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    Module 3 Activity No. 2

    Uploaded by

    Ariel Gamboa
    This document contains two problems related to calculating contact stresses in spur gears. Problem 1 involves a 22-tooth steel pinion driving a 60-tooth cast iron gear, transmitting 15 HP at 1200 rpm. The contact stress is calculated to be 65.49 ksi. Problem 2 involves a 20-tooth cast iron pinion driving a 32-tooth cast iron gear, transmitting 10 kW at 1000 rpm. The contact stress is calculated to be 616.39 MPa. Both problems provide the given information and show the step-by-step workings to arrive at the contact stress values.

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    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Module 3 Activity No. 2

    Uploaded by

    Ariel Gamboa
    62 views5 pages
    This document contains two problems related to calculating contact stresses in spur gears. Problem 1 involves a 22-tooth steel pinion driving a 60-tooth cast iron gear, transmitting 15 HP at 1200 rpm. The contact stress is calculated to be 65.49 ksi. Problem 2 involves a 20-tooth cast iron pinion driving a 32-tooth cast iron gear, transmitting 10 kW at 1000 rpm. The contact stress is calculated to be 616.39 MPa. Both problems provide the given information and show the step-by-step workings to arrive at the contact stress values.

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    Module 3 Activity No. 2.docx

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    This document contains two problems related to calculating contact stresses in spur gears. Problem 1 involves a 22-tooth steel pinion driving a 60-tooth cast iron gear, transmitting 15 HP at 1200 rpm. The contact stress is calculated to be 65.49 ksi. Problem 2 involves a 20-tooth cast iron pinion driving a 32-tooth cast iron gear, transmitting 10 kW at 1000 rpm. The contact stress is calculated to be 616.39 MPa. Both problems provide the given information and show the step-by-step workings to arrive at the contact stress values.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    62 views5 pages

    Module 3 Activity No. 2

    Uploaded by

    Ariel Gamboa
    This document contains two problems related to calculating contact stresses in spur gears. Problem 1 involves a 22-tooth steel pinion driving a 60-tooth cast iron gear, transmitting 15 HP at 1200 rpm. The contact stress is calculated to be 65.49 ksi. Problem 2 involves a 20-tooth cast iron pinion driving a 32-tooth cast iron gear, transmitting 10 kW at 1000 rpm. The contact stress is calculated to be 616.39 MPa. Both problems provide the given information and show the step-by-step workings to arrive at the contact stress values.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 5

    Module 3: Activity No.

    2
    Spur Gear Tooth Stresses

    Name: Gamboa, Ariel C.


    Student No.: 20151157958

    Problem No. 1 (14 – 11)


    A speed reducer has 20◦ full-depth teeth and consists of a 22-tooth steel spur pinion
    driving a 60-tooth cast-iron gear. The horsepower transmitted is 15 at a pinion speed of
    1200 rev/min. For a diametral pitch of 6 teeth/in and a face width of 2 in, find the contact
    stress.
    Given:
    ∅=20° ( full depth)
    N p=22−teeth(steel)

    N g=60−teeth(cast−iron)
    P=15 HP
    n p =1200 rpm

    teeth
    P=6
    ¿
    F=2∈.

    Solution:
    1/ 2
    Wt Kv 1 1
    σ C =Cp
    [ ( + )
    Fcos ∅ r 1 r 2 ]
    1200+ v
    Kv=
    1200
    Np
    P=
    dP
    v=π n p d P
    22
    6=
    dP

    d P=3.67∈¿

    v=π ¿
    ft
    v=1152.96
    min
    1200+ 1152.96
    Kv=
    1200
    Kv=1.96

    Wt ( v )
    P=
    33000
    Wt ( 1152.96 ft /min )
    15 HP=
    33000
    Wt=429.33lb

    dp 3.67
    r 1= sin 20 ° ; r 1= sin 20°
    2 2
    r 1=0.63

    dg Ng 60
    r 2= sin 20 ° ; P= ; 6= ; d g=10∈.
    2 dg dg

    10
    r 2= sin20 °
    2
    r 2=1.71∈¿

    For Cp, Use table 14-8:


    Cp=2100 psi

    1 /2
    (429.33)(1.96) 1 1
    σ C =2100 [ 2 cos 20 °
    ( +
    0.63 1.71
    ) ]
    σ C =65489.95 psi

    σ C =65.49 ksi

    Problem No. 2 (14 -14)


    A 20◦ 20-tooth cast-iron spur pinion having a module of 4 mm drives a 32-tooth cast-iron
    gear. Find the contact stress if the pinion speed is 1000 rev/min, the face width is 50
    mm, and 10 kW of power is transmitted
    Given:
    ∅=20°
    N p=20−teeth(cast−iron)

    N g=32−teeth (cast−iron)
    m=4 mm
    n p =1000 rpm

    F=50 mm
    P=10 kW

    Solution:
    1/ 2
    Wt Kv 1 1
    σ C =Cp
    [ ( + )
    Fcos ∅ r 1 r 2 ]
    3.05+ v
    Kv=
    3.05
    v=π n p d P

    dp
    m=
    NP
    dp
    4=
    20
    d P=80 mm

    1m 1 min
    v=π (80 mm)( )(1000 rev/ min)( )
    1000 mm 60 s
    v=4.19 m/ s
    3.05+ 4.19
    Kv=
    3.05
    Kv=2.37
    P=Wt (v)
    Nm m
    10 x 103 =(Wt )(4.19 )
    s s
    Wt=2386.63 N

    dp
    r 1= sin 20 °
    2
    80
    r 1= sin 20°
    2
    r 1=13.68 mm

    dg
    r 2= sin 20 °
    2
    dg
    m=
    Ng
    dg
    4=
    32
    d g=128 mm

    128
    r 2= sin20 °
    2
    r 2=21.89mm

    Cp=163 MPa

    1/ 2
    Wt Kv 1 1
    σ C =Cp
    [ ( + )
    Fcos ∅ r 1 r 2 ]
    1/ 2
    (2386.63)(2.37) 1 1
    σ C =163 [
    50 cos 20 °
    ( +
    13.68 21.89
    ) ]
    σ C =616.39 MPa

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