Gyuláné Vincze, Gergely György Balázs
Budapest University of Technology and Economics Department of Electric Power Engineering
Table of Contents
Forces acting in vehicle movement can be divided into four groups:
forces pointing parallel to vehicle movement,
forces perpendicular to path of motion,
lateral forces acting on the vehicle,
inertial forces influencing the movement.
Forces a), b) and c) arise between the path (or medium of movement) and the vehicle.
Secure movement can be realized with strict monitoring and controlling the above forces. Main requirements of secure movement are:
vehicle moves with the expected constant speed and direction on straight-line path, it does not slip during acceleration or deceleration.
It does not (or with allowable degree) leave the planned path during change of direction.
canting, pitching and oscillation of vehicle body is damped properly and kept to acceptable level under operational circumstances.
Vector sum of active and passive forces pointing to movement direction determines whether vehicle accelerates, decelerates or moves with constant speed.
Active force in the movement direction can be:
motive force (pushing or pulling) F acting in the movement direction controlled by the vehicle driving engine and
brake force F brake acting on opposite direction, controlled by several braking actions.
In vehicles rolling on wheels, motive and brake force acts between the path and the surface of the wheels and depends on the adhesive conditions. Such a limit does not appear with levitated, linear motor-driven vehicles.
Passive force in mov ement direction is the vector sum of forces acting against the movement. Force opposite to movement is so-called tractive resistance F m. Most part of tractive force is air resistance (windage), which depends quadratically on vehicle speed, usually. Also, part of the tractive resistance is the rolling resistance and, in case of levitation, the so-called magnetic resistance depending on levitation mode. If the gradient angle of the path is α then gravitational force m * g calculated from the vehicle mass m * has passive component m * gsinα parallel to the movement, which is opposite to movement when climbing up and in the same direction (additional) when going down the slope. Gradient of the road is given by tgα: i * =100tgα[%].
Vector sum of active and passive forces in the movement direction determines acceleration of the vehicle dv/dt:
m* red is resultant accelerated mass of the vehicle. If we have to accelerate a rotating mass inside the vehicle, for example the motor with inertia Θ m, resultant mass is m* red ≥m*, where m* red=m * +(ω m 2 /v 2 )Θ m. (ω m: rotational speed of motor).
If F=F m +m*gsinα, which means that motive force equals to passive forces, then vehicle moves with constant speed, its acceleration is zero.
If F>F m +m*gsinα, then vehicle accelerates, if F<F m +m*gsinα, it decelerates.
If F goes to negative, then vehicle is in brake mode.
Forces acting perpendicular to movement path cannot be controlled in most of the land crafts, which transfer to road or rail. Exceptions are levitated vehicles.
Passive forces perpendicular to movement has two components, gravitational force pointing down, and lifting force pointing up. Gravitational force is usually much bigger. On horizontal surface, the whole weight of vehicle m * g acts perpendicularly to path, on non-horizontal surface only its perpendicular projection m * gcosα, as can be seen in Figure 1.1.b. Lifting F lf force is a component of air resistance and depends on the shape and speed of vehicle.
Controllable perpendicular active forces arise only in levitated vehicles. If active levitation forces equal to passive forces, then levitation distance is constant, otherwise the distance changes.
At traditional vehicles moving on wheels, sum of forces perpendicular to path (m * gcosα-F lf) play an important role. Part of this force G w appearing on one wheel presses the wheel to the road, and this force determines the possible tractive and brake forces. Circumferential force F tk that can be transferred on one wheel depends on pressing force and grip coefficient μ w of the wheel (k is number of wheels):
μ w grip coefficient depends on the conditions of the road and wheel, weather, velocity of the vehicle and is different for each wheel, usually. Sum of the transferable forces F t is limited because of the limited gripping coefficient, F t ≤F tmax. An ideal tractive (or brake) force can be calculated for vehicles with wheels, which can be transferred to horizontal road (α=0) with low speed (F lf ≈0), in good road conditions and dry weather. This ideal force is called gripping limit, F μ:
If tractive force of the motor or brake force of the brake system is lower than the limit, then traction is realized with normal rolling. If tractive force is higher than momentary transferable force F t, then wheel spins, if brake force if higher, then wheel blocks (see more details in Section 1.5). Such spinning or block effect does not appear in levitated vehicles.
Lateral forces cannot be controlled in most of land crafts, they are passive forces and are transferred to the road or rail. Rail or wheel counteracts these forces coming from turning or side-wind.
However active controlled lateral forces are needed to counteract lateral passive forces in levitated vehicles or to control lateral movement.
Inertial forces influencing movement of the vehicle body generate canting, pitching and oscillation of the body. Dumping of these forces is required for stabilization of the vehicle. There are special solutions for damping and stabilization.