Chapter 19 Springs

Chapter 19: Springs Springs Characterized By: Ability to deform significantly without failure Ability to store/release PE over large deflections Provides an elastic force for useful purpose

Chapter 19: Springs How used in mechanical design? Shock/Vibration protection Store/Release PE Offer resisting force or reaction force for mechanism  Example: Valve spring pushes rocker arm so lifter follows cam VCR lid – torsion springs keeps door closed

Types of springs

Chapter 19: Springs Our focus will be on Helical Compression Springs Standard round wire wrapped into cylinder, usually constant pitch We will cover design process and analysis

Chapter 19: Springs - Terminology Helical Compression Springs: ID –inside diameter of helix OD – outside diameter of helix D m – mean diameter of helix L f – free length L s – solid length L i – installed length L o – operating length F f – zero force F s – solid force F i – min. operating force F o – max. operating force

k – spring rate C – spring index = Dm/Dw N – number of coils N a – number of active coils (careful N a may be different from N – depends on end condition – see slide 9) p – pitch λ – pitch angle cc – coils clearance K – Wahl factor f – linear deflection G – shear modulus  – torsional shear stress  o – stress under operation  s – stress at solid length  d – design stress Chapter 19: Springs - Terminology

Spring Rate

Chapter 19: Springs

Chapter 19: Springs – Analysis Process: Determine: K, τ o, τ s to determine if OK for your application 1.) Calc spring rate : 2.) Based on geometry: Shear mod table 19-4Wire dia. Table 19-2 C = spring index = D m /D w **Need to know k to get spring forces to get spring stresses** 3.) Shear stress in spring: (accounts for curvature of spring) **Compare τ o & τ s to material allowable (Figure 19-8 – 19-13)** Key Equations: Show slide

Chapter 19: Springs – Analysis Process: 4) Buckling Analysis – usually final analysis done to make sure there’s no stability issue. If so, may be as simple as supporting the spring through id or od Calculate Lf/Dm From Fig 19-15, get fo/Lf fo = buckling deflection – you want your maximum deflection to be less than this!! Buckling procedure

2 Categores: Spring Analysis – spring already exists – verify design requirements are met (namely, stiffness, buckling and stress is acceptable) Spring Design – design spring from scratch – involves iterations!!

Given:Spring- 34ga Music Wire D m = 1.0 “ L f = 3.0”L i = 2.5”L o = 2.0” Na = 15 (squared and ground end) Find:Spring rate, τ o, τ s D w =.100” (table 19-2) Spring Analysis Example:

Fo = k ΔL = lb/in (1 in) = lb operating force L f - L o 3” – 2” IS this stress ok? See figure 19-9 (severe or average service) Spring Analysis Example: o

Squared and ground (Max force) Spring Analysis Example: IS this stress ok? See figure 19-9 (light service since only happens once!!) CHECK FOR BUCKLING!!!

Given:L o = 2.0 inF o = 90lb L i = 2.5 inF i = 30 lb Severe service Find:Suitable compression spring Looks OK compared to ~ 3 in. length Spring Design Example: Generally all that’s given based on application!!

Guess: D m =.75 in.Try: Cr – Si Alloy, A-401 Guess: τ allow = 115 ksi (Figure 19-12) Try: 11 gage =.1205 in. (Table 19-2) Spring Design Example: o

FROM APPENDIX 19-5: τ severe allow = 122 ksi (operating max.) τ light allow = 177 ksi (solid max.) ( > 5, so OK ) Spring Design Example:

OK < 122 ksi Spring Design Example: o

(squared and ground ends assumed) 294 ksi > 177 ksi -  WILL YIELD, NOT ACCEPTABLE Spring Design Example:

How to check buckling: Critical ratio = ? For any f o /L f This spring is below fixed end line and fixed-pinned. If pinned-pinned critical ratio = >.23: So it would buckle Spring Design Example:

Trials Select one of these Spring Design Example:

But…. Τ allow and K depend on D w So……Guess K is mid-range, about 1.2 Then: Side Info: How determine initial estimate for D w Equation for shear stress where geometry is known Re-arrange…. This D w is about where to start for spring design. Both K and τ allow may be found for selected D w.