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Road Identification for Anti-Lock Brake Systems
Equipped with Only Wheel Speed Sensors
Abstract :Anti-lock brake systems (ABS) are now widely used on motor vehicles .To reduce cost and to use currently available technologies ,standard ABS uses only wheel speed sensors to detect wheel angular velocities ,which is not enough to directly obtain wheel slip rations needed by the control unit ,but can be used to calculate reference slip ratios with measured wheel angular velocities and the estimated vehicle speed .Therefore ,the road friction coefficient, which determines the vehicle deceleration during severe braking , is an important parameter in estimating vehicle speed .This paper analyzes wheel acceleration responses in simulations of severe braking on different road surfaces and selects a pair of specific points to identify the wheel acceleration curve for each operating condition ,such as road surface , pedal-braking torque and wheel vertical load .It was found that the curve using the selected points for each road surface clearly differs from that of the other road surface. Therefore, different road surfaces can be distinguished with these selected points which represent their corresponding road surfaces. The analysis assumes that only wheel speed sensors are available as hardware and that the road cohesion condition can be determined in the initial part of the severe braking process.
Key words: anti-lock brake systems (ABS); road identification; wheel angular acceleration; tire characteristics
Introduction
For anti-lock brake systems(ABS),the road cohesion condition is one of the most important factors .Standard ABS can identify road cohesion conditions while braking and decide whether the road friction is high (asphalt) or low (snow , ice),so that the control unit activates the corresponding control logic . Only wheel speed sensors are available in standard ABS to identify the road conditions, with no other sensors needed. Road identification research is currently a popular topic in automotive control, but researchers usually assume extra equipment is available for measuring vehicle motion and other state parameters besides wheel speed sensors, to continuously monitor the road condition. But standard ABS only needs to identify road conditions during the initial braking period, and then obtain road information to ensure necessary operations of the control unit. Obviously, the standard ABS demands less strict identification, therefore less hardware and cost. However, the method to identify the conditions is not obvious. This paper investigates the road identification method for the standard ABS configuration.
The analysis is based on the wheel angular acceleration, which is acquired from the measured wheel angular speed. Since tire-road friction characteristics differ on different road surfaces, the wheel responses while braking on different surfaces are also different, so the wheel responses must contain road cohesion information. Therefore, we simulated braking situations and then chose two typical values on the wheel acceleration curve as criteria to distinguish between different road surfaces. Influence of uncertainties in the measurements is also discussed.
1 Modeling
A one quarter vehicle model (Fig.1) is used with the Dugoff tire model. The peak values of the tire slip-friction curve (i.e., cohesion coefficient) are different for different road surfaces, such as dry asphalt 0.8-0.9, wet asphalt 0.5-0.7, snow about 0.2 and ice about 0.1.Furthermore, when the slip ratio increases above zero, the friction coefficient increases at a different rate. This is especially true for the increase of the friction coefficients on snow or ice which are much lower than on asphalt. This feature is important since the control unit makes decisions about road conditions before the friction coefficient reaches a maximum .Once the friction coefficient is close to the maximum, the control unit starts to regulate the braking pressure. Generally, the friction coefficient rate of increase with the increasing slip ratio on asphalt is at least double that on snow or ice. To reflect this difference, the initial slope of the characteristic curve on asphalt was assumed to be twice that of snow. If the difference is even greater, the results using the assumption will be even more effective.
Fig.1 one quarter vehicle model
A first-order braking model is given by:
dTp/dt=(Tp-Tb)/ て (1)
where Tp is the pedal-braking torque, Tb is the actual braking torque, and てis the brake constant.
2 Results and Discussion
Full load for the quarter-vehicle model is 400 kg. The maximum pedal-braking torque is 1000Nm, which is theoretically enough to produce a vehicle deceleration of 1g. On snow (0.2), the maximum ground-braking torque is 200Nm so if the pedal-braking torque is over 200Nm, the wheel will lock. On wet asphalt (0.5), the maximum ground-braking torque is 500Nm so the wheel will lock at a pedal-braking torque higher than 500Nm.Wheel acceleration curves are shown in Fig.2 for braking on wet asphalt (0.5) and snow (0.2) using different pedal-braking torques. In each case, the pedal-braking torque is high enough to lock the wheel. On either road surface, increasing the pedal-braking torque cause the wheel to decelerate more rapidly and the slip ratio to increase. On snow, when the pedal-braking torque is very, the wheel decelerate much more rapidly than on asphalt, so the system can easily judge when the road is covered with snow. However, when the pedal-braking torque is not very high but enough to cause lockup, the wheel deceleration process may resemble that on asphalt, the control unit may not be able to decide which type of road surface has been encountered. This case needs further analysis.
---------- Snow Wet asphalt
Fig.2 Wheel acceleration for different pedal braking torques on wet asphalt and snow
Each acceleration curve in Fig.2 can be described with two points on the curve. One is the acceleration at the time 0.05s, and the other is the time when the acceleration reaches – 50 rad/s2. (Braking starts at time 0.) We refer to these as the acceleration-time criteria and the curve defined by these points is referred to as the acceleration-time curve. Acceleration-time curves for asphalt (0.9, 0.7, and 0.5) and snow (0.2) are drawn in Fig.3 for maximum ground-braking torques of 900, 700, 500, and 200 Nm. None of the curves intersect which means the acceleration –time criteria corresponds to a particular road surface or maximum ground braking torque.
The previous analysis assumed a fully-loaded vehicle. If the wheel vertical load changes, the wheel will behave differently which will result in different acceleration-time curves. Three acceleration-time curves for a half-loaded wheel on asphalt (0.9 and 0.5) and snow (0.5) are shown in Fig.4 with the full-load curves. Their maximum ground braking torque are 450, 250, and 100 Nm. Assuming that the acceleration-time curve for a wheel with a partial load between “full” and “half”
on asphalt (0.9) will be located between the curves for braking torque of 900 Nm and 450Nm, then a partial load curve would be similar to the curve for braking torque of 700Nm and 500Nm. Therefore, the acceleration-time criteria do not correspond to the road surface, but to the maximum ground braking torque. It is physically reasonable that the wheel response depends on the difference between the pedal-braking torque and the road friction potential (ground-braking Torque), In cases where the wheel load does not vary greatly, such as in passenger cars, the full load of a car may not be double the load of empty car, then the acceleration-time curves for asphalt and snow will always be separated for any operating conditions. In such cases, asphalt and snow can be distinguished by the acceleration-time criterion.
3 Conclusions
This paper analyzes the relationships between the wheel load. The proposed wheel acceleration-time criteria, which can be measured by a control unit with wheel speed sensors, can reflect the road friction potential resulting from the road surface and wheel load. For passenger cars, the criteria can even determine the road conditions, whether the wheel is in contact with asphalt or snow.