Spiral Cylindrical Torsion Spring Analysis

Transcription

1 Spiral Cylindrical Torsion Spring Analysis Theory & FEA JingheSu:

2 Introduction A torsion spring is a spring that works by torsion or twisting; that is, a fleible elastic object that stores mechanical energy when it is twisted. cited from wiki

3 Introduction Torsion coefficient (k) is one of the most important parameters of torsion springs. depend on coil diameter (), coil number (), wire diameter (axb for rectangular wire) elastic modulus (E) Application we can calculate the torque and the energy stored in spring as following, theta is the torsion angle united in radian. τ -κθ U κθ

4 Introduction In the industrial the following formula is widely used for cylindrical torsion spring design, in order to meat the torsion coefficient requirement. M is united in [ m], which is equal to πk. M 4 E d.8 for round wire spring M 3 E a b 6.6 rectangular wire spring Here, we just give brief derivation of the formula and verify it using finite element methods (implemented by ABAQUS).

5 Theory All the following interpretation is under the presupposition of elastic and small deformation. Also, plane section is an other hypotheses during the derivation. For simplification, we assume the wire diameter (a,b) as well as the pitch (p) is relatively small comparing with spring diameter (), which will result in really brief but useful formula. We assume the spring wire is in pure bending during working. Actually, the formula is derived in the similar way as classic beam theory, also known as Euler Bernoulli beam theory. The one who want to know the detail can refer to google.

6 Theory Some denotation: a p b : coil diameter before twist (mm), : coil number before twist (-), E: elastic modulus (Mpa) p: coil pitch (mm) a,b: rectangular wire diameter (mm) : coil diameter after twist (mm), : coil number after twist (-),

7 Theory Theory Theory Theory We start from the basic idea that the spring diameter will decrease when torsion spring is twisted π. neutral line /. θ After twist, ----, θ ----θ, the following relations eist, p p π π π π θ θ, p << The first two relation is due to pure bending and neutral line length does not change.

8 Theory Theory Theory Theory, << θ θ θ ε ( ) 3 6 b a E b d E M a a ε We can calculate the strain in position ( is the distance to neutral line) as, After that, we can calculate the torque M as, using the same method you can get the formula of round wire spring.

9 Theory As reflected during derivation, we should prevent from abusing these formula in some etreme situations.. the torsion spring with small only have limited capacity for elastic twist, otherwise wire will be plastically deformated.. diameter of the wire and spring is critical to guarantee good result of the formula. 3. Bigger a can result in bigger torsion coefficient but also an easy damaged spring because of plastic deformation. 4. sometimes buckling problem may occur for rectangular wire spring if a is much bigger than b.

10 FEA verification Two kinds of simulation is implemented using, beam element and solid element. Solid simulation: C3R element 3 elements in thickness Beam simulation: B3 elements 6 elements in a pitch

11 FEA verification iameter-pitch Ratio influence Some tips:.beam simulation is reliable as solid one..theory formula produce wrong prediction when pitch is really large. 3.Beam simulation can save a lot time.

12 FEA verification iameter-pitch Ratio influence Some tips:.theory formula get good result when spring diameter is much bigger than thickness. (b ratio> guarantee 5% error).buckling problem reduce the spring maimum load capacity.

13 FEA verification Buckling problem in torsion spring Capacity will go down and buckling will be severe if, * () b/a () pitch() The one who want to go further can search 'bend buckling' in google and you will get a lot of informations.

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