9. A DC electric motor is connected to a wheel via a gearbox. The aim is to find when to engage the gear so that the torque at the wheel is always the largest possible. On its own, the motor generates a torque M (52) (in Nm) that depends on the rotation speed 52 (in rpm) of the motor shaft: M (52) = 0.3 (1-600) The torque T() exerted at the wheel depends on the rotation speed of the wheel, and on whether the gear is engaged: To(w) - M(w). if the gear is not engaged, T₁ (@)-M). if the gear is engaged. (a) Write explicit expressions for To(a) and 7, (a) as functions of a given the definition of M (92). (b) Plot the two functions you found in (a) on a same graph for positive values of . (c) Find the optimal gear shifting point that ensures that the forque 7(a) is always as large as possible. Hint: Look for a graphical solution first by using the graph from Part (b).
9. A DC electric motor is connected to a wheel via a gearbox. The aim is to find when to engage the gear so that the torque at the wheel is always the largest possible. On its own, the motor generates a torque M (52) (in Nm) that depends on the rotation speed 52 (in rpm) of the motor shaft: M (52) = 0.3 (1-600) The torque T() exerted at the wheel depends on the rotation speed of the wheel, and on whether the gear is engaged: To(w) - M(w). if the gear is not engaged, T₁ (@)-M). if the gear is engaged. (a) Write explicit expressions for To(a) and 7, (a) as functions of a given the definition of M (92). (b) Plot the two functions you found in (a) on a same graph for positive values of . (c) Find the optimal gear shifting point that ensures that the forque 7(a) is always as large as possible. Hint: Look for a graphical solution first by using the graph from Part (b).
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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Transcribed Image Text:9. A DC electric motor is connected to a wheel via a gearbox. The aim is to find when to engage
the gear so that the torque at the wheel is always the largest possible.
On its own, the motor generates a torque M (2) (in Nm) that depends on the rotation speed 52
(in rpm) of the motor shaft:
M
(2) = 0.3 (1-600)
The torque T() exerted at the wheel depends on the rotation speed of the wheel, and on
whether the gear is engaged:
To(w) - M(w). if the gear is not engaged,
Ti (0) - M (2).
if the gear is engaged.
(a) Write explicit expressions for To(a) and 7₁ (4) as functions of a given the definition of
M (92).
(b) Plot the two functions you found in (a) on a same graph for positive values of .
(c) Find the optimal gear shifting point that ensures that the forque 7() is always as
large as possible.
Hint: Look for a graphical solution first by using the graph from Part (b).
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