A permanent magnet BLDC motor has torque constant 0.12 Nm/A referred to DC supply. Find no load speed when connected to 48 V dc supply. Find stall current and stall torque if armature resistance is 0.15,per phase and drop in controller transistor is 2V.
The Correct Answer and Explanation is :
To analyze the permanent magnet brushless DC (BLDC) motor, we start by calculating the no-load speed, stall current, and stall torque using the given parameters.
1. No Load Speed
The no-load speed ( N_0 ) of a BLDC motor can be calculated using the formula:
[
N_0 = \frac{V – I_a \cdot R_a – V_{drop}}{K_t} \times 60
]
where:
- ( V ) = supply voltage (48 V)
- ( I_a ) = armature current (0 A at no load)
- ( R_a ) = armature resistance per phase (0.15 Ω)
- ( V_{drop} ) = voltage drop across the controller (2 V)
- ( K_t ) = torque constant (0.12 Nm/A)
Substituting the values:
[
N_0 = \frac{48 V – 0 A \cdot 0.15 Ω – 2 V}{0.12} \times 60
]
[
N_0 = \frac{46 V}{0.12} \times 60
]
[
N_0 = \frac{46}{0.12} \times 60 \approx 23000 \text{ RPM}
]
2. Stall Current
The stall current ( I_{stall} ) occurs when the motor is not rotating (i.e., speed is zero). This can be calculated using the formula:
[
I_{stall} = \frac{V – V_{drop}}{R_a}
]
Substituting the values:
[
I_{stall} = \frac{48 V – 2 V}{0.15 Ω}
]
[
I_{stall} = \frac{46 V}{0.15} \approx 306.67 A
]
3. Stall Torque
The stall torque ( T_{stall} ) can be calculated using the formula:
[
T_{stall} = K_t \cdot I_{stall}
]
Substituting the values:
[
T_{stall} = 0.12 \text{ Nm/A} \cdot 306.67 A \approx 36.8 \text{ Nm}
]
Summary
- No Load Speed: Approximately 23000 RPM
- Stall Current: Approximately 306.67 A
- Stall Torque: Approximately 36.8 Nm
Explanation
In this analysis, we use fundamental principles of electric motor operation. The no-load speed reflects how quickly the motor can turn when not under load, directly influenced by supply voltage, armature resistance, and internal drops. The stall current is critical for determining how much current the motor will draw when it cannot turn, which is vital for sizing the power supply and protecting the circuit. Finally, stall torque represents the maximum torque the motor can produce when starting or under heavy load, illustrating the motor’s capacity to perform work. These calculations are essential in applications where precise motor performance is required, such as robotics or industrial drives.