ME 454 Exam 2 Hw 6-8

Is it invertible, over its entire range?

The sensor is invertible if the slope is nonzero over the entire range. The sensor is invertible over its usable range but not the entire range. The slope is close to zero at the extremes of the operating range

[a,b] = butter(2, 300/500);

This is a low pass filter so noise at high frequency will be removed and theoretically completely removed at ∞ frequency. Given the above MATLAB command, will noise of ∞ Hz: Be completely removed

At a certain speed, a DC motor typically has maximum efficiency. For the average motor, what is the speed of maximum efficiency?

Efficiency = Mechanical power out/Electrical power in = Torque*Speed/Voltage*Current:Eff = T*S/(V*I) = (Tmax - S*Tmax/Smax)*S/(V*(V - Vb)/R)Numerator is parabolic in S. Vb increases linearly with speed so denominator decreases linearly with speed. Thus, the maximum will occur somewhere above the max power point, typically around 90% of the no-load speed Smax. Brushed DC motors typically run below 10,000 rpm because the centrifugal forces above that speed tend to tear them apart. So the best answer is 7,000 rpm

The maximum torque that a brushed DC electric motor can create is proportional to the voltage applied

For the standard brushed DC electric motor the maximum torque = V*kt/R, where V = voltage, Kt =torque constant, and R = winding resistance. Maximum torque is at zero speed (stall torque), so the current is simply V/R and torque = Kt*current. True

a,b] = butter(2, 300/500);

From Matlab: [b,a] = butter(n,Wn) returns the transfer function coefficients of an nth-order lowpass digital Butterworth filter with normalized cutoff frequency Wn. Thus, this Matlab command creates a 2nd order lowpass digital Butterworth filter with normalized cutoff frequency Wn = 300/500. The cutoff frequency is normalized by dividing the cutoff frequency by half of the sample frequency. So for Wn = 300/500, and the sample frequency = 1 kHz, then the cutoff frequency is 300 Hz. Noise of 200 Hz is below the cutoff frequency for this low pass filter, so it will not be significantly reduced. Given the above MATLAB command and a sample frequency of 1 kHz, will noise of 200 Hz: Mostly stay

A PMDC motor generates constant torque across all operating speeds.

PMDC motor is a Permanent Magnet DC motor which is the same as a brushed DC motor. We know that torque decreases linearly with speed for a PMDC motor. False

Which one(s) of the above sensors can theoretically respond to its input without any phase delay?

Phase delay occurs whenever the filter has dynamics. Phase = angle(G) = atan2(imag(G),real(G)), where G is evaluated at s = jw. Only transfer function d has no "s". A transfer function is a static relationship (no dynamics) so it has no phase delay. Output is in phase with input for all frequencies. (Need diagram)

The maximum power output of a brushed DC motor occurs at half of its no load speed

Power output = Torque*speed = (Tmax - Tmax*S/Smax)*S. Calculate dP/dS = 0 (maximum) and youget S = Smax/2. True

The no-load speed is equal to the maximum possible speed of a motor.

Speed can only decrease if we load the motor. Generally speaking, the motor is designed to go tothe no load speed and no faster (windings might explode). Protect against cases where the motor is overdriven (e.g., a runaway vehicle going downhill). True

Is this sensor approximately linear in behavior, in its usable range?

True

For the application below, which motor type makes the most sense to use: PMDC,brushless motor, a stepper, hobby servo, AC induction, universal motor?

A very cheap motor that needs to move at a constant, slow velocity with little torque, preferably not requiring any position sensor to obtain position. C. Stepper

Explain why stepper motors are frowned upon for paper printers in terms of environmental impact:

A. Consume more power in motion B. Consumer more power when held D. Low efficiency

A wheelchair motor operating at maximum speed (180 RPM) provides a desired wheelchair speed. What gearbox ratio r = Input Speed/Output Speed is needed on this motor to make it run at maximum efficiency?

Assume the gearbox is lossless so it doesn't change efficiency. For maximum efficiency, we want to run somewhere between Smax/2 and Smax, typically around 80% of Smax. So we want input(motor) speed = .8(180 RPM) while the output speed = 180 RPM. This means that r = 0.8(180 RPM)/(180RPM) = 0.8. A

What is the difference between full-step and half-step sequences on a stepper motor, in terms of the number of steps needed?

B to see diagram HW 8 Q 22

For the application below, which motor type makes the most sense to use: PMDC, brushless motor, a stepper, hobby servo, AC induction, or universal motor? A motor that needs to have very precise position control.

B. Brushless Motor

For the application below, which motor type makes the most sense to use: PMDC, brushless motor, a stepper, hobby servo, AC induction, or universal motor?

Universal Motor

A wheelchair motor operating at maximum speed (180 RPM) provides a desiredwheelchair speed. What gearbox ratio r = Input Speed/Output Speed is needed on this motor so itprovides max power at that same desired wheelchair speed?

Assume the gearbox is lossless so it doesn't change power. Power is maximum when motor is runningat Smax/2 = 90 RPM. Thus, r = 90 RPM/180RPM = .5. A

The efficiency of the motor peaks when the motor outputs maximal power

Efficiency = Mechanical power out/Electrical power in = Torque*Speed/Voltage*Current:Eff = T*S/(V*I) = (Tmax - S*Tmax/Smax)*S/(V*(V - Vb)/R) The numerator is parabolic in S. Vb increases linearly with speed so the denominator decreases linearly with speed. Thus, the maximum will occur somewhere above the max power point, typically around 90% of no load speed Smax. False

Why is graphite used as the commutator for DC motors?

Graphite brushes need low friction and good conduction

A sequence of first-order low-pass filters in series will make a higher order low-pass filter with the same cutoff frequency.

passive filters only work if they are connected to a high impedance load so the output current is almost zero. This is true if you hook up the filter to an ADC input channel, for example. If you connect one passive filter to another passive filter, however, they draw current from each other, and the high impedance load assumption is no longer valid. There is no guarantee that multiple first-order low-pass filters in a series will make a higher-order low-pass filter with a similar cutoff frequency. False

Select the optimum motor for each application among: A) Brushless motor B) stepper motor C) AC induction D) universal motor E) servo 1. A very cheap motor that needs to move at a constant, slow velocity with little torque, preferably not requiring any position sensor to obtain the position 2. Motor that needs very precise position control 3. A motor that needs to produce large power (10 HP or more), with large torque at large speeds. 4. A motor that needs to be extremely cheap to move across a limited angle. It doesn't have to be reliable but needs to go to a position command that it's given and hold that position on its own 5. A motor that needs to be cheap but produces a lot of torque, but speed doesn't matter that much. Strong preference to run on AC or DC

1: B, 2: A, 3:C, 4: E, 5: D

For each of the applications below, which technology should most likely be used (and justify your answers): hydraulic, pneumatic, or electric motors? 1. You need to select an actuator to aim a cannon turret on a tank. It needs to be extremely powerful and extremely accurate. 2. You are building a brain-surgery robot and need extreme precision and repeatability, as well as a very clean operational environment. 3. You are building a device to push apples off a conveyor belt that does not appear to be high-enough quality. It needs to be fast, can be all on/off, but cannot contaminate the food

1: Hydraulic, 2: Electric, 3: Pneumatic

For the application below, which motor type makes the most sense to use: PMDC, brushless motor, a stepper, hobby servo, AC induction, or universal motor?

A motor that needs to be extremely cheap to move across a limited angle. It doesn't have to be reliable, but needs to go to a position command that it's given and hold that position on its own. D. Hobby Servo

For the application below, which motor type makes the most sense to use: PMDC, brushless motor, a stepper, hobby servo, AC induction, or universal motor?

A motor that needs to produce large power (10 HP or more), with large torque at large speeds. E. AC Induction

For a DC motor, what do A, B, and C correspond to in the given plot if X-axis is speed? (UsingVoltage, Power, and Torque)

A: Power versus Speed, B: Voltage versus speed, C: Torque versus speed HW 7 Q8

Based on trends in paper printers, what motor technology could better replace steppermotors in 3D printers?

C. Brushless Motor

Of the following sensor transfer functions, which will have the lowest sensitivity?

To determine DC sensitivity, substitute s = jw in transfer function and let w -> 0. Or, justset s = 0 in the transfer function and the result is the DC sensitivity.

Which stepper motors can do both 4 wire and 5/6 wire connections?

4 wire can only do a 4 wire connection. 5 and 6 wire can do both 4-wire4-wire and 5/6 wire connections. B and C see HW 8 Q 23 to see the diagram

Which number(s) of wires will give the most position accuracy?

4 wire can only power two sets of windings. 5/6 wire can power four sets of windings so they canhave higher position accuracy. A. and B.

When a motor (with motor rotary inertia JM) is driving a load (with inertia JL) through agearhead with a gear ratio r = Input Speed/Output Speed.To maximize the acceleration of the motor shaft itself, what gear ratio, r, should we use? Larger than,equal to, or less than the gear ratio that maximizes the acceleration of the load?

A See HW 8 Q 27

When a motor (with motor rotary inertia JM) is driving a load (with inertia JL) through a gearhead with a gear ratio r = Input Speed/Output Speed.To minimize the power going into the motor inertia, what gear ratio, r, should we use? Larger than, equal to, or less than the gear ratio that maximizes the acceleration of the load?

A See Hw 8 Q 28

When a motor (with motor rotary inertia JM) is driving a load (with inertia JL) through a gearhead with a gear ratio r = Input Speed/Output Speed To maximize the acceleration of the load, what gear ratio, r, should we use?

A and C see hw 8 Q 26

For a low-pass RC filter, all of the frequency components of the input signal higher than its cutoff frequency will be completely removed by the filter

A low-pass filter reduces signals above the cutoff frequency and passes signals below the cutoff frequency. Attenuation is never perfect, however, so there will always be some frequency components in the output above the cutoff frequency False

For the application below, which motor type makes the most sense to use: PMDC, brushless motor, a stepper, hobby servo, AC induction, or universal motor?

A motor that can change its speed, be very efficient, and needs to be VERY reliable (for a space mission). A. Brushless Motor

Why, as mechanical engineers, do we rarely encounter the use of AC induction motors in our mechatronic designs?

Because it is harder to do position control.

Why do AC induction motors make sense for vehicle powertrains?

Because of their high power and speed control

Why is it so difficult to control the position of a device that has a large coulomb friction term,but not a viscous friction term?

Both Coulomb friction is a nonlinear behavior. and Stopping and starting are difficult to control

Why are stepper motors commonly used in 3D printers, despite almost identical motionand precision requirements as for paper printing where they are not preferred?

C. Cheap

What is the likely overall electrical to mechanical conversion efficiency of the motor with gearbox?

DC motors can be 70 - 95% efficient. The gearbox can be 70 - 90% efficient. Overall efficiency = 50 -86% efficiency. Best answer is B

A DC servo's response is measured in time for an angle command of 30 degrees when the angle starts at 0 degrees. It takes 0.5 seconds to move this arc. An engineer wants to predict the behavior for a command of 60 degrees. Which situation is likely to give a more accurate prediction?

DOUBLE the angular speed during motion, so the servo should take 0.5 seconds, and move twice as quickly.

student is building a Battlebot robot, and wants to use a brushed DC wheelchair motor that is rated for 200 RPM max, with a max torque of 1.3 in-lbs. The robot needs to produce 1.0 in-lbs of force at just 100 RPM. Will this motor meet the student's needs?

Gears have the following effects on the output: Tout = g*Tin, Sin = g*Sout where g > 1 forgearing down (Sout < Sin & Tout > Tin). Thus, we can rewriteTout = g*(Tmax - g*Sout*Tmax/Smax) = g*Tmax - g^2*Sout*Tmax/SmaxNote that gearing does not change the power: 2 | P a g ePout = Tout*Sout = (g*Tmax - g^2*Sout*Tmax/Smax)*Sout = (g*Tmax - g*Sin*Tmax/Smax)*Sin/g = (Tmax - Sin*Tmax/Smax)*Sin = PinThe maximum power occurs atd(Tmax*S - S^2*Tmax/Smax)/dS = Tmax - 2*S*Tmax/Smax = 0 => S = Smax/2Thus, for this motor, power is maximum at S = 100 rpm and T = 0.65 in-lb, so Pmax = 100rpm*0.65 in-lb = 65 in-lb-rpm. Gears do not change the amount of power that the motor can provide. At 100 rpm, the maximum powerPout = Tout*Sout = Tout*100 < 65 => Tout < .65 in-lb. Can't do it! False

For a low-pass RC filter, all of the frequency components of the input signal higher than its cutoff frequency will be reduced in amplitude.

HW 6 Q 7 to see diagram

What are the pros of using a series winding for traction motors on locomotives?

High torque at low speeds

For a stepper motor with 200 teeth, how many times must one coil be pulsed in full-steptwo-phase mode to move 90 degrees? __________ pulses. What if it is operated in half-step mode?___________ pulses

In Full Step Mode, each coil is pulsed twice per tooth. For example, Coil A is pulsed during Steps 1 and 2. Pulses/degree = (2 pulse/tooth)*(200 teeth/rev)*(1 rev/360 deg). For 90 degrees: Pulses =90*2*200/360 = 100 pulses n half step mode, each coil is pulsed thrice per tooth. For example, Coil A is pulsed in Steps 1-2 and 8.For 90 degrees: Pulses = 90*3*300/360 = 150 pulses D see hw 8 Q 25

Adding inertia to the motor output shaft will reduce its steady-state output speed.

In a steady state, a = 0, so motor torque = load torque, and inertia does not affect the answer. For example, if load torque = 0, then steady state speed = no load speed which is independent of inertia. False

adding inertia to the motor output shaft will reduce its acceleration.

Neglecting non-inertial loads on the motor, acceleration = T/J, where J = inertia. If we increase J, then a decreases. True

[a,b] = butter(2, 300/500);

Noise at 400 Hz is above the cutoff frequency so it will be reduced but not completely.Given the above MATLAB command and a sample frequency of 1 kHz, will noise of 400 Hz: Be dropped in amplitude

The following calibration curve is from the distance sensors used in the lab. Which two operating points should be avoided (other than the origin)?

This sensor is highly sensitive (steep slope) between 0 and 5 cm so this is a good operating range. The sensor gives the same output for different distances around 7 cm (Point B) so this is not a good operating point. For example, distances of 7 and 8 cm both give an output of 3 V, so it is impossible to tell where you are. For distances between 10 cm and 50 cm, the sensor is reasonably sensitive so around Point B would be an acceptable operating point. At Point D, however, the sensitivity is getting very low (low slope) so it should be avoided. Band D

the student is building a Battlebot robot and wants to use a brushed DC wheelchair motor that is rated for 200 RPM max, with a max torque of 1.3 in-lbs. The robot needs to produce 1.0 in-lbs office at just 100 RPM. Will this motor meet the student's needs?

Torque versus speed for a brushed DC motor is a linear relationship. We can determine the equation of the line from the maximum torque Tmax and maximum speed SmaxT = Tmax - S*Tmax/Smax = 1.3 - ((1.3)/200)*S = 1.3 - .0065S Where S = speed and T = torque. At 100 RPM, T = 0.65 in-lb < 1.0 in-lbs. Not enough torque! NO

DC motors typically have at least 3 pairs of field windings (producing 6 different contacts on the commutator brushes) because: More field windings give less torque ripple BUT with more fields to be wound, each field has fewer wires that we can package in the motor which results in less torque

True

The impedance of the capacity Zc = 1/Cs. So, by the voltage divider rule, vout = vin(Zc/(Zc+R)). Thus, the transfer function 𝑣𝑜𝑢𝑡(𝑠)𝑣𝑖𝑛(𝑠) = 1𝑅𝐶𝑠 + 1If we substitute s = jw into the transfer function, we see that the amplitude of all input frequencies is reduced because vout/vin < 1. The reduction is more pronounced, however, above the cutoff frequency w > wc = 1/RC

True

Using the same circuit of the low-pass RC filter discussed in the class, instead of measuring the voltage across the capacitor, if we measure the voltage across the resistor (shown below), do we have a low pass or a high pass filter?

We know that a capacitor looks like an open circuit at DC and a short circuit at very high frequencies (Zc(w) = 1/jwC, Zc(0) = ∞, Zc(∞)=0). Looking at the circuit above, at low frequency, the capacitor is an open circuit so the output is connected to ground and equal to zero. At high frequencies, the capacitor directly connects the output to the input, so the gain = 1. This is a high-pass filter. High pass

We want to filter a signal. The original signal has a frequency component of 50 Hz. However, the original signal is corrupted with measurement noise. The noise frequency is 500Hz. Now, we want to design an RC filter to remove the noise. If we have a 500 ohm resistor, which capacitor could be used to remove the noise?

We want to design our RC filter cutoff frequency to be greater than 50 Hz but less than 500 Hz. The cutoff frequency fc = 1/(2*pi*RC). Check the three possibilities:1 uF -> fc = 1/(2*pi*500*1e-6) = 318 Hz <- Little reduction of original signal and significant reduction of noise6.3 uF -> fc = 1/(2*pi*500*6.3e-6) = 50 Hz <- Some reduction of original signal0.63 uF -> fc = 505 Hz <- Little reduction of noise answer: 1 uF

Adding friction to the output shaft of a brushed DC motor will reduce its steady-state output speed

n steady state, motor torque = load torque = friction. This requires non-zero current and Voltage >back emf voltage. Thus, speed must be less than no load speed. True