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
Magnitude and direction of force: Determine magnitude and direction of smallest force P which is required to start the wheel over the block. As shown in the figure. So

Find out the motion of the system: Block (A) of mass M A = 40 kg is resting on coarse table having coefficient of friction = 0.1. This is tied up with an inextensible rope (

Q. Shut-off valves on major zone? Are shut-off valves on major zone branches and on the bottom and top of riser? Are balancing valves on return branches? Are control valves on

Prove the torsion equation T/J=τ/R=C. θ/L for the solid circular shaft. State the various assumptions used on above said equation.

what is clearance?what is the need of clearance?differences between with clearance and with out clearance?

Specific Properties of a System The extensive properties while estimated on the unit mass basis result in intensive property that is as well known as specific property. For exa

Design Problem:  Design a pipeline and pump station to pump 100 MGD of water to the Mississippi river.  To reduce the required horsepower of the pumps, the flow will be pressurized

Consider radar with a PRF of 5 kHz. What is the maximum unambiguous range R ua of this radar, in km?  If a target is located at a range of 50 miles, how many pulses will the r

A Wilson-Hartnell governor is illustrated in given Figure. In this, the balls are associated by two springs that are known as main springs. The main springs are symmetrically arran

Scope of strength of materials: What is the scope of strength of materials? Sol.: Strength of materials is science that deals with the relations between externally appl