Alva Industries highlights the importance of motor constant (Km) as a primary performance indicator for motors in drones and robotics, going on to explain how FiberPrinting™ can deliver motors with a higher Km than comparable alternatives available.
Explanation of motor constant (Km)
In certain scenarios, a high Km can serve as crucial performance metric. This value demonstrates torque production relative to heat generated within a device due to inefficiencies.
Km is defined and calculated as follows:
Km = T/sqrt(Pl), (1)
T represents torque (Nm), Pl indicates power dissipation (W).
Under specific assumptions detailed later, Km may also be expressed through another parameter – torque constant Kt:
Km = Kt/sqrt(R), (2)
Kt measured in Nm/A, R denotes resistance (Ohms).
Kt illustrates potential torque delivery when supplied particular current amount.
When utilizing expressions (1) and (2), ensuring correct parameters and units is vital. For instance, if Kt uses Nm/Arms, then R (in formula 2 above) must reflect three-phase equivalent resistance, not measured line-line value RL-L:
R = 3/2*RL-L, (3)
Employing Km as Primary Performance Indicator
It’s crucial to recognize that using Km, especially defined by expression (2), assumes all generated heat originates from copper losses caused by current flowing through motor winding (Pl =I2R). Other loss sources are disregarded. Thus, Km accurately depicts losses only when a motor delivers torque without movement or at low velocities.
Consequently, designs where additional losses aren’t negligible prove less suitable for evaluations based on Km value. Typically, other inefficiencies like core losses, magnet-related issues, windage effects become more pronounced at higher operational speeds.
Utilization of motor constant in comparative analysis
Keeping aforementioned assumptions in mind, it can still be said that Km proves highly useful when comparing multiple motors of similar dimensions, voltage ratings, speed capabilities, and power output. The motor with higher Km can be expected to provide greater torque, maintain lower surface temperature, and consume less energy (i.e., exhibit improved efficiency).
When conducting benchmarking, ensuring parameters and units used are accurate and consistent across compared cases is crucial. For example, verifying R represents three-phase equivalent resistance rather than measured line-to-line value (as previously mentioned).
Motor constant as the factor in sizing considerations
Examining motor constant value becomes particularly important when determining appropriate motor sizes for applications where heat dissipation options are limited and the device surface cannot reach excessive temperatures, such as medical equipment or humanoid robotic systems.
Engineers must evaluate how much thermal energy can be comfortably absorbed into the system. Typically, thermal resistances are identified and subsequently used to establish limits on heat generation. If it is known that a robotic joint can dissipate no more than 100 W before surface temperature exceeds design threshold, this information helps determine allowable Km.
For instance, if 10 Nm torque is required, and the mechanical structure can only dissipate 100 W, a motor with minimum Km of 1 Nm/W1/2 becomes necessary. This motor must also fit available space and operate from given power source at specified speed.
Caution when using motor constant as the primary metric
As previously noted, Km proves less useful in power conversion applications where motors constantly run at several thousand RPM compared to low-speed, high-precision scenarios. Again, the reason lies in non-ohmic losses becoming considerable at higher velocities.
In slotless motors, speed-dependent losses are lower than in iron-cored slotted counterparts. For slotless designs, even at 3000-5000 RPM, fundamental conduction losses can comprise around 90% of total inefficiencies.
Therefore, comparing slotless vs slotless motors based on Km remains viable for relatively high speeds. However, when evaluating slotless against slotted for high-speed operation, Km becomes less reliable parameter.
Nonetheless, Km can still serve as useful performance indicator when considered alongside other application-specific criteria.
Derivative figures of merit
Depending on intended use, various Km derivatives may prove beneficial as performance metrics, such as Km/weight and Km/volume ratios.
For example, low weight is crucial for exoskeletons and aerospace applications. This means that Km/weight ratio might be employed as key indicator. However, size also matters, so Km/volume could be equally valuable metric.
Significance of Elevated Motor Constant in Specific Applications
For medical devices, assuming 25°C operating room temperature is often reasonable. When considering robotic-assisted surgery systems, large heat sinks for thermal dissipation are unlikely, making thermal considerations paramount.
If a patient’s surface temperature limit is set to 45°C, the available temperature rise above ambient (dictating power dissipation) is merely 20°C. Consequently, minimizing generated heat through high-Km motor technology becomes essential.
Gimbal systems frequently rely on battery power. Higher Km translates to reduced energy consumption, resulting in extended operational time.
In practice, elevated Km yields either cooler motor running at the same torque or increased torque production while maintaining identical surface temperature.
FiberPrinting™ Yields Motors with Superior Motor Constant
Due to inherent advantages of FiberPrinting™ technology, such as enhanced copper fill factor and optimized winding geometry, Alva’s motors typically exhibit higher Km than comparable alternatives available in market (Fig. 1).
In Alva’s devices, motor constant remains unaffected by core saturation under heavy loads, maintaining validity even at extremely high peak currents and torques.
Fig. 1. Benchmarking of several iron-cored (slotted) and slotless motors with outer diameter of 75 mm and axial length of 20 mm.
