A motor-load system is simplified depicted by Fig. 1 below. The system work at different condition as shown in Fig. 1 b and Fig. 1c, check the stability of each equilibrium equ ilibrium points.

TM

Motor

Load

Jm wM

JL

TL

b)

a)

c)

Fig. 1. Simplified motor-load system

Prob. 2

An electrical drive system is as in Fig. 1a. The load has constant torque Tload = 50Nm, the system’s total moment of inertia Jt = 0.5 kgm2. a) Determine the motor torque Tm(t) to obtain speed trajectory as shown in Fig. 2a. b) If the motor torque is as shown in Fig. 2 b, determine the speed of the system, assume the system is standstill at initial. (rad/s)

w

Tm (Nm)

376.8

0

80 50 20 0.2

0.8

1 t (s)

0

5

a)

15

2 0 t(s)

b) Fig. 2. Motor’s speed demand a) and Torque demand b)

Prob. 3

An electrical drive system is as in Fig. 1a. The total moment of inertia is 3 kgm 2. a) The load is accelerated from a speed of 500 rpm to 1000 rpm in 10 seconds. What is the total torque of the motor needed when the constant load torque is 50 Nm? b) How fast will the motor decelerate to 0 rpm speed if the motor’s electric supply is switched off? Prob. 4

A hoist system is simplified depicted in Fig. 3a below. The total moment of inertia consists of J1 =10 kgm2, J2=30 kgm2, r = 0.2m and m = 100 kg. A gearbox with gear ratio i = n1:n2=2. The mass m is driven to follow the speed profile as in Fig. 3 b. b. a) Determind the motor speed b) Calculate the motor torque.

Motor

n1

Gearbox i=2

v (m/s)

Drum

10 2r

n2

J1

24

20

0

J2

4

12

28

32

16

t (s)

v

m

15

a) Simplified structure

b) speed trajectory Fig. 3. Hoist system

Prob. 5

An electric car has a mass of 900 kg including the passengers. Air drag coefficient is Cw = 0.3, cross-sectional area A = 1.8m2. A single motor mounted on the front wheels drives the car, and the radius of the wheel is 0,3 m. The car is going uphill at a speed of 50 km/h. The slope of the hill is 30o. The friction coefficient of the road surface is 0,3. Ignore the motor loses, Determine a) The torque and speed of the motor b) The power consumption of the motor

u

wM

M (kg)

TM

r

q

Fig. 4. Up hill electrical vehicle

Hint

FL u

F1 F2

F fr F L

F M

Mg sin q

FM

Mg cos q

F1

Mg cos q

0.046Cw Au

F2

Ffr

M

wM TM

F2 Ffr

2

FL

F1

du M dt

Fg q

Prob. 6

A conveyor system is simplified depicted by Fig. 5a bellow. The total moment of inertia of the motor and the driving pulley is Jt = 1 kgm2. The driving pulley has diameter of D = 0.8m. The load is m = 1000 kg. The friction coefficient of the conveyor surface is = 0,3. a) Determine the minimum starting torque of the motor to move the load b) For a speed profile of the load as shown in Fig. 5 b, determine: - The motor speed and motor torque - Average power consumption of the motor

Load

v (m/s) 10 20 0 4

Motor

12

24

28

16

Driving Pulley

15 a) System structure

b) Desired Load Speed Profile Fig. 5. Simplified conveyor system

32 t (s)

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