Lab 1: Fluctuating Stresses
Jinyuan Zhang
Due Date: Wednesday, October 14, 2015
Lab Section: 5
Objectives:
There are three objectives for this lab. The first objective is applying stresses calculation on a bicycle crank shaft with real-world load. Second objective is visualization of stresses’ fluctuate in process of fatigue failure analysis. The last objective is using the stresses model to find the force is applied on the crank shaft.
Sample Calculation:
For collecting the data, a bicycle crank shaft is pedaled. In the sample calculation, a 1N for a crank angle of θ= 90 degree will be calculated. Strain Gage 2 Pedal Force = 1 N θ= 90 degree …show more content…
Strain Gage 1 Crank Shaft
Figure 1: Right side view of the crank set when θ = 90 degree Figure 2: The position of strain gage on the crank shaft when θ = 90 degree
For strain gage 1, y
Figure 3: The stress element on strain gage 1
Known: Diameter of the shaft d
Pedal force F
Angel θ
Normal Stress: I=〖πd〗^4/64 σ_x= My/I=32M/(πd^3 )
Shear Stress: τ(h)=Tr/j=Fh sinθ*r/j j=〖πd〗^4/32
Max Transverse Shear Stress: Max σ_t=4γ/3A=4F/(3πr^2 )
When θ=90 degree
For strain gage 1 τ(h)=Tr/j=Fh sinθ*r/j=(1N)*(175mm)*1*8mm/((〖(π16mm)〗^4/64)＝0.218MPa σ_x=0
〖 σ〗_y=0
〖 σ〗_y=4γ/3A=4F/(3πr^2 )=0.0063MPa
Theta (degree) Strain Gage Normal Stress(MPa) x Shear
Stress (MPa) Transverse Shear Stress (MPa) Normal Stress(MPa) y or z
90 1 0 -0.218 -0.0063 0
90 2 0.254 0.218 0 0
180 1 -0.254 0 0 0
180 2 0 0 0.0063 …show more content…
My weight is approximately 800N, compare with my weight, the pedal force is 1/4 of my weight, which is reasonable, for the seat supports another portion of the weight.
From figure2, one typical cycle takes 3.15s. So ω=2π/T=2π/3.15=1.99
The power is P=Tω=Fsω=66.076W=0.08854hp
The horsepower output is 6.435*〖10〗^(-4)hp
The power out put in horsepower is very low according to my opinion，an expectation higher than that was made before calculation.
The light bulb can be illuminated is about 60-70 watts.
Conclusion:
This experiment provides an experience on how to apply stresses test in real-world problems. For solving a problem economically, multiple factors should be considered, for example, the crank set’s power efficiency, maximum possible normal and shears stress; weight should be tested for manufacturing. Before building a prototype of a design, build its mathematical model can solve many potential problems in advance, in this experiment, it mathematical model predicts the performance of the system very close to the experiment result. The stress out put of the system is not consistent, for the rider’s speed is not necessarily consistent, further experiment can be performed under consistent speed, for it can influence experiment result a
Jinyuan Zhang
Due Date: Wednesday, October 14, 2015
Lab Section: 5
Objectives:
There are three objectives for this lab. The first objective is applying stresses calculation on a bicycle crank shaft with real-world load. Second objective is visualization of stresses’ fluctuate in process of fatigue failure analysis. The last objective is using the stresses model to find the force is applied on the crank shaft.
Sample Calculation:
For collecting the data, a bicycle crank shaft is pedaled. In the sample calculation, a 1N for a crank angle of θ= 90 degree will be calculated. Strain Gage 2 Pedal Force = 1 N θ= 90 degree …show more content…
Strain Gage 1 Crank Shaft
Figure 1: Right side view of the crank set when θ = 90 degree Figure 2: The position of strain gage on the crank shaft when θ = 90 degree
For strain gage 1, y
Figure 3: The stress element on strain gage 1
Known: Diameter of the shaft d
Pedal force F
Angel θ
Normal Stress: I=〖πd〗^4/64 σ_x= My/I=32M/(πd^3 )
Shear Stress: τ(h)=Tr/j=Fh sinθ*r/j j=〖πd〗^4/32
Max Transverse Shear Stress: Max σ_t=4γ/3A=4F/(3πr^2 )
When θ=90 degree
For strain gage 1 τ(h)=Tr/j=Fh sinθ*r/j=(1N)*(175mm)*1*8mm/((〖(π16mm)〗^4/64)＝0.218MPa σ_x=0
〖 σ〗_y=0
〖 σ〗_y=4γ/3A=4F/(3πr^2 )=0.0063MPa
Theta (degree) Strain Gage Normal Stress(MPa) x Shear
Stress (MPa) Transverse Shear Stress (MPa) Normal Stress(MPa) y or z
90 1 0 -0.218 -0.0063 0
90 2 0.254 0.218 0 0
180 1 -0.254 0 0 0
180 2 0 0 0.0063 …show more content…
My weight is approximately 800N, compare with my weight, the pedal force is 1/4 of my weight, which is reasonable, for the seat supports another portion of the weight.
From figure2, one typical cycle takes 3.15s. So ω=2π/T=2π/3.15=1.99
The power is P=Tω=Fsω=66.076W=0.08854hp
The horsepower output is 6.435*〖10〗^(-4)hp
The power out put in horsepower is very low according to my opinion，an expectation higher than that was made before calculation.
The light bulb can be illuminated is about 60-70 watts.
Conclusion:
This experiment provides an experience on how to apply stresses test in real-world problems. For solving a problem economically, multiple factors should be considered, for example, the crank set’s power efficiency, maximum possible normal and shears stress; weight should be tested for manufacturing. Before building a prototype of a design, build its mathematical model can solve many potential problems in advance, in this experiment, it mathematical model predicts the performance of the system very close to the experiment result. The stress out put of the system is not consistent, for the rider’s speed is not necessarily consistent, further experiment can be performed under consistent speed, for it can influence experiment result a