An extension spring from music wire with full twisted end shall work in an environment where its maximum outer diameter shall be less than 0.9 inch and the free length of the spring must be smaller than 7.5 inch. The initial preload shall be 10 lbf. Spring rate shall be 8 lbf/inch. Available wire size for the production of the spring are 0.069, 0.080, 0.090, 0.105, and 0.112 in. From the given information:

(a) Determine the wire diameter to satisfy the design requirements.

(b) Find the factors of safety under a maximum static 45 lbf load. (Hook radii
will be R_{2} =
0.25 in)

Extension Spring with Twisted End

Location of Maximum Bending and Torsion Stresses in Twisted Loops |

Step 1 : Write down input parameters which are defined in the sample example.

INPUT PROPERTIES SUMMARY | ||||

d (in) |
R_{2}(in) |
F_{max}(lbf) |
F_{i}(lbf) |
Material |

0.069 | 0.25 | 45 | 10 | Music wire |

0.080 | ||||

0.090 | ||||

0.105 | ||||

0.112 |

Step 2 : Visit dimensional extension spring design and solve the problem for each of the wire size. Known parameters are spring rate and preload so this option is selected for the solution of the problem Physical parameters generated by the calculator are tabulated as follows.

INPUT PROPERTIES SUMMARY | ||

d (in) |
L_{o} (in) |
OD (in) |

0.069 | 13.38 | 0.35 |

0.080 | 10.2 | 0.48 |

0.090 | 8.59 | 0.61 |

0.105 | 7.32 | 0.84 |

0.112 | 7.01 | 0.95 |

According to dimensional requirements (L

Step 3 : For the initial preload stress conditions, visit "Stress Analysis of Extension Spring for Static Loading" calculator. Select Maximum working load as the known parameter. Remember that d and OD is found as 0.105 and 0.84 respectively in step 2 so use this number during stress calculations. Following input parameters are used and results generated by the calculator are as follows. Note that R1 is used as the half of mean diameter (D).

INPUT PROPERTIES SUMMARY | ||

Parameter | Value | |

Wire diameter [d] | 0.105 | inch |

Spring outer diameter [OD] | 0.84 | inch |

Radius-1 [R1] | 0.3675 | inch |

Radius-2 [R_{2}] |
0.25 | inch |

Maximum working load [F_{max}] |
45 | lbf |

Material | Music wire | |

Allowable torsional strength for the spring body (% of Sut) * | 45 | % |

Allowable torsional strength for the spring end (% of Sut) * | 40 | % |

Allowable bending strength for the spring end (% of Sut) * | 75 | % |

Note 1 : ^{*} Values are taken from the
table which is given in the supplement section of extension spring design for static loading

RESULTS | ||

Parameter | Value | |

SPRING MATERIAL & STRESS RELEATED PARAMETERS | ||

Maximum working load [F_{max}] |
45 | lbf |

Shear stress at point B for maximum working load
[τ_{B}] |
87.26 | ksi |

Allowable torsional strength at point B
[S_{all_B}] |
111.264 | |

Factor of safety at point B [fos_{B}] ^{+} |
1.28 | --- |

Tensile stress at point A for maximum working load
[σ_{A}] |
168.03 | ksi |

Allowable tensile strength at point A
[S_{all_A}] |
208.621 | |

Factor of safety at point A [fos_{A}] ^{+} |
1.24 | --- |

Shear stress at spring body for maximum working load
[τ_{sb}] |
88.24 | ksi |

Allowable torsional strength for spring body
[S_{all_sb}] |
125.173 | |

Factor of safety at spring body [fos_{sb}] ^{+} |
1.42 | --- |

Ultimate tensile strength of material
[S_{ut}] |
278.16 | ksi |

Material ASTM No. | A228 |

According to calculations, the weakest point of the extension spring is point A
and fos_{A} is 1.24. If the
design margin is lower than 1.24, this design is satisfactory and can be used.

- Courtesy of Associated Spring (1987)., Design Handbook
- Budynas.R , Nisbett.K . (2014) . Shigley's Mechanical Engineering Design . 10th edition. McGraw-Hill

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