讲解MIE 313 Fall 、解析MathCAD、Matlab编程讲解留学生、Matlab调试
- 首页 >> Matlab编程MIE 313 Fall 2018
Mini Project No. 1
Due Monday Sept 24 11:55 pm
Like all Mini Projects, this is an individual assignment. It is is to be done in a professional manner using
MathCAD1
, printed to a pdf file and submitted electronically as a Moodle assignment.
A mechanical deep drawing press uses a crank-connecting rod-piston mechanism to draw a thin sheet of
metal, called a blank, into the shape of the receiving die (see Figure 1). The force exerted on the blank by the
ram as a function of crank angle is given by the curve shown in Figure 2.
where crank angle ? is measured from bottom dead center. Thus, the beginning of the pressing operation
occurs when the crank is at bottom dead center (i.e. ? = 0 deg). Between zero and 140 degree crank angle, a
fifth order polynomial can be used to approximate the press force:
1 A CAD tool will need to be used for part f). The department offers both Creo and SolidWorks in ELAB 203.
Figure 1: Crank-Connecting Rod-Ram Mechanism for Mechanical Press
( )
5
0
1
0 1 2 3 4 5
where
0.0015 , 1.522 , 194.93 , 247.3 , 115.69 , 19.05
i
press i
i
F a a
a kN a kN a kN a kN a kN a kN
? ?
=
= +
= = ? = = ? = = ?
?
(1)
In Eq. (1) ? must be dimensionless, i.e. it must have units of radians. A simple linear function may be used to
approximate the pressing force between 140 deg and 180 deg, and the press force is zero during the return
stroke. The crank shaft of the press rotates at 60 rpm and is driven by a motor operating at a speed of 360
rpm. A 6:1 speed-reducing system (i.e. pulley-belt system) connects the output shaft of the motor to the
input shaft of the press. Power losses in the speed-reducing system may be neglected. Let the crank radius r
= 20 mm and the connecting rod length lrod = 70.0 mm. Let y(?) denote the displacement of the ram from
bottom dead center as a function of crank angle. From simple trig one can show that
2
( ) (1 cos ) 1 1 sin rod
rod
r
y r l
l
? ? ?
? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ?
(2)
a) (10 pts) Plot the ram displacement as a function of ? for crank radius r = 20 mm and the connecting
rod length lrod = 70 mm and determine the total work done in the deep drawing operation.
b) (20 pts) Neglecting friction and inertial effects, use principles of statics (i.e. free body diagram) to
derive an expression for the instantaneous torque that must be delivered by the crank shaft for the
deep drawing operation as a function of crank angle ?? crank radius r? and connecting rod length lrod.
Determine the maximum required crank shaft torque and the average required crank shaft torque
over one crank revolution for crank radius r = 20 mm and the connecting rod length lrod = 70 mm.
c) (10 pts) Determine the required instantaneous motor torque as a function of crank angle ?? crank
radius r? and connecting rod length lrod. Determine the maximum required motor torque, and the
average motor torque over one crank revolution for crank radius r = 20 mm and the connecting rod
length lrod = 70 mm.
d) (10 pts) Determine the instantaneous power required of the motor as a function of crank angle
?? crank radius r? connecting rod length lrod, and motor angular velocity ?motor. Determine the
required maximum power and the required average power motor for crank radius r = 20 mm, the
connecting rod length lrod = 70 mm, and ?motor = 360 rpm.
e) (10 pts) Plot as a function of crank angle the crank shaft torque, average crank torque, motor torque,
average motor torque, motor power, and average motor power.
f) (40 pts) Motors are sized based on maximum torque and power requirements. Design a reasonable
minimum-weight flywheel that will enable the motor to be sized based on required average torque.
Include a CAD image of your flywheel design and supporting information from the CAD tool that
confirms the flywheel has the required mass moment of inertia about its axis of rotation. Be sure to
provide specs on your flywheel, i.e. dimensions, weight, material, etc. The speeds of the motor
output shaft and press crank shaft should not vary more than ± 10% from their nominal values.