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
Aluminum-lithium alloys have been developed by the aircraft industry to reduce the weight and improve the performance of its aircraft. A commercial aircraft skin material having a

Write a report on the procedure along with the MATLAB code. The subject is Gas Dynamics

Explain the working of Michelson's interferometer. How circular fringes he produced with it. (a) What are antireflection films and interference filters? (b) Find the reflecti


Q. Identification of Defects of coating? All holidays and other coating defects, including without limitation primer blister, excess powder mounds, crazed coating, lifted and u

In class, we derived and solved a model of a non-isothermal, insulated, CSTR with an exothermic reaction (model6.m). We want to derive and solve a very similar model of a system wi

define thormodynamics and its laws

Find out the centre of gravity of a wire: Find out the C. G. of a wire of uniform cross-section bent into shape of a semicircle as illustrated in Figure. Solution

Flow Work and Flow Energy - thermodynamics: Flo w Work:  The flow work is energy needed to move the working substance against its pressure It is called as flow or displac