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