Engineering/Failure Engineering/Failure AnalysisAnalysisTeam Icarus John Brooks Ivan Olendan Kyle Reno Endalk Tegegne David Wu

Last Week: Design LayoutDecided to go with a modified

triangular design rather than T design

A lot of room for improvement in the caster wheel design

Maintenance/Failure is a major area for improvement over current designs

Topics for TodayQualitative Caster Angle/Trail effects. Trail effect Positive vs. Negative caster angleFailure Analysis Static Analysis – Pin shear and bending with

factor of safety. Load Rating of wheels. Impact Analysis – Spring model of wheel

assembly to estimate impact forces using strain-energy.

Materials Selection Wheel selection Frame Bearings/PinsNew Design Idea

Qualitative Caster AnalysisMechanical Trail (distance between steering arm and

wheel contact)Although the scientific understanding of bicycle steering

remains incomplete,[Whitt] mechanical trail is certainly one of the most important variables in determining the handling characteristics of a bicycle. A higher mechanical trail is known to make a bicycle easier to ride "no hands" and thus more subjectively stable.

Whitt, Frank R.; Jim Papadopoulos (1982). "Chapter 8", Bicycling Science, Third edition, Massachusetts Institute of Technology. 

For our purposes, trail will increase how well the dolly tracks, but it will also increase bending stresses that exist in the caster pin (due to a larger moment arm).

Qualitative Caster AnalysisCaster Angle (source is based on cars)

Positive caster angle◦ Improves tracking◦ Makes wheels harder to turn (in cars and motorcycles

power steering is often required for significant caster)◦ Reduces FlutterNegative caster angle◦ “Vehicle might wander as a result of negative caster”◦ Too much negative caster can cause sensitive steering

at high speeds.

Unequal caster angles cause the vehicle to steer toward the side with less caster. For us, if one pin bends and changes the caster angle and the other pins doesn’t bend as much this would be problematic.

Static Failure AnalysisW 250 lb 1112 NL dolly 7 ft 2.1336 mCg dolly 0.333333333 (fraction of length away from front)L_fork 10 in 0.254 mtheta_fork 45 deg

D_pin 0.75 in 0.01905 mI_pin 6.46472E-09 m^4

F_wheel 370.6666667 N 83.48348 lbsM 66.57363204 NmV 919578 Pa 0.00092 GPasigma_bending 104218869 Pa 0.104219 GPaFailure=yieldingSy 1.7 GPa <-- harder steelSy 0.2 Gpa <--weaker steel

good_n 16.31182546bad_n 1.919038289

This is for a ¾” pin with current fork length and fork angle. They currently use a 5/8” pin.

Modeling Impact (to determine max force that arises)Spring model

mNk

kkk

net

wheelforknet

/241787

111

For springs in series:

Max force exerted on tires=3620N=814 lbsMax bending stress in pin = 1.655 GPaBending factor of safety (failureyielding) for a ‘hardened’ steel~1.027

When 50 lb dolly is dropped 1 foot

Wheel Spring Model

Assume a rectangular shape carries load in tire

LEAkwheel 254000 N/m

Fork Spring Model

3

32LEIk fork

Treated both sides of fork as cantilevers. Bending spring rate is much smaller than axial compression spring rate, so axial component is neglected.

12

3bhI

K=3556000 N/m

Pin Stresses

NmFLMNkxF

mxkxmgh

wheel

1.650)45sin(3619

01425.02

2

3

32

pinbending d

MIMc

There’s also a shearing stress in the pin because the fork is in compression, but the static analysis showed this is 100 times smaller than the max bending stress

From our model, the bending stresses exceed the yield strength for many metals. The pin may be permanently deforming without fatigue.

New Dolly Design

Wheel Rub

Keel Rest

Interference Problem with Pilot

Cradle Support Bar

Material SelectionsSquare tube steel for the front part of

frame, aluminum used as much as possible elsewhere.

Decided on urethane Never-Flat Tires. They come up to a 10 inch diameter and have a load rating of 350 lbs.

Hardened steel for caster pin (need very high yield strength). Looking at aircraft grade chromoly steel steerer tubes for pin connection (used in bikes, easy to add bearings with this)

Galvanized steel for bolt connections.

Next WeekPart Drawings

◦Fully dimensioned drawings of dolly.