braking acceleration to increase, as shown in Equation (1a). For this reason, the downward damping force should be increased according to Equations (14), (14a) and (14b). The rules related to this case are described as follows:

If Δ P (i) > 0 & & Δ \overset{\cdot\cdot}{φ} (i) < 0, Δ F_{z} (i) > 0

(24)

If the wheel accelerates or does not decelerate although ABS increases the brake pressure, the friction torque remains higher than the braking torque, as shown in Equation (3). For this reason, the wheel load should be decreased to reduce the friction torque. In this way, the friction decreases and the wheel becomes free to slow down, as shown in Equation (4b). Therefore, the wheel deceleration is brought closer to zero in a short time according to Equation (4). For this reason, the downward damping force should be decreased, as shown in Equations (14) and (14b). The rule related to this case is described as follows:

If Δ P (i) > 0 & & Δ \overset{\cdot\cdot}{φ} (i) > 0, Δ F_{z} (i) < 0

(25)

If the wheel accelerates while the brake pressure is reducing, the friction torque becomes higher than the braking torque, as shown in Figure 3. For this reason, the wheel load should be decreased to reduce the friction torque with a view to accelerating the wheel in a short time, as shown in Equation (4). Therefore, the friction decreases, as shown in Equation (4b) and the wheel acceleration is brought closer to zero in a short time according to Equation (4). For this reason, the downward damping force should be increased. The rule related to this case is as follows:

If Δ P (i) < 0 & & Δ \overset{\cdot\cdot}{φ} (i) > 0, Δ F_{z} (i) < 0

(26)

If the wheel decelerates or does not accelerate while brake pressure is reduced, the braking torque is higher than the friction torque, as shown in Equation (3). This causes the wheel to rotate in the limit of locking due to high slip, according to Equation (4). For this reason, the wheel load should be increased to make the friction torque higher than the braking torque in a short time, as shown in Equation (4). In this way, the friction or road contact increases, as shown in Equation (4b). For this reason, the downward damping force should be increased according to Equations (14) and (14b). The rule related to this case is as follows:

If Δ P (i) < 0 & & Δ \overset{\cdot\cdot}{φ} (i) < 0, Δ F_{z} (i) > 0

(27)

Furthermore, the changes in wheel load are determined depending on the direction of piston motion.

In order to determine the direction, the following rules are designed, where z₁ is axle height.

If z₁(i+1)>z₁(i), the damper is moved to upwards and the direction of damper is defined as 1.

If z₁(i+1)<z₁(i), the damper is moved to downwards and the direction of damper velocity is defined as −1.

Then, the damper stage is determined according to direction of piston. For this, the wheel load influence matrix suggested by Reul et al. (2009) is used, as shown in Table 4.

Table 4.

Wheel load influence matrix.

Damper stage	Compression (1)	Rebound (−1)
Hard to medium-hard	Decrease in wheel load	Increase in wheel load
Medium-hard to hard	Increase in wheel load	Decrease in wheel load

After the direction of piston is determined, the control strategy rules are established, as shown in Table 5.

Table 5.

Control rules for wet and slippery roads.

The road type – wet road and ΔP>0
Condition	Motion ofdamper piston	Damperstage	Wheel loadchange
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==1	Rebound	Hard	Decrease
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==−1	Compression	Medium-hard	Decrease
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==1	Rebound	Medium-hard	Increase
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==−1	Compression	Hard	Increase
The road type – slippery road and ΔP<0
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==1	Rebound	Hard	Decrease
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==−1	Compression	Medium-hard	Decrease
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==1	Rebound	Medium-hard	Increase
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==−1	Compression	Hard	Increase

As shown in Table 5, the control rules determine the damper stages based on the interactions between brake pressure change rate and wheel acceleration with reference to the direction of the piston valve. This is defined as the controlled damper.

In order to assess the performance of these control rules according to that of damper stages obtained with only a medium-hard or hard damper, the rules are applied to these damper stages, as shown in Table 6. Here, the damper is constantly set to the medium-hard or hard stage, irrespective of the direction of damper motion and road type.

Table 6.

Rules for medium-hard and hard damper stages on wet and slippery roads.

The road type – wet road and ΔP>0
Condition	Motion ofdamper piston	Damperstage	Wheel loadchange
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==1	Rebound	Medium-hard/hard	Increase/decrease
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==−1	Compression	Medium-hard/hard	Decrease/increase
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==1	Rebound	Medium-hard/hard	Increase/decrease
If ΔP(i)>0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==−1	Compression	Medium-hard/hard	Decrease/increase
The road type – slippery road and ΔP<0
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==1	Rebound	Medium-hard/hard	Increase/decrease
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ <0 && v_d(i)==−1	Compression	Medium-hard/hard	Decrease/increase
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==1	Rebound	Medium-hard/hard	Increase/decrease
If ΔP(i)<0 && $Δ \overset{\cdot\cdot}{φ} (i)$ >0 && v_d(i)==−1	Compression	Medium-hard/hard	Decrease/increase

Performance of control strategy

In order to apply these rules to an ABS braking system, the brake pressure change rate, wheel deceleration and direction of piston motion acquired in ABS tests are applied to the control strategy as an input signal, as shown in Figure 7. These signals are obtained by filtering the measured signals through a low-pass Butterworth filter. The cut-off frequency of the filter is selected as 25 Hz, as the axle resonance frequency occurs in the 7–20 Hz frequency ranges. In the direction of the piston motion signals, the compression motion of the piston is represented by 1 and the rebound motion of piston is represented by −1. Therefore, the input signal is divided into four sections to evaluate the performance of the control strategy according to both wet and slippery road surfaces. The first and third sections are established with wet road signals measured. The second and fourth sections are established by using slippery road signals, as shown in Figure 7.

Assessment of time reponses

The wheel load request results show that all damper settings need different wheel load requests, as shown in Figure 8.

The wheel load requests needed by the control strategy are similar to that of the hard damper on slippery road surface sections and to that of the medium-hard damper on wet road sections, as shown in Figure 8. This is confirmed with dynamic wheel load variations, as shown in Figure 9. Figure 9 clearly shows that the control algorithm exploits the dynamic wheel load characteristics, providing the shortest braking distance according to road type.

This shows that the controlled damper stages take advantage of the hard and medium-hard dampers according to road type, because the medium-hard damper stage obtains the shortest braking distance on the wet road surface, and the hard damper stage has obtained the shortest braking distance on the slippery road surface, as shown in Table 7.

Table 7.

Braking distances for medium-hard and hard dampers.

		Dampers
		Hard	Medium-hard
Braking distance (m)	Wet rough road	73.04	64.90
	Slippery rough road	83.67	91.96

Thus, the damper is triggered by the control algorithm in accordance with the damper stages shortening braking distance. This is a novel result, because the control strategy provides damper stages that are suitable to road type without using any algorithm for identifying the road type. It can also vary the brake pressure without directly intervening in the ABS control unit. The damper stages provided by the control algorithm are compared with hard and medium-hard dampers to determine the performance of the control algorithm, as shown in Figures 10 –13. These figures clearly show the developed control strategy enabling the brake pressure to be altered by means of the wheel load changes. Therefore, the brake pressure is increased to a high level by the wheel load changes. Also, the number of increases in brake pressure is more than that of the other dampers; however, the number of decreases in brake pressure is less than that of other dampers. In this way, the control algorithm requires less brake pressure reduction. This shows that the control algorithm applies enough brake pressure to the wheel during braking with an activated ABS.

These brake pressure changes provide the level of wheel acceleration or deceleration to reduce gradually, as the braking effects decrease, as shown in Figure 11. Also, the number of peaks related to wheel deceleration is more than that of the other dampers. Nevertheless, the number of peaks related to wheel acceleration is less than that of the other dampers. Therefore, the wheel is effectively decelerated with a high level of brake pressure change rate.

As shown in Figure 12, the friction coefficient changes in the 0.4–0.6 range; however, hard and medium-hard dampers cause a friction coefficient in the 0.2–0.7 range. Thus, the obtained wheel accelerations keep the tyre–road contact at a certain level. Therefore, this provides the friction coefficient, which has less oscillation, as shown in Figure 12.

Assessment of frequency responses

In this section, the effects of the control algorithm on wheel acceleration oscillations are investigated in the frequency domain. For this, firstly the impact of the control strategy on brake pressure oscillations is determined by using fast Fourier transform (FFT) of the brake pressure change rate as follows:

X (j ω) = \int_{- \infty}^{\infty} x (t) e^{- j ω t} dt

(28)

where X(jω) is FFT response and x(t) is brake pressure change rate in the time domain. The FFT results are shown in Figure 13.

As shown in Figure 13, medium-hard and hard dampers greatly increase the peaks; however, the control algorithm greatly reduces the level of peaks. Therefore, the brake pressure that has less oscillation is applied to the wheel by the control algorithm; in addition, the brake pressure is increased to a high level, as shown in Figure 10.

In this study, secondly, the frequency response function (FRF) is used to determine the effects of brake pressure change rate on the dynamic wheel load, friction coefficient and wheel acceleration in the frequency domain. FRF is described as follows:

H (f) = \frac{S_{AB} (f)}{S_{BB} (f)}

(29)

where H(f) is the FRF, A the excitation signal, B the response signal, SAB(f) the cross power spectrum of A and B, and SBB(f) the power spectrum of B. In this study, the brake pressure change is used as an excitation signal. The response signals are dynamic wheel load, friction coefficient and wheel acceleration, as shown in Figures 14, 15(a) and 15(b), respectively. The horizontal scale of Figures 14, 15(a) and 15(b) represents the pumping frequencies of the ABS hydraulic unit. The frequency responses of the dynamic wheel load are shown in Figure 14.

Figure 14 clearly shows that the control algorithm reduces the dynamic wheel load oscillations. Hence, the control algorithm provides a dynamic wheel load that has less of a disturbance effect on wheel acceleration or deceleration.

The effects of changes in brake pressure on friction coefficient and wheel acceleration are investigated in the frequency domain, as shown in Figures 15(a) and 15(b), respectively.

Therefore, as shown in Figure 15(a), the hard damper increases the level of friction coefficient oscillations at low pumping frequencies. Also, it greatly increases the level of wheel acceleration oscillations at high pumping frequencies, as shown in Figure 4(b). The medium-hard damper causes more peaks than that of the hard damper. In addition, it causes the level of both oscillations to increase at all frequencies. However, the controlled brake pressure reduces these oscillations, irrespective of the changes in pumping frequencies of the ABS. It is worth pointing out that the control algorithm has a greatly improved effect on the friction coefficient and wheel acceleration. This is very important for increasing the braking performance of the ABS.

These improved effects of the control strategy on the braking performance are obtained by using braking acceleration and braking distance, as shown in Figure 16.

Therefore, the braking acceleration increases and maintains a high level, as shown in Figure 16. Also, the changes in braking acceleration are more stable than those of the other dampers. These braking accelerations also shorten the braking distance, as shown in Figure 17.

The braking distance results are computed as follows:

d_{br} = \frac{d}{dt} (V_{x, measured})

(30)

In Equation (30), the braking distances of the medium-hard and hard dampers are obtained by using the vehicle speed results of the medium-hard and hard damper, respectively. That of the controlled damper is computed by substituting the vehicle speed results of the medium-hard and hard damper test into the control algorithm. In other words, if the hard damper setting is needed in the control algorithm, the vehicle speed result of the hard damper is used. However, if the medium-hard damper setting is needed, the result of the medium-hard damper is used. This is a suitable method for determining braking distance, as the tests are conducted under the same conditions.

Consequently, the control strategy decreases the braking distance by 8.25 m relative to that of hard damper, and it may decrease the braking distance by 7.73 m relative to that of medium-hard damper, as shown in Figure 17.

Conclusions

In this study, a control strategy is developed to reduce the rotational acceleration oscillations of the wheel. For this, a suspension system is integrated into an ABS by designing the control rules. The control rules are based on accordance between the brake pressure change rate and wheel acceleration. The performance of the control strategy is assessed for time and frequency responses.

Therefore, the time results state that the control algorithm can obtain different brake pressure characteristics to reduce the rotational acceleration and friction coefficient oscillations of the wheel by taking advantage of the damper obtaining the shortest braking distance. The frequency responses show that both the medium-hard and hard damper stages increase the dynamic wheel load and wheel acceleration oscillation at most pumping frequencies of the ABS hydraulic unit. However, the control algorithm greatly reduces the oscillations, irrespective of the changes in pumping frequency. Also, these reductions increase the braking acceleration throughout the braking manoeuvre with an activated ABS. This shortens the braking distance by 9.88% and 10.48% relative to that of medium-hard and hard damper, respectively.

As a result, adaptation of this control strategy to a self-tuning damper–ABS braking system integration can allow the braking distance to be shortened, as the oscillations in wheel acceleration and friction coefficient are reduced with high level brake pressure.

Footnotes

Acknowledgements

The authors are grateful to the individuals and companies who contributed to this study.

Declaration of Conflicting Interests

The authors declare that there is no conflict of interest.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the Grants from the Scientific and Technological Research Council of Turkey (Project No. 107M188) and Scientific Research Foundation of Kocaeli University (Project No. 2007/31). Also, these projects were supported by Frenteknik and HED Academy companies.

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