Topic A Analyzing Motor Performance
(detailed objectives) (available resources)
Goal: Students complete a realistic mathematical analysis of a real industrial electric motor.
[standards: NM-ALG.6-8.2, NM-ALG.6-12.2, NM-DATA.6-8.1, NM-DATA.9-12.2, NM-PROB.CONN.PK-12.2-3, NL-ENG.K-12.8] (please license the curriculum if you wish to view Enrichment Module PowerPoint presentations)
Summary
Though the electromagnetic phenomena that make a DC motor work can be very complicated the bulk effect is easily predicted by a few simple algebraic equations relating torque, current, and some measured motor parameters.  This topic allows the students to exercise their knowledge of Newton's laws, interpret real motor data sheets, and apply simple algebra to perform a realistic engineering analysis.

Background
Though there are many types of motors used in industry, DC motors are very commonly used in high torque applications.  Two foundational electromagnetic principles allow electric motors to work.  First, if a current passes through a conductor (a wire) in the presence of an external magnetic field, there will be a force exerted on the conductor.  Second, if a loop of wire moves through an external magnetic field, there will be an induced voltage in the loop of wire (one end will become more positively charged than the other).   We don't know why, the phenomena are simply observable facts...like gravity is a fact even though we don't really know what causes it.  A DC motor is very easy to create and it makes a fairly simple "science" experiment.  Just type "build your own dc motor" into an Internet search engine and you'll find out how.  Basically, it is simply a coil of wire that is free to rotate among some permanently mounted magnets.  When you apply a voltage to the coil (by attaching a battery), current flows through the coil and this induces a force on the coil.  The coil then rotates.  The more current you put it, the stronger the induced forces...and, hence, the higher the output torque of the motor.

Doing a mathematical analysis requires a little more background.  Students will need a basic understanding of Ohm's Law (also easy to find information online). Ohm's law says that if there is a current passing through any resistor, there will be a voltage drop across the resistor that is proportional to the current.  The equation is often written  V = I R.  So, if you measure the electrical resistance (using an inexpensive multimeter) and you apply a known voltage (like from a battery), you can precisely predict how much current will flow through the system.

This topic allows you an opportunity to apply what you know about Newton's laws.  When we put current through a DC motor a torque is induced on the motor shaft.  The only thing opposing this torque is some small amount of bearing friction.  Yet, the shaft does NOT continually accelerate (as Newton suggests would happen if an unbalanced force is applied to a system).  The motor quickly reaches some steady speed at which it will continually operate.  The phenomenon that keeps the motor from continually accelerating is the second electromagnetic principle mentioned above. Because the coil is moving in an external magnetic field, there is an induced voltage in the coil.  This voltage polarity is such that it opposes the battery and, hence, reduces the current through the coil.  In reality, the current going through the motor will only be enough to generate enough torque to overcome friction and the inertial load on the shaft...that is if the motor is strong enough to turn the shaft at all. If we apply such a heavy load to the shaft that the motor cannot turn it, we say the motor is "stalled."  Imposing such conditions on a motor for any length of time is a sure way to ruin a motor.

Motor specification sheets report a lot of data but there are three types of data that should gain our attention: the no-load condition, the stalled condition, and the rated conditions.  "No-load" represents the speed and current drawn by the motor when there is no external load applied to the shaft.  "Stalled" represents the torque and current drawn by the motor when the shaft is overloaded so that the motor cannot spin the shaft at all.  "Rated" conditions are the maximum loading conditions at which the motor can be operated indefinitely without damaging the motor.

There are a lot of steps in the motor analysis process.  Taken as a whole, it can be overwhelming.  However, use the motor worksheet one step at a time and the effort should be manageable even by young students.  The only caution is to watch the conversions between krpm (thousand revolutions per minute) and rpm (revolutions per minute).

Teacher Preparation
1. Gather motor specification sheets for your actual DC motors.
2. Compile a worksheet for the students to complete by interpreting information from the specification sheets.
3. Obtain a multimeter and verify the published resistance of your motor and the published voltage of your power source.
4. Design an experimental setup appropriate for your motor and intended test.
Classroom Activities
Explain to the students the basic operational principles of a DC motor and the basic electrical concept of Ohm's law.  Guide them through interpreting data values from the DC motor specification sheets for no-load and stalled conditions.  As a class use Ohm's law for the various states to recreate published motor performance graphs.  Demonstrate the actual motor performance and compare the speed to the predicted speed of the motor.