Principles of Form Synthesis II

1. Principles of Form Synthesis II Images: www.freeimage.co.uk

2. Form Synthesis Principles 1. Triangle Principle 2. Tetrahedron Principle 3. Hollow Shaft principle 4. Mating Surface Principle 5. I-Beam Principle 6. Supplementary Shape Principle 7. Anti-Buckling Principle 8. Direct Path Principle 9. Force Flow Principle 10. Metal Removal Principle 11. Redundancy Avoidance Principle 12. Leverage Principle 13. Shape Merging Principle 14. Roughly Uniform Size Principle 15. Symmetry Principle.

3. Triangle Principle • Football stadium structures • Bicycle frame • Airplane landing gear • Roof trusses • Automobile frame component

4. Tetrahedron Principle • Antenna supports • Drilling platforms • Jack stands • Wire spoked wheels • Guyed power poles

5. Hollow Shaft Principle

6. Mating Surface Principle Examples: • All lower kinematic pairs (surface contact) • Journal bearings • Scotch yoke • Piston • Roller chain • Press fit on a shaft • V-belt (instead of a gear) • Wobble plate shoe

7. Mating Surface Summary

8. I-Beam Principle

9. Examples of I-Beam Principle

10. Supplementary Shape Principle A supplementary shape often can be added to provide a load path leading to a strong stress pattern

11. More on Supplementary Shapes

12. Anti-Buckling Principle • As sections become thin, buckling becomes possible • Buckling requires: • Compressive load • Thin or long section • Sources of Buckling • Geometry change • Material change

13. Examples of Buckling

14. More Examples of Buckling

15. Buckling Stiffeners Buckling stiffeners add a small amount of material to stiffen (not necessarily strengthen) structure • Flange stiffeners Flat plate stiffeners Wing stiffeners

16. More Buckling Stiffeners • Tube stiffeners for bending Tapered column House floor braces

17. More Buckling Stiffeners (cont’d) • Derrick boom lacing Use of internal pressure

18. Direct-Path Principle • Put material in a straight-line path between loads and supports

19. Force-Flow Principle • Internal forces flow like fluids in laminar flow

20. Example of force flow

21. Flow Line examples

22. Metal Removal Principle • After selecting a strong stress pattern • After visualizing the flow of forces • Remove all material where stresses are low • Consider economics, function, and manufacturing processes

23. Examples of Metal Removal

24. Examples of Metal Removal (cont’d)

25. Another Example of Metal Removal Principle

26. Examples of Material Removal

27. Redundancy Avoidance Principle Identify optimum load paths, and do not put in structure at other places unless absolutely necessary

28. Load Leverage Principle When moments or torques must be carried, regions of force application should be separated as much as possible

29. Load Leverage Example

30. Limitations on Leverage • Weight can increase due to extra length, and supplementary shapes needed to achieve leverage • Sections can become so thin that buckling occurs • Space may be too large to achieve good leverage • Manufacturing problems caused by the introduction of leverage may make the part too expensive

31. Shape/stiffness Merging When a large force must be accommodated and widely distributed to a general area, use shape merging

32. General Regions Involved in Shape Merging • Compact region where there is a highly concentrated load • Merge region • Thin walled region into which the load must be transferred

33. Types of Merging Regions • Tapered Sections (thickness or diameter changes with length) • Fan Sections (width changes with length)

34. Types of Merging Regions (cont’d) • Ribs (height and possibly thickness changes with length) • Branching Ribs

35. Roughly Uniform Size Principle • Adjoining portions of a part should be roughly the same size

36. Symmetry Principle • Unless there is a reason to the contrary, make a part symmetric • Makes parts easy to machine on a lathe • Makes assembly easier • Reduces inventory needs

37. Rules of Thumb for Part Shapes Ranking according to order of expense • Rectangular solids • Planes with general boundaries • Circular cylinders • Cones • Axisymmetric geometries • Spheres • General geometries

38. Limits to Form Synthesis Principles Space limitations Function limitations Cost limitations

39. Limits to Form Synthesis Principles (cont’d) Manufacturing process limitations (e.g., hollow crankshaft) Fastening constraints; for example, the mounting brackets on engine block Appearance

40. Examples of Limits

41. Summary • Many different principles for Form Synthesis • Use of each principle depends on the application and the driving factors • Engineers determine the appropriate principle for the “best” design

42. Credits • This module is intended as a supplement to design classes in mechanical engineering. It was developed at The Ohio State University under the NSF sponsored Gateway Coalition (grant EEC-9109794). Contributing members include: • Gary Kinzel ……………………………………..Primary author • Walter Starkey……………Primary source of original material • Phuong Pham and Matt Detrick ……….…….. Module revisions

43. Disclaimer This information is provided “as is” for general educational purposes; it can change over time and should be interpreted with regards to this particular circumstance. While much effort is made to provide complete information, Ohio State University and Gateway do not guarantee the accuracy and reliability of any information contained or displayed in the presentation. We disclaim any warranty, expressed or implied, including the warranties of fitness for a particular purpose. We do not assume any legal liability or responsibility for the accuracy, completeness, reliability, timeliness or usefulness of any information, or processes disclosed. Nor will Ohio State University or Gateway be held liable for any improper or incorrect use of the information described and/or contain herein and assumes no responsibility for anyone’s use of the information. Reference to any specific commercial product, process, or service by trade name, trademark, manufacture, or otherwise does not necessarily constitute or imply its endorsement.