1. Scaling Down - The Optimal Choice? Fritz B. Prinz Departments of Mechanical Engineering and Materials Science and Engineering Stanford University Stanford, CA 94 305

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

3. A World Apart 10 4 - 10 2 10 -4 mm -1 10 -1 mm -1

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

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

6. Physics of Scaling (forget heat loss)

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

8. Scaling of Mass For v << c Relativisitic:

9. Scaling of Power

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

11. Constant Field E = constant In practice:

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

13. A Manufacturing Issue Determined by manufacturing process Determines quality of machine Traditional mechanical machines Integrated circuits Even May not be achievable

14. Turbine Combustion Engines Power Density (1/l) - Thrust to Weight T/W = 5.6 T/W= 7.6

15. 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

16. From RP and CNC to... 2000 1960 1990 Shape Deposition Manufacturing ( SDM) RPCNC

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

18. Ceramic Inlet Nozzle Fully dense Silicon Nitride RMS ~ 0,5 micro meter Strength ~ 400 - 600 Mpa as sintered

19. ‘Shape Assembled’ Mechanism

20. Micro Flaps for Aero Elastic Control Maximize flight time of Unmanned Air Vehicle (UAV) Front view

21. Suggested Solution Aeroelastic control using trailing edge effects –Concept Span-wise lift control via micro-flaps Micro-flaps

22. Approach Design & Manufacture Micro-flaps Small size (6 mm) Large deflection (± 75°) Frequency (10s HZ) Material strength Requirements Airfoil Flap Surface 6 mm

23. Actuating Mechanism

24. Build Sequence in SDM 3 2 6 5 4 1

25. SDM Fabrication of Multiple Flaps

26. Micro Flap for Aero - Elastic Control Clearance ~ 50 micron

27. The Mesicopter: a Miniature Helicopter

28. Aerodynamics New results for very low Re airfoils Very thin sections required Maximum lift increases as Re decreases below 10,000

29. 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)

30. 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

31. 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

32. Scaled Down Mesicopter Insect-Scale Aerodynamics 3D Micro- Manufacturing Power / Control / Sensors

33. Mesomotor REM-Aufnahme des 2mm-Motors Explosions- ansicht des Motors Rotor Stator Anker- spule

34. Shaping of Electrodes Sputtering of seed layer SEM Micro- graph of etched silicon Plating SEMMicro- graph of plated electrode

35. EDM of Amorphous Metals Electro Discharge Machining

36. Massively Parallel Mechanical Systems One Electro Static MotorMany Electro Static Motors