Showing posts with label Contra. Show all posts
Showing posts with label Contra. Show all posts

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.