Torque Ratios

Torque Ratios

The performance of the motor is sometimes expressed interms of comparison of various torques such as full load torque, starting torque and maximum torque. The comparison is obtained by finding out ratios of these torques.

1. Full Load and Maximum Torque Ratio

2. Starting Torque and Maximum Torque Ratio

Again starting with torque equation as,

Infact using the same method, ratio of any two torques at two different slip values can be obtained.

Sometimes using the relation, R₂ = aX₂ the torque ratios are expressed interms of constant a as,

Example 5.12.1 A 746 kW, 3-phase, 50 Hz, 16-pole induction motor has a rotor impedance of (0.02 + j0.15) Ω at standstill. Full load torque is obtained at 360 r.p.m. Calculate

1) The ratio of maximum to full-load torque.

2) The speed at maximum torque and

3) The rotor resistance to be added to get maximum starting torque.

4) The ratio of maximum torque to starting torque. AU : May-14, Marks 12

Solution :

Example 5.12.2 Calculate the torque exerted fey an 8 pole 50 Hz, 3 phase induction motor operating with a 4 % slip which develops a maximum torque of 150 kgm at a speed of 660 r.p.m. The resistance per phase of the rotor is 0.5 Ω.

Solution :

Example 5.12.3 A 3 phase induction motor has a starting torque of 100% and a maximum torque of 200% of the full load torque. Determine :

1) Slip at which maximum torque occurs;

2) Full load slip

3) Rotor current at starting in per unit of full – load rotor current

Soultion

Dividing numerator and denominator by X²₂,

Dividing numerator and denominator by X²₂, 

So rotor current at start is 3.7345 times full load rotor current.

Examples for Practice

Example 5.12.5 A 24 pole, 50 Hz, star connected induction motor has rotor resistance of 0.016 Ω per phase and rotor reactance of 0.265 Ω per phase at standstill. It is achieving its full load torque at a speed of 247 r.p.m. Calculate the ratio of

i) Full load torque to maximum torque ii) Starting torque to maximum torque

[Ans.: i) 0.3824, ii) 0.1203]

Example 5.12.6 A 3-phase, 50 Hz, induction motor has a starting torque which is 1.25 times full-load torque and a maximum torque which is 2.5 times full-load torque. Neglecting stator resistance and rotational losses and assuming constant rotor resistance, find i) The slip at full-load ii) The slip at maximum torque and iii) The rotor current at starting in per unit of full-load rotor current.

[Ans.: i) 26.79 %, ii) 1.28,5.5 %, iii) Ist = 4.7673 IFL]

Example 5.12.7 A 8 pole, 50 Hz, 3-phase, induction motor develops a maximum torque of 150 N-m at 650 r.p.m. The rotor resistance is 0.6 ohm/phase. Find torque at 4 % slip. Neglect stator impedance.

[Ans.: 82.5854 Nm] 

Example 5.12.8 A 3.3 kV, 20 pole, 50 Hz, 3-phase star-connected induction motor has a slip ring rotor of resistance 0.025 ohm and standstill reactance of 0.28 ohm per phase. The motor has a speed of 294 r.p.m. when ful-load torque is applied. Compute slip at maximum torque and the ratio of maximum to full-load torque. Neglect stator impedance.

[Ans.: 8.92 %, 2.344]

Example 5.12.9 A 6 pole, 50 Hz 3-phase slip-ring induction motor has a resistance and reactance of 0.5 Ω and 5 Ω per phase respectively. Calculate i) at what speed the torque is maximum ? ii) The ratio of maximum torque/starting torque. What must be the external resistance per phase have so that the starting torque is half of the maximum torque ?

[Ans.: i) 900 r.p.m. ii) 5.05 iii) 0.839 Ω]

Example 5.12.10 A 6-pole, 3-phase, 50 Hz induction motor runs on full-load with a slip of 4 percent. The rotor standstill impedance/phase is (0.01+j 0.05) Ω, calculate the available maximum torque interms of full-load torque. Also determine the speed at which the maximum torque occurs.

 [Ans.: 2.6 Tp £Z 800 r.p.m.]

Example 5.12.11 A 6-pole, 50 Hz, 3^, induction motor has rotor resistance of 0.2 Q/phase. Maximum torque is 200 N-m at 850 r.p.m. Find

i) torque at 4 % slip

ii) additional rotor resistance to get two-thirds of maximum torque at starting. Neglect stator impedance  

 [Ans.: 99.56 Nm, 0.3092 Ω]

Example 5.12.12 A 6 pole, 3 phase, 50 Hz induction motor develops a maximum torque of 30 Nm at 960 r.p.m. Determine the torque exerted by the motor at 5 % slip. The rotor resistance per phase is 0.6 Ω.

[Ans.: 29.2683 Nm]

Example 5.12.13 A 4 pole, 50 Hz, 7.46 kW motor has, at rated voltage and frequency, at starting torque of 160 percent and a maximum torque of 200 percent of full-load torque. Determine : 1) Full-load speed 2) Speed at maximum torque.

[Ans.: 1299.15 rpm, 750 rpm]

Review Question

1. Derive the following torque ratios in term of slip and rotor parameters