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Chapter 5 – Torsion - PowerPoint PPT Presentation


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Chapter 5 – Torsion. Torsional failures (ductile, buckling, buckling):. 1 3/8” Isolator ( Assembly). Drill Bit. Torsional induced shear stresses throughout – where is it maximum? Other loadings to consider? (welcome to my nightmare). Drill Bit Isolator (QC-19835, 1 /38” or QC-20036, 1”).

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1 3 8 isolator assembly
1 3/8” Isolator ( Assembly)

Drill Bit

Torsional induced shear stresses throughout – where is it maximum?

Other loadings to consider? (welcome to my nightmare)

Drill Bit Isolator (QC-19835, 1 /38” or QC-20036, 1”)

Drill Rod

Torsion Load=300 lb-ft

Chuck Isolator (QC-19836, 1 3/8”)

slide4

Ch 5 - Torsion

Recall: External loads (T) produce internal loads which produce deformation, strain and stress.

slide5

Before Torque

After Torque

slide6

5.1 Torsional Deformation of a Circular Shaft

f(x) = angle of twist (varies linearly along the length, 0 at x = 0, max at x = L)

slide7

Recall g = shear strain (rad)

Notice, shear strain, g varies linearly with radial distance, r, and is max on the outer surface!!

slide8

Notice, shear strain, g varies linearly with radial distance, r, and is max on the outer surface!!

Distance from center to point of interest

Distance from center to outer fiver (i.e. outer radius)

what have we learned so far
What have we learned so far?
  • f = angle of twist varies from zero at fixed support to max at end.
  • g = shear strain varies from zero at center to max at outer fiber.
what about stress
What about stress???
  • Deformation = strain
  • Strain = stress
  • If you can visualize deformation, you can visualize stress
  • The stress is a shear stress!!
slide11

5.2 The Torsion Formula

If linear elastic, Hooke’s law applies, t = Gy

Therefore, stress follows same profile as strain!!

slide12

EMCH13

Derivation – simple Torque balance. The torque produced by the stress distribution over the entire cross section must be equal to the resultant internal torque, or:

This is simply polar moment of inertia, J (an area property)

slide13

The torsion formula (see derivation):

Torque (N-m, N-mm or lb-in, lb-ft, etc)

Outer radius of shaft (m or in)

Polar moment of inertia (m4 or in4)

Max shear stress in shaft (MPa, psi/ksi, etc.)

or

j polar moment of inertia
J = polar moment of inertia
  • Solid shaft:
  • Hollow shaft:
slide15

Stress Profiles:

Shear stress profile – YOU MUST UNDERSTAND THIS!!!!

Where is shear stress max? zero? How does it vary along the length and circumference?

examples
Examples:
  • Analysis:

Want << tallow

Find geometry

2. Design:

5 3 power transmission
5.3 Power Transmission
  • Nothing new, just calculate Torque, T, from power equation:

P = Tw

Careful with units!

Power (watts, ft-lb/s or hp)

Angular velocity (rad/s or Hz)

Torque (N-m, lb-ft)

Note: 1 hp = 550 ft-lb/s

f = Hz or rev/s

examples english
Examples (English):
  • Shaft powered by 5 hp electric motor spins at 10 Hz, find Torque in shaft.
  • P = Tw

5 hp (550 ft-lb/s/hp) = 2,750 ft-lb/s

10 Hz (2p rad/rev) = 62.83 rad/s

T = 2750 ft-lb/s

= 43.76 lb-ft

62.83 rad/s

examples si
Examples (SI):
  • Shaft powered by 500 W electric motor spins at 10 Hz, find Torque in shaft.
  • P = Tw

10 Hz (2p rad/rev) = 62.83 rad/s

T = 500 N-m/s

= 7.96 N-m

62.83 rad/s

slide27

Your HW prob 5.39: Find stress throughout shaft:

  • Steps:
  • Find Torque throughout shaft
  • Solve for stress throughout shaft
slide28

Prob 5.42: The motor delivers 500 hp to the steel shaft AB which is tubular and has an inside dia of 1.84 in and outside of 2 in. Find: smallest angular velocity at which the shaft can rotate if tallow = 25 ksi

  • Design or Analysis:
  • Steps:
  • Find allowable torque
  • Back solve for speed using P=Tn