The dynamic performance of a road vehicle depends largely by the characteristics of the tire. The torque generated by the powertrain is applied at the wheel through the tire. The tire it’s the point of contact of the vehicle with the road, so its properties are critical for the dynamic behavior of the vehicle.
The “point of contact” of the tire with the road is in fact a surface. When the tire is inflated, the weight of the vehicle applies a normal (vertical) load on the wheel which causes the deflection of the tire. The surface of contact between the tire and the road is called contact patch.
In order to be able to analyze the forces and moments which are acting on a vehicle tire, especially during cornering, we need to define an axis (coordinate) system. Since the wheel can move in three directions, we need a 3-D coordinate system. There are several axis systems defined, the most common being the tire axis system defined by the Society of Automotive Engineers (SAE) and by ISO (International Organization for Standardization).
The SAE standard which defines the tire axis system and terminology is SAE J670 – Vehicle Dynamics Terminology.
Image: Tire axis system and terminology defined by SAE standards (right-hand road wheel)
Legend:
x – longitudinal axis (direction of wheel heading)
y – lateral axis
z – vertical axis
O – origin of the axis system
v – linear speed of the wheel
α – positive slip angle
γ – positive inclination angle
Ω – angular velocity of the wheel
Fx – tractive force
Fy – lateral force
Fz – normal force
Mx – overturning torque (moment)
My – rolling resistance torque (moment)
Mz – aligning torque (moment)
The origin (O) of the axis system it is located in the center of the contact patch. The origin is the point defined by the intersection of three planes: horizontal (defined by xOy), longitudinal (defined by xOz) and vertical (defined by yOz).
The x-axis is contained in the wheel plane and it’s parallel with the longitudinal axis of the vehicle. The positive direction of the x-axis is pointing towards the front of the vehicle.
The y-axis is perpendicular on the x-axis and the positive direction is pointing to the right side of the wheel.
The z-axis is normal to the road, the positive direction being downwards. In the ISO standard (ISO 8855) the positive direction of the z-axis is pointing upwards.
All three axes are mutually orthogonal, which means that they are perpendicular to each other. The origin (O) is the point of intersection of x,y and z axes.
For the forces and torques action on the wheel, we will define which is the positive direction.
The tractive force Fx is a longitudinal force and it’s positive in the forward direction (pointing to the front of the vehicle.
The lateral force Fy is positive towards the right, when the vehicle is moving forwards along the x-axis.
The normal force Fz is the force applied by the road to the wheel. It is negative pointing upwards and positive pointing downwards.
The overturning torque (moment) Mx is the torque which is trying to rotate the wheel around the x-axis (the wheel is falling over). The direction of rotation obtained by collapsing the y-axis onto the z-axis gives the positive direction of rotation for Mx.
The rolling resistance torque (moment) My is the torque which opposes the wheel to turn around the y-axis. The direction of rotation obtained by collapsing the z-axis onto the x-axis gives the positive direction of rotation for My.
The aligning torque (moment) Mz is the torque which rotates the wheel around the z-axis. The direction of rotation obtained by collapsing the x-axis onto the y-axis gives the positive direction of rotation for Mz.
On front-wheel drive (FWD) vehicles there is an additional torque, the drive torque. The drive torque is the opposite of the rolling resistance torque and it is the one responsible for the vehicle acceleration.
For further details regarding the tire axis system and terminology please read the standards:
- SAE J670_200801 – Vehicle Dynamics Terminology
- ISO 8855:2011 – Road vehicles — Vehicle dynamics and road-holding ability — Vocabulary
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toto
Hello, can I take your picture and quote you as a referent?