An undersized motor overheats and fails prematurely; an oversized motor wastes energy and capital — and both problems are avoidable with a systematic motor sizing process that starts from the actual load requirements, not from guesswork or “the same as last time.”
Motor selection is a core mechanical engineering task that appears in almost every machine design project — conveyors, pumps, spindles, robotic joints, packaging machinery, HVAC systems. The selection process requires calculating the required torque and speed at the motor shaft, accounting for the duty cycle and thermal behavior, and choosing from the available motor technologies based on performance, cost, and control requirements. This guide covers the methodology and the key decision points.
Step 1: Calculate Load Torque at the Output
Start at the load — not the motor. Calculate the torque required at the driven shaft or actuator output to overcome all resisting forces:
Linear load (conveyor, slide, cylinder): T_load = F × r, where F is the total force (load force + friction + gravity component if inclined) and r is the effective moment arm (drive pulley radius, pinion pitch radius, or lead / 2π for a leadscrew).
Rotary load (fan, pump, machine tool spindle): Torque is the resistance at the output shaft. For centrifugal fans and pumps: T = P_fluid / ω (power ÷ angular velocity). For machining spindles: T = cutting force × tool radius.
Friction and efficiency: Add friction torque from all mechanical elements in the drive train. Account for drive train efficiency (η): a worm gear with 70% efficiency requires the motor to deliver 1/0.70 = 1.43× the theoretical output torque. Chain and belt drives: 95–98% efficiency. Helical gearboxes: 96–99% per stage. Ball screws: 85–95% forward drive efficiency.
Acceleration torque: To accelerate a load with moment of inertia J_load at angular acceleration α: T_accel = J_load × α. The motor also has its own rotor inertia J_motor. Total acceleration torque referred to the motor shaft: T_total_accel = (J_motor + J_load_referred) × α. J_load_referred = J_load / i² × η, where i is the speed ratio (gear ratio) and η is efficiency. Acceleration torque can significantly exceed steady-state torque for high-inertia loads — cranes, flywheels, and large rotating tables.
Step 2: Determine Required Speed
Calculate the required motor speed from the output speed requirement and the gear/drive ratio: n_motor = n_output × i (where i is the speed ratio = motor speed / output speed). For direct-drive applications, motor speed equals output speed. For VFD-controlled motors, the operating speed range (minimum to maximum) must be within the motor’s useful speed range (typically 3:1 to 20:1 turndown for AC induction, up to ∞:1 for servo/stepper).
Standard motor speeds (4-pole AC induction motor at 50 Hz): 1450–1480 rpm no-load; full-load speed approximately 1400–1450 rpm. Common gearing: to achieve 100 rpm output from a 1450 rpm motor requires a 14.5:1 reduction (use 14.5:1 or 15:1 standard gear unit). Match the required output speed to standard motor speed + standard gear ratio combinations to minimize cost and lead time.
Step 3: Account for Duty Cycle
Motor ratings are based on the motor reaching thermal equilibrium at rated load — this is the S1 continuous duty rating (IEC 60034-1). Most industrial motors are rated S1. If the actual load cycle is intermittent, the motor can deliver higher peak power without overheating:
S1 (Continuous duty): Constant load, indefinite running time. Rating is the continuous output power at which the motor reaches rated temperature rise (typically 80 K above ambient, Class B insulation).
S2 (Short-time duty): Constant load for a specified short period (10, 30, 60, 90 min), then off long enough to cool to ambient. A motor rated S2-30 min can deliver 120–150% of its S1 rating for 30-minute bursts.
S3 (Intermittent periodic duty): Repeated cycles of running at constant load and stopped. Defined by cyclic duration factor (CDF) = run time / (run time + stop time). A motor with S3-40% CDF can operate at 120–130% of S1 rating.
For crane hoists, press drives, and other intermittent machinery: calculate the RMS (root mean square) torque over the duty cycle rather than the peak torque. The motor must deliver peak torque during acceleration phases, but the thermal rating needs only to match the RMS torque: T_rms = √[(T₁² × t₁ + T₂² × t₂ + …) / (t₁ + t₂ + … + t_rest × k)], where k is the cooling factor during rest (typically 0.2–0.5 for TEFC motors).
Motor Technology Selection
AC Induction Motor (ACIM): The standard industrial workhorse. Squirrel-cage induction motors are robust, low-maintenance (no brushes), low-cost, and widely available. IE2, IE3, IE4 efficiency classes per IEC 60034-30. Run directly on line voltage for constant-speed applications; with VFD for variable speed. Speed control range: 10:1 with VFD; torque at low speed requires either a VFD with closed-loop control or a motor designed for VFD duty (reinforced insulation, thermally monitored). Best for: pumps, fans, compressors, conveyors, blowers — any continuous-duty constant or variable-speed application where position control is not required.
Servo Motor: Permanent magnet synchronous motor with encoder feedback and servo drive amplifier. Provides precise position and speed control, high dynamic response, and operation at rated torque from near-zero speed. Significantly more expensive than ACIM — motor + drive system cost is typically 5–15× the cost of an equivalent ACIM + VFD. Best for: CNC machine tool axes, robotic joints, pick-and-place systems, packaging machinery with precise motion profiles, any application requiring position accuracy and dynamic response.
Stepper Motor: Open-loop position control (no encoder required for basic positioning) by driving the motor through discrete angular steps (typically 200 steps/rev = 1.8°/step; microstepping to 1/256 step). Simple, low-cost position control for light loads at low speed. Limitations: resonance at certain speeds, loss of position if torque is exceeded (stall without indication), low efficiency at high speeds, limited speed range. Best for: 3D printers, small CNC machines, laboratory equipment, low-cost automation where positional loads are predictable and modest.
DC Brushless Motor (BLDC): Permanent magnet motor with electronic commutation — used extensively in robotics, e-bikes, drones, and small machine tools. Excellent power density, wide speed range, high efficiency. Requires a BLDC controller. Increasingly used in servo applications as an alternative to traditional AC servo motors.
Inertia Matching
The ratio of load inertia to motor inertia (referred to the motor shaft) significantly affects dynamic performance. For servo systems, a load-to-motor inertia ratio above 10:1 produces poor dynamic response — the servo struggles to control a high-inertia load and may oscillate. Rule of thumb: match inertia ratio to 1:1 to 5:1 for high-performance servo systems; up to 10:1 for lower-performance applications; above 10:1, the system will have sluggish response and may require detuned gains that reduce accuracy.
If the inertia ratio is too high: add a gear reduction between motor and load (referred load inertia = J_load / i²), select a motor with higher rotor inertia, or accept reduced dynamic performance.
Thermal Class and Temperature Rise
Motor winding insulation is rated by thermal class (IEC 60085): Class B (130°C max), Class F (155°C max), Class H (180°C max). Most industrial motors are wound with Class F or Class H insulation. The allowable temperature rise above ambient (40°C standard) determines the continuous output capacity. A motor specified as “Class F, Class B rise” uses Class F insulation but is derated to Class B temperature rise (80 K above ambient) — providing a substantial insulation life reserve and enabling higher ambient temperature operation. Always check the thermal class and the specified temperature rise, not just the power rating.
Motor Selection Checklist
| Parameter | Calculate/Determine | Verify Against Motor Spec |
|---|---|---|
| Continuous output torque | T_continuous (from load analysis) | T_rated ≥ T_continuous |
| Peak torque (acceleration) | T_peak = T_continuous + T_accel | T_peak_rated ≥ T_peak (servo: typically 3× T_rated) |
| Output speed (max) | n_output_max from process | n_motor_max ÷ gear ratio ≥ n_output_max |
| Duty cycle | CDF = run time / cycle time | RMS torque ≤ continuous rated torque |
| Inertia ratio (servo) | J_load_ref / J_motor | Ratio ≤ 5:1 for high performance |
| Ambient temperature | Max ambient in installation location | Motor rated for ambient + rise ≤ insulation class max |
| Enclosure / IP rating | Environment (dust, water, washdown) | IP55 min for outdoor; IP65 for washdown; TEFC standard |
| Mounting | Foot, flange (B3, B5, B14 per IEC 60034-7) | Match frame and mounting type to installation |
Conclusion
Systematic motor sizing — starting from the load, calculating torque at every point in the speed-torque curve, applying duty cycle factors, and checking inertia ratio for servo applications — produces reliable, cost-effective motor selections. The most common sizing errors are ignoring acceleration torque in high-inertia applications, underestimating friction losses through the drive train, and selecting on S1 continuous rating for an inherently intermittent application. Verify your motor selection with the supplier’s application engineering team for non-standard applications — manufacturers like ABB, Siemens, Yaskawa, Mitsubishi, and Panasonic all offer application engineering support.
コメント