AC Servo Motor and Drive Sizing Calculator

AC Servo Motor and Drive Sizing Calculator

Vendor-neutral sizing and technical procurement engine for permanent magnet synchronous servomotors, matched digital servo drives, high-resolution feedback encoders, and fieldbus motion interfaces.

1. Motor Power & Mechanical Frame STEP 1
2. Drive Inverter, Encoder & Industrial Network STEP 2
Engineering Sizing Summary [OK] SIZED
Continuous Rated Torque
2.39 N·m
80mm Flange
Peak Transient Torque
7.16 N·m
300% Peak Headroom
[OK] Specification Feasible & Standard Compliant
Flange dimensions, continuous phase ampacities, and DC bus levels satisfy standard thermal constraints.
Procurement Scope Matched Motor + Inverter Drive Package
Output Power & Frame 750 W | 80mm Flange | Keyway Shaft with Oil Seal
Torque Envelope 2.39 N·m (Rated) / 7.16 N·m (Peak)
Speed Envelope 3000 rpm (Rated) / 6000 rpm (Max)
Supply & DC Bus 3-Phase 380-415V AC (540V DC Bus)
Drive Output Ampacity Cont. ≥ 5.5 A | Peak ≥ 15.1 A
Position Encoder 23-bit Multi-Turn Absolute (8,388,608 PPR) | Brake: None
Control Protocol & Cables EtherCAT (CoE CiA402) | Cables: 5m Flexible Shielded Cable
ENGINEERING SIZING NOTICE: This sizing schedule is provided for preliminary technical estimation and sizing reference only. Calculations do not constitute professional engineering certification or guarantee under specific commercial conditions. Ambient thermal derating, switching harmonics, cable run inductance, and duty cycle require site verification against certified manufacturer data sheets.

AC Servo Motor and Drive Sizing Calculator: Technical Selection & Application Manual

This ac servo motor sizing calculator establishes an automated, vendor-neutral methodology to evaluate industrial permanent magnet synchronous servomotors, matched PWM servo drives, absolute position feedback systems, and motion fieldbus architectures. Formulated in accordance with IEC 60034 and DIN 42955 electromechanical standards, this tool enables automation engineers to verify rated continuous RMS torque, peak dynamic acceleration torque, reflected load inertia ratios, and internal inverter DC bus voltages across standard industrial utility feeds.

1. Dynamic Torque Sizing

Maintain continuous duty cycle RMS torque within rated S1 thermal boundaries while reserving transient peak torque headroom (up to 300%) for rapid kinematic acceleration.

2. Inertia Ratio Control

Ensure reflected mechanical load-to-rotor inertia ratios remain within stable closed-loop bandwidth limits (≤ 5:1 for dynamic positioning axes, ≤ 10:1 for general transfer).

3. Deterministic Feedback

Eliminate external homing limit switches using high-resolution multi-turn absolute encoders (up to 24-bit resolution) equipped with mechanical gear trains or non-volatile registers.

1. Core Electromechanical Mathematical Models

Rigorous servomotor selection requires matching continuous thermal dissipation limits against cyclic kinematic profiles while verifying sufficient instantaneous torque during acceleration phases.

Equation 1: Motor Rated Continuous Torque & Cyclic RMS Thermal Torque
Trated = 9550 × Prated (kW) nrated (rpm)   [N·m]   |   TRMS = √ ( Σ Ti2 · ti ) / tcycle  ≤ Trated
Equation 2: Peak Dynamic Acceleration Torque
Tpeak = Tfriction + [ Jrotor + Jload(reflected) η ] × 2π × Δn 60 × taccel   [N·m]
Equation 3: Inverter DC Bus Rectification Voltage
VDC(Loaded) ≈ 1.35 × VAC_RMS(Line)   |   VDC(NoLoad) = √2 × VAC_RMS(Line) ≈ 1.414 × VAC_RMS   [V DC]
Equation 4: Reflected Load-to-Rotor Inertia Ratio
Jload(reflected) = Jload i2   →   Rinertia = Jload(reflected) Jrotor ≤ Rallowable   (Dynamic Axis: ≤ 3:1 to 5:1 | Continuous: ≤ 10:1)

2. Standard Industrial AC Servo Motor Frame Dimensions & Capacities

Permanent magnet synchronous servomotors follow standardized metric flange envelopes and shaft configurations defined under IEC 60034-7 and DIN 42955:

Standard Power Rating Flange Frame Size Rated Torque (N·m) Peak Torque (N·m) Rated / Max Speed Nominal Bus Voltage
100 W 40 mm Flange 0.32 N·m 0.96 N·m 3000 / 6000 rpm 110V/220V AC, 24V/48V DC
200 W / 400 W 60 mm Flange 0.64 / 1.27 N·m 1.91 / 3.82 N·m 3000 / 6000 rpm 200V – 240V AC, 48V DC
750 W / 1.0 kW 80 mm Flange 2.39 / 3.18 N·m 7.16 / 9.55 N·m 3000 / 5000 rpm 200V – 240V AC, 380V AC
1.5 kW – 3.0 kW 130 mm Flange 7.16 – 14.3 N·m 17.9 – 35.7 N·m 2000 / 3000 rpm 220V AC / 380V – 415V AC
4.5 kW – 7.5 kW 180 mm Flange 28.6 – 47.7 N·m 71.5 – 119.0 N·m 1500 / 2500 rpm 380V – 480V AC 3-Phase
11.0 kW – 15.0 kW 220 mm Flange 70.0 – 95.5 N·m 175.0 – 238.0 N·m 1500 / 2000 rpm 380V – 480V AC 3-Phase

3. Step-by-Step Engineering Sizing Verification Example

Consider a direct-coupled ball-screw linear actuator stage (gear reduction ratio i = 1:1) operating under dynamic pick-and-place indexing conditions:

  • Payload Mass: m = 45 kg
  • Ball Screw Lead: p = 10 mm/rev (0.01 m/rev)
  • Screw Shaft & Coupling Inertia: Jscrew = 0.13 × 10-4 kg·m2
  • Mechanical Transmission Efficiency: η = 90% (0.90)
  • Maximum Axis Velocity: v = 0.5 m/s → Angular velocity n = (0.5 / 0.01) × 60 = 3000 rpm
  • Target Acceleration Time: tacc = 0.05 s → Angular acceleration α = (2π × 3000 / 60) / 0.05 = 6283.2 rad/s2
  • Constant Friction Force: Ffric = 60 N

Step 1: Calculate Reflected Linear Mass Inertia & Total Load Inertia:

Jload_linear = m × p2 4π2 = 45 × (0.01)2 4 × (3.1416)2 ≈ 1.14 × 10-4 kg·m2   →   Jload(reflected) = Jload_linear + Jscrew = 1.27 × 10-4 kg·m2

Step 2: Calculate Continuous Friction Torque:

Tcont = Ffric × p 2π × η = 60 × 0.01 2 × 3.1416 × 0.90 ≈ 0.106 N·m

Step 3: Evaluate Motor Sizing Margins:

Evaluating against a standard 750W 80mm flange servomotor (Jrotor = 1.40 × 10-4 kg·m2, Trated = 2.39 N·m, Tpeak = 7.16 N·m):

  • Inertia Ratio Check: Rinertia = (1.27 × 10-4) / (1.40 × 10-4) ≈ 0.91:1 (Rigid coupling, complies strictly with the ≤ 5:1 dynamic threshold).
  • Dynamic Acceleration Torque: Taccel = (1.40 + 1.27 / 0.90) × 10-4 × 6283.2 ≈ 1.766 N·m.
  • Total Peak Required Torque: Ttotal_peak = 0.106 + 1.766 = 1.872 N·m ≤ 7.16 N·m (Demands only 26.1% of the 7.16 N·m dynamic peak capacity, leaving abundant acceleration headroom).
  • Engineering Assessment: Continuous friction torque (0.106 N·m) consumes only 4.4% of continuous rated capacity (2.39 N·m), while transient peak torque during rapid 50 ms acceleration is safely capped well below the amplifier inverter limit.

4. Industrial Automation Integration & Commissioning FAQ

When should an engineer specify a smooth round shaft versus a keyed shaft?
Specify a smooth round shaft paired with zero-backlash friction clamping couplings (such as curved jaw or servo disc couplings) for cyclic reversing, high-speed indexing, and precise electronic camming. Shaft keys subjected to continuous dynamic torque reversal experience micrometric fretting corrosion, keyway deformation, and backlash hysteresis. Restrict keyed shafts to unidirectional continuous rotation or direct keyed industrial gearhead mounts.
How does AC utility input voltage govern motor torque across rated speed?
The incoming AC supply establishes internal inverter DC bus potential (VDC ≈ 1.35 to 1.414 × Vline). In permanent magnet synchronous motors, back-EMF increases linearly with angular velocity. Low bus voltages (such as 110V AC or 24V/48V DC) cause back-EMF to match the DC bus rail at low rotational speeds, causing premature torque roll-off. Higher bus supplies (380V to 480V AC, generating 540V to 680V DC) sustain rated continuous and peak acceleration torque across the full speed envelope up to maximum RPM.
What operational differences exist between battery-backed and mechanical gear multi-turn encoders?
Battery-backed multi-turn encoders rely on an auxiliary 3.6V lithium cell to power the revolution counter during system power-down. Battery exhaustion while powered off results in coordinate loss, necessitating mechanical re-homing upon reboot. Mechanical gear multi-turn encoders integrate optical or magnetic sensors across an internal miniature reduction geartrain. These devices retain absolute multi-turn position indefinitely without battery maintenance, making them standard for critical industrial machinery.
Why is 360-degree circumferential shield bonding mandatory on servo power cables?
Servo drive output stages utilize pulse-width modulation (PWM) switching frequencies (8 kHz to 16 kHz) with steep voltage slew rates (du/dt exceeding 5 kV/μs). This generates common-mode high-frequency noise currents that flow through cable parasitic capacitances. Terminating shielded motor cables across a full 360-degree circumference using brass EMC cable glands or metallic grounding clamps ensures low impedance diversion to ground, preventing cross-coupling into sensitive encoder channels and fieldbus networks (EtherCAT, PROFINET).