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Outline

Outline. Spring Functions & Types Helical Springs Compression Extension Torsional. The Function(s) of Springs. Most fundamentally: to STORE ENERGY. Many springs can also: push pull twist. Parallel. Series. k total =k 1 +k 2 +k 3. Some Review. linear springs: k=F/y. F. k.

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Outline

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  1. Outline • Spring Functions & Types • Helical Springs • Compression • Extension • Torsional

  2. The Function(s) of Springs Most fundamentally: to STORE ENERGY Many springs can also: push pull twist

  3. Parallel Series ktotal=k1+k2+k3 Some Review linear springs: k=F/y F k nonlinear springs: y

  4. Compression Extension Torsion Types of Springs Helical:

  5. More Springs Washer Springs: Power springs: Beams:

  6. Helical Compression Springs d diameter of wire D mean coil diameter Lf free length p pitch Nt Total coils may also need: Do and Di

  7. Length Terminology minimum of 10-15% clash allowance Assembled Length Max Working Load Bottomed Out Free Length Lf La Lm Ls

  8. Plain Plain Ground Square Square Ground End Conditions Na= Active Coils

  9. F F T F F T F F Stresses in Helical Springs Spring Index C=D/d

  10. Curvature Stress Inner part of spring is a stress concentration • under static loading, local yielding eliminates stress concentration, so use Ks • under dynamic loading, failure happens below Sy: use Ks for mean, Kw for alternating (see Chapter 4) Kw includes both the direct shear factor and the stress concentration factor

  11. Spring Deflection

  12. Spring Rate k=F/y

  13. Helical Springs • Compression • Nomenclature • Stress • Deflection and Spring Constant • Static Design • Fatigue Design • Extension • Torsion

  14. Static Spring Design • Inherently iterative • Some values must be set to calculate stresses, deflections, etc. • Truly Design • there is not one “correct” answer • must synthesize (a little bit) in addition to analyze

  15. Material Properties • Sutultimate tensile strength • Figure 13-3 • Table 13-4 with Sut=Adb • Systorsional yield strength • Table 13-6 – a function of Sut and set

  16. Spring/Material Treatments • Setting • overstress material in same direction as applied load • increase static load capacity 45-65% • increase energy storage by 100% • use Ks, not Kw (stress concentration relieved) • Load Reversal with Springs • Shot Peening • What type of failure would this be most effective against?

  17. d, C, D*, Lf*, Na*, clash allowance ()**, material** + design variables What are You Designing? Given F, y k, y Find k F Such that: Safety factor is > 1 Spring will not buckle Spring will fit in hole, over pin, within vertical space * - often can calculate from given ** - often given/defined

  18. Na,  d, C DEFLECTION STRESSES D, Ks, Kw Ns=Sys/ Lf, yshut, Fshut material strengths for shut spring if possible if not, for max working load material CHECK ITERATE? buckling, Nshut, Di, Do Nshut=Sys/shut Static Spring Flow Chart if GIVEN F,y, then find k; If GIVEN k, y, then find F • Three things to know: • effect of d • shortcut to finding d • how to check buckling

  19. Based on Ns=Ssy/ and above equation for : use Table 13-2 to select standard d near calculated d Km=Sys/Sut *maintain units (in. or mm) for A, b **see Example 13-3A on MathCad CD Static Design: Wire Diameter • Three things to know: • effect of d • shortcut to finding d • how to check buckling

  20. Buckling • Three things to know: • effect of d • shortcut to finding d • how to check buckling

  21. Helical Springs • Compression • Nomenclature • Stress • Deflection and Spring Constant • Static Design • Fatigue Design • Extension • Torsion

  22. Material Properties • Susultimate shear strength • Sus0.67 Sut • Sfw´torsional fatigue strength • Table 13-7 -- function of Sut, # of cycles • repeated, room temp, 50% reliability, no corrosion • Sew´torsional endurance limit • for steel, d < 10mm • see page 816 (=45 ksi if unpeened, =67.5 ksi if peened) • repeated, room temp., 50% reliability, no corrosion

  23. Repeated C Sfs B 0.5 Sfw A 0.5 Sfw Sus Modified Goodman for Springs • Sfw, Sew are for torsional strengths, so von Mises not used a m

  24. load line mload Sa a mgood i m Fatigue Safety Factor a Fi=Fmin Fa=(Fmax-Fmin)/2 Fm=(Fmax+Fmin)/2 Sfs 0.5 Sfw m 0.5 Sfw Sus a,load = a,good at intersection …on page 828

  25. d, C, D*, Lf*, Na*, clash allowance ()**, material** design variables What are you Designing? Given Fmax,Fmin, y k,  y Find k F + Such that: Fatigue Safety Factor is > 1 Shut Static Safety Factor is > 1 Spring will not buckle Spring is well below natural frequency Spring will fit in hole, over pin, within vertical space * - often can calculate from Given ** - often given/defined

  26. Na,  DEFLECTION STRESSES D, Ks, Kw Lf, yshut, Fshut material strengths material CHECK ITERATE? buckling, frequency, Nshut, Di, Do Nshut=Sys/shut Fatigue Spring Design Strategy if GIVEN F,y, then find k; If GIVEN k, y, then find F d, C • Two things to know: • shortcut to finding d • how to check frequency

  27. *maintain units (in. or mm) for A, b **see Example 13-4A on MathCad CD Fatigue Design:Wire Diameter as before, you can iterate to find d, or you can use an equation derived from relationships that we already know: use Table 13-2 to select standard d near calculated d • Two things to know: • shortcut to finding d • how to check frequency

  28. Natural Frequency: Surge Surge == longitudinal resonance for fixed/fixed end conditions: (Hz) ideally, fn will be at least 13x more than fforcing… it should definitely be multiple times bigger • Two things to know: • shortcut to finding d • how to check frequency …see pages 814-815 for more

  29. Review of Design Strategy ITERATIVE USING d EQUATION Find Loading Select C, safety factor Find Loading Select C, d Solve for d, pick standard d Find stresses Determine material properties Check safety factor Find stresses Determine material properties Find safety factor

  30. Strategy Review Continued Find spring constant, Na, Nt Find FSHUT (must find lengths and y’s to do this) Find static shut shear stress and safety factor Check Buckling Check Surge Check Di, Do if pin to fit over, hole to fit in

  31. Consider the Following:

  32. Helical Springs • Compression • Nomenclature • Stress • Deflection and Spring Constant • Static Design • Fatigue Design • Extension • Torsion

  33. Extension Springs As before, 4 < C < 12 surge check is same as before However, no peening, no setting, no concern about buckling Lb=d(Na+1)

  34. “preloading” Fi F=Fi+ky Difference 1: Initial Force force F deflection y

  35. Difference 1a: Deflection

  36. Difference 2: Initial Stress take initial stress as the average stress between these lines, then find Fi

  37. Difference 3: Ends!: Bending standard end

  38. Difference 3a: Ends: Torsion C2=2R2/d pick a value >4

  39. Materials • Sut – Same • Sys, Sfw, Sew – same for body • Sys, Sfw, Sew – see Tables 13-10 and 13-11 for ends

  40. Strategy similar to compression + end stresses - buckling

  41. Helical Springs • Compression • Nomenclature • Stress • Deflection and Spring Constant • Static Design • Fatigue Design • Extension • Torsion

  42. Torsion Springs • close-wound, always load to close Deflection & Spring Rate

  43. For Fatigue – Slightly lower Outside Tensile Stress – Outside of Coil Stresses Compressive is Max – Use for Static – Inside of Coil

  44. Materials see Tables 13-13 and 13-14, page 850 follow book on Sewb=Sew/0.577… for now

  45. Strategy Select C, d  • fit over pin (if there is one) • don’t exceed stresses M K

  46. Helical Springs • Compression • Nomenclature • Stress • Deflection and Spring Constant • Static Design • Fatigue Design • Extension • Torsion

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