The document is a project report on vibration analysis of a wheelchair. It analyzes the wheelchair as a single degree of freedom (SDOF) system, then a two degree of freedom (TDOF) system, and finally as a multi degree of freedom (MDOF) system to account for increased complexity. Key steps include developing models of the wheelchair as a SDOF system, calculating natural frequency and response, then expanding the analysis to a TDOF and MDOF model considering additional masses and degrees of freedom. Graphs and equations are provided to analyze vibration properties at each level of complexity.
High Bandwidth suspention modelling and Design LQR Full state Feedback Contro...
vibration of machines and structures
1. 1
In the fulfill of the requirement of the
Vibration of machines and structures
(MECH 6311)
Summer 15
A project report on
Vibration analysis of wheelchair
Submitted to
Dr. R Ganesan, Ph.D., Eng
By
Aniruddhsinh barad [7180217]
Bhoomirajsinh barad [7180225]
Viral kale [7677871]
Department of Mechanical and Industrial Engineering
Faculty of Engineering & Computer Science
2. 2
Abstract
In this project, we concerned the vibration analysis of half portion of
the wheel chair. First we considered the different properties of the system and get
the values for all parameters from the real life examples. Then, we considered the
whole system as one equivalent SDOF model system and developed one
elementary model and we calculated the all the parameters and responses of
system. In the next step we analyzed magnification factor and transmissibility of
the system. At last the whole system is studied for multi degree of freedom system
for more complexity.
3. 3
Index
1. Vibration model of wheel chair…………………………………4
2. SDOF system of wheelchair …………………………………….6
3. Two DOF system analysis……………………………………...11
4. MDOF system analysis…………………………………………13
5. References……………………………………………………….20
Figures
1. Wheelchair suspension system….………………………………4
2. SDOF suspension system………….…………………………….6
3. Two DOF suspension system……...………………………...…11
4. MDOF suspension system...……………………………………13
5. 5
Contractions:
Mh = mass of human
Mf = mass of frame
Mu = mass of tyre(wheel)
Kc = stifness of tyre
Kc = stifness of cushion
Kf = stifness of frame suspension
Cf = damping of frame
Cc = damping of cushion
v = velocity
ξ = Damping Ratio
Data:
Mh = 50 kg
Mf = 13 kg
Mu = 1.2 kg
Ku = 56 ∗ 104 N
m
Kc = 1.161 ∗ 104 N
m
Kf = 104 N
m
Kcf = 2.16 ∗ 104 N
m
Cf = 150
Ns
m
Cc = 115
Ns
m
Ccf = 265
Ns
m
v = 0.5
m
s
ξ = 0(no damping)
y = 0.01sin(
2πvt
2.5
)
= 0.01sin(
2π ∗ 0.5 ∗ t
2.5
)
ω = (
2πv
2.5
)
6. 6
= (
2π ∗ 0.5
2.5
)
∴ ω = 1.256 rad/sec
2. SDOF system of wheelchair:
Fig.2 SDOF suspension system
Kinetic energy:
T =
1
2
Muẋ 2
t+
1
2
Mhfẋ 2
t
=
1
2
(Mu + Mhf)ẋ 2
t
7. 7
Meq = (Mu + Mhf)
= (1.2 + 63)
∴ Meq = 64.2 kg
Potential energy:
U =
1
2
Kuẋ2
t +
1
2
Kcfẋ 2
t
=
1
2
(Ku + Kcf)ẋ2
t
Keq = (Ku + Kcf)
Keq = 2.16 ∗ 104
N
m
Damping:
C = ∫ Ccf xt
2̇
Ceq = Ccf
Ceq = 265 Ns/m
Natural frequency:
ωn = √
Keq
Meq
= √
58.16 ∗ 104
64.2
ωn = 95.18 rad/sec
8. 8
Frequency ratio:
r =
ω
ωn
=
1.256
95.18
r = 0.01319
Damped frequency:
ωd = ωn√1 − ξ2
ωn = 95.15 rad/sec
Critical Damping ratio:
Cc =2Meqωn
=2*64.2*95.18
Cc = 1.2 ∗ 104
Ns/m
Damping ratio:
ξ =
C
Cc
ξ =0.022
Amplitude of Vibration:
X
Y
= √
1 + (2ƺr)2
(1 − r2)2 + (2ƺr)2