Sample Problems

Uncertainty

A rotating mass creates an unbalanced force given be the formula F = mrw². Determine the nominal unbalanced force, F, and the uncertainty in the force, U_F, for the following nominal values and uncertainties. Use units of lbf for force.

Mass, m = 0.0026 ± 0.0001 lbm
Radius, r = 0.367 ± 0.015 inch
Speed, w = 1750 RPM ± 2%

Op-Amp

For each of the op-amp circuits given below, assume you have a large supply of 741 op-amps and a large supply of 4.7 kW , 10 kW , 22 kW , 47 kW , and 100 kW resistors.

You are NOT required to compute uncertainties for the gain in this homework.

Be sure to show all input and output voltages, as well as all ground references for each sketch.

Minimize the number of resistors when possible - it will make your life easier!

1) Sketch a schematic showing all resistor selections for a single input, inverting amplifier with a gain of -5 ± 2% (i.e. -4.9 to -5.1)

2) Sketch a breadboard layout showing all resistor selections for a dual input, difference amplifier with a gain of 2.2 ± 2%

Sensor Selection

You have been hired by a faculty member to assist on a research project. The project needs a measurement of angular position over a 270 degree range, with a resolution of at least 0.25 degrees and an accuracy of at least ± 0.5 degrees.

Describe 5 different transducers (name or written description) or transducer/mechanical component combinations (sketches required) that will satisfy these criteria.
Give the part number and price of three transducers that will satisfy this criteria (check links from 360 website, catalogs in Design Clinic - don't ask any faculty members!) Each of these transducers can use the same physical principle for sensing position.

DC Motor

A DC permanent magnet motor has an armature resistance of 17 ohms and a theoretical no-load speed of 6000 RPM at an applied voltage of 42 volts. When operated at an armature voltage of 42 volts and a speed of 3600 RPM it develops 24.9 watts of output power.

Determine from the data at this operating point:

a) the motor’s output torque,
b) the motor’s theoretical back-EMF constant,
c) the motor’s theoretical torque constant,
d) the motor's theoretical stall torque, and
e) the motor’s efficiency.

PLC Design

Draw a PLC wiring diagram and design a ladder logic control system for the long stroke cylinder below. Two normally open pushbuttons are provided, PB-1 and PB-2, along with a double solenoid activated, three position, tandem center directional control valve.

The desired task is:

If the cylinder is fully retracted, pressing either pushbutton will fully extend the cylinder (by activating Sol. B).
If the cylinder is fully extended, pressing either pushbutton will fully retract the cylinder (by activating Sol. A).
While the cylinder is in motion (i.e., between the two limit switches), a warning light, PL-1, should be activated.
Once the cylinder reaches either the fully extended or fully retracted position, "center the valve" (by turning off both solenoids) to unload the pump.

Do not be concerned with starting or stopping the system at intermediate positions.

The hydraulic pump is controlled by a separate system and runs continuously.

PLC De-bugging

A fluid power system and its ladder logic controls are shown below. The circuit does not work as intended, but it is supposed to do the following:

cycle the cylinder (out, then back = 1 cycle) three times when C43 is pressed, also
cycle the cylinder two times when C45 is pressed.

Describe the operation of the system given below if the C43 button is pressed. Be complete and thorough in your description.
Describe the operation of the system given below if the C45 button is pressed. Be complete and thorough in your description.
Modify the ladder logic diagram such that the system works "correctly." Note that NO NEW LIMIT SWITCHES, PUSHBUTTONS, OR SOLENOIDS can be used!