Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driver is 10 inches, find the center distance between cylinders. A. 15 in B. 10 in C. 25 in. D. 20 in. Please solve the Problem elaborately. Your solution will be use as reference for my studies. Thank you so much your work will be appreciated much!
Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driver is 10 inches, find the center distance between cylinders. A. 15 in B. 10 in C. 25 in. D. 20 in. Please solve the Problem elaborately. Your solution will be use as reference for my studies. Thank you so much your work will be appreciated much!
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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Two cylinders rolling in the opposite direction has a speed ratio of 3. If the diameter of driver
is 10 inches, find the center distance between cylinders. A. 15 in B. 10 in C. 25 in. D. 20 in.
Please solve the Problem elaborately. Your solution will be use as reference for my studies. Thank you so much your work will be appreciated much!
Transcribed Image Text:Machine Elements
1. Cylinders Rolling in opposite direction:
A. Tangential speed V = Va =n D. N == D, N:
D. N. = D. Na
B. Relation of diameter and speed
Speed of Driver
Speed of the Driven
C. Speed Ratio=
D. Center Distance- R, + R, D, + D2
2
2. Cylinders Rolling in the same direction
A. Tangential speed VVn D, N = D, N,
B. Relation of diameter and speed D: N = D, Na
Speed of Driver
Speed of the Driven
.
C. Speed Ratio =
D. Center Distance = R, -R,- D-D,
2
Stresses
1. Stress (S) = a total resistance that a material offers to an applied load, Ibin, kg/cm, KN/m?
2. Ultimate stress (S.) - is the stress that would cause failure
3. Yield stress(S,) - maximum stress without causing deformation
4. Allowable stress(Sa) = Ultimate stress/Factor of Safety
5. Design stress(S.) - stress used in determining the size of a member. S= or S=
where: FS factor of safety
1. Tensile Stress (S)
S = 4
For solid circular cross-section: A = D
For hollow circular cross-section: A = (D, -D)
For rectangular cross-section: A = base x height = b xh
2. Compressive Stress(S.)S.
3. Shearing Stress(S.)
A. For single bolt of rivet needed to join to plates together. S, =
For single rivet: A= z4 D
For double riveted joint: A= 2(m/4 D)
where:
B. Shearing due to punching of hole.
S= where A DI (for punching a hole) A4S1 (for square hole)
Where: S= length of side of
t= plate thickness
Where: d= hole diameter, in
4. Bearing Stress(S) S, F IA
C. Pressure needed to punch a hole, F: Fdxtx 80, tons
t= thickness, in
where: A= DL
She
a aa
5. Factor of safety(FS) a. Based on yield strength FS = S, /S
b. Based on ultimate strength FS = s./ S
6. Torsional Shear Stress(S.)
Projected Area
where: J = polar moment of inertia = T D' /32 (for solid shaft)
T= torque c - distance from neutral axis to the farthest fiber
C-r (for circular cross section)
d- diameter
6 M
7. Bending Stress(S)
S- For rectangular beam S
bh
where: M = moment
C= distance of farthest fiber from neutral axis
|- moment of inertia about the neutral axis
= bh/12 (for rectangular cross section)
Z = section modulus =
c S
8. Strain and Elongation Strain = !
E. Stress . FL
Strain
Y= FL
AE
Stress a F
- AV
L- original length
S stress
where: y- elongation due to applied load
F force A area
9. Thermal Elongation; Stresses
y = kL (t - t:) s = EL = kE (t - t)
where: k = coefficient of thermal expansion, m/m-C
For steel k- 6.5 x 104 inin-F- 11.7 x 104 m/m-C
E = 30 x 10 psi
Relation betwoen shearing and tensile stress based on theory of failure:
Suna- Sy 12
Swa- S
10. Variable Stress
1. S.
FS S, S.
S, - yield point
S = mean stress
where: FS = factor of safety
S. endurance limit
Smax + Sn
S. = variable component stress
S.. maximum stress
Sen minimum stress
11. Poisson's Ratio(u) = is the ratio of lateral unit deformation to axial unit deformation.
F
E- strain
=
AE
where: G = shear modulus of elasticity
2G
Lateral Strain
Wa-W
Longitudin al Strain
E, -L
E, Ex
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