
(a)
The values of pitch diameter.

Answer to Problem 63A
25mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Pitch diameter (D) is given by,
D=mT where m=Module,T=No. of teeth.
Using above formula,
Pitch Diameter(D)=mT⇒Pitch Diameter(D)=2.5×10 mm⇒Pitch Diameter(D)=25 mm.
Hence, pitch diameter of given spur gear will be 25 mm.
(b)
The values of circular pitch of given metric spur gear.

Answer to Problem 63A
7.854mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Circular pitch (Pc) is given by,
Pc=πm where m=Module,T=No. of teeth.
Using above formula,
Circular pitch (Pc)=πm⇒Circular pitch (Pc)=3.14×2.5 mm⇒Circular pitch (Pc)=7.854 mm.
Hence, circular pitch of given spur gear will be 7.854 mm.
(c)
The values of outside diameter of given metric spur gear.

Answer to Problem 63A
30mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Outside diameter (Do) is given by,
D0=D+2m where m=Module,D=Pitch diameter.
From part a of this exercise, pitch diameter D=
117 mm.
Using above formula,
Outside diamter (D0)=D+2m⇒Outside diamter (D0)=25+2×2.5 mm⇒Outside diamter (D0)=30 mm.
Hence, outside diameter of given spur gear will be 30 mm.
(d)
The values of addendum of given metric spur gear.

Answer to Problem 63A
2.5mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Addendum (a) of a spur gear is given by,
a=1.00m where m=Module,a=addendum.
Using above formula,
Addendum(a)=1.00m=1.00×2.5 mm⇒Addendum(a)=2.50 mm
Hence, addendum of given spur gear will be 2.5 mm.
(e)
The values of working depth of given metric spur gear.

Answer to Problem 63A
5mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Working depth (w) of a spur gear is given by,
w=2m where m=Module,w=working depth.
Using above formula,
Working depth (w)=2m⇒Working depth (w)=2×2.5 mm⇒Working depth (w)=5 mm
Hence, working depth of given spur gear will be 5 mm
(f)
The tooth thickness depth of given metric spur gear.

Answer to Problem 63A
3.917mm
Explanation of Solution
Given information:
Module(m)=2.5mm;No of teeth (T)=10
Calculation:
Tooth thickness (t) of a spur gear is given by,
t=Pc2 where Pc=circular pitch,t=tooth thickness.
Using above formula,
Tooth thickness (t)=Pc2⇒Tooth thickness (t)=7.8542 mm⇒Tooth thickness (t)=3.917 mm
Hence, tooth thickness of given spur gear will be 3.917 mm.
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Chapter 46 Solutions
Mathematics for Machine Technology
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- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL

