Gyuláné Vincze, Gergely György Balázs

Budapest University of Technology and Economics Department of Electric Power Engineering

Acceleration of a vehicle *dv/dt* with mass *m*
^{*} is determined by the vector sum of active and passive forces in the movement direction, as can be seen on equation (1.1). Force *m*
^{*}
*gsinα* resulting from the gradient of the road depends on what terrain the vehicle is designed for. Tractive resistance *F*
_{m} is determined by the type and shape of the vehicle and increases non-linearly with velocity. Sum of the passive forces is called running resistance *F*
_{e}, where *F*
_{e}
*=F*
_{m}
*+m*
^{*}
*gsinα*. Running resistance vs. velocity for different road gradients are shown in Figure 1.2.a. Tractive resistance *F*
_{m} can be got from running resistance *F*
_{e} where gradient *i*
^{*}
*=0%*.

From the viewpoint of motive force, vehicle drive has to be designed so that motive force available is greater than running resistance characteristic used for design in the whole velocity range. Based on equation (1.1), acceleration reserve is the difference of momentary motive force and running resistance *F-F*
_{e}. If the available motive force of the vehicle drive is that shown in Figure 1.2.a. then acceleration reserve is the greatest at starting and reduces to zero when *v=v*
_{max}, on a horizontal *i*
^{*}
*=*0%* *road. Final speed on a horizontal road is limited by this, as motive force *F* is not greater than momentary running resistance *F*
_{e,vmax}, i.e. the vechicle cannot accelerate. In this operating point, motive power required to keep velocity *v*
_{max} is:

Drives are designed for this final *P=P*
_{motive,max} power, and this designed power is usually available in a wide range of velocity, as can be seen in Figure 1.2.b. Motive power is constant in a wide velocity range if *P=Fv* is constant, which means that motive force decreases hyperbolically when increasing velocity. Constant power range can be used until maximal motive force *F*
_{start}, i.e. between *v*
_{0 }and *v*
_{max}. *F*
_{start} is calculated from the required starting acceleration (according to equation 1.1). Gripping limit calculated in equitation 1.3 shouls also be taken into account when designing vehicles running on wheels, as motive force greater than grip limit cannot be transferred via wheels.

Such an ideal motive force characteristic can be seen in Figure 1.2.a. This characteristic, of course, is a limit characteristic. Under this curve, motive force has to be controllable freely, according to the demanded momentary acceleration. A starting and acceleration process, which takes full advantage of the ideal motive force curve, can be seen in Figure 1.3. Motive force *F* is set to value *F*
_{e,vmax} when final velocity is reached, and acceleration reserve decreases to zero. Dynamic behavior is usually described by starting acceleration value *v*
_{0}
*/t*
_{0}. Acceleration that can be seen in the figure is used rarely; instead, softer acceleration is used that is more convenient to passengers.

Motive force and running resistance of different vehicle types are shown in Figure 1.4. and 1.5.

In the figure, specific motive force and power characteristics are shown, relative to vehicle mass *m*
^{*}.

Urban vehicles are designed for relatively low speed and high gradient angle. For example, angle *i*
^{*}=20-25% is used for garage ramp, and this slope must be performed.

Figure 1.4 is prepared for urban vehicles and gives minimal motive force and power that have to be taken into account during design.

Figure 1.5 shows motive force characteristics of locomotive series V43, popular in Hungary, for two different gradient angles and pulled masses.

Locomotive was designed for various applications (goods, slow and express trains). Allowable starting force *F*
_{start} is limited by grip limit *F*
_{μ} in equation (1.3).

Characteristics of motive force of engines with maximal voltage and current are indicated by lines 1 and 2. Line 1 is for maximal excited motor, and line 2 is for maximal allowable field weakening (42%).

Motive force range under line 3 can only be used for continuous and long time mode, under motive force *F*
_{hour}. Constant motive power is used between points A and B. Motive force for momentary acceleration demand can be set with voltage regulation and field weakening under limit characteristics. Voltage of the motor and field weakening can be changed with steps for locomotives V43.