I write about Propulsion, Aerodynamics and Renewable Energy (Wind/Hydro Turbines).
Showing posts with label Graph. Show all posts
Showing posts with label Graph. Show all posts
Monday 13 February 2017
Sunday 12 February 2017
Friday 10 February 2017
Bond Graph Representation of the Coaxial Contra-Rotating Propeller (with the Bond-Graph)
A contra rotating propeller, with five gears and seven shafts.
Se
|
Source of effort; voltage supplied by
the power source; a Li-Po battery in this study.
|
Rw
|
Motor winding resistance.
|
Iw
|
Motor winding inductance.
|
GY
|
dc Motor; a Gyrator.
|
T
|
Gyrator Modulus.
|
bs1
|
Bearing resistance on shaft number
one.
|
Js1
|
JS1=Js’1+Jg1+Jr.
|
Js1
|
Total inertia for shaft number one.
|
Js’1
|
Inertia of shaft number one.
|
Jg1
|
Inertia of gear number one.
|
Jr
|
Inertia for dc motor rotor.
|
Ks1
|
Stiffness of shaft number one.
|
Ms1
|
Ms1=Ms’1+Mm+Mg1.
|
Ms1
|
Total mass for the shaft number one.
|
Ms’1
|
Mass for the shaft number one.
|
Mm
|
Mass for the dc motor.
|
Mg1
|
Mass for the gear number one.
|
m1
|
Distance from the center of mass of
the Ms1 to the shaft number one; moment arm to transform the
torque in to force to be applied to the Ms1.
|
TF
|
Transformer, mechanical transformer in
this study, spur gear mesh.
|
Rs12
|
Transformer Modulus, transmission
ratio between shaft number one and two.
|
bs2
|
Bearing resistance on shaft number
two.
|
Js2
|
JS2=Js’2+ Jg2+Jg6.
|
Js2
|
Total inertia for shaft number two.
|
Js’2
|
Inertia of shaft number two.
|
Jg2
|
Inertia of gear number two.
|
Jg6
|
Inertia of gear number six.
|
Ks2
|
Stiffness of shaft number two.
|
Ms2
|
Ms2=Ms’2+Mg6+Mg2.
|
Ms2
|
Total mass for the shaft number two.
|
Ms’2
|
Mass for the shaft number two.
|
Mg6
|
Mass for the gear number six.
|
Mg2
|
Mass for the gear number two.
|
m2
|
Distance from the center of mass of
the Ms2 to the shaft number two; moment arm to transform the
torque in to force to be applied to the Ms2.
|
Rs23
|
Transformer Modulus, transmission
ratio between shaft number two and three.
|
bs3
|
Bearing resistance on shaft number three.
|
Js3
|
JS3=Js’3+ Jg3+Jg4.
|
Js3
|
Total inertia for shaft number three.
|
Js’3
|
Inertia of shaft number three.
|
Jg3
|
Inertia of gear number three.
|
Jg4
|
Inertia of gear number four.
|
Ks3
|
Stiffness of shaft number three.
|
Ms3
|
Ms2=Ms’2+Mg3+Mg4.
|
Ms3
|
Total mass for the shaft number one.
|
Ms’3
|
Mass for the shaft number three.
|
Mg3
|
Mass for the gear number three.
|
Mg4
|
Mass for the gear number four.
|
m3
|
Distance from the center of mass of
the Ms3 to the shaft number three; moment arm to transform the
torque in to force to be applied to the Ms3.
|
Rs34
|
Transformer Modulus, transmission
ratio between shaft number three and four.
|
bs4
|
Bearing resistance on shaft number
four.
|
Js4
|
JS4=Js’4+ Jg5+Jp1.
|
Js4
|
Total inertia for shaft number four.
|
Js’4
|
Inertia of shaft number four.
|
Jg5
|
Inertia of gear number five.
|
Jp1
|
Inertia of propeller number one.
|
Ks4
|
Stiffness of shaft number three
|
Ms4
|
Ms4=Ms’4+Mg5+Mp1.
|
Ms4
|
Total mass for the shaft number four.
|
Ms’4
|
Mass for the shaft number four.
|
Mg5
|
Mass for the gear number five.
|
Mp1
|
Mass for the propeller number one.
|
m4
|
Distance from the center of mass of
the Ms4 to the shaft number four; moment arm to transform the
torque in to force to be applied to the Ms4.
|
Rs25
|
Transformer Modulus, transmission
ratio between shaft number two and five.
|
bs5
|
Bearing resistance on shaft number five.
|
Js5
|
JS5=Js’5+ Jg7+Jp2.
|
Js5
|
Total inertia for shaft number five.
|
Js’5
|
Inertia of shaft number five.
|
Jg7
|
Inertia of gear number seven.
|
Jp2
|
Inertia of propeller number two.
|
Ks5
|
Stiffness of shaft number five.
|
Ms5
|
Ms4=Ms’5+Mg5+Mp2.
|
Ms5
|
Total mass for the shaft number four.
|
Ms’5
|
Mass for the shaft number five.
|
Mg7
|
Mass for the gear number seven.
|
Mp2
|
Mass for the propeller number two.
|
m5
|
Distance from the center of mass of
the Ms5 to the shaft number five; moment arm to transform the
torque in to force to be applied to the Ms5.
|
RPS
|
RPS=KT1/(KQ1*D1)
|
RPS
|
Transformer Modulus, for propeller
number one.
|
KT1
|
Coefficient of thrust for propeller
number one.
|
KQ1
|
Coefficient of torque for propeller
number one.
|
D1
|
Diameter for propeller number one.
|
KT1
|
KT1=Tp1/(Rho*n12*D14)
|
KQ1
|
KQ1=Qp1/(Rho*n12*D15)
|
Tp1
|
Thrust from propeller number one.
|
n1
|
Speed for propeller number one, in
rev/s.
|
Qp1
|
Torque required to rotate propeller
number one.
|
P1
|
Propeller number one, mounted on the
shaft number four.
|
RPH
|
RPH=KT2/(KQ2*D2)
|
RPH
|
Transformer Modulus, for propeller
number 2.
|
KT2
|
Coefficient of thrust for propeller
number two.
|
KQ2
|
Coefficient of torque for propeller
number two.
|
D2
|
Diameter for propeller number two.
|
KT2
|
KT=Tp2/(Rho*n22*D24)
|
KQ2
|
KQ=Qp2/(Rho*n22*D25)
|
Tp2
|
Thrust from propeller number two.
|
Rho
|
Density of the fluid, air in this
study.
|
n2
|
Speed for propeller number two, in
rev/s.
|
Qp2
|
Torque required to rotate propeller
number two.
|
P2
|
Propeller number two, mounted on the
hollow shaft; only of the system, shaft number five.
|
mc1
|
Distance from the center of mass of
the chassis to the shaft number one; moment arm to transform torque in to
force to be applied to the chassis.
|
mc2
|
Distance from the center of mass of
the chassis to the shaft number two; moment arm to transform torque in to
force to be applied to the chassis.
|
mc3
|
Distance from the center of mass of
the chassis to the shaft number three; moment arm to transform torque in to
force to be applied to the chassis.
|
mc4
|
Distance from the center of mass of
the chassis to the shaft number four; moment arm to transform torque in to
force to be applied to the chassis.
|
mc5
|
Distance from the center of mass of
the chassis to the shaft number five; moment arm to transform torque in to
force to be applied to the chassis.
|
Mc
|
Mass of the chassis.
|
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