Excavator structural stress - hand calculations B. Ravindra Excavator design engineers need to be familiar with methods to calculate pivot forces ar...
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Excavator design engineers need to be familiar with methods to calculate pivot forces arising out of the specific kinematics of excavator and structural stresses. Finite Element Analysis methods notwithstanding, doing calculations by hand provides engineers with a keen insight on the magnitude of forces at play and stresses that are set up in his structural designs. These are key inputs to avoid expensive FEA iterations. iterations. This document gives gives a method to compute section stresses once pivot forces are know. It is assumed that readers are familiar with basic strength of materials and applied mechanics concepts. Below is an image of an excavator dipper arm with bucket in maximum breakout force position. Just for the purposes of this sample calculation let’s assume the maximum breakout force is 45kN and acting at the corner of the bucket. Link lengths and position for maximum force are assumed to be known to arrive at forces in the links. Section dimensions of Arm structure are given in later images. Once the Breakout force vector is completely defined it is not necessary to calculate the link & pivot forces to get sectional stresses. It is given here only to let readers get a feel for the magnitude of the forces in links arising out of breakout force and a nd the linkage system. A Breakout force of 4.5 Tons sets-up pin forces of 16.5 Tons in the Arm. That is what you get as a consequence of the excavator 4-bar mechanism. A similar feel for forces in boom pivots can rationally explain why an excavator boom is more generously dimensioned than the Arm. For sectional calculations, Arm is oriented with the horizontal axis passing through bucket pivot and the arm cylinder pivot (on the arm). A typical hand calculation of stresses would require about four to six sections analyzed and about ten sections analyzed in the boom. Sections in the arm are numbered from 1 to 4. There would be at least a couple more passing through the two end pivots. We would demonstrate the hand calculation in section 3-3. There is nothing sacrosanct about the orientation of the section. Sections can be taken any which ways but then interpretations of stresses become meaningless when section orientations results in plate thicknesses very different from actual. Also one is interested not just in stresses at one section but in a number of sections along the length of the structure and a non-uniform distribution of sections just doesn’t help.
LOAD CASE: MAX BREAKOUT FORCE of 45kN (Forces left of section 3-3)
Force at Pin joint F Ff
16414daN
Force at Pin joint J F j
13835daN
Width of bucket
Subtended angle w.r.t section 5-5 1.6 deg deg
f
Subtended angle w.r.t 5-5 87.9deg
j
Half width of bucket W
Wb
710 710 m
Breakout force Fbr
4500daN
W
hb
b
2
Subtended angle w.r.t section 5-5
br
54.2deg
Section properties: 3-3
Sectional area
Acc
2
Area moment of Inertia X-X Ixx
Iyy
31924067mm
Area moment of Inertia, Polar Ip
84121402mm
Area moment of Inertia Y-Y
5369mm
4
52197335mm
Dimension to outer fiber of top plate (for stress due to bending about X axis)
d bx
127.2m
Dimension to outer fiber of side plate (for stress due to bending about Y axis of section) d by
102.5m
ds
Arm side plate thickness (for stress due to torsion & transverse shear stress)
6m
Torsion area = Area bounded by the center line of the wall cross-section At
Section modulus X-X
Wx
Ixx
( 185
6) mm ( 2 54 . 4 Iyy
Wy
Section modulus Y-Y
dbx
6) m
d by
Shear area
Areas of side half plates
area area1 1
2
72 727.2m 7.2mm m
ar area ea2 2
2
12 1230mm 30mm
First moment of areas for transverse shear stress along X-X A sx
2 area1 area1 60.6 60.6 mm
Resolution of forces & moments about axes 5-5
Horizontal component of forces
Vertical component of forces
Ffh
Ffv
Horizontal component of Breakout force
Vertical component of Breakout force
Ff c os
Ff sin
f
f
F jh
F j c os j
F jv
F j sin j
Fbrh
Fbr c os
br
Fbrv
Fbr sin
br
area2 area2 124.2m 124.2m
Vertical distances from 5-5 axis to section centroid (refer section dimensions above)
d fv
254.4 2
69.8 m
d jv
d fv
26.1m
Horizontal distances to section 3-3 centroid
dfh
800 800 m
Stress analysis at section 3-3
d jh
dfh
203.3m
Mbx
Bending moment at section 3-3
Ffh d fv
Ffv d fh
Mbx
Stress due to bending along X-X at 3-3
bx
bx
Wx
Bending moment on Arm perpendicular to Axes 5-5 due to bucket corner loading
F jh d jv
169.541MPa
Mby
Fbrh W hb
by
30.003MPa
Mby
Stress due to bending along Y-Y at 3-3
by
Wy Ffh
Direct stress due to horizontal components d
Torsion
F jv d jh
F jh
.d
29.616MPa
Ac c 3
Fbrv W hb
f
.f
1.29 1.296 6 10 daN m
.s
24.283MPa
f
Torsional stress
s
2 A t ds
Transverse/horizontal shear stress due to varying bending moment along X-X F jv
