Ceiling-mounted bicycle lift structural analysis

From DDL Wiki

(Difference between revisions)
Jump to: navigation, search
m
m
Line 132: Line 132:
|}
|}
-
==Part # 001: V-Bracket==
+
==Part # 012: V-Bracket==
{| class="wikitable" border="0"  
{| class="wikitable" border="0"  
|- align="left"
|- align="left"
Line 148: Line 148:
(P = 50 lbs)<br />
(P = 50 lbs)<br />
|-  align="left"
|-  align="left"
-
| [[Image:Team1-FBD-VBracket.JPG|300px]] || '''Bending along X-axis'''<br />
+
| [[Image:Team1-FBD-VBracket.JPG|300px]] || '''Bending at Neck'''<br />
-
Distance between support forces: 200 mm<br />
+
Distance from support force: 10 mm<br />
-
Vertical centroid: -7.57 mm (measure from top surface)<br />
+
Cross sectional area: 19.5 mm<sup>2</sup>
-
Second moment of area about centroidal axis: 3510 mm<sup>4</sup><br />
+
Second moment of area about centroidal axis: 2.42 mm<sup>4</sup><br />
-
Maximum bending moment:  5,560 N*mm<sup>2</sup><br />
+
Maximum bending moment:  5,56 N*mm<sup>2</sup><br />
<br />
<br />
-
Maximum x-bending stress: 9.47 N/mm<sup>2</sup> = 9.47 Mpa<br />
+
Maximum bending stress: 9.47 N/mm<sup>2</sup> = 15.2 Mpa<br />
|-  align="left"
|-  align="left"
-
| [[Image:Team1-Stress-Vbracket.JPG|300px]] || '''Bending along Z-axis'''<br />
+
| [[Image:Team1-Stress-Vbracket.JPG|300px]] || '''Stress Concentration'''<br />
-
Distance between support forces: 70 mm<br />
+
r: 2 mm<br />
-
Vertical centroid: -.66 mm (measure from top surface)<br />
+
d: 16 mm<br />
-
Second moment of area about centroidal axis: 37.8 mm<sup>4</sup><br />
+
D: 18 mm</sup><br />
-
Maximum bending moment: 1,946 N*mm<sup>2</sup><br />
+
D/d = 1.1    r/d = .13
-
<br />
+
K = 1.6 -  From table A-15-5 of (Shigley, Mechanical Engineering Design)<br />
-
Maximum z-bending stress: 3.4 N/mm<sup>2</sup> = 3.4 Mpa<br />
+
'''<big>Actual Maximum Stress = 24.3 Mpa<br /></big>'''
-
<br />
+
'''<big>Safety Factor = 9.1 Mpa<br /></big>'''
-
'''Maximum net bending stress: 10.1 Mpa'''<br />
+
|}
|}
-
'''Stress Concentration Factor'''<br />
 
-
h = 1.22 mm (sheet thickness)<br />
 
-
w = 50 mm (section width)<br />
 
-
d = 6 mm (hole size)<br />
 
-
<br />
 
-
d/w = .12    d/h = 5<br />
 
-
K = 1.7  -  From table A-15-12 of (Shigley, Mechanical Engineering Design)<br />
 
-
<br />
 
-
'''<big>Actual Maximum Stress = 17.1 Mpa<br /></big>'''
 
-
'''<big>Safety Factor = 12.9 Mpa<br /></big>'''
 
-
<br />
 

Revision as of 02:49, 8 March 2007

Contents

Part # 001: Ceiling Bracket

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Bending along X-axis

Distance between support forces: 200 mm
Vertical centroid: -7.57 mm (measure from top surface)
Second moment of area about centroidal axis: 3510 mm4
Maximum bending moment: 5,560 N*mm2

Maximum x-bending stress: 9.47 N/mm2 = 9.47 Mpa

Bending along Z-axis

Distance between support forces: 70 mm
Vertical centroid: -.66 mm (measure from top surface)
Second moment of area about centroidal axis: 37.8 mm4
Maximum bending moment: 1,946 N*mm2

Maximum z-bending stress: 3.4 N/mm2 = 3.4 Mpa

Maximum net bending stress: 10.1 Mpa

Stress Concentration Factor
h = 1.22 mm (sheet thickness)
w = 50 mm (section width)
d = 6 mm (hole size)

d/w = .12 d/h = 5
K = 1.7 - From table A-15-12 of (Shigley, Mechanical Engineering Design)

Actual Maximum Stress = 17.1 Mpa
 Safety Factor = 12.9 Mpa

Part # 002: U-Pulley Mount

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Bending along X-axis

Distance between support forces: 20 mm
Vertical centroid: -.66 mm (measure from top surface)
Second moment of area about centroidal axis: 3.03 mm4
Maximum bending moment: 556 N*mm2

Maximum x-bending stress: 12.1 N/mm2 = 12.1 Mpa

Stress Concentration Factor

h = 1.22 mm (sheet thickness)
w = 48 mm (section width)
d = 6 mm (hole size)

d/w = .13 d/h = 5
K = 1.7 - From table A-15-12 of (Shigley, Mechanical Engineering Design)

Actual Maximum Stress = 20.6 Mpa
 Safety Factor = 10.7 Mpa


Part # 003: Pulley Wheel

Images Calculations
Material: Injection molded plastic

E = 3,500 N/mm2
v = .4 Yield strength = 103 Mpa

Loads
P/2 = 111.2 N
Ft = force resulting from tension in rope
(P = 50 lbs)

Contact Stress

Diameter 1: 5.3 mm
Diameter 2: 4.9 mm
Contact length = 13.5mm
Half-width of contact surface = 2 mm

Maximum Compressive Stress = 4.2 Mpa
 Safety Factor = 24.5

Part # 004: Pulley Rivet

Images Calculations
Material: Aluminum

E = 69,000 N/mm2
Yield strength = 95 Mpa

Loads
P/2 = 111.2 N
P/4 = 55.6 N

(P = 50 lbs)

Shear Stress

Diameter: 4.9 mm
Length = 20 mm

Maximum shear force = 55.6 N
Shear area = 18.9 mm2

Maximum Compressive Stress = 2.9 Mpa
 Safety Factor = 32.3

Part # 012: V-Bracket

Images Calculations
Material: Carbon steel

E = 202,700 N/mm2
Yield strength = 220 Mpa

Loads
P/2 = 111.2 N
P/4 = 55.6 N
Mz = 1780 N*mm
(P = 50 lbs)

Bending at Neck

Distance from support force: 10 mm
Cross sectional area: 19.5 mm2 Second moment of area about centroidal axis: 2.42 mm4
Maximum bending moment: 5,56 N*mm2

Maximum bending stress: 9.47 N/mm2 = 15.2 Mpa

Error creating thumbnail: convert: unable to open image `/ux0/websites/wiki.ece.cmu.edu/wiki/virtual-hosts/ddl/images/Team1-Stress-Vbracket.JPG': No such file or directory @ error/blob.c/OpenBlob/2882.
convert: no images defined `/ux0/websites/wiki.ece.cmu.edu/wiki/virtual-hosts/ddl/images/thumb/Team1-Stress-Vbracket.JPG/300px-Team1-Stress-Vbracket.JPG' @ error/convert.c/ConvertImageCommand/3235.
 Stress Concentration

r: 2 mm
d: 16 mm
D: 18 mm</sup>
D/d = 1.1 r/d = .13 K = 1.6 - From table A-15-5 of (Shigley, Mechanical Engineering Design)
Actual Maximum Stress = 24.3 Mpa
 Safety Factor = 9.1 Mpa

Retrieved from "http://wiki.ece.cmu.edu/ddl/index.php/Ceiling-mounted_bicycle_lift_structural_analysis"
Personal tools