2. Factors in spring design Materials Torsional
Types
Factors in spring design
Materials
Torsional
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3. Types of Springs
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4. Types of spring cont.
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5. Types of springs cont.
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6. Types of springs cont.
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8. 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
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9. Common materials for springs
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10. Influence of diameter on ultimate stress
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11. Influence of diameter on ultimate stress cont.
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12. Design of helical compression springs
Length nomenclature
Free
Assembled
Solid or shut height
Working deflection
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13. Stresses in Helical Spring
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14. 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)
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15. 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
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16. 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
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17. 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.
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18. 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,
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19. Deflection of a helical spring
Using Castigliano’s theorem, strain energy is equal to
Substituting
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20. Deflection cont.
Using the spring index
Spring scale is
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21. Spring design – end treatment
End details affect active coils
Plain ends
Squared ends
Squared
Ground
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22. Number of active coils
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23. Stability of a column
Euler Formula
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24. 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
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25. 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
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26. End constraint alpha given by
Instability cont.
End constraint alpha given by
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27. For absolute stability
Instability cont.
For absolute stability
For steels it turns out
For square and ground ends
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28. Static design flow chart
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29. Flow chart cont.
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30. Recommended design conditions
Figure of merit (fom)
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31. 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
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32. 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
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33. 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
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34. S-N and Modified Goodman
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35. 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
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36. 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
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37. End stresses
Bending stress:
Torsional stress:
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38. 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
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39. Goodman curve
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40. 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
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41. Torsional
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42. Read chapter 10 of Shigley
Homework
Read chapter 10 of Shigley
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