scaling down - the optimal choice?
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Scaling Down - The Optimal Choice?
Fritz B. PrinzDepartments of Mechanical Engineering
and Materials Science and Engineering
Stanford University
Stanford, CA 94 305
Outline
• Scaling laws– Physics
– Engineering performance (power, power density)
– Mechanical tolerances
• Manufacturing Processes• Examples
– Turbine engine
– Mites (millimeter sized flaps)
– Mesicopter
A World Apart
Surface
Volume
l 2
l 3
1
l
104 - 102 10-4mm-1 10-1mm-1
Scaling of Strength and Stiffness
Ff
fA Failure Load
Ff
m
Ff
W 1
lFailure Load per Weight
SB
W 1
l 2Bending Stiffness per Weight
Beam S CEI
l 3
Scaling of Moving Objects
• Find relation between:
–Mass m
–Length l
–Time t
Physics of Scaling(forget heat loss)
E T U
2
2lmT
U U(l) U( l ) kU( l )
2)(
2
2
2 lmlT
l l t t
Scaling of Length and Time
2
2 k t
t
l
l
1 1
2k
k = 2 elasticK= -1 electro - static motor, gravity (Kepler’s third law)
t
t
l
l
3/2
Scaling of Mass
m l 3For v << c
m m0 1Ý r 2
c2Relativisitic:
Scaling of Power
P mass* acceleration * speed
P l 3 l
t2
l
t
l5
l3 3
2k
P
V
l 2
l3 3
2k
Electro Static Motors
In theory: k 1
P l1
2
P
Vl
5
2
Assuming all dimensions e.g. gaps can be scaled down
Constant Field
E U / l
E = constant
In practice: k 0
P l 2
P
Vl 1
Scaling of Critical Dimensions?
Electro static /magnetic motors
Tolerance l
ll
A Manufacturing Issue
l Determined by manufacturing process
l
lDetermines quality of machine
10 5 Traditional mechanical machines
10 2 Integrated circuits
P
V
1
lEven May not be
achievable
Turbine Combustion Engines Power Density (1/l) - Thrust to Weight
T/W = 5.6 T/W= 7.6
M-Dot Micro Engine for Drone Aircraft
0
5
10
Thrust (N)
950
1000
1050
1100
1150
1200
1250
Operating Temp. (OC)
0
2
4
6
8
10
12
14
Thrust-to-weight ratio
0
10
20
30
40
50
60
70
80
90
Weight (g)
Current (metal) design Design incorporating ceramics
From RP and CNC to . . .
2000
1960
1990Shape Deposition Manufacturing ( SDM)
RP CNC
Mold Shape Deposition Manufacturing
– Builds wax molds via SDM using Soldermask temporary part material
– Gel cast ceramic slurry into
– sacrificial mold
Ceramic Inlet Nozzle
Fully dense Silicon Nitride
RMS ~ 0,5 micro meter
Strength ~ 400 - 600 Mpa
as sintered
‘Shape Assembled’ Mechanism
crank rod piston
Micro Flaps for Aero Elastic Control• Maximize flight time of Unmanned Air Vehicle (UAV)
Front view
Suggested Solution• Aeroelastic control using trailing edge effects
– Concept
• Span-wise lift control via micro-flaps
Micro-flaps
Approach• Design & Manufacture Micro-flaps
Small size (6 mm)Large deflection (± 75°)Frequency (10s HZ)Material strength
Requirements
Airfoil
Flap Surface
6 mm
Actuating Mechanism
Build Sequence in SDM
32
654
1
SDM Fabrication of Multiple Flaps
Micro Flap for Aero - Elastic Control
Clearance ~ 50 micron
The Mesicopter: a Miniature Helicopter
Aerodynamics
• New results for very low Re airfoils
• Very thin sections required
• Maximum lift increases as Re decreases below 10,000
Rotor Optimization
• Chord, twist, RPM, blade number designed using nonlinear optimization
• 3D analysis based on Navier-Stokes section data
• Rotor matched with measured motor performance (50 000rpm)
Aerodynamics
• Navier-Stokes analysis of rotor sections at unprecedented low Reynolds number
• Novel results of interest to Mars airplane program
• Nonlinear rotor analysis and optimization code
SDM Rotor Manufacturing
1. Micro-machine bottom surface of rotor on wax 2. Cast epoxy
3. Remove excess epoxy
4. Machine top surface of rotor
5. Melt wax
Scaled Down Mesicopter
• Insect-Scale Aerodynamics
• 3D Micro-Manufacturing
• Power / Control / Sensors
Mesomotor
REM-Aufnahme des 2mm-Motors
Explosions-ansicht des
Motors
Rotor
Stator
Anker-spule
Shaping of Electrodes
+ -
Sputtering of seed layer
SEM Micro-graph ofetchedsilicon
Plating
SEMMicro- graph of plated electrode
EDM of Amorphous MetalsElectro Discharge Machining
Massively Parallel Mechanical Systems
One Electro Static Motor Many Electro Static Motors
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