Time – Part 2

Time is the single variable that ties all of motion control and mechatronics together.  And if that is so, its impact on our design work cannot be underestimated.

The most basic feature of time is its relationship to work.  The work done in a mechatronic system is defined through displacement over time.  So a bunch of important variables get picked up.  The force exerted in mechanical terms can be a torque for a rotating load or thrust for a linear load.   The torque of a rotating load is the same as the current through the motor and drive.  And this makes sense of why these performance characteristics are related.

The power rate of electricity usage is the Kilowatt Hour.  The measure of work done over a period of time.

The horsepower is the mechanical unit of measure of work.  One horsepower is the work done to move a 550 pound load 1 foot in one second.  One horsepower is the equivalent of 746 Watts.  Now we have a direct correspondence between the mechanical and electrical definitions.

If electric motors are rated in horsepower, the implied property is the amount of work that can be done using that motor to power a load.  And an interesting anomoly occurs.  In most situations the motor is built based on an arbitraty size, like 10HP, and not based on the load requirement, unless the application has sufficiently high volume to merit a custom design.  A hard disk drive spindle motor is a case in which, because of the millions of units that will be sold, the motor design is unique.  So its construction is specifically designed for the load it is applied to, the hard disk platter turning in a vacuum.

So in general application, electric motors are poorly matched to their loads because of the economics that drive motor manufacturing.  The mis-match can be speed matching or power matching.  This impacts energy efficiency more than the inherent efficiency of the motors themselves.  Efficiency data is usually measured at rated power and can fall off dramatically for all load conditions less than maximum power.

The Power Rate of the system is directly related to the specification of the power semiconductors and mechanical contactors that are used to control motors.  So when we think of torque being equal to amperes, the current rate dI/dt is the power rate throught the electronics side of motor control.  In fact, the definition of the failure threshold in the power semiconductor, also called shoot through, is dI/dt.

Thinking about the relationship of torque and time, what happens when we consider acceleration?  Acceleration is measured in units per second squared.  Exponential.  So when we start pushing system performance for a given load, as the allowable time for the motion decreases (cycle time decreases or throughput increases) then the torque requirement goes up exponentially, and the current requirement goes up exponentially as well.  This requires a big increase in motor and drive size and cost, and in some cases reducing cycle times cannot be achieved.

Unless you change the inertia of the load.  Aluminum is one third the mass of steel, and engineering plastics are often half the inertia of aluminum.  So when you have the need for speed, don’t overlook material substitution as part of your strategy.