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# Why torque density is important for machine design

## Smarter machine design

In the design of mechanical systems, torque density can be used to make smarter design decisions. When considered during the concept evaluation stage of mechanical designs, torque density can be used to evaluate the potential success of various concepts. Multiple design solutions might be available, but when space is limited, the relative torque densities of the solution may help determine which design has the most efficient footprint.

### Did you know there is a difference between torque and torque density?

In pursuit of improved design and performance of mechanical systems, designers, manufacturers and end users must consider numerous parameters and scenarios. One often overlooked parameter is torque density. While not as commonly considered as other measurements, torque density can help designers make smarter decisions by focusing on “where the work gets done.”

Torque is defined as the measure of the turning force on an object being rotated, such as a bolt or an automotive flywheel.

Torque density expresses the ratio of torque capability to volume, in units of Joules per cubic metre or foot-pounds per cubic foot.

In short, torque density measures the torque-carrying capability of a component in a given weight and space envelope.

Power and torque fundamentals

Before exploring torque density, a brief review of power and torque can help set the stage for the importance of torque density as a design parameter.

Power is often defined as the rate of doing work. In physics terms, this is expressed as: P = W/t  where P = power, W = work, and t = time.

The metric (SI) unit of measurement for power is the Watt, also expressed as Joules per second. The English (Imperial) unit is horsepower as depicted in Figure 1. For the purpose of rating motors, one horsepower equals approximately 746 Watts.

Torque is a measure of the turning force on an object being rotated, such as a bolt or an automotive flywheel. Again returning to basic physics: T = F*r where T = torque, F = the force applied and r = the radius of the arc along which the force is applied, as shown in Figure 2. Torque is usually expressed in units of Newton-metres or foot-pounds.

Figure 1: Horsepower has been used to measure power for decades
Figure 2: Torque is a measure of the turning force on an object being rotated

Torque can also be expressed in terms of power. Through a mathematical conversion that will be omitted here for brevity, one can state power as follows: P = T*ω where P = power, T = torqueand ω = angular speed in revolutions per minute.

By re-arranging the terms, power in horsepower can be expressed as follows:

HP = (T*ω)/5252

This becomes important when designing machine systems with motors and gear boxes. Torque from a motor at the input end of a gear box can be converted to a lower rotational speed and transmitted to the output end to drive a machine, as shown schematically in Figure 3.

In a motor vehicle, the transmission adapts the output of the engine to the drive wheels, reducing the engine speed to an appropriate wheel speed, increasing torque in the process to accomplish work (i.e., propel the vehicle).

To evaluate how much power can be generated in a given space, system designers sometimes use the term power density. This is typically expressed as the amount of power per unit volume, such as Watts per cubic metre (W/m3).

Torque density is a similar concept, except instead of quantifying power, it expresses the ratio of torque capability to volume, in units of Joules per cubic metre or foot-pounds per cubic foot. In short, it measures the torque-carrying capability of a component in a given weight and space envelope.

Figure 3: Schematic diagram of a motor-gearbox arrangement to drive a machine

Why torque density is important in machine design

In the design of mechanical systems, torque density can be used to make smarter design decisions. Using consumer product analogies, purchase choices are often incorrectly made based on “brute force” factors such as how many Watts an amplifier puts out, or the horsepower rating of an engine in a pressure washer. More in-depth considerations review how efficiently an amplifier delivers a signal to its speakers, or how much water flow the pressure washer delivers at a certain pressure.

Industrial example - mining equipment

As an example, consider an industrial gear box used for mining equipment, as shown in Figure 4. If the gear box size is based on the power requirements in an electro-mechanical system, with the electric motor mounted near the gear box, large counterweights would be required to provide balance to the machine.

Based on torque requirements and a hydraulic solution, the power unit can be located where it is most convenient, such as shown in Figure 5. The actuator can then make use of superior torque density, lowering the requirements for additional counterweights and saving substantial machine structural weight and cost.

Figure 4: Mining equipment with motor located near gear box

Figure 5: Mining equipment with reduced counterweight

Paybacks from using torque density for product design and selection

The need to deliver torque is often a complex challenge. A traditional approach based on power or rotational speed might lead to unnecessarily bulky solutions. By using torque density as a key parameter, numerous paybacks can be achieved, such as:

• More efficient operation through space savings
• Cost savings due to optimal component selection
• Innovative designs and new products
• Extended equipment life due to better-matched components
• Noise reduction due to smaller motors

With torque density at the forefront, designers, manufactures and end users can all benefit from smarter machine designs.