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Sheet Metal Forming (MIT 2.008x Lecture Slides)
- 1. 2.008x Sheet Metal Forming MIT 2.008x Prof. David E. Hardt
- 2. Manufacturing Key Topics • Products and Processes • The Process Taxonomy • Demonstrations – Pure Bending – Adding Stretch • Processes and Mechanics • Comparison Criteria – Rate – Quality – Flexibility – Cost 10/12/16 2.008 Fall 2016
- 3. Manufacturing Process Taxonomy • Shape Change Mechanism? – Removal (2-D) • Mechanical Shear • Water Jet (Fluid Shear) • Thermal Ablation or Melting – Plastic Deformation (2 and 3-D) • Simple Bending (Along a Line) • Bending + Stretching • 3D Draw-Forming 2.008 Fall 201610/12/16
- 4. Manufacturing The “Big Four” • Rate – What Limits This? • Quality – What Causes Dimensions/Shape/Properties to Vary from Specifications? • Cost – Material/Machine/Labor • Flexibility – Ease of Product Changeover 2.008 Fall 201610/12/16
- 5. Manufacturing Amada CNC Automated Shear Punch • Removal (Cutting) • What Determines the Part Geometry? 2.008 Fall 201610/12/16 Amada CNC Punch Press
- 6. Manufacturing Processes • Removal (Cutting) – Serial Thermal Energy • What Determines the Part Geometry? 2.008 Fall 201610/12/16 CNC Laser Cutter
- 7. Manufacturing Simple Bending 2.008 Fall 201610/12/16 • Plastic Deformation Via Bending Stresses
- 8. Manufacturing Processes: Bending • Local High Bending Stress • Plastic Deformation • What Determines the Part Geometry? 2.008 Fall 201610/12/16
- 9. Manufacturing Combined Die Cutting and Bending 2.008 Fall 201610/12/16 • “Progressive” Dies • Strip of Sheet Sequences Through a “Progression” of Cutting and Bending Tools http://stampingworld.com/stripjoint/highspeedstamping/10 Electrical Connectors
- 10. Manufacturing Making Airplane Skins: Large Smooth Panels with Compound Curvature: 2.008 Fall 201610/12/16 From Cyril Bath Co. Why do we need the Stretch? What Determines the Part Geometry? Stretch Forming Process
- 11. Manufacturing 3D Sheet Stamping for Car Bodies 2.008 Fall 201610/12/16 Simultaneous Deformation over the Area of the Part What Determines the Part Geometry?
- 12. Manufacturing Process Mechanics • Removal – Serial Shear (Shearing) – Parallel Shear (Punching) • Planar Deformation – Focus on Simple Bending but with Plasticity • Elastic Springback – Effect of Adding Stretch • Reduction of Springback • Potential for Tensile Failure • General 3D Deformation – Bending, Tension and Compression • Buckling! 2.008 Fall 201610/12/16
- 13. Manufacturing Processes and Mechanics • Cutting – Similar to Machining – Large Shear at Tool - Material interface 10/12/16 2.008 Fall 2016 Looks just like machining at the interface
- 14. Manufacturing Processes and Mechanics • Simple Bending – Bending Only – Low Forces – Large Springback • Low accuracy 10/12/16 2.008 Fall 2016
- 15. Manufacturing M M ε σ Brake Bending of Sheet 10/12/16 2.008 Fall 2016 • Simple Process • Complex Mechanics • Variable Moments • Variable Curvature • Combined Elastic- Plastic Zones
- 16. Manufacturing Simple Model : Pure Moment Bending Constant Radius Tool Springback 10/12/16 2.008 Fall 2016
- 17. Manufacturing Simple Bending Mechanics: • Tool Shape (Rtool) determines the shape under load • Can Model as Pure Moment Beam Bending • Elastic Springback determines the final shape • What determines the Springback? 10/12/16 2.008 Fall 2016
- 18. Manufacturing h b M r = 1/K y e=K y M K = curvature of the tooling h = thickness of the sheet e(y) = through thickness strain What is M(K) (or K(M)) ? Simple Bending Model 10/12/16 2.008 Fall 2016
- 19. Manufacturing Moment – Curvature for Bending 2.008 Fall 201610/12/16 • Relates the Shape to the Applied Moment • Is the Bending Equivalent to Force- Displacement or Stress-Strain • Will look similar: K M
- 20. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 21. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 22. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016 In Elastic Range Stress is Proportional to Strain
- 23. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016 NB: Yield exceeded
- 24. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016 NB: Yield exceeded
- 25. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016 NB: Yield exceeded
- 26. Manufacturing h b M r = 1/K y e=K y M ε(y) = Ky σ = f (ε) M = σ (y)ybdy −h/2 h/2 ∫ dA moment arm Given K, M = ? Analysis: Simple Beam Theory ds y dA b h dy 10/12/16 2.008 Fall 2016 From 2.001 Elastic Beam Bending (stress-strain curve)
- 27. Manufacturing s e E eY sY Idealized Material Model: Elastic Perfectly Plastic s= E e e <eY s= sY e >eY 10/12/16 2.008 Fall 2016
- 28. Manufacturing K h 2 = εmax < εY If the die curvature K is such that: Then only elastic deformation will take place and: M = σ(y)ybdy−h/ 2 h / 2 ∫ = EKy 2 bdy−h/ 2 h / 2 ∫ = loaded curvature bending stiffness = KE bh3 12 = KEI Moment - Curvature Relationship M(K) 10/12/16 2.008 Fall 2016 (All strains are below yield)
- 29. Manufacturing Moment - Curvature Relationship As K increases, eventually: K h 2 > εY ∴yielding occurs But for all e> e Y, s= s Y (i.e. constant stress) From M = Melastic + M Plastic M = 3 2 My 1− 1 3 Ky K " # $ % & ' 2 " # $ % & ' KY =εY /(h / 2) MY = EI KY 10/12/16 2.008 Fall 2016 We can get
- 30. Manufacturing The Resulting M-K Curve M K EI KY MY 3/2 MY Loading EI Unloading KtoolKpart DK 10/12/16 2.008 Fall 2016 Mmax
- 31. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 32. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 33. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 34. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 35. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 36. Manufacturing Stress and Strain in Bending K M 10/12/16 2.008 Fall 2016
- 37. Manufacturing Final Shape: Springback ΔK = Mmax EI ∴Kpart = Ktool − ΔK K = shape of tool E= material modulus I = 1 12 bh3 cubic dependence on thickness Mmax = ? Mmax = Φ (KY, EI) 10/12/16 2.008 Fall 2016 M K EI KY MY 3/2 MY EI KtoolKpart DK Mmax
- 38. Manufacturing Effect of Material Variations: Increase in Yield Stress M K EI KY MY Ktool DK Kpart MY DK 10/12/16 2.008 Fall 2016
- 39. Manufacturing Other Possible Variations • Yield Stress (+ 10%reported) – Chemistry, working history • Thickness – Rolling mill quality – Design vs. manufacturing specs • Tooling Errors 10/12/16 2.008 Fall 2016
- 40. Manufacturing Conclusions for Simple Bending • High Degree of Springback • Strong Material Dependence • Yield Strength • Strain Hardening • Thickness • Low Forming Forces 10/12/16 2.008 Fall 2016
- 41. Manufacturing More Precision? • Bend + Stretch – Reduction in Springback • Higher Accuracy – Increase in Forces – Increase in strain: more failure 10/12/16 2.008 Fall 2016
- 42. Manufacturing Adding Stretch to Pure Bending 10/12/16 2.008 Fall 2016 F F
- 43. Manufacturing Effect of Tensile Strain with Bending 2.008 Fall 201610/12/16 M M F F ε(y) Pure Bending Moment “M” Added Tensile Force “F” Bending Strains are Biased toward Tensile !
- 44. Manufacturing Effect on Stresses? 2.008 Fall 201610/12/16 M M σ(y) F F Stresses Are Likewise Biased Toward Tensile
- 45. Manufacturing Effect on Springback? 2.008 Fall 201610/12/16 M M F F ε(y) ε(h/2) = εY M M F F σY Uniform Stress: No Springback
- 46. Manufacturing Processes and Mechanics • Deep Drawing (3D Bend + Stretch) – Extreme Deformation – Large Compressive Strains • Buckling Failure possible – Large Forces – Critical Flow Control • Sheet Formability – Balance of Biaxial Strains (++ and +-) 10/12/16 2.008 Fall 2016
- 47. Manufacturing The Big Four • Rate Limits – Deformation Speed (Usually “Fast”) – Parallel Processes – Large Areas “Fast” • Quality – Springback – Strong Material Property Dependence • Cost – High Volumes – Material Dominates, but Low Waste in General – Low Volumes – Tooling and Machine Dominates • Flexibility – Serial Processes – Trajectory Easily Changed – Parallel Processes – Low – Complex and Costly Tooling 10/12/16 2.008 Fall 2016
- 48. Manufacturing Process Comparisons • Rate • Quality • Cost • Flexibility Sheet Forming Machining 10/12/16 2.008 Fall 2016 High High High Low Moderate Low Low Moderate-High