SHIGLEY'S MECHANICAL ENG.DESIGN W/CODE
SHIGLEY'S MECHANICAL ENG.DESIGN W/CODE
10th Edition
ISBN: 9781260243314
Author: BUDYNAS
Publisher: MCG CUSTOM
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Chapter 14, Problem 1P

A steel spur pinion has a pitch of 6 teeth/in, 22 full-depth teeth, and a 20° pressure angle. The pinion runs at a speed of 1200 rev/min and transmits 15 hp to a 60-tooth gear. If the face width is 2 in, estimate the bending stress.

Expert Solution & Answer
Check Mark
To determine

The bending stress on teeth of gear.

Answer to Problem 1P

The bending stress on teeth of gear is 7.63 kpsi.

Explanation of Solution

Write the expression for pitch diameter of gear.

d=NP (I)

Here, the pitch diameter is d, the number of teeth is N and the pitch of gear is P.

Write the expression for linear velocity of gear.

V=πdn (II)

Here, the linear velocity is V and the rotation per unit time is n.

Write the expression for dynamic factor of cut or milled gear profile.

Kv=1200+V1200 (III)

Here, the dynamic factor is Kv and the linear velocity in ft/min is V.

Write the expression for transmitted load.

Wt=33000HV (IV)

Here, the transmitted load in lbf is Wt, the power to be transmitted in hp is H and the linear velocity in ft/min is V.

Write the expression for bending stress.

σ=KvWtPFY (V)

Here, the bending stress in psi is σ, the face width in in is F and the Lewis form factor is Y.

Conclusion:

Substitute 22teeth for N and 6teeth/in for P in Equation (I).

d=22teeth6teeth/in=3.667 in

Substitute 3.667 in for d 1200rotation/minute for n in Equation (II).

V=π(3.667in)(1200rotation/min)=(13824.26in/min)(1ft12in)1152ft/min

Substitute 1152ft/min for V in Equation (III).

Kv=1200+1152ft/min1200=1.96

Substitute 1152ft/min for V and 15hp for H in Equation (IV).

Wt=(33000)(15hp1152ft/min)=429.7lbf

Refer to Table 14-2 “Values of the Lewis Form factor Y(These Values Are for a Normal Pressure Angle of 20°, Full-Depth Teeth and a Diametral Pitch of Unity in the Plane of Rotation)” to obtain value of Lewis form factor as 0.331 at 22 number of teeth.

Substitute 429.7lbf for Wt, 1.96 for Kv, 6teeth/in for P, 2in for F and 0.331 for Y in Equation (V).

σ=1.96(429.7lbf)(6teeth/in)(2in)(0.331)=7633psi(1kpsi1000psi)7.63kpsi

Thus the bending stress on teeth of gear is 7.63kpsi.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A pair of helical gears transmit 15 KW power and the pinion is rotating at 1000 rpm. The helix angle is 0.50 radians and the normal pressure angle is 0.35 radians. The pitch diameter of the pinion is 70 mm and the pitch diameter of the gear is 210 mm. Determine the tangential, radial, and axial forces between the gear teeth.
A 20◦ helical gear has tangential force of 200lb and helix angle of 16◦ and face width of 0.6”.If the machining error is 0.6 and pitchline velocity is 400ft/min. Determine radial force, axial force, normal force, normal pressure angle and dynamic load.
A Coniflex, straight-tooth bevel gearset is supported on shafts with centerlines intersecting at a 90° angle. The gear is straddle mounted between closely positioned bearings, and the pinion overhangs its support bearing. The 15-tooth pinion rotates at 900 rpm, driving the 60-tooth gear, which has a di- ametral pitch of 6, pressure angle of 20°, and face width of 1.25 inches. The material for both gears is through-hardened Grade I steel with a hardness of BHN 300 (see Figure). It is desired to have a reliability of 90 percent, a design life of 10° cy- cles, and a governing safety factor of 2.5. Estimate the maximum horsepower that can be transmitted by this gear re- ducer while meeting all of the design specifications given.

Chapter 14 Solutions

SHIGLEY'S MECHANICAL ENG.DESIGN W/CODE

Knowledge Booster
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
    • SEE MORE QUESTIONS
    Recommended textbooks for you
  • Elements Of Electromagnetics
    Mechanical Engineering
    ISBN:9780190698614
    Author:Sadiku, Matthew N. O.
    Publisher:Oxford University Press
    Mechanics of Materials (10th Edition)
    Mechanical Engineering
    ISBN:9780134319650
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Thermodynamics: An Engineering Approach
    Mechanical Engineering
    ISBN:9781259822674
    Author:Yunus A. Cengel Dr., Michael A. Boles
    Publisher:McGraw-Hill Education
  • Control Systems Engineering
    Mechanical Engineering
    ISBN:9781118170519
    Author:Norman S. Nise
    Publisher:WILEY
    Mechanics of Materials (MindTap Course List)
    Mechanical Engineering
    ISBN:9781337093347
    Author:Barry J. Goodno, James M. Gere
    Publisher:Cengage Learning
    Engineering Mechanics: Statics
    Mechanical Engineering
    ISBN:9781118807330
    Author:James L. Meriam, L. G. Kraige, J. N. Bolton
    Publisher:WILEY
  • Elements Of Electromagnetics
    Mechanical Engineering
    ISBN:9780190698614
    Author:Sadiku, Matthew N. O.
    Publisher:Oxford University Press
    Mechanics of Materials (10th Edition)
    Mechanical Engineering
    ISBN:9780134319650
    Author:Russell C. Hibbeler
    Publisher:PEARSON
    Thermodynamics: An Engineering Approach
    Mechanical Engineering
    ISBN:9781259822674
    Author:Yunus A. Cengel Dr., Michael A. Boles
    Publisher:McGraw-Hill Education
    Control Systems Engineering
    Mechanical Engineering
    ISBN:9781118170519
    Author:Norman S. Nise
    Publisher:WILEY
    Mechanics of Materials (MindTap Course List)
    Mechanical Engineering
    ISBN:9781337093347
    Author:Barry J. Goodno, James M. Gere
    Publisher:Cengage Learning
    Engineering Mechanics: Statics
    Mechanical Engineering
    ISBN:9781118807330
    Author:James L. Meriam, L. G. Kraige, J. N. Bolton
    Publisher:WILEY
    Power Transmission; Author: Terry Brown Mechanical Engineering;https://www.youtube.com/watch?v=YVm4LNVp1vA;License: Standard Youtube License