E1C12 09/14/2010
13:54:20 Page 560
where
y ¼ displacement in cm
t ¼ time in s
The seismic instrument is to have a damping ratio of 0.7.
a. Select a combination of seismic mass, spring constant, and damping coefficient to yield less than a
6% amplitude error in measuring the input signal. Under what conditions would the output signal
experience significant distortion?
b. Plot and describe the phase response of the system, either in a plot or tabular form.
12.7 A seismic instrument has a natural frequency of 20 Hz and a damping ratio of 0.65. Determine the
maximum input frequency for a vibration such that the amplitude error in the indicated displacement
is less than 5%.
12.8 A seismic instrument consists of a housing and a seismic mass. To measure vibration, the seismic
mass should remain stationary in an absolute frame of reference. To measure acceleration, the
magnitude ratio should be unity. Explain in detail the requirements for mass, spring constant, and
damping ratio to satisfy these requirements.
12.9 A seismic instrument consists of a housing and a seismic mass. To measure vibration, the seismic
mass should remain stationary in an absolute frame of reference. To measure acceleration, the
magnitude ratio should be unity. Using Labview, develop a model of the seismic instrument for both
vibration and acceleration measurement.
12.10 Determine the bandwidth for a seismic instrument employed as an accelerometer having a seismic
mass of 0.2 g and a spring constant of 20,000 N/m, with very low damping. Discuss the advantages
of a high natural frequency and a low damping ratio. Piezoelectric sensors are well suited for the
construction of accelerometers, since they possess these characteristics.
12.11 In Example 12.2, integration is identified as a method for reducing the effects of noise in a signal.
Discuss how a moving average can be used to reduce the effects of noise in a velocity measurement,
through the integration of an acceleration signal. Discuss the effects of averaging time on the
elimination of noise. Assume that the noise has significant amplitude, but higher frequency content
than the velocity being measured.
12.12 Consider a moving coil transducer having a coil diameter D c of 0.8 cm and a coil length of 2 cm. The
nominal range of velocities to be measured is from 1 to 10 cm/s. The resulting emf is measured by a
PC-based data acquisition system with an 8-bit A/D converter and a range of À1 to 1 V. The
accuracy is 0.1% full-scale. Plot the number of turns as a function of magnetic field strength to
provide an accuracy of 1% in the resulting velocity measurement.
12.13 Consider measuring a rotational speed using a stroboscope. The rotational speed is higher than the
flash rate of the stroboscope. The stroboscope is observed to synchronize at 10,000, 18,000, and
22,000 flashes/s. Determine the rotational speed.
12.14 Research the state-of-the art specifications for load cells designed to measure the smallest possible
forces. What applications exist for such precise measurements of small forces?
12.15 Design a proving ring load cell appropriate to serve as a laboratory calibration standard in the range
of 250 to 1000 N. The proving ring material is steel.
12.16 Power transmitted through the drive shaft of a car results in a rotational speed of 1800 rpm with a
power transmission of 40 horsepower. Determine the torque that the driveshaft must support.
12.17 Discuss the importance of a dynamometer for automotive emissions testing.
12.18 Research applications for linear actuators. For each application that you identify suggest the most
appropriate linear actuator. Why was the actuator chosen for the particular application? For many
applications, a choice is made to convert rotary motion to linear motion.
560 Chapter 12 Mechatronics: Sensors, Actuators, and Controls
13:54:20 Page 560
where
y ¼ displacement in cm
t ¼ time in s
The seismic instrument is to have a damping ratio of 0.7.
a. Select a combination of seismic mass, spring constant, and damping coefficient to yield less than a
6% amplitude error in measuring the input signal. Under what conditions would the output signal
experience significant distortion?
b. Plot and describe the phase response of the system, either in a plot or tabular form.
12.7 A seismic instrument has a natural frequency of 20 Hz and a damping ratio of 0.65. Determine the
maximum input frequency for a vibration such that the amplitude error in the indicated displacement
is less than 5%.
12.8 A seismic instrument consists of a housing and a seismic mass. To measure vibration, the seismic
mass should remain stationary in an absolute frame of reference. To measure acceleration, the
magnitude ratio should be unity. Explain in detail the requirements for mass, spring constant, and
damping ratio to satisfy these requirements.
12.9 A seismic instrument consists of a housing and a seismic mass. To measure vibration, the seismic
mass should remain stationary in an absolute frame of reference. To measure acceleration, the
magnitude ratio should be unity. Using Labview, develop a model of the seismic instrument for both
vibration and acceleration measurement.
12.10 Determine the bandwidth for a seismic instrument employed as an accelerometer having a seismic
mass of 0.2 g and a spring constant of 20,000 N/m, with very low damping. Discuss the advantages
of a high natural frequency and a low damping ratio. Piezoelectric sensors are well suited for the
construction of accelerometers, since they possess these characteristics.
12.11 In Example 12.2, integration is identified as a method for reducing the effects of noise in a signal.
Discuss how a moving average can be used to reduce the effects of noise in a velocity measurement,
through the integration of an acceleration signal. Discuss the effects of averaging time on the
elimination of noise. Assume that the noise has significant amplitude, but higher frequency content
than the velocity being measured.
12.12 Consider a moving coil transducer having a coil diameter D c of 0.8 cm and a coil length of 2 cm. The
nominal range of velocities to be measured is from 1 to 10 cm/s. The resulting emf is measured by a
PC-based data acquisition system with an 8-bit A/D converter and a range of À1 to 1 V. The
accuracy is 0.1% full-scale. Plot the number of turns as a function of magnetic field strength to
provide an accuracy of 1% in the resulting velocity measurement.
12.13 Consider measuring a rotational speed using a stroboscope. The rotational speed is higher than the
flash rate of the stroboscope. The stroboscope is observed to synchronize at 10,000, 18,000, and
22,000 flashes/s. Determine the rotational speed.
12.14 Research the state-of-the art specifications for load cells designed to measure the smallest possible
forces. What applications exist for such precise measurements of small forces?
12.15 Design a proving ring load cell appropriate to serve as a laboratory calibration standard in the range
of 250 to 1000 N. The proving ring material is steel.
12.16 Power transmitted through the drive shaft of a car results in a rotational speed of 1800 rpm with a
power transmission of 40 horsepower. Determine the torque that the driveshaft must support.
12.17 Discuss the importance of a dynamometer for automotive emissions testing.
12.18 Research applications for linear actuators. For each application that you identify suggest the most
appropriate linear actuator. Why was the actuator chosen for the particular application? For many
applications, a choice is made to convert rotary motion to linear motion.
560 Chapter 12 Mechatronics: Sensors, Actuators, and Controls