Mechanical system shown in the figure represents a motor drive unit The motor drives a load imertia through a gear pair and massless nigid shafts. VisCOus damping is assumed to be at the bearings. System elements are described as follows: ba T(t) Mass moment of inertia Torsional damping coefficients at bearing i Motor torque Rotational posıtion of shaft i Reduction ratio Number of teeth on gear i : Pitch radius of gear i The angular velocity of the second shaft (6,(t) is the system output) is desired to be controlled via driving torque (T(t) is the desıred input). For the given system a) Draw necessary free-body diagrams (FBD's) for the system. Then, identifying the forces with given elements (parameters) in the figure, wmte all elemental equations used in the FBD's. [ Note 1: Do not ignore the force which shows up on the contact point between the gear pair. Note 2: Please pay attention to the positive and negative signs that indicate the direction. Note 3: Remember that the radius of a gear is proportional to its teeth number (R,/R, = n)| b) Obtain the equation of motion (EoM) for the system in terms of imput & output using Newton's Laws (Le. Continuty Eqn's) c) Take Laplace transform of the EoM. Then find the tansfer function of the system
Mechanical system shown in the figure represents a motor drive unit The motor drives a load imertia through a gear pair and massless nigid shafts. VisCOus damping is assumed to be at the bearings. System elements are described as follows: ba T(t) Mass moment of inertia Torsional damping coefficients at bearing i Motor torque Rotational posıtion of shaft i Reduction ratio Number of teeth on gear i : Pitch radius of gear i The angular velocity of the second shaft (6,(t) is the system output) is desired to be controlled via driving torque (T(t) is the desıred input). For the given system a) Draw necessary free-body diagrams (FBD's) for the system. Then, identifying the forces with given elements (parameters) in the figure, wmte all elemental equations used in the FBD's. [ Note 1: Do not ignore the force which shows up on the contact point between the gear pair. Note 2: Please pay attention to the positive and negative signs that indicate the direction. Note 3: Remember that the radius of a gear is proportional to its teeth number (R,/R, = n)| b) Obtain the equation of motion (EoM) for the system in terms of imput & output using Newton's Laws (Le. Continuty Eqn's) c) Take Laplace transform of the EoM. Then find the tansfer function of the system
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Mechanical system shown in the figure represents a motor drive unit The motor drives a load imertia
through a gear pair and massless nigid shafts. VisCOus damping is assumed to be at the bearings.
System elements are described as follows:
ba
T(t)
Mass moment of inertia
Torsional damping coefficients at bearing i
Motor torque
Rotational posıtion of shaft i
Reduction ratio
Number of teeth on gear i
: Pitch radius of gear i
The angular velocity of the second shaft (6,(t) is the system output) is desired to be controlled via
driving torque (T(t) is the desıred input). For the given system
a) Draw necessary free-body diagrams (FBD's) for the system. Then, identifying the forces with
given elements (parameters) in the figure, wmte all elemental equations used in the FBD's. [
Note 1: Do not ignore the force which shows up on the contact point between the gear pair.
Note 2: Please pay attention to the positive and negative signs that indicate the direction.
Note 3: Remember that the radius of a gear is proportional to its teeth number (R,/R, = n)|
b) Obtain the equation of motion (EoM) for the system in terms of imput & output using
Newton's Laws (Le. Continuty Eqn's)
c) Take Laplace transform of the EoM. Then find the tansfer function of the system
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