AGV Motor Torque Calculation Guide: Formulas, Worked Examples & Выбор двигателя

AGV Motor Torque Calculation Guide: Formulas, Worked Examples & Выбор двигателя

Torque calculation errors are the single most common root cause of AGV drive system failures — overheating under continuous duty, wheel slip during acceleration, and insufficient climbing power on ramps. Many engineering teams select motors based on catalog peak torque or prior project experience, then discover the AGV cannot maintain speed under real-world floor conditions.

This guide provides a complete, standards-referenced methodology for calculating AGV drive motor torque — from the force balance model through gearbox ratio selection, inertia matching, thermal validation, and motor specification by payload class. It follows calculation principles consistent with МЭК 60034-1 (rotating electrical machines — rating and performance) а также NEMA MG 1 (двигатели и генераторы), and references technical documentation from Maxon, Faulhaber, and Yaskawa.

For a broader overview of AGV motor types and selection criteria, see our companion guide: Как выбрать двигатель для AGV.

1. Why Torque Calculation Matters

An AGV drive motor does not operate at a single steady-state point. It cycles through acceleration, constant-speed cruising, замедление, turning, and slope climbing — each imposing a different torque demand on the motor shaft. Selecting a motor by rated torque alone, without mapping the full duty cycle, leads to one of two outcomes:

As Yaskawa notes in its servo motor selection white paper, proper sizing requires analyzing the mechanism’s motion profile, calculating the required torque at each phase, and verifying that both continuous (RMS) and peak torque fall within the motor’s safe operating envelope [1]. The same principle applies to BLDC двигатели used in AGV drive systems.

2. AGV Driving Resistance Model

For industrial AGVs operating at speeds below 2 РС, aerodynamic drag is negligible. The total driving force must overcome three primary resistances, plus a fourth condition (turning) that applies to differential-drive configurations [2][3].

The fundamental force balance is:

Ф_total = F_roll + Ф_grade + Ф_acc

Only when the motor-driven traction force equals or exceeds F_total can the AGV maintain stable motion.

2.1 Rolling Resistance (Ф_roll)

Rolling resistance arises from elastic deformation between the wheel and the floor surface. It is the dominant resistance during constant-speed operation on flat ground.

Ф_roll = m × g × C_rr × cos(я)

On flat ground (θ = 0), cos(я) = 1, simplifying the expression to F_roll = m × g × C_rr.

2.2 Slope / Grade Resistance (Ф_grade)

When the AGV climbs a ramp, gravity produces a component along the incline that opposes forward motion.

Ф_grade = m × g × sin(я)

For small angles commonly found in warehouses (2–5% grade), the approximation sin(я) ≈ tan(я) ≈ grade ratio is acceptable. Для 3% grade:

Ф_grade ≈ m × 9.81 × 0.03 = 0.294 × m (N per kg of vehicle mass)

Для 500 kg AGV on a 3% grade: Ф_grade ≈ 147 Н. This is roughly equal to the rolling resistance on smooth concrete — meaning slope resistance can double the total traction force requirement compared to flat-floor operation.

2.3 Acceleration Inertia Resistance (Ф_acc)

Newton’s second law governs the force required to accelerate the vehicle mass:

Ф_acc = m × a

2.4 Turning Resistance (Differential Drive)

For differential-drive AGVs (two powered wheels, multiple casters), in-place rotation is typically the most demanding torque condition — often 2 к 5 times higher than straight-line torque [3]. During rotation, caster wheels generate significant steering resistance, and one drive wheel moves forward while the other moves backward.

An engineering approximation of the spin resistance force is:

Ф_spin = (2 × F_roll × √(W² + L²)) / Вт

Where W is the wheel track (distance between left and right drive wheels) and L is the vehicle length. The resulting torque per wheel:

Т_spin = F_spin × (Д / 2)

In most real AGV applications, the in-place rotation torque defines the пик motor torque requirement, while straight-line motion defines the continuous torque requirement [3]. This distinction is critical for proper motor selection — see our Motor for AGV: Полное руководство по выбору for motor type comparisons.

3. Core Torque Calculation Formulas

Once the total driving force is determined, convert it to wheel-side torque, then to motor-side torque through the gearbox.

3.1 Wheel-Side Torque

Т_wheel = (Ф_total × r) / не_{водить машину}

Engineering note: Always use the loaded wheel radius, not the nominal diameter from the catalog. Polyurethane wheels compress 3–8% under load, reducing the effective radius and increasing the required torque [4].

3.2 Motor-Side Torque (After Gearbox)

Т_{двигатель} = T_wheel / (i × η_г)

For a detailed comparison of spur vs. planetary gearboxes for AGV applications, see Прямозубый мотор-редуктор против планетарного мотор-редуктора. The choice between gearbox types directly affects both the efficiency term η_г and the reflected inertia calculation.

3.3 Power Verification

п_wheel = F_total × v

п_{двигатель} = P_wheel / (тот_г × η_{двигатель})

Where η_{двигатель} for BLDC motors typically ranges from 0.85 к 0.92 at rated load and speed, as documented in Maxon’s motor selection guide [5] and Faulhaber’s DC motor technical information [6]. The motor’s continuous power rating must exceed P_{двигатель} with a 30–50% margin to account for thermal transients and duty cycle variations.

3.4 Speed Calculation

В_м = (v × 60) / (2π × r) × i (motor RPM)

The target motor speed under load should fall within the motor’s peak efficiency range, typically 60–80% of no-load speed for BLDC motors [5][6]. Operating below 1,000 RPM increases cogging torque and torque ripple; operating above 3,500 RPM increases bearing wear and audible noise [4].

4. Worked Example 1: 200 kg AMR (Goods-to-Person)

This example demonstrates torque calculation for a lightweight AMR used in e-commerce fulfillment.

4.1 Input Parameters

4.2 Step-by-Step Calculation

Recommended system: 2 × 24V 100W BLDC motors with 20:1 two-stage planetary коробка передач, controlled by dual-channel motor controllers via RS485 Modbus RTU.

5. Worked Example 2: 1,200 kg Heavy AGV (Manufacturing Line)

5.1 Input Parameters

5.2 Step-by-Step Calculation

Recommended system: 2 × 48V 400W BLDC motors with 50:1 двухступенчатый планетарный редуктор, BLD6010-class controllers with regenerative braking enabled. The regenerative braking circuit dissipates back-EMF energy during deceleration of the 1,200 kg mass, protecting the controller from overvoltage trips [4].

6. Inertia Matching and Gear Ratio Selection

Torque is only half the sizing equation. Inertia matching between the load and the motor rotor determines dynamic response quality — how quickly the AGV accelerates, how cleanly it stops, and whether the control loop remains stable.

6.1 Equivalent Load Inertia

The vehicle mass, reflected through the wheel and gearbox, appears as an equivalent rotational inertia at the motor shaft:

Дж_{нагрузка} = (м / не_{водить машину}) × r² / i²

Where i is the gearbox ratio. The gearbox reduces the reflected load inertia by the square of the ratio — a 20:1 gearbox reduces load inertia by a factor of 400. This is why high-ratio planetary gearboxes are so effective at improving motor control stability in AGV applications.

6.2 Inertia Ratio Guidelines

These ratios are consistent with the servo motor selection guidelines published by Yaskawa [1] and the motor sizing methodology described in Maxon’s motor type selection document [5]. For stepper motor applications in AGVs, see our Servo Motor vs Stepper Motor comparison.

6.3 Gear Ratio Selection Method

The optimal gear ratio satisfies three simultaneous constraints:

1. Speed constraint: i = RPM_{двигатель,target} / об/мин_wheel, where RPM_{двигатель,target} is 1,500–3,000 RPM (peak efficiency range for most BLDC motors) [5][6]
2. Torque constraint: i must be high enough that T_{двигатель} falls within the selected motor’s continuous torque rating
3. Inertia constraint: i must be high enough that J_{нагрузка}/Дж_ротор falls within the recommended ratio

На практике, start with the speed constraint to determine a candidate ratio, then verify torque and inertia constraints. If the inertia ratio is too high, increase the gear ratio or select a motor with higher rotor inertia. For applications requiring high positioning accuracy, а direct-drive motor vs gear motor trade-off analysis may be warranted.

7. Peak vs. Непрерывный крутящий момент: Термическая проверка

Motor datasheets specify two torque values: пик (максимум) and continuous (rated). The continuous torque is limited by the motor’s thermal capacity — the winding insulation class and the cooling method determine how much heat the motor can dissipate under steady-state operation.

7.1 МЭК 60034-1 Duty Cycles

МЭК 60034-1 defines ten duty cycle classes (S1 through S10) that specify how a motor’s thermal rating applies to different operating patterns [7]. For AGV applications, the most relevant are:

For S5 duty (the most common AGV profile), the RMS (root-mean-square) torque over the full cycle determines the effective continuous torque requirement:

Т_RMS = √[(Т_acc² × t_acc) + (Т_run² × t_run) + (Т_dec² × t_dec)] / (Т_acc + Т_run + Т_dec + Т_{останавливаться})

The motor’s continuous (С1) torque rating must exceed T_RMS, and the motor’s peak torque rating must exceed the maximum instantaneous torque (typically T_acc or T_spin). Oriental Motor’s AGV sizing tool implements this RMS calculation with configurable acceleration, run, замедление, and stopping time parameters [8].

7.2 NEMA MG 1 Torque Classifications

NEMA MG 1 classifies motors into four design types based on torque characteristics [9]. While NEMA standards primarily apply to AC induction motors, the torque classification framework is useful for understanding motor behavior:

For BLDC and servo motors used in AGVs, the analogous parameters are the peak torque (corresponding to locked rotor or starting torque), the continuous torque (corresponding to rated or breakdown torque), and the torque-speed curve shape. Faulhaber’s technical documentation recommends operating the motor in the range where load torque is less than 50% of the stall torque and speed is higher than 50% of no-load speed for optimal efficiency and lifetime [6].

7.3 Термическое снижение номинальных характеристик

Motor torque ratings in datasheets are specified at a reference ambient temperature (typically 25°C per Maxon [5] or 40°C per IEC 60034-1 [7]). At higher ambient temperatures, the motor must be derated:

For AGVs operating in environments above 40°C (литейные заводы, сталелитейные заводы, outdoor summer operations), specify motors with Class F (155°С) или класс H (180°С) insulation to maintain rated torque capacity. Наш electric motor testing standards page details how GreenSky validates thermal performance under IEC 60034-1 conditions.

8. Rolling Resistance Coefficient Reference

The rolling resistance coefficient (С_rr) has the largest variance of any input parameter — it can vary by a factor of 8× depending on the wheel-floor combination. Using an incorrect value is the most frequent calculation error identified by AGV drive system suppliers [2][3][4].

Recommendation: Always measure or calibrate C_rr with field data before finalizing the motor selection. The AGV Drive Wheel manufacturer’s torque calculation guide recommends using the upper bound of the range for initial sizing, then validating with a loaded coast-down test on the actual installation floor [2].

9. Common Calculation Mistakes

10. Motor Selection by Payload Class

Once the torque calculation is complete, map the results to motor specifications by payload class. The table below provides starting-point configurations validated across multiple AGV deployments [4][10].

For custom motor configurations outside these standard ranges, GreenSky offers custom electric motor design services with IEC 60034-1 compliant testing. To understand the broader AGV vs AMR platform differences that influence motor selection, see our АГВ против АМР comparison guide.

11. 7-Step Torque Calculation Workflow

The following workflow consolidates the complete calculation process into a repeatable engineering procedure:

12. Adhesion and Wheel Slip Verification

Torque calculation ensures the motor can производить sufficient force. Adhesion verification ensures the wheel can transmit that force to the floor without slipping. These are independent checks — a motor can generate enough torque to spin the wheel without moving the vehicle.

The adhesion constraint is:

μ × F_{нормальный} ≥ F_traction

If adhesion is insufficient, options include: increasing the normal force via preload springs, adding driven wheels, or reducing the acceleration target. The required preload force is F_{нормальный} = F_traction / μ, with a 10–20% fatigue margin on the spring rate [3].

13. Motor Torque Constants and Datasheet Interpretation

Motor manufacturers specify torque in terms of a torque constant (К_Т), which relates motor current to output torque. Understanding K_Т is essential for translating the calculated motor torque into the controller current setting.

Т_{двигатель} = K_Т × I

Where K_Т is in N·m/A and I is the motor phase current in amperes. Per Maxon’s motor data documentation, К_Т has tolerances of up to ±10% and decreases with motor temperature due to magnet weakening [5]. Faulhaber’s technical information similarly notes that the torque constant is specified at 25°C and may vary under operating conditions [6].

For BLDC vs servo motor comparisons in AGV applications — including torque constant differences, control loop bandwidth, and encoder requirements — see our BLDC против серводвигателей для AGV анализ.

14. Academic and Standards References

The torque calculation methodology described in this guide is grounded in classical mechanics and validated by multiple academic and industry sources. Key references include:

• МЭК 60034-1:2022 — Rotating electrical machines — Part 1: Rating and performance. Defines duty cycle classes (S1–S10), thermal classification, and torque definitions [7].
• NEMA MG 1-2021 — Motors and Generators. Defines NEMA Design A/B/C/D torque classifications and IEC Design N/H equivalencies [9].
• Maxon Motor Type Selection — Technical document covering torque constant, speed-torque curves, and motor sizing methodology for DC and BLDC motors [5].
• Faulhaber DC Motors Technical Information — Technical manual covering coreless DC motor torque-speed characteristics, thermal limits, and operating range recommendations [6].
• Yaskawa SigmaSelect Sizing Software White Paper — Application note describing servo motor selection methodology including mechanism analysis, torque profile calculation, and RMS torque verification [1].
• Motor Parametric Calculations for Robot Locomotion (MDPI, 2022) — Peer-reviewed paper presenting motor-transmission coupling selection methodology for mobile robot drive systems, including dynamic operating range analysis [11].
• How to Model Brushless Electric Motors for the Design of Robotics Applications (arXiv, 2023) — Tutorial describing governing equations for BLDC motor modeling, including torque production, back-EMF, and thermal constraints [12].
• Michigan Technological University — Motor Calculations — Engineering reference document covering torque-speed curve construction from raw data measurements, useful for interpreting AGV motor datasheets [13].

15. Часто задаваемые вопросы

What is the formula for AGV motor torque?

The core formula is T_wheel = (Ф_total × r) / не, where F_total = F_roll + Ф_grade + Ф_acc, r is the loaded wheel radius, and n is the number of driven wheels. Motor-side torque is T_{двигатель} = T_wheel / (i × η_г), where i is the gearbox ratio and η_г is the gearbox efficiency.

What safety factor should I use for AGV motor torque?

For standard industrial AGVs, apply 1.5–2.0× to the calculated wheel torque. For safety-critical applications (медицинский, переработка пищевых продуктов, human-robot collaboration), use 2.5×. The safety factor accounts for floor condition degradation, payload variation, and long-term mechanical wear [2][4].

How do I calculate RMS torque for an AGV duty cycle?

RMS torque is the root-mean-square of the torque profile over one complete cycle: Т_RMS = √[Σ(Т_я² × t_я) / Σt_я]. Include acceleration, constant-speed, замедление, and stop phases. The motor’s continuous (С1) torque rating must exceed T_RMS. This is consistent with IEC 60034-1 S5 duty cycle analysis [7][8].

What rolling resistance coefficient should I use for AGV calculations?

For polyurethane wheels on smooth concrete (the most common AGV floor), use C_rr = 0.018–0.025. For epoxy floors, use 0.015–0.025. For rough concrete with joints, use 0.020–0.040. Always use the upper bound for initial sizing and validate with field measurements [2][3].

What inertia ratio is acceptable for AGV motors?

For closed-loop servo and BLDC servo systems, maintain J_{нагрузка}/Дж_ротор ≤ 5:1. For standard BLDC with Hall commutation, ≤ 10:1 к 15:1. For open-loop steppers, ≤ 10:1. Higher ratios cause control instability, колебание, and reduced bandwidth [1][5].

Can I use a motor with higher torque than calculated?

Да, oversizing by 20–50% is acceptable and provides thermal margin. Однако, excessive oversizing (>2×) wastes battery energy, increases controller cost, and may cause the motor to operate below its efficient speed range. Verify that the motor still operates at 60–80% of no-load speed under typical load [5][6].

Ссылки

1. Yaskawa America, Инк., “SigmaSelect Sizing Software: Proper Servo System Selection,” White Paper WP.MTN.13. [Online]. Доступный: https://www.yaskawa.com/delegate/getAttachment?documentId=WP.MTN.13
2. AGV Drive Wheel, “How to Calculate AGV Drive Wheel Torque and Motor Sizing,” Apr. 2026. [Online]. Доступный: https://agvdrivewheel.com/blog/how-to-calculate-agv-drive-wheel-torque-and-motor-sizing
3. Yikong Intelligent Equipment (Bicontrols), “Differential Drive Wheel AGV Motor Sizing Guide: Torque Calculation and Inertia Matching,” июнь. 2026. [Online]. Доступный: https://en.bicontrols.com/news_detail/104.html
4. Shenghe Motor (NBshzl), “AGV Drive System Design — BLDC + Коробка передач + Controller Engineering Reference,” июнь. 2026. [Online]. Доступный: https://www.nbshzl-motor.com/agv-drive-system/
5. Максон Групп, “Motor Type Selection,” Technical Document, Aug. 2019. [Online]. Доступный: https://www.maxongroup.us/medias/sys_master/root/8835096313886/5-Motor-Type-Selection.pdf
6. доктор. Fritz Faulhaber GmbH & Ко. КГ, “DC-Motors Technical Information,” Apr. 2026. [Online]. Доступный: https://www.faulhaber.com/fileadmin/Import/Media/EN_TI_DC-MOTORS.pdf
7. Международная электротехническая комиссия, МЭК 60034-1:2022 Rotating electrical machines — Part 1: Rating and performance, Geneva, Швейцария: МЭК, 2022. [Online]. Доступный: https://webstore.iec.ch/publication/60796
8. Oriental Motor U.S.A. Corp., “AGV — Automatic Guided Vehicle Sizing Tool,” июнь. 2026. [Online]. Доступный: https://www.orientalmotor.com/motor-sizing/agv-sizing.html
9. Национальная ассоциация производителей электротехники, NEMA MG 1-2021: Motors and Generators, Rosslyn, VA: ЗДЕСЬ НЕТ, 2021. Torque classification reference: https://www.engineeringtoolbox.com/iec-nema-standards-torques-d_741.html
10. Yikong Intelligent Equipment (Bicontrols), “AGV Drive System Selection Guide: Dynamic Calculation Method for Drive Wheels, Low Voltage Servo Motors and Servo Drives,” Jul. 2026. [Online]. Доступный: https://en.bicontrols.com/news_detail/111.html
11. С. Т. Yen and Y. ЧАС. Tsai, “Motor Parametric Calculations for Robot Locomotion,” Engineering Proceedings, vol. 20, no. 1, п. 8, Jul. 2022. [Online]. Доступный: https://www.mdpi.com/2673-4591/20/1/8
12. С. п. Н. Singh and C. Е. Hubert, “How to Model Brushless Electric Motors for the Design of Robotics Applications,” arXiv preprint arXiv:2310.00080, Oct. 2023. [Online]. Доступный: https://arxiv.org/pdf/2310.00080
13. Michigan Technological University, “Motor Calculations — Constructing Torque-Speed Curves from Raw Data,” июнь. 2003. [Online]. Доступный: https://pages.mtu.edu/~wjendres/ProductRealization1Course/DC_Motor_Calculations.pdf

Need help calculating torque for your AGV project? Contact GreenSky Power with your vehicle parameters — mass, скорость, ускорение, slope, wheel diameter — and our engineering team will return a calculation sheet with recommended motor, коробка передач, and controller specifications. Explore our full product catalog or learn more about GreenSky Power.