Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
10th Edition
ISBN: 9780073398204
Author: Richard G Budynas, Keith J Nisbett
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
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
2. In a particular section of a fluid system, a 30% ethylene glycol mixture is flowing through a 6- nom xs cast iron pipe at a temperature of 0°C. In this section of piping, the velocity must be maintained in the range 1.5 m/s
1. Steam leaves the boiler of a power plant at 5 MPa, 500°C as shown in the following figure. As the steam passes to the turbine, the temperature drops to 496°C before it enters the turbine due to a heat loss through the pipe's insulation. The pressure drop in the pipe connecting the boiler to the turbine is negligible. The steam then passes through an adiabatic turbine and exits at 10 kPa. The turbine has an isentropic efficiency of 85% and is delivering 1000 MW of power. Determine the following. P = 5 MPa T₁ = 500°C Boiler P₁₂ =5 MPa Τ =496°C 7 = 85% W = 1,000 MW P=1 atm To=25°C Turbine 3+ P = 10 kPa a. The heat transfer rate from the pipe connecting the boiler to the turbine (in MW) b. The change in flow exergy rate as the steam flows through the pipe (MW). This represents exergy that is lost to the environment and unavailable for power delivery. Comment on the magnitude of this exergy loss compared to the power delivered by the turbine. What factor(s) would warrant better…
An aluminum rod of length L = 1m has mass density p = 2700 kg and Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact natural eigenfrequencies of the rod are wexact E = √ ρ for n=1,2,3,. . . . 1. What is the minimum number of linear elements necessary to determine the fundamental frequency w₁ of the system? Discretize the rod in that many elements of equal length, assemble the global system of equations KU = w² MU, and find the fundamental frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact Sketch the fundamental mode of vibration. 2. Use COMSOL to solve the same problem. Show the steps necessary to find the fundamental frequency and mode of the rod. What is the relative error using linear elements and a normal mesh?

Chapter 14 Solutions

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

Knowledge Booster
Background pattern image
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
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
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