弹簧的有限元分析.ppt

Spiral Cylindrical Torsion Spring Analysis Theory FEA JingheSu: alwjybai@ Introduction Introduction Torsion coefficient (k) is one of the most important parameters of torsion springs. depend on coil diameter (D), coil number (N),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. 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 [N?m], which is equal to 2πk. 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 (D), 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. Theory Theory We start from the basic idea that the spring diameter will decrease when torsion spring is twisted 2π. Theory 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 deformated. 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 verification Two kinds of simulation is implemented using,beam element and solid element. Solid simulation: C