Hooks Law

[markc]

Can anyone explain Hooks law - and how I would calculate spring strength using it.

 

 

Many thanks

 

Mark C

 

[Peter Carmichael]

Formula appears to be:

 

=(12000000*d^4)/(8*C*D^3)

 

where:

d is the wire diameter

D is the coil diameter

C is the count of working coils

 

So 5 coils of 1/4 inch diameter on a 2.25in spring gives: 103 lbs/in

 

[R2D2]

Hooke’s Law states that the amount an elastic body (Spring) stretches is in direct proportion to the force acting upon it.

 

It is usually expressed in simple terms as F= kx

 

Where F is the force acting on the spring, x is the extension and k is a constant of proportionality which depends on material.

 

This formula is only useful for springs which have a linear behaviour.

 

This law is only true if the elastic limit of the object has not been reached.

 

Calculated Spring Rate ® = Gd^4/8nD^3 pounds per inch

 

where

 

R = Rate, pounds of load per inch of deflection

G = modulus of rigidity of material, pounds per square inch

d = wire diameter, inches

n = number of active coils, which is one less than the total number of coils (for an open spring with ground ends.)

D = mean coil diameter, inches

 

There are 4 types of compression spring that need to be considered:

 

1. Open ends not ground ( n is the same as the total number of coils)

 

2. Open ends ground (n is one less than the total number of coils)

 

3. Closed ends not ground (n is two less than the total number of coils)

 

 

4. Closed ends ground (n is two less than the total number of coils)

 

G for Chrome Vanadium Spring Steels is 11.5 x 10^6 psi

 

Mean coil diameter = inner diameter of coil + wire diameter

 

Some care is needed to ensure that the operating stress in the coils does not exceed the yield strength of the material that has been used to manufacture the spring.

 

[scooby dooby doo]

Hooke's Law is simply that exptension is proportional to force (within the elastic limit- it also doesn't apply to rubber bands etc)

 

Chris's very applied version of this law seems feasible. I'm slightly surprised at Peter quoting (something that is equally feasible as its the same with a few values filled in) without the rider that it is for a given type of material etc. etc. 😬

 

To get any values out of the physics it all stems from the calculation for the torsional stiffness of a cylinder. This is the 4th power of its diamater (1st year degree stuff). a spring is then just a coiled version of a torsion spring (done for compactness and stability reasons)

 

HOOPY R706KGU what's a 'hood' 🤔 😬

[EFA]

Nobody has considered the pitch of the coil helix.

 

This issue is more usually addressed by calculating the sectional area of the spring wire perpendicular to the spring load.

 

Taking the wire diameter and converting to setcional area perpendicular to the wire is not good engineering practice and leads to inconsistant results.

 

 

 

 

 

Fat Arn

Visit the K2 RUM website

See the Lotus Seven Club 4 Counties Area Website here

 

[scooby dooby doo]

at that level of accuracy surly the shape of the cross section should be properly integrated. springs can be a long way off a circular corss-section, I'm sure I've seen examples where the wire is at least 2 or 3 times wider than it is thick...

 

HOOPY R706KGU what's a 'hood' 🤔 😬

[neilsjuke]

boing time for bed

[scooby dooby doo]

said zebedee

 

HOOPY R706KGU come to cam7 - we don't bite ❗