Determine mean coil radius - close coiled helical spring, Mechanical Engineering

Determine Mean coil radius - close coiled helical spring:

 A close coiled helical spring contains a stiffness of 1 kN/m in compression to a maximum load of 50 N and a maximum shearing stress of 150 N/mm2. The solid length of the spring is equal to 45 mm. Resolve out the wire diameter, mean coil radius, and number of coils. Take G = 40 GPa.

Solution

W = 50 N, k = 1 kN/m = 1 N/mm, τmax = 150 N/mm2, solid length = 45 mm, d = ?,

R = ?, n = ?

Use Eq. (10) for stiffness

k = W/ Δ          = G d 4/            64 R3 n

or         1 = (40 × 103 ) d 4 / 64 R3 n

∴ R3 n/ d 4     = 625             ---------- (1)

Use Eq. (3) for maximum shearing stress with K = 1

τmax      = 16 W R  /π d3

or         150 =16 × 50 × R /π d 3

∴          R / d 3  = 0.6                          ------------- (2)

or         R = 0.6 d3

Note solid length of spring is length while all coils are touching each other, so

            nd = 45

         n = 45 /d         ---------- (3)

Use R from Eq. (2) and n from Eq. (3) in Eq. (i)

 (0.6 d 3 )3 ( 45/d)(1/d4)  = 625

Or  d 4  = 64.3

∴   d = 2.83 mm

From Eq. (3)

n =   45 /2.83 = 15.9      (say 16)

R = 0.6 d 3  = 0.6 (2.83)3  = 13.6 mm

Posted Date: 1/21/2013 1:09:34 AM | Location : United States







Related Discussions:- Determine mean coil radius - close coiled helical spring, Assignment Help, Ask Question on Determine mean coil radius - close coiled helical spring, Get Answer, Expert's Help, Determine mean coil radius - close coiled helical spring Discussions

Write discussion on Determine mean coil radius - close coiled helical spring
Your posts are moderated
Related Questions
Explain Clamping Devices A clamp is a device that holds the work piece firmly against the locators provided and also resists all forces generated by the cutting action of

What us the duff between direct stress and bending stress

How does the Two Stage Reciprocating Air Compressor works?


Explain the Methods of solid modeling The various methods for representing the solids are : (i)  Half-space method (ii)  Boundary representation method (b-rep) (iii)

Determine elongation of bar: A conical bar tapers uniformly from diameter of 4 cm to 1.5 cm in length of 40 cm. If axial force of 80 kN is applied at each end, determine elon


Fourth Gear Position: When gear M4 on the main shaft is in mesh with gear C4 on the countershaft then this is known as fourth gear position. The free gear M4 rotates with the

Find out the horizontal and vertical components of the force: A force of 120 N is exerted on a hook in the ceiling as illustrated in Figure. Find out the horizontal and vertic