4. The maximum vertical force applied to the machine by the unbalanced mass (in Newtons) if the motor is spinning at Win,1 = 500 RPM. 5. The percent reduction in vibration transmitted to the foundation if the motor is spinning at Win,1 = 500 RPM. (Note: the percentage is the transmission ratio (TR) multiplied by 100.) 1 Problem Consider the following scale prototype of a measurement unit operating in the presence of vi- brations from an unbalanced motor. Dynamic vibration absorber Measuring point at measuring probe position Unbalance motor Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration isolator base that the unit rests on. Image source: [1]. Before adding the DVA (shown above) the original system (machine and isolator mounts) were modeled using a lumped-parameter model (sketched below). The model approximated this sys- tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine: k W r m нич 1. The natural frequency in rotations per minute (RPM). 2. The resonant frequency in rotations per minute (RPM). 3. The phase shift at resonance in degrees. M
4. The maximum vertical force applied to the machine by the unbalanced mass (in Newtons) if the motor is spinning at Win,1 = 500 RPM. 5. The percent reduction in vibration transmitted to the foundation if the motor is spinning at Win,1 = 500 RPM. (Note: the percentage is the transmission ratio (TR) multiplied by 100.) 1 Problem Consider the following scale prototype of a measurement unit operating in the presence of vi- brations from an unbalanced motor. Dynamic vibration absorber Measuring point at measuring probe position Unbalance motor Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration isolator base that the unit rests on. Image source: [1]. Before adding the DVA (shown above) the original system (machine and isolator mounts) were modeled using a lumped-parameter model (sketched below). The model approximated this sys- tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine: k W r m нич 1. The natural frequency in rotations per minute (RPM). 2. The resonant frequency in rotations per minute (RPM). 3. The phase shift at resonance in degrees. M
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:4. The maximum vertical force applied to the machine by the unbalanced mass (in Newtons)
if the motor is spinning at Win,1 = 500 RPM.
5. The percent reduction in vibration transmitted to the foundation if the motor is spinning at
Win,1 = 500 RPM. (Note: the percentage is the transmission ratio (TR) multiplied by 100.)
![1 Problem
Consider the following scale prototype of a measurement unit operating in the presence of vi-
brations from an unbalanced motor.
Dynamic vibration
absorber
Measuring point at
measuring probe position
Unbalance motor
Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration
isolator base that the unit rests on. Image source: [1].
Before adding the DVA (shown above) the original system (machine and isolator mounts) were
modeled using a lumped-parameter model (sketched below). The model approximated this sys-
tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a
distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration
isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine:
k
W
r
m
нич
1. The natural frequency in rotations per minute (RPM).
2. The resonant frequency in rotations per minute (RPM).
3. The phase shift at resonance in degrees.
M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbce6c3fc-5060-4ca2-88c7-1140020dfd1b%2F2dd0491c-eea7-486d-9f2b-0c3a036d873e%2F9ty2wb5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 Problem
Consider the following scale prototype of a measurement unit operating in the presence of vi-
brations from an unbalanced motor.
Dynamic vibration
absorber
Measuring point at
measuring probe position
Unbalance motor
Figure 1: Left: A dynamic vibration absorber (DVA) mounted above the unit. Right: A vibration
isolator base that the unit rests on. Image source: [1].
Before adding the DVA (shown above) the original system (machine and isolator mounts) were
modeled using a lumped-parameter model (sketched below). The model approximated this sys-
tem as a rotating machine of total mass M = 50 kg with a unbalanced mass m = 0.08 kg at a
distance r = 0.05 m from the center of a spinning motor shaft that is mounted on a vibration
isolator with stiffness k = 50,000 N/m and damping b = 0.8 N-s/m. For this system, determine:
k
W
r
m
нич
1. The natural frequency in rotations per minute (RPM).
2. The resonant frequency in rotations per minute (RPM).
3. The phase shift at resonance in degrees.
M
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