Mathematical model of braking process of car
Omil Kasimov, Sobit Tukhtamishov
Abstract
A mathematical model of braking a car using differential equations has been compiled. The calculation scheme of the plane-parallel motion of the car during braking is given. When braking a car, three forces are considered in the contact of each wheel with the road: the braking force, the slip resistance force, and the normal reaction of the road. A diagram of the components of the braking force acting in the plane contact of the wheel with the road when sliding. A scheme has been drawn up to determine the normal reactions on the wheels of a car. To assess the preservation of the car's controllability, a function of the driver's control action is introduced into the mathematical model, imitating the algorithm of his action. The angular speed of the steering wheel is limited by the driver's capabilities, and in emergencies is 250 ... 350 deg / s. If the heading angle decreased with the introduction of the driver's control action function, then the skid was considered controlled.