Scaling Down - The Optimal Choice? Fritz B. Prinz Departments of Mechanical Engineering and Materials Science and Engineering Stanford University Stanford, CA

Outline Scaling laws –Physics –Engineering performance (power, power density) –Mechanical tolerances Manufacturing Processes Examples –Turbine engine –Mites (millimeter sized flaps) –Mesicopter

A World Apart mm mm -1

Scaling of Strength and Stiffness Failure Load Failure Load per Weight Bending Stiffness per Weight Beam

Scaling of Moving Objects Find relation between: –Mass m –Length l –Time t

Physics of Scaling (forget heat loss)

Scaling of Length and Time k = 2 elastic K= -1 electro - static motor, gravity (Kepler’s third law)

Scaling of Mass For v << c Relativisitic:

Scaling of Power

Electro Static Motors In theory: Assuming all dimensions e.g. gaps can be scaled down

Constant Field E = constant In practice:

Scaling of Critical Dimensions? Electro static /magnetic motors Tolerance l

A Manufacturing Issue Determined by manufacturing process Determines quality of machine Traditional mechanical machines Integrated circuits Even 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 Thrust (N)Operating Temp. ( O C) Thrust-to-weight ratio Weight (g) Current (metal) design Design incorporating ceramics

From RP and CNC to Shape Deposition Manufacturing ( SDM) RPCNC

Mold Shape Deposition Manufacturing –Builds wax molds via SDM using Soldermask temporary part material –Gel cast ceramic slurry into –sacrificial mold Sangkyun Kang:

Ceramic Inlet Nozzle Fully dense Silicon Nitride RMS ~ 0,5 micro meter Strength ~ Mpa as sintered

‘Shape Assembled’ Mechanism

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

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 of etched silicon Plating SEMMicro- graph of plated electrode

EDM of Amorphous Metals Electro Discharge Machining

Massively Parallel Mechanical Systems One Electro Static MotorMany Electro Static Motors