Machine ElementShaft

Shaft

1. Strength of Shaft

(2) Bending load

2. Strength of Key

(3) Torsion load

(1) Material

3. Fracture surface

Shaft

𝑊 : h𝑊𝑒𝑖𝑔 𝑡𝐹 :𝐹𝑜𝑟𝑐𝑒𝜎=

𝑀𝑍

𝑀 :𝑀𝑜𝑟𝑚𝑒𝑛𝑡𝜎 :𝑆𝑡𝑟𝑒𝑠𝑠

Strength of Shaft (1) Bending load

Shaft

I: geometrical moment of inertia, Z: section modulus

Shaft

Formula of statically determinate beam

BMD: Bending Moment Diagram SFD: Shear Force Diagram

Shaft

BMD: Bending Moment Diagram SFD: Shear Force Diagram

Shaft

𝑊=12 𝑡𝑜𝑛𝜎 𝑎=46𝑁

How much diameter we need ?

allowable stress

< Q. 1 >

Shaft

𝑊 : h𝑊𝑒𝑖𝑔 𝑡𝐹 :𝐹𝑜𝑟𝑐𝑒𝑀 :𝑀𝑜𝑟𝑚𝑒𝑛𝑡𝜎 :𝑆𝑡𝑟𝑒𝑠𝑠

Strength of Shaft

𝑇 :𝑇𝑜𝑟𝑠𝑖𝑜𝑛

𝑇

(2) Torsion load

Shaft

Shaft

Stress concentration

Fig. Stepped Shaft

fatig

ue n

otch

fact

or β

Shaft

Stress concentration

Fig. Torsion of Shaft having key

stre

ss c

once

ntra

tion

fact

or α

Shaft

Stress concentration

Fig. Torsion of Stepped shaft

stre

ss c

once

ntra

tion

fact

or α

Shaft

< Q. 2 >

𝜏𝑎=98𝑁

How much torsion each shaft resist ?

allowable stress

𝜏=𝑇𝑍𝑃

=16𝑇𝜋 𝑑3

This shift have stress concentration

Shaft

Stress concentration

boss

shaft

Shape and stress distribution of Tight fit

contact edge

Distance from contact edge r

Stre

ss σ

Shaft

Countermeasure

boss

shaft

boss

shaft

boss

shaft

ditchditch

Shaft

𝐹=12h𝑙𝑝

𝐹=𝑏𝑙𝜏 𝑘

(2) contact pressure strength

(1) shear strength

Strength of Key

𝑙≥1.5𝑑

Shaft

ShaftFatigue Fracture Surface

Chevron Pattern

Beach Mark

Chevron Pattern

Beach Mark

starting point

Final fracture section

Shaft

Fracture surface

pulsating bending

fully-reversed bending

rotary bending

pulsating tension, tension and compression

cyclic torsion

high stress low stressnotch

(sharp)notch (dull)smooth

notch (sharp)

notch (dull)smooth

ShaftMaterial for Shaft

small shaft, motor shaft car shaft, common shaft crank shaft, induction hardening shaft cam shaft, piston shaft small shaft, piston pin crank shaft, cam shaft, drive shaft, common shaft small shaft, middle shaftcommon shaftcrank shaft, large shaft, piston pin cam shaft, spline shaft middle shaft, large shaft

common shaft, piston pin piston pin

crank shaft, car shaft, various shaft large shaft

Carbon Steels for Mechanical Structure

Chromium Molybdenum Steel

Chromium Steel

Nickel Chromium Molybdenum Steel

Nickel Chromium Steel