# Performance Advantages with Active Cooling

The heat generated during servo motor operation poses significant challenges to system integrators. This paper presents a review of passive motor cooling, the pros and cons of liquid and forced-air active cooling. It concludes with an outline of the impact of liquid cooling on motor performance and size.

## Passive Cooling

Electric motors convert electrical energy to mechanical energy through the interaction of magnetic fields in the stator and the rotor. This process is not entirely efficient, and energy is lost due to heat generation in the motor.

$${Power}_{in}={Power}_{out}+{Power}_{losses}$$

Note that total power losses include both heat losses and core losses. For simplicity, assume core losses are negligible. Heat is dissipated to the surroundings (heat sink or housing) through conduction, called passive cooling. The ability of the motor to dissipate heat is characterized by its thermal resistance.

$$R_{th}=\ \frac{∆T}{P_d}$$

where Rth is thermal resistance, ∆T is the temperature rise from ambient to the maximum winding temperature of the motor, and Pd is the allowable power dissipated. Thermal resistance is dependent on the surface area and thermal properties of the motor and housing. A motor with a high thermal resistance, such as a housing with low surface area in contact with the motor, dissipates less heat than a motor with a low thermal resistance, such as a motor in a large aluminum housing.

Thermal resistance affects the maximum continuous torque (Tc) rating of the motor.

Starting with the equation for motor constant (Km),

$$K_m=\ \frac{T_c}{\sqrt{P_d}}$$

Rearrange to isolate for Pd.

$$P_d=({\frac{T_c}{K_m})}^2$$

Rearrange the equation for thermal resistance to isolate for Pd.

$$P_d=\ \frac{∆T}{R_t{_h}}$$

Substitute Pd in the equation for Km and isolate for Tc.

$$T_c=\ K_m{\sqrt \frac{∆T}{R_t{_h}}}$$

An increase in thermal resistance reduces the continuous torque rating. This equation also highlights the relationship between continuous torque and allowable temperature rise (∆T). A decrease in temperature rise, caused by either reducing the maximum winding temperature or increasing the ambient temperature, decreases the continuous torque.

## Design Considerations

Motor manufacturers assume a heat sink size and material to generate motor specifications. Integrators should design a housing with a thermal resistance similar to the specified heat sink to avoid overheating the motor. In some cases, motor manufacturers assume large heat sink sizes to gain competitive advantage. If the actual heat sink design is smaller, the motor will not achieve the performance shown in the manufacturer’s specifications.

Motor specifications may be rated at high winding temperatures (e.g., 140 – 155 °C) to achieve a larger allowable temperature rise. While this increases the allowable power dissipated and torque capacity, the large temperature rise increases the likelihood of thermal expansion, bearing degradation, and reduced overall motor lifetime. To avoid these effects, the torque must be de-rated by reducing the current supplied to the motor. Additionally, motor manufacturers may limit maximum winding temperature due to restrictions of adjacent components such as encoders. When selecting a motor, these factors should be considered to accurately compare motor performance between manufacturers. Exceeding the maximum winding temperature can cause overheating, reduced lifetime, winding shorts, or adjacent component failure.

## Challenges with Passive Cooling

There are three main challenges with passive cooling: thermal limitations, heavy loads and high dynamic response.

### Thermal Limitations

Temperature rise may be restricted by the integrator due to process or material sensitivity, human contact, high ambient temperature or altitude.

• Process or material sensitivity: high precision applications cannot tolerate thermal expansion. As the motor temperature rises, materials become susceptible to expansion which can reduce the accuracy of the system.
• Human contact: when humans are near or touching the system, temperature limitations may be employed to ensure the outer touch temperature of the housing is safe (50-60°C).
• High ambient temperature: maximum winding temperature is fixed, so allowable temperature rise decreases as the ambient temperature increases.
• High altitude applications: reduced air density.

As shown in the previous equations, limiting the allowable temperature rise reduces the continuous torque available from the motor. This may require integrators to oversize motors, which increases system cost.

Applications with heavy loads and vertical moves require a motor with a high continuous RMS torque. This can be calculated for a simple trapezoidal motion profile using the following equation.

$$T_{RMS}=\ \sqrt{\frac{{T_A}^2t_A+{T_R}^2t_R+{T_D}^2t_D+{T_H}^2t_H}{t_A+t_R+t_D+t_H}}$$

where TA is acceleration torque, TR is run torque, TD is deceleration torque, and TH is holding torque. tx is the respective time per move.

Consider a trapezoidal motion profile for a vertical move (Figure 1).

TG is torque due to gravity. TAU is torque to accelerate upward and oppose gravity. TRU is torque to oppose gravity and maintain speed in the upward direction, TDU is torque to decelerate upwards aided by gravity, and TH is holding torque that is non-zero to maintain position against gravity. TAD is torque to accelerate downward, aided by gravity. TRD is torque to overcome gravity and maintain speed in the downward direction and TDD is torque to decelerate downward, opposing gravity.

If the motion profile is symmetric, as shown in Figure 1, continuous RMS torque can be calculated using either the upward or downward move. For completeness, both moves are considered in the equation below.

$$T_{RMS}=\ \sqrt{\frac{{T_{AU}}^2t_{AU}+{T_{RU}}^2t_{RU}+{T_{DU}}^2t_{DU}+{T_H}^2t_H+{T_{AD}}^2t_{AD}+{T_{RD}}^2t_{RD}+{T_{DD}}^2t_{DD}+{T_H}^2t_H}{t_{AU}+t_{RU}+t_{DU}+t_H+t_{AD}+t_{RD}+t_{DD}+t_H}}$$

Although motion profiles aren’t typically as simple as a trapezoidal velocity move, the example highlights the relationship between load torques and continuous RMS torque requirements.

### High Dynamic Response

When frequently moving and settling, high acceleration and deceleration is necessary to improve throughput. However, the ability of a motor to accelerate the load with total inertia (J) is limited by the available torque.

$$T=J\ast\alpha$$

For low duty cycles, the motor can operate under peak conditions to achieve higher torque. If the application requires high duty cycles, the motor can experience overheating when operating too long above the continuous torque. A motor with higher continuous torque can help achieve high dynamic response.

## Active Cooling

Active cooling systems use air or liquid flow to decrease the thermal resistance of the housing and subsequently increase the amount of heat dissipated from the motor. The motor can achieve higher torque capacity without overheating the system or maintain torque while operating at a lower temperature rise.

Additional benefits include reduced motor footprint, increased mean time before failure (MTBF), performance stability under varying external conditions, and improved system accuracy.

There are two types of active cooling: forced air and liquid cooling.

Forced air requires a fan to blow air onto the motor housing or coils. This a lower cost solution than liquid cooling but less effective in dissipating heat. Fans collect dust and require extra maintenance. The rotor of a motor can also be used to create air flow in the motor as it rotates, however this method is speed dependent and not effective for low-speed applications.

Liquid cooling requires a water supply, pump, and machined sleeve or heat sink with cooling channels. Proximity to motor windings, channel dimensions, flow rate, liquid type and temperature limit the allowable heat dissipation. The closer the cooling system is to the motor windings, the more effective it will be in dissipating heat. The channel structure is particularly important. It effects the distribution and speed of liquid. Poor distribution reduces the efficiency of heat dissipation. Unlike forced air, liquid cooling does not require ventilation or frequent cleaning, reducing maintenance costs. Higher performance and reduced maintenance costs can make up for the higher upfront costs incurred with liquid cooled motors.

### Higher Continuous Torque

While peak torque is limited by the current saturation point of the motor, continuous torque is limited by the allowable temperature rise of the motor winding. Peak torque can only be achieved for short duty cycles (< 3 seconds typical) before overheating occurs. Under continuous operation at the rated torque and ambient temperature, the motor reaches the maximum winding temperature. With active cooling, the motor can achieve the rated continuous torque with a reduced temperature rise. Alternatively, the continuous current can be increased, enabling higher-than-rated continuous torque without exceeding the maximum winding temperature. With active cooling, the motor could theoretically operate at peak torque continuously without exceeding the maximum winding temperature (dashed line in Figure 2).

However, there are caveats that limit the continuous torque capacity of a motor. To achieve higher torque, current must be increased up to the peak current rating of the motor. The servo drive and connectors must be able to accommodate the higher continuous current. Additionally, the cooling channels must be designed to evenly distribute cool liquid to avoid overheating. Flow rates and inlet/outlet dimensions must also be considered.

To operate continuously at the peak torque in Figure 2, the current must be increased from 14.4 Arms to 27 Arms. To ensure the motor does not overheat beyond the maximum winding temperature, the active cooling system must be able to dissipate the heat difference between the continuous and peak regimes.

If the torque speed point increases from 2.25 Nm at 1000 RPM to 3.5 Nm at 1000 RPM with active cooling, the increase in power losses needs to be calculated to determine the amount of heat the cooling system needs to dissipate. Since the speed is not changing, core losses can be ignored.

$${Power}_{losses}=\ I^2R$$
$${Power}_{l{osses}_{passive}}={14.4\ A_{rms}}^2\ast0.248\ Ω= 51.4 W$$
$${Power}_{l{osses}_{active}}=\ {27\ A_{rms}}^2\ast0.248\ Ω= 180.8 W$$

Power losses increase by approximately 130 W. The resistance does not change under the assumption that the winding temperature remains constant.

To maintain the maximum winding temperature while operating at the peak torque, the cooling system must be able to dissipate 130 W of heat from the motor. The servo drive must be able to supply 27 A of continuous current and the connector must be able to pass through the same amount.

### Reduced Form Factor

A benefit of increased torque capacity is reduced motor form factor. Although the cooling sleeve increases the motor form factor radially, the torque capacity with active cooling allows integrators to downsize their motor (Figure 3).

Figure 4 compares a 160 mm outer diameter motor with a 25mm stack length (Motor A) to a 135 mm outer diameter motor with a 25 mm stack length (Motor B). With passive cooling, Motor A has a maximum continuous torque of 16 Nm while Motor B has 12 Nm.