REAR WHEELS SAFETY FACTOR ANALYSIS OF
WHEELCHAIR
A PROJECT
Submitted as a partial fulfillment for the Subject
MS 2210 Elemen Mesin Dasar (Basic Design of Machine Elements)
by:
Fatah Banyunuki Raziqin
13120030
Class 03
Lecturer:
M. Agus Kariem, S.T.,M.T.,Ph.D
MECHANICAL ENGINEERING STUDY PROGRAM
FACULTY OF MECHANICAL AND AEROSPACE ENGINEERING
INSTITUT TEKNOLOGI BANDUNG
2021
Table of Contents
Table of Contents ............................................................................................................................. i
1.
Introduction .............................................................................................................................. 1
1.1 Background ………………………………………………………………………….. 1
1.2 Specification ………………………………………………………………………… 2
1.3 General Assumption ………………………………………………………………… 3
2. Objective ……………………………………………………………………………………… 3
3. Methodology ………………………………………………………………………………….. 4
3.1 Methodology ………………………………………………………………………… 4
3.2 Theoretical Background ……………………………………………………………... 5
3.2.1 Axle ………………………………………………………………………... 5
3.2.2. Bearing ……………………………………………………………………. 6
3.2.3 Bolt ………………………………………………………………………… 7
4. Data ………………………………………………………………………………………….. 9
4.1 Bearing ………………………………………………………………………………..9
4.2 Axle …………………………………………………………………………………. 9
4.3 Bolt …………………………………………………………………………………. 9
5. Analysis ………………………………………………………………………………… …10
5.1 Bearing ……………………………………………………………………………... 10
5.2 Axle ………………………………………………………………………………… 10
5.3 Bolt …………………………………………………………………………………. 11
6. Conclusion …………………………………………………………………………………... 14
i
1. Introduction
1.1 Background
Wheelchair is something most people know, although not everyone use one but some
people has a family that need to use wheelchair nowadays the newest wheelchair electric one is
easier to use but due to it’s build it is quite expensive not everyone can use it so the traditional
wheelchair is still be used in many places including a hotel, but does this wheel chair is safe to
use is the main topic of the safety analysis of this paper we use wheel chair from a hotel in
bandung, grand tjokro hotel for analysis
1
1.2 Specification
Figure 1. side view of wheelchair
Figure 2. front view of wheelchair
2
1.3 General Assumption
2. Weight of the person sat on the wheelchair = 60 Kg
3. The Wheelchair is massless
4. The weight is distributed equally
5. Safety factor = 1 means safe
2. Objective
1. Find the estimated safety factor of nut on wheelchair.
2. Find the estimated safety factor of axel on wheelchair.
3. Find the estimated safety factor of bearing on wheelchair
3
3. Methodology and theoretical background
3.1 Methodology
Diagram 1. Methodology
4
3.2 Theoretical background
3.2.1 Axle
Assumption
Because the axle and the bolt is connected permanently, thus we assume the length of the axle
start from the right side thread until the part before the left thread started.
Failure analysis of Axle
In order to find the safety factor of axle, we could use the modified goodman formula
5
3.2.2 Bearing
Failure analysis of Bearing
In order to find the safety factor of bearing, we could use the formula below
𝑆𝐹 =
Whereas:
CO = Basic Static Loading
FE= Xi x V x F radial + Yi x F axial
V = Rotation factor
F radial = combined radial load
F axial = Combined axial load
6
𝐂𝐎
𝐅𝐄
3.2.3 Bolt and Nut
𝑺𝑭 =
𝐂𝟎
𝐅𝐄
Assumption
Because the Bolt is permanently connected to the axel, thus we assume the length of the bolt is
the thread from the left until the head of the Bolt. Hence the diameter of the Bolt is the same as
the diameter of the Axel.
Failure analysis of Bolt :
In order to calculated the safety factor of bolt we use the formula below.
Fi= 0.75 × 𝐹𝑝
Fp=𝐴𝑡 × 𝑆𝑝
Sp = Minimum proof Strength
At = Tensile stress area
7
K𝑏
𝐶 = Kb+Km
E = Elastic Strength
A and B from table 8-8
d = nominal major diameter
l = length
8
4. Data
4.1 Bearing
No Description
1 Bearing
Inner
Diameter
2 Bearing
outer
Diameter
3 Material
4
Type of
Bearing
5
Basic
Dynamic
load rating
Basic Static
Load rating
6
Symbol
d
Value
11.5
Unit
mm
Remarks
measured
D
32
mm
measured
-
-
Assumed
-
C10
Stainless
Steel
Deep
grove
ball
6.89
kN
https://www.skf.com/group/products/rollingbearings/ball-bearings/deep-groove-ballbearings
Table 11-2
C0
3.1
kN
Table 11-2
-
4.2 Axle
No
1
2
3
Description
Shaft Diameter
Shaft Length
Material
Symbol
D
L
-
4
Ultimate Tensile Strength
Sut
Value
12
85
AISI 1018
Steel
341
Unit
mm
mm
-
Remarks
measured
measured
Assumed
MPa
Table A-22,
Shigley
mechanical
engineering
Table A-22,
Shigley
mechanical
engineering
5
Yield strength
Sy
220
MPa
Description
Bolt Length
Bolt Diameter
Material
Symbol
L
D
-
Value
50
12
Low carbon
Steel
225
400
207
Unit
mm
mm
-
Remarks
measured
measured
Assumed
MPa
MPa
GPa
Table 8-11
Table 8-11
Table 8-8
4.3 Bolt
No
1
2
3
4
5
6
Proof strength
Tensile strength
Modulus of Elasticity
Sp
Sut
E
9
5. Analysis
5.1 Bearing
FBD of Bearing
Fa = 0
Fn = Fr = 150N
Fr = 150N
Calculation of the safety factor
𝑆𝐹 =
C0 = 3.1 kN
FE = 𝑋𝑖 × 𝑉 × 𝐹𝑟𝑎𝑑𝑖𝑎𝑙 + 𝑌𝑖 × 𝐹𝑎𝑥𝑖𝑎𝑙
FE = 1 × 1 × 150 + 0
FE = 150
Thus,
𝑆𝐹 =
3100
150
SF = 20.67
5.2 Axle
FBD of Axle
10
CO
FE
With
P = 150 N
N = 150 N
Therefore, we get bending moment diagram
By using the modified goodman formula, we can calculate the safety factor
Ma = T a= Tm = 0 ( because axel as a static road )
Kf = 1
1
16
= ( 3.14(12×10−3 ))^ 2 )( 0 + ( 4 × (1 × 3187,5)2 )/(341 × 106 )
𝑛
1
𝑛
= 0.35082
n = 2.8
5.3 Bolt
FBD of Bolt
Ld = L – LT
LT = 2 ( 𝐷 ) + 6 = 2 × 12 + 6 = 30 mm
11
Ld = 20 mm
π 𝐷2
𝐴𝑑 =
4
Ad = 113.04 𝑚𝑚2
At = from Table 8-1 = 84.3
Based from the FBD of the Wheel chair (4 wheels)
W = 60 × 10 = 600 N
G = 10 m/𝑠 2
P=
600
4
=150 N
N = P = 150 N
Assume the location of N is in the middle of the Bolt and the location of P is in the middle of the
Axle
L Bolt = 50 mm
50
2
= 25 mm
L axle = 85 mm
85
2
= 42.5 mm
𝑥 = 50 − 42.5 = 7.5 mm
Ma = 150 ( 7.5 ) + 150 ( 25 ) = 4875 N.mm
Therefore, we get the Internal force
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Calculation of the Safety Factor
Sp = 225
Fp = 𝐴𝑡 × 𝑆𝑝 = 18967.5
Fi = 0.75 × 𝐹𝑝 = 14225. 625
Kb =
113.04 × 84.3×207
( 113.04×30 )
+ ( 84.3 ∗ 20 )
Kb = 388.513
𝐾𝑚
207 ×12
12
= 0.78715 × 𝑒( 0.62873 × 50 )
Km = 2273.6
𝐶=
388.513
388.513 + 2273.6
𝑛𝑝 =
225(84.3)
0.146 + 14225.625
C = 0.146
np = 1.3
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5. Conclusion
the safety factor of axle is 2.8, means it’s safe to use, the safety factor of bolt is 1.3 also
means it is safe to use and the safety factor of bearing is 20.67 also means it is safe to use,
therefore the conclusion the wheelchair is safe to use at least the rear wheel parts, do take note
that the measurement did not use proper tools to it has low precision, a better tools may provide
different result than the one in analysis and more precise
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