Electric braking is essential for controlling motor speed and ensuring safety in industrial applications. Calculating the correct electric brake parameters optimizes performance and prevents damage.
This article covers detailed calculations for electric brakes based on IEC and IEEE standards. It includes formulas, tables, and real-world examples for precise motor braking design.
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- Calculate braking torque for a 15 kW motor at 400 V, 50 Hz.
- Determine stopping time for a 10 HP motor with a 0.2 inertia constant.
- Compute brake resistor value for a 7.5 kW motor under IEC standards.
- Find braking current and torque for a 20 kW motor using IEEE guidelines.
Common Values for Electric Brake Parameters – IEC and IEEE Standards
| Parameter | Typical Range | Units | IEC Reference | IEEE Reference |
|---|---|---|---|---|
| Motor Power (P) | 0.75 – 500 | kW | IEC 60034-1 | IEEE Std 112 |
| Rated Voltage (V) | 230 – 690 | Volts (V) | IEC 60038 | IEEE Std 141 |
| Rated Frequency (f) | 50 / 60 | Hz | IEC 60038 | IEEE Std 141 |
| Inertia Constant (J) | 0.01 – 0.5 | kg·m² | IEC 60034-1 | IEEE Std 112 |
| Braking Torque (Tb) | 0.5 – 2.0 × Rated Torque | Nm | IEC 60034-1 | IEEE Std 112 |
| Stopping Time (ts) | 0.5 – 10 | seconds | IEC 60034-1 | IEEE Std 112 |
| Brake Resistor Value (Rb) | 5 – 50 | Ohms (Ω) | IEC 60034-1 | IEEE Std 112 |
Fundamental Formulas for Electric Brake Calculations
Electric braking calculations rely on several key formulas derived from motor physics and electrical engineering principles. Below are the essential formulas with detailed explanations.
1. Braking Torque (Tb)
The braking torque is the torque applied by the electric brake to decelerate the motor shaft.
- Tb: Braking torque (Nm)
- k: Braking torque factor (typically 0.5 to 2.0)
- Tr: Rated motor torque (Nm), calculated as Tr = (9550 × P) / n
- P: Motor power (kW)
- n: Motor speed (rpm)
Typical values for k depend on the braking method and motor type, with dynamic braking often requiring k ≈ 1.5.
2. Rated Motor Torque (Tr)
Rated torque is the torque output of the motor at rated power and speed.
- Tr: Rated torque (Nm)
- P: Motor power (kW)
- n: Motor speed (rpm)
This formula assumes mechanical power output and is standard in IEC and IEEE calculations.
3. Stopping Time (ts)
Stopping time is the duration required for the motor to come to a complete stop under braking torque.
- ts: Stopping time (seconds)
- J: Moment of inertia of the motor and load (kg·m²)
- ω: Angular velocity (rad/s), ω = (2 × π × n) / 60
- Tb: Braking torque (Nm)
Stopping time is inversely proportional to braking torque and directly proportional to inertia and speed.
4. Brake Resistor Value (Rb)
Brake resistors dissipate the energy generated during braking. Their value is critical for safe operation.
- Rb: Brake resistor value (Ohms)
- Vb: Braking voltage (Volts)
- Pb: Power dissipated by the resistor (Watts)
IEC 60034-1 and IEEE Std 112 provide guidelines for selecting resistor power ratings based on braking energy.
5. Braking Current (Ib)
Braking current is the current flowing through the brake resistor during braking.
- Ib: Braking current (Amperes)
- Vb: Braking voltage (Volts)
- Rb: Brake resistor value (Ohms)
Ensuring Ib does not exceed motor or resistor ratings is critical for safety and reliability.
Detailed Real-World Examples of Electric Brake Calculations
Example 1: Calculating Braking Torque and Stopping Time for a 15 kW Motor
A 15 kW, 4-pole, 50 Hz induction motor runs at 1450 rpm. The moment of inertia of the motor and load is 0.12 kg·m². Calculate the braking torque and stopping time if the braking torque factor k is 1.2.
Step 1: Calculate Rated Torque (Tr)
Step 2: Calculate Braking Torque (Tb)
Step 3: Calculate Angular Velocity (ω)
Step 4: Calculate Stopping Time (ts)
Result: The motor will stop in approximately 0.15 seconds with a braking torque of 118.55 Nm.
Example 2: Determining Brake Resistor Value for a 7.5 kW Motor
A 7.5 kW motor operates at 3000 rpm and 400 V. The braking voltage is 400 V, and the power dissipated by the brake resistor is estimated at 2000 W. Calculate the required brake resistor value.
Step 1: Calculate Brake Resistor Value (Rb)
Step 2: Calculate Braking Current (Ib)
Result: A brake resistor of 80 Ω with a power rating of 2000 W is required, and the braking current will be 5 A.
Additional Technical Considerations for Electric Brake Calculations
- Thermal Ratings: Brake resistors must be rated for continuous and peak thermal loads to avoid overheating.
- Motor Type: Synchronous, induction, and DC motors have different braking characteristics affecting calculations.
- Braking Methods: Dynamic braking, regenerative braking, and plugging each require unique parameter adjustments.
- Standards Compliance: Always verify calculations against the latest IEC 60034 series and IEEE Std 112 for motor testing.
- Safety Margins: Incorporate safety factors (typically 1.25 to 1.5) in torque and resistor sizing for reliability.