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

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

Sensing elements Load Cells - examples Hydraulic Capacitive Piezoelectric

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

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

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

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

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”

Gaging of Bicycle Crankshaft Strain gage rosettes

The Instrumented Bicycle Crankshaft Strain gage rosettes 90o apart

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

Sir Charles Wheatstone DR  Measured DV Samuel Christie Sir Charles Wheatstone 1802-1875 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.)

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’

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)

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