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The final design of the wheel of the agriculture robot is designed to be strong, flexible, and stable. This will allow the robot to support the 25lbs weight of the robot plus heavy payloads. The final design consists of 11 wheel spokes, a wheel hub and a motor cruciform. The 11 wheel spokes are designed to help the robot to operate over rough terrain. The wheel hub help equally spacing out the wheel spokes and securing them in place; this helps the robot maintain its stability. Lastly, the motor cruciform helps connect the wheel to the rest of the robot.
Figure #: The exploded views of the final design of the wheel assembly.
Buckling Analysis:
Based on the wheel analysis the reaction forces applied to the ground to the wheel is 1/4 of the total weight of the robot. The robot’s weight is 250 lb (W=250/4 lb)
Figure 7: Buckling with different types of constraint
https://www.sciencedirect.com/topics/engineering/euler-buckling
The case of =0.8with Fixed-Pivot ends matches the model of the spoke and ground contact.
Cross Area: 0.2 x 1.75 inches. (Figure)
Second Moment of Area
I=bh312=wt312=1.17x10-3in4
w is the width of the cross section, t is the thickness of the cross section
Material: Aluminium 6061 T6
E=107 Psi Elastic Modulus
y=40000 Psi Yield strength
L=23 inches Active length of spoke
Critical Buckling Load:
Pcr=2EI(L)2=345 lbf
The loading force applied to the spoke is P=250/4 = 62.5 lbf
The spoke wouldn’t be buckled due to ratio of Pcrand P is 5.52
We attach a foot to improve the efficiency in motion and contact with ground of robot, as picture below:
Critical Buckling Load:
Pcr=2EI(L)2
E young modulus of material
I area moment of inertia
L the length of the spoke
effective length factor
Figure 6: buckling model and cross section
For the end loaded spoke, the equation of deflection is :
(x)=[P.L3/(6EI)][3(x/L)2-(x/L)3]
x is maximum at L.
Therefore, max(x=L)=P.L3/(3EI)
Figure 8: Eccentric buckling due to the offset of loading and central line
The eccentric buckling would be considered in this analysis due to the offset of loading and the centerline of spoke. Maximum stress in the spoke is calculated by the following formula.
max=PA[1+e.C.AIsec(2PPcr]
e: offset distance (e= 0.1 in)
A: area of cross section.
C: the maximum distance from a point in section to neutral axis. (C=t/2)
max= 859 psi
Factor of safety:
n=ymax=46.5
The spoke is safe.
Deflection Analysis:
Find the the deflection of the spoke based on the calculation in the deflection analysis, we had . Cantilever deflection modeling
=FL33EIF=3EIL3
Material is Aluminium 6061 T6:
Sut=45000 Psi Ultimate Strength
Se=14000 Psi Fatigue Strength
Bending stress of the spoke:
=M.CI=FL(t/2)I=3Et.2L2
max=14.5 kpsi
min=0
m=max+min2
a=max-min2
Factor of safety:
1n=mSut+aSe
n = 1.5
The spoke will pass the fatigue failure check.
Deflection of the spoke: =PT.L33.E.I (1)
PT: Traction force applied on the spoke
Bending stress of the spoke:
=M.CI=PT.L.CI PT=.IL.C (2)
M: Bending moment in t the spoke
From (1) and (2), the deflection of the spoke can be calculated:
=.L23.E.C
Maximum deflection before plastic deformation:
=y, where y is the yield stress.
Maximum deflection of the spoke is:
max=y.L23.E.C=7.05 in.
Fatigue:
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