PURE TENSION
Guide
⁄ ⁄⁄
1) Assume intermediate column/JB Johnson 2) Check using 3) If < 2, dims stays, governs design! 4) If > 2, recomputed using Eu ler ’s formula!
CASE 3 -
PURE COMPRESSION
CASE 1 -
CASE 2 -
THIN-WALLED PRESSURED VESSEL
(intermediate column)
Euler Formula
PINS FIXED-PIN FIXED FREE-FIXED
n=1 n=2 n=4 n=1/2
Limiting Criteria :
THICK-WALLED PRESSURE VESSEL Hoop Stress on Inner Fiber
(HP)
T lb-ft
N rpm
(HP)
kgf-m
rpm
POWER FORMULA Formula
SPHERICAL
FOR JOINTED SEAM ; For a good design
IF L NOT GIVEN ASSUME 20D IF NOT IN TABLE OF PROPERTIES USE
LONGITUDINAL GOOD DESIGN
(long column)
PURE TORSION
(pure compression block)
CYLINDRICAL
CIRCUMFERENTIAL
(kW)
kN-m
rpm
(HP)
lb-in
rpm
PURE BENDING
→
Hoop Stress on Outer Fiber
Longitudinal Longitudinal Stress
Computing for the thickness of the plate,
Brittle
[ ]
If BHN < 400
VARIABLE STRESS ANALYSIS *W/O STRESS CONCENTRATION
b)
For Cast Steel
Soderberg Equation (MyAn, Ductile)
c)
For Cast Iron
d)
For Nodular Iron
Goodman Equation (MuAn, Brittle)
Surface Factor (Fig AF5) Assume machined if not specified.
Size Factor
Axial
* +
Torsion
Bending Vessel
FOR INDEFINITE LIFE BASIS Axial/ Bending Rotating Bending Torsion
: : :
FOR DEFINITE LIFE BASIS Axial/ Bending
:
First assumption : Size = 0.85 If range is 0.5” -2”, assumption stays. Otherwise, recomputed with size = 1
Endurance Strength
TYPES OF VARIABLE STRESSES
SHAFT DESIGN SHAFT UNDER PURE TORSION
SHAFT UNDER PURE BENDING
SHAFT UNDER COMBINED BENDING & TORSION Maximum Shear Stress Theory (Ductile)
* + Maximum Normal Stress Theory (Brittle)
Equivalent Bending Moment
Equivalent Torque
1) Reversed
2) Repeated
3)Fluctuating
SHAFT UNDER VARIABLE COMBINED LOADS Equivalent Stress Theory
() () Equivalent Normal Stress
Shaft Design Using Code 1) ASME Code A. For commercial shafting ***without keyway***
***with keyway***
2) PSME Code
Where the allowable sharing stress are as follows:
B. For line shafts
2) For allowable twist not exceeding 1⁰ per 20D length
C. For small, short shafts, countershafts
For English units
Allowance for Keyways
For combined stresses:
√ √
***without keyway***
1) For allowable twist not exceeding 0.08⁰ per ft. length
For bending torsion alone:
Diameter of Shaft
In SI units (allowable twist 0.26⁰ per meter length) A. For main power transmitting shafts
B. For shafts with definite specifications
Empirical Formula for Machinery’s Handbook
A. For main power transmitting shafts
B. For line shafts
C. For small, short shafts, countershafts
√ 3) For short, solid shaft, subject only to heavy transverse shear
Linear Deflection of Shafting Maximum Distance 1) For shafting subjected to bending action except its own weight
2) For shafting subjected to bending action of pulleys etc.
Design of Keys Design Considerations
c. Determine the length of the key using elementary failure
analysis.
a. Bolt Fail in compression
If
then, square. Otherwise, flat key.
b. Determine the key dimensions.
Failure Analysis 1. Key fails in shear ***Induced stress: shearing stress
2) Key fails in compression
3) Hub Fails a. Hub fails in shear
4) Shaft Fails
***Induced stress: compressive or bearing stress
Design of Couplings Failure Analysis 1) Key Fails a. Shearing
FLEXIBLE TRANSMITTING MATERIALS V-BELTS
√
, Use Std L from 17.3
Open Belt
+ big pulley, - small pulley Crossed Belt
Design Considerations
Compute Design hp
Add 0.2 for continuous, wet Subtract 0.2 for intermittent, seasonal
Compute for adjusted rated hp/belt
from 17.5, 5.
Use larger value.
1.
4.
from 17.6
Compute the number of belts required
FLAT BELTS Belt Tension Ratio
* +*+ √ √ √ If no
; SI unit, otherwise English
Initial Tension in the Belt, 2.
Choose belt section (ABCDE)
Neglecting centrifugal tension: Table 17.3, Figure 17.4 3.
Compute the rated hp/belt
a,c,e from 17.3 assume %slip=0 if not given from 17.4
Considering centrifugal tension:
But in actual practice:
Net Belt Pull/Net Belt Tension, F
Torque Developed
Power Transmitted by the Belt
Maximum Tension
ROLLER CHAINS 1.
2.
@Absolute Maximum Power
Belt Speed %Slip mentioned
%Slip not mentioned
For a Good Design
Installation of Idler Pulley
[ ] [ ] Rated Capacity of Leather Belts
Recommended Min. No. of Teeth Smaller Sprockets
Speed of Belt for Maximum Power
Estimation Formula for Chain Pitch
3.
Compute for Pitch Diameter and Outside Diameter
4.
[]
Compute for No. of Strands
⁄ By Formula:
Hp/strand:
)() (
[ ] Choose lower value.
⁄ By Table:
Rated Capacity of Rubber Belts
Assume different no. of strands so that hp rating on
ACA tables is greater than computed hp/strand. 5.
Compute for Chain Length and Center Distance
6.
7.
Compute for Chain Speed
Compute for Chain Pull
For safe design,
Silent Chain or Inverted Tooth Chain 1.
Hp/in of width
2.
Chain width
3.
Length of Chain
] [ ⁄
WIRE ROPES
Considering bending effect:
Considering fatigue failure:
For indefinite life:
Traction Drive Application:
Assume bending effect if not given
SPRINGS Coil Ends Plain Ground Squared S&G
Actual (N) n n n+2 n+2
BRAKES
Solid Length nd+d nd nd+3d nd+2d
Free Length np+d np np+3d np+2d
Mean Diameter of the Coil
Spring Index
Shear Stress on Spring
Deflection of Spring
Spring Rate of Spring Constant
Series Springs
LEAF SPRINGS Flexural Stress on Spring
Pure Rotation
Wahl’s Stress Factor
Energy Absorbed by the Spring
Unequal
Potential Energy
∆
Braking Torque
Power Needed by the Brake
Simple Band Brake Clockwise Rotation
⁄
Counter Clockwise
Differential Band Brake Clockwise Rotation
Counter Clockwise
Torque Equation
Concentric Springs Equal
Heat to be Dissipated during Braking
Spring under Kinetic Energy Source
Combination
Spring under Impact Load (Potential Energy)
Parallel Connected Springs
Pure Translation
CLUTCHES Cone Clutch Uniform Pressure (New Clutch) Uniform Wear (Old Clutch)
⁄
Self-Energizing or Self-Locking Brakes
Designing the Band
Block or Shoe Brakes
[ ] () [ ]
( )
Wear Constant
Force to Engage the Clutch
/
=
Mean Diameter of Clutch
Mean Friction Diameter of Clutch
Disc Clutch Uniform Pressure (New Clutch)
[ ] () [ ]
Uniform Wear (Old Clutch)
( )
FLYWHEEL
THREADED FASTENERS Rim Speed
Volume of Rim
Specific Weight
/
Angular Speed
Stress Area
Formula from Machinery’s Handbook a) Working Stress of Bolts
b) Power and Torque Transmitted by a Single Set Screw
POWER SCREW
Solving for the Rim Weight
Torque Required to Raise Load by Square Threaded Screws
Kinetic Energy Stored in Flywheel
Mass Moment of Inertia,
For Lowering the Load
Pitch
Energy Released by the Flywheel
() 1.
2.
Coefficient of Fluctuation
Coefficient of Steadiness
⁄
Application Energy Line
Lead Bolt Stress Area a) American National Thread and United Thread Series
b) Metric Thread Series
Strength Consideration
Linear Velocity
Lead Angle
Torque Required to Turn the Screw (Any Thread),
° [ ] ° ° ° [ ] a) Raising the Load
b) Lowering the Load
Torque Required to Overcome Collar Friction,
Total Torque Required to Operate the Screw,
Output Power of Screw,
Input Power of Screw,
Velocity Ratio
° a) For Square Thread
b) For Acme Thread,
SPUR GEARS
Circular Pitch
Base Pitch
Base Circle
Backlash
Lewis Equation
Velocity Factor Case 1 – ordinary industrial gears
] [
Case 2 – accurately cut gears
] [
Case 3 – precision gears cut
] [√ Dynamic Loads on Gear Teeth
Module
Contact Ratio
Tangential Force from hp
Diametral Pitch
⁄ ⁄ Length of Action
Efficiency of Power Screw,
Center Distance
Face Width
Design of Spur Gears for Wear
Dynamic Stress
Stress Concentration
° °
If not given, assume : Steady Load 8-10 hrs/day Enclosed
NOTE: If both gears were to be made of the same material, only the weaker pinion would have to be considered. If pinion and gear were made of different material, the weaker gear is to be considered which is the one with the smallest product of and For a good design, For a good design,
.
