Factors in spring design Materials Torsional Types Factors in spring design Materials Torsional 11/26/2018
Types of Springs 11/26/2018
Types of spring cont. 11/26/2018
Types of springs cont. 11/26/2018
Types of springs cont. 11/26/2018
Factors in spring design High strength High yield Modulus may be low for energy storage Cost Environmental factors Temperature resistance (e.g. valve springs) Corrosion resistance 11/26/2018
Common materials for springs 11/26/2018
Influence of diameter on ultimate stress 11/26/2018
Influence of diameter on ultimate stress cont. 11/26/2018
Design of helical compression springs Length nomenclature Free Assembled Solid or shut height Working deflection 11/26/2018
Stresses in Helical Spring 11/26/2018
Stresses in Helical springs cont. At the inside of the spring Substituting for Gives 4<C<12 Defining the spring index Therefore the stress is Equation(1) 11/26/2018
Effect of curvature on Stress Equation (1) is based on the wire being straight However the curvature increases the stress on the inside of the wire For static stress the effect of curvature can be neglected For fatigue the effect of curvature is important 11/26/2018
Effect of curvature cont. Wahl factor Bergstrasser factor The results of the two equations differ by less than 1%. Bergstrasser factor is preferred due to simplicity 11/26/2018
Deflection The external work done on an elastic member in deforming it is transformed into strain, or potential, energy. If the member is deformed a distance y, and if the force-deflection relationship is linear, this energy is equal to the product of the average force and the deflection, or This equation is general in the sense that the force F can also mean torque, or moment, provided, that consistent units are used for k. 11/26/2018
Deflection cont.. By substituting appropriate expressions for k, strain-energy formulas for various simple loadings may be obtained. For tension and compression and for torsion, 11/26/2018
Deflection of a helical spring Using Castigliano’s theorem, strain energy is equal to Substituting 11/26/2018
Deflection cont. Using the spring index Spring scale is 11/26/2018
Spring design – end treatment End details affect active coils Plain ends Squared ends Squared Ground 11/26/2018
Number of active coils 11/26/2018
Stability of a column Euler Formula 11/26/2018
We know a column will buckle when the load is too large Stability of a spring We know a column will buckle when the load is too large A compression coil spring will also buckle ycr is the deflection corresponding to onset of instability 11/26/2018
Is called the effective slenderness ratio Deflection cont. Is called the effective slenderness ratio Alpha = end condition constant Lo is the spring length D is the Coil diameter 11/26/2018
End constraint alpha given by Instability cont. End constraint alpha given by 11/26/2018
For absolute stability Instability cont. For absolute stability For steels it turns out For square and ground ends 11/26/2018
Static design flow chart 11/26/2018
Flow chart cont. 11/26/2018
Recommended design conditions Figure of merit (fom) 11/26/2018
Yield strength for static loading Depends on set Materials for springs Yield strength for static loading Depends on set Before set removed use Wahl factor After set removed no stress concentration used 11/26/2018
Properties for fatigue Fatigue Strength Torsion is relevant loading- could use von Mises stress Materials testing specific to helical compression springs is available, however Correct for temp., reliability, environment 11/26/2018
Properties - endurance Endurance Strength (steels) unlimited cycles For high ultimate strengths, endurance limits max out at 45 kpsi (unpeened) and 67.5 kpsi (peened) Small wires have high ultimate strength Tests have been done specific to spring wire Temperature may require compensation Corrosion Reliability 11/26/2018
S-N and Modified Goodman 11/26/2018
Requirements Design Choices Constraints (other) Functionality Designing springs Requirements Design Choices Functionality Stiffness Lengths Diameter Forces Reliable operation Static factor of safety Fatigue factor of safety Buckling and surge Manufacturability Index C Material Wire and coil diameter Number of turns End treatment and constraint Set and shot peen Constraints (other) Bend radius 11/26/2018
Helical extension spring Similar in most ways to compression springs Usually wound to be closed coil at zero force Thus a preload is required to stretch any, i.e. y=k(F-Fi ) Spring hook is a source of failure in bending and torsion No set is used One coil not considered active 11/26/2018
End stresses Bending stress: Torsional stress: 11/26/2018
Application often has preload… how to use? Design for fatigue Data available for springs with loading from zero to some compresion value Application often has preload… how to use? First construct (or find) S-N curve Next construct Mod-Goodman chart Apply load line for given preload and design stress Find factor of safety to failure point 11/26/2018
Goodman curve 11/26/2018
A word about torsional springs The wire in a torsional spring is primarily in bending Spring constant is rotary M=k Loading should act to wind up coil Design process resembles compression springs 11/26/2018
Torsional 11/26/2018
Read chapter 10 of Shigley Homework Read chapter 10 of Shigley 11/26/2018