NEW YORK – This is the first of two parts of a post by Prof. John Fieldhouse for The Brake Academy on a straightforward look at bringing a road vehicle to a halt:
A pragmatic approach to braking a road vehicle: Part 1 of 2
During acceleration, the power unit has to provide all the torque necessary to move the vehicle as a rigid body. In addition to accelerating the rigid body, the power unit has to provide additional torque to accelerate the rotational parts of both the driveline (including the driven wheels) and the non-driven wheels. As such there needs to be sufficient adhesion at the tire/road interface of the non-driven wheels to cause them to rotate. The rotational inertia of a vehicle may be reduced to a “mass equivalent,” so acceleration may be determined using the vehicle mass plus the mass equivalent.
That is not the case for braking. The tires do not need to be in contact with the ground for the rotational parts to be decelerated.
Consider the vehicle being raised off the ground and all wheels, and driveline. caused to rotate at the same speed. When the brakes are applied all the rotational parts will decelerate dependent on the braking torque at each axle. As such the wheels do not need to be in contact with the ground. If this is accepted, the brakes will need to be designed to account for the different rotational inertias at each axle plus the braking force at each axle, due to linear deceleration on the rigid body, taking account of the load transfer. It must be noted that the mass equivalent has no influence on the load transfer effect. The driven axle brake needs to take account of all the driveline inertia, plus the driven wheel rotational inertias, plus the linear braking force (at the driven axle). Whereas the non-driven axle brake has only the wheels to decelerate and the linear braking force. In essence, the brakes need to decelerate the vehicle as a rigid body, which is dependent on the tyre/road adhesion, in addition to the rotational inertia at each axle. It is not correct to simply treat braking as the inverse of acceleration, the braking analysis should be related to each axle.
The front braking force (torque) would include the total braking force (torque) proportioned to the front axle plus the force (torque) necessary to decelerate the non-driven wheels. The rear braking force (torque) would include the total braking force (torque) proportioned to the rear axle plus the force (torque) needed to decelerate the rotational parts of the driveline including the driven wheels.
The following analyses will consider three differing braking approaches –
1) where rotational parts are not taken into accounted,
2) where mass equivalent is not distributed to each axle but simply added to vehicle mass, and
3) where mass equivalent is distributed to each axle – referred to as the pragmatic approach.
Consider the base vehicle to be as follows, and with a general specification:
Driveline Rear wheel drive
Each wheel rotational inertia 2.1 kgm2
Total mass equivalent 10% of “m”
Tyre rolling radius 300 mm
Tyre/road adhesion 0.8 giving deceleration “d” 0.8g
Density of Cast Iron 7250kg/m3
Analysis on my next blog the following week.
Professor John Fieldhouse is currently an advisor to industry and provider of short courses regarding braking and NVH issues. He is a National Teaching Fellow and has for many years been a visiting professor at The University of Leeds – teaching chassis systems and vehicle performance. He holds a BSc from the University of Leeds and gained a PhD at the University of Huddersfield where he was awarded professorial status. John is a member of and an instructor in Brake Academy.