Braking Formulas for Heavy Trucks

[KianaN]

I am working on virtual modeling, simulation & analysis of Heavy Trucks with Adams/truck.

I need to check the Braking distance at Emergency Braking , I found some results from my simulation , Now I need the fundamentals of braking formula to know more about the theory , please help to find:

1) Relationship between (Formula) : Truck weight (m: mass), Wheel Normal Force , Braking force ,Braking torque , Friction coefficient (μ )

2) Min braking force that lock up Wheels , how it change with truck load? I mean the braking force that need to lock up the wheels is different for empty & fully loaded Truck??

3) Weight effect on Braking force that cause wheel lock up

If there is any books or publication refer
Please give me some ideas to connect my analysis results with theory.

 

[Valerie Park]

The fundamental relationship between the weight of a heavy truck, wheel normal force, braking force, braking torque, and friction coefficient is that the greater the weight of the truck, the higher the wheel normal force, the greater the braking force required to stop the vehicle, the higher the braking torque, and the higher the friction coefficient needed to lock up the wheels. This relationship can be expressed mathematically as follows: F_w = m*a F_b = μ*F_w T_b = F_b*r where F_w is the wheel normal force, m is the mass of the truck, a is the acceleration due to gravity, F_b is the braking force, μ is the friction coefficient, and r is the radius of the wheel. The minimum braking force that will cause the wheels to lock up is dependent on the friction coefficient between the tires and the road surface. A higher friction coefficient will require a lower braking force to cause the wheels to lock up. The friction coefficient is also affected by the weight of the vehicle, and thus the heavier the vehicle, the higher the friction coefficient needed to lock up the wheels. Finally, the effect of weight on the braking force that causes the wheels to lock up can be expressed mathematically as follows: F_b = μ*m*a where F_b is the braking force, μ is the friction coefficient, m is the mass of the truck, and a is the acceleration due to gravity. For further information, you may find the following publications helpful: 1. Vehicle Dynamics: Theory and Application, by G.R. Hauler 2. Braking and Stability Systems for Heavy Vehicles, by S.N. Singh 3. Dynamics of Ground Vehicles, by J.Y. Wong 4. Fundamentals of Automotive and Engine Technology, by B.A. Wiehle