1、Spiral Cylindrical Torsion Spring Analysis,Theory that is, a flexible elastic object that stores mechanical energy when it is twisted. cited from wiki,Torsion coefficient (k) is one of the most important parameters of torsion springs. depend on coil diameter (D), coil number (N),wire diameter (aXb f

2、or 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.,Introduction,Introduction,In the industrial the following formula is widely used for cylindrical torsion spring design, in order

3、to meat the torsion coefficient requirement. M is united in Nm, which is equal to 2k.,for round wire spring rectangular wire spring,Here, we just give brief derivation of the formula and verify it using finite element methods (implemented by ABAQUS).,Theory,All the following interpretation is under

4、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 (D), which will result in really brief but useful f

5、ormula. 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 EulerBernoulli beam theory. The one who want to know the detail can refer to google.,Theory,D0: coil diameter before twist (mm), N0: coil num

6、ber before twist (-),E: elastic modulus (Mpa) p: coil pitch (mm) a,b: rectangular wire diameter (mm) D1: coil diameter after twist (mm), N1: coil number after twist (-),Some denotation:,D,p,b,a,Theory,We start from the basic idea that the spring diameter will decrease when torsion spring is twisted

7、2.,neutral line,D0/2.0,0,After twist, D0-D1, 0-1, the following relations exist,The first two relation is due to pure bending and neutral line length does not change.,Theory,We can calculate the strain in x position (x is the distance to neutral line) as,After that, we can calculate the torque M as,

8、using the same method you can get the formula of round wire spring.,Theory,As reflected during derivation, we should prevent from abusing these formula in some extreme situations. the torsion spring with small N only have limited capacity for elastic twist, otherwise wire will be plastically deforma

9、ted. diameter of the wire and spring is critical to guarantee good result of the formula. Bigger a can result in bigger torsion coefficient but also an easy damaged spring because of plastic deformation. sometimes buckling problem may occur for rectangular wire spring if a is much bigger than b.,FEA

10、 verification,Two kinds of simulation is implemented using,beam element and solid element. Solid simulation: C3D20R element 3 elements in thickness Beam simulation: B31 elements 60 elements in a pitch,FEA verification,Diameter-Pitch Ratio influence,Some tips: Beam simulation is reliable as solid one

11、. Theory formula produce wrong prediction when pitchis really large. Beam simulation can savea lot time.,FEA verification,Diameter-Pitch Ratio influence,Some tips: Theory formula get goodresult when spring diameteris much bigger than thickness.(Db ratio10 guarantee 5%error) Buckling problem reduce the spring maximum load capacity.,FEA verification,Buckling problem in torsion spring,Capacity will go