1. ME3221: Fundamentals of Design & Manufacturing
Lab: Fluctuating Stresses
in a Bicycle Crankshaft

2. Lab Problem & Content Describe stress state in bicycle crankshaft
Measure stresses – Electrical resistance strain gages
Stress analysis - Mechanical analysis of system

3. Sensing elements Load Cells - examples Hydraulic Capacitive
Piezoelectric

4. Load Cells - examples
Electrical resistance strain gages
Most common, by far
Sensitive to strain along gage longitudinal direction

5. So, we’ve decided to measure bending stress and shear stress at an accessible location.
How to do this?
Measurement concept – Use electrical resistance strain gages on crankshaft
System Design - Specify number and orientation of gages

6. Strain gages – “easy-to-use” – how do they work?
Measure strain, egage, then use,
stress – strain relations
esurface
esurface = egage => DR
a meander pattern foil resistor
bonded to the test surface
loading applied to test structure
deforming structure deforms gage => resistance change
measure DR
calibration of gage to give strain in terms of resistance change
gages designed to be sensitive only to axial strain

7. Measure Strains Gage responds to strain
Lead tabs
Gage
Physical process in gage is DR due to e
Advance alloy
Calibrate gage:
DR as function of e => Gage factor, Sg

8. Measure Stresses – Surface of Part
Measure DR and calculate e
(Valid for uniaxial tension only!)
DR, and so e, more usefully measured as DV using a “bridge circuit”

9. Gaging of Bicycle Crankshaft Strain gage rosettes

10. The Instrumented Bicycle Crankshaft
Strain gage rosettes 90o apart

11. Strain Gage Measurement – Bending stress
Gages are sensitive to strain along length of gage x y z F
M about z M x y e
Use Gage 2, which is aligned with the x-axis: x z

12. Sir Charles Wheatstone
DR  Measured DV
Samuel Christie
Sir Charles Wheatstone
Vout
Vin A D B C R2 R3 R1 R4
SG Rosette
Gage 2
“Dummy gage”
for temperature
compensation
(on “dummy”
crank shaft
taped to
down tube)
R3 & R4 are “bridge completion resistors”
included on strain gage amp circuit board
Note: DVout is amplified by a factor of ≈ 3500!
(Any noise in the “slip ring” can cause jitters in your data.)

13. How to measure txy? Wire in gages 1&3 as bridge resistances 1&2: 45○
Vout
Vin A D B C R2 R3 R1 R4
SG Rosette
Gage 3
Gage 1
Wire in gages 1&3 as bridge resistances 1&2: x y
45○ x’ y’
Bridge will measure a function of sx’ – sy’

14. Now apply Mohr’s Circle:2 sx
txy
sx’
sy’ q
(90○– q) r sx
txy y x x y’
txy’
sx’
sy’ x’
45○
sx’ = sx /2 + r cos(90 ○– q)
sy’ = sx /2 - r cos(90 ○– q)
sx’ - sy’ = 2 r cos(90 ○– q)= 2 r sinq
But sinq = txy / r
So: sx’ - sy’ = 2txy
(The 2X factor is included in the final V->s scale factor)

15. Typical Results
What to do with them? - In lab writeup