As a cutting-edge field of robotics, humanoid robots face unique technical challenges in designing their joint motors. Unlike traditional applications such as industrial automation and automobiles, humanoid robot joints place more stringent and complex requirements on motors.
This article systematically elaborates on the design requirements and optimization methods for humanoid robot joint motors from three core dimensions: power density, temperature rise control, and cogging torque.
I. Power Density
Power density is a key indicator for measuring motor performance, reflecting the ability to achieve maximum power output within a limited space. For humanoid robots, power density requirements can be broken down into the following three dimensions.
1.1 Dimensional Constraints
The space in the joints of humanoid robots is extremely limited, which imposes strict constraints on the physical dimensions of the motors:
Outer diameter limitation: The outer diameter of most joints is unlikely to exceed 120mm, while the outer diameter of small joints such as the wrist and elbow is usually within 80-90mm. This limitation stems from the biomimetic design concept, which requires robots to simulate the size proportions of human joints.
Axial length: The joints of humanoid robots adopt a highly integrated “hamburger” structure, stacking components such as motors, reducers, sensors, and actuators. Therefore, the axial length of the motors must be compressed as much as possible to make room for other critical components.
Hollow diameter: A hollow channel needs to be reserved inside the joint for purposes including:
- Routing channels for signal lines and power lines
- Installation space for the lead screw nut in the linear joint
- Input shaft channel of the planetary reducer in the rotary joint
These constraints cause the joint motors of humanoid robots to exhibit a typical “hollow and flat” structural feature.
1.2 Lightweight Requirements
Power density is essentially the power output capability per unit volume or unit mass. As a mobile platform, the overall weight of a humanoid robot directly affects its motion performance and energy efficiency. Therefore, motor design must minimize weight while ensuring power output.
This requires systematic design in terms of material selection and structural optimization, such as using a high-strength aluminum alloy shell and optimizing the magnetic circuit structure to reduce the amount of iron core used.
1.3 Torque Overload Capacity
Humanoid robots frequently accelerate and decelerate during movement, and have a large load inertia. This places stringent requirements on the instantaneous torque output capability of the motors.
Overload capacity: The industry generally requires motors to have a torque overload capacity of 3-5 times. For example, a motor with a rated torque of 10 Nm needs to output a peak torque of 30-50 Nm for a short period of time.
Overload duration: The peak torque duration is typically required to be 3-10 seconds. This duration covers most of the robot’s dynamic motion requirements, such as rapid standing up, jumping, and landing.
1.4 Power Density Optimization Design Method
To meet the above requirements, the following design strategies were adopted in engineering practice:
Slot fill factor improvement: Filling stator slots with as much copper wire as possible improves space utilization. By adopting technologies such as flat wire winding and segmented winding, the slot fill factor can be increased from the traditional 40-50% to 60-70% or even higher.
Electromagnetic topology optimization: Through finite element simulation analysis, parameters such as stator tooth profile, air gap length, and pole slot fit are optimized to improve torque density and overload capacity without increasing volume.
High-performance magnet applications: Humanoid robot motors commonly use high-grade neodymium iron boron permanent magnet materials, such as N52. These rare-earth magnets have extremely high remanence and coercivity, enabling them to generate strong magnetic fields within a small volume. Although the cost is higher, it is a necessary choice for applications that require ultimate performance.
Segmented magnet design: Dividing the permanent magnet into multiple small pieces not only increases the number of pole pairs, thereby improving torque, but also effectively reduces eddy current losses inside the magnet, improving motor efficiency.
II. Temperature Rise Control
Temperature control is a key challenge in the design of joint motors for humanoid robots. Compared with traditional applications, humanoid robots face unique heat dissipation difficulties.
2.1 Special characteristics of the heat dissipation environment
The problem with floating bases: Industrial robots are usually fixed to the ground or workbench, and can effectively conduct heat through the base. However, humanoid robots are mobile platforms with their joints suspended in the air, and cannot utilize a base for heat dissipation.
Limited heat dissipation methods: Humanoid robot joints can only rely on the following two methods for heat dissipation:
- Natural air convection for heat dissipation (low efficiency)
- Heat dissipation is achieved through heat conduction via joint structural components (limited pathways).
Traditional active cooling methods, such as forced air cooling and water cooling, are difficult to implement on humanoid robots, making temperature rise control a major design challenge.
2.2 Heat generation analysis under key operating conditions
Stalled state: When the robot maintains a specific posture and bears a load without moving, the motor is in a stalled state. At this time, the motor outputs a constant torque, but the speed is zero, and all electrical energy is converted into copper losses, generating a huge amount of heat. This is the worst operating condition for the motor.
Under stalled conditions, the copper loss (resistive loss) of the motor is dominant, and its power calculation formula is as follows:
Copper loss P = I² × R
Where I is the phase current, and R is the winding resistance.
Dynamic operating conditions: During robot movement, the speed and torque of the joint motors constantly change. Although the operating conditions at a single moment may not be the worst, equivalent rated operating conditions need to be considered.
Under dynamic operating conditions, the motor experiences both copper losses and iron losses (eddy current losses and hysteresis losses). The total losses are:
Total loss = Copper loss + Iron loss = I²R + Eddy current + Hysteresis
2.3 Systemic effects of temperature rise
Excessive motor temperature rise can trigger a chain reaction, affecting the performance of the entire joint module:
Gearbox performance degradation: High temperatures can cause a decrease in the viscosity of the gearbox grease, deterioration of lubrication performance, accelerated gear wear, and reduced gearbox life.
Reduced reliability of electronic components: Electronic components such as PCB boards and power modules integrated inside the joint are sensitive to temperature. For every 10°C increase in temperature, the failure rate of electronic components approximately doubles.
Decreased mechanical precision: Thermal expansion caused by temperature changes can lead to deformation of structural components, affecting the zero-point stability of the sensor and the precision of mechanical transmission.
2.4 Temperature Rise Optimization Design Method
Current density control: Current density is a key parameter for measuring the degree of heating in a winding, defined as the current flowing per unit conductor cross-sectional area.
J=AI
Where J is the current density (A/mm²), I is the current (A), and A is the conductor cross-sectional area (mm²).
Ideally, the current density should be controlled below 8 A/mm². However, in practical engineering, due to space and performance requirements, the current density of small articulated motors may reach 12-15 A/mm², while large articulated motors are relatively easier to control at lower levels.
Reduce winding resistance: The total winding resistance can be reduced by increasing the conductor cross-sectional area, using thicker copper wire, and increasing the number of parallel turns, thereby reducing copper loss and heat generation.
Application of ultra-thin silicon steel sheets: Traditional motor stators and rotors are made of silicon steel sheets with a thickness of 0.35-0.5mm stacked together. However, frameless torque motors for humanoid robots generally use silicon steel sheets with a thickness of 0.2-0.25mm or even thinner.
The thinner the silicon steel sheet, the lower the eddy current loss. According to the principles of electromagnetism, eddy current loss is directly proportional to the square of the thickness of the silicon steel sheet:
P eddy current ∝ d2
Where d represents the thickness of the silicon steel sheet. Therefore, reducing the thickness from 0.5 mm to 0.2 mm can reduce eddy current losses to 16% of the original value.
Epoxy resin potting: Thermally conductive epoxy resin is injected into the motor ends and slots to quickly conduct the heat generated by the windings to the outer casing. After the epoxy resin cures, it forms a monolithic structure, which not only enhances thermal conductivity but also improves the mechanical strength and protection level of the windings.
Magnetic circuit optimization design: By optimizing the magnetic circuit structure of the stator and rotor, magnetic resistance is reduced, leakage flux is decreased, and motor efficiency is improved. Every 1% increase in efficiency means a reduction of approximately 1% in heat generation, which is of great significance for temperature rise control.
III. Cogging Torque: The Key to Smooth Operation
Cogging torque is an inherent physical phenomenon of permanent magnet motors and has a decisive influence on the smoothness of humanoid robot motion.
3.1 The physical nature of cogging torque
Cogging torque refers to the periodic resistance torque felt by the rotor when it rotates due to the magnetic field interaction between the stator cogging structure and the rotor permanent magnet when no power is applied.
The mechanism is as follows: when the relative position of the rotor permanent magnet and the stator slot changes, the magnetic reluctance of the magnetic circuit changes periodically. The system tends to stay at the position with the minimum magnetic reluctance, thereby forming a torque pulsation that hinders or promotes rotation.
3.2 Performance Influence of Cogging Torque
Humanoid robots have extremely strict requirements for toothed torque, typically requiring its peak value to not exceed 2-3% of the rated torque, and high-end applications even require it to be controlled within 5%.
Smoothness of motion: Cogging torque can cause fluctuations in rotational speed, resulting in periodic vibrations in the robot’s joint movements. This vibration not only affects motion accuracy but can also induce structural resonance, damaging the mechanical lifespan.
Control system challenge: Cogging torque, as a periodic disturbance, places an additional burden on the servo control system. Although it can be compensated for through advanced control algorithms, fundamental optimization at the hardware level is more important.
3.3 Gear Cogging Torque Optimization Design Method
Pole-slot matching optimization: By selecting appropriate pole and slot numbers, the cogging torque at different positions can be mutually canceled out. The least common multiple principle is to choose the least common multiple of the number of poles and slots as large as possible.
For example, a 12-pole, 14-slot configuration is better than a 12-pole, 12-slot configuration because the former has a shorter cogging torque cycle and a smaller amplitude.
Fractional slot concentrated winding: This design uses a fractional slot ratio, where the ratio of stator slots to poles is a fraction rather than an integer, which can further reduce cogging torque. Common fractional slot configurations include 10 poles with 12 slots and 14 poles with 12 slots.
Stator tooth groove shape optimization: The magnitude of tooth groove torque is closely related to the shape of the stator tooth groove opening. By optimizing parameters such as groove width, tooth tip shape, and groove chamfer, the magnetic field distribution can be effectively smoothed, reducing tooth groove torque.
Finite element simulation analysis shows that using a semi-closed groove or waist-reduced groove design can reduce the tooth groove torque by 30-50% compared to an open groove.
Permanent magnet shape design: The shape of a permanent magnet directly affects the distribution of the air gap magnetic field. Common magnet shapes include:
- Rectangular magnets: simple to process, but the air gap magnetic field is a rectangular wave with high harmonic content.
- Bread-shaped magnets: The surface is arc-shaped, the air gap magnetic field is nearly sinusoidal, and the cogging torque is relatively small.
- Tile-shaped magnets: The curvature matches the inner circle of the stator, resulting in optimal magnetic field distribution.
Slanted pole design: The stator teeth or rotor magnetic poles are tilted along the axial direction by a tooth pitch angle, so that the tooth cogging torque phases at different axial positions are staggered and cancel each other out through the integral effect.
The slant angle is usually chosen as a slot pitch angle, and the calculation formula is:
θ_slope = 360 ° / Ns
Where Ns is the number of stator slots.
It should be noted that while the slanted pole design reduces cogging torque, it also causes a 3-5% decrease in rated torque, so a comprehensive balance needs to be struck.
3.4 Key Issues in Engineering Practice
There is often a significant gap between theoretical design and actual testing. In electromagnetic simulation, the cogging torque may be only 1% of the rated torque, but the measured value is as high as 10%, a difference of an order of magnitude.
The root cause of this phenomenon lies in the precision of manufacturing and assembly :
Cylindricity error of stator and rotor: Cylindricity error of the inner circle of the stator and the outer circle of the rotor will lead to uneven air gap, local increase in magnetic flux density, and sharp increase in cogging torque.
Coaxiality error: The runout error after the stator and rotor are assembled will cause the air gap to be uneven along the circumferential direction, which will aggravate the magnetic field distortion.
Stator core stacking quality: If misalignment or warping occurs during the stacking of silicon steel sheets, it will lead to an inconsistent tooth groove shape and increase tooth groove torque.
Therefore, in applications requiring extremely low cogging torque, strict control over machining accuracy and assembly processes is essential. Typical accuracy requirements include:
- Stator inner circle cylindricity: ≤0.02mm
- Rotor outer cylindricity: ≤0.02mm
- Radial runout after assembly: ≤0.03mm
IV. Systematic Design Concept
The three core indicators mentioned above are not isolated but interconnected and mutually restrictive. Excellent motor design requires finding the optimal balance among multiple objectives.
The trade-off between power density and temperature rise: Pursuing high power density means cramming more copper wire and using stronger magnets into a limited space, which inevitably leads to increased current density and heat generation. However, temperature rise control requires reducing losses and improving heat dissipation, which in turn consumes valuable space resources.
The trade-off between cogging torque and torque output: Many measures to reduce cogging torque (such as slanted poles and magnet forming) will lead to a reduction in effective magnetic flux and a decrease in torque output capability. Therefore, one should not blindly pursue extremely low cogging torque, but should set a reasonable target value based on application requirements.
Balancing cost and performance: High-grade magnets, ultra-thin silicon steel sheets, and precision machining processes all significantly increase costs. In commercial products, manufacturing costs must be controlled while meeting performance requirements.
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