Abstract In diesel engines, engine torque fluctuation inevitably produces torsional vibration。 A sleeve spring-type damper commonly is used to reduce this vibration。 In this paper, closed form equations to predict the spring constant of a sleeve spring and the torsional characteristics of a torsional vibration damper are proposed for calculation of the stiffness of the damper。 The equations were verified through finite 82797

 element analysis (FEA) and experiments。 In addition, the stability of the sleeve spring-type torsional vibration damper was verified in an analysis of the inner star and outer star (the core components of the damper)。 A two-roll bending process, proposed in this paper, was determined to be the most suitable for manufacture of the sleeve springs。 A closed form equation to calculate the forming radius, taking account of the springback effect, was derived, and a FEA method used to analyze the elasto-plastic problem was verified through an analysis of a 90° bending process。 The results of the analysis were in good agreement with the experiment。 It is recommended that our proposed method, an advanced technique that can significantly reduce production costs, replace the conventional forming process。

Keywords: Sleeve spring; Spring constant; Torsional vibration damper; Two-roll bending

1。Introduction

Torsional vibration of a crankshaft due to variation of tor- que is inevitable in a diesel engine, which is a reciprocal en- gine with a crank mechanism。 Such vibration can be reduced through installation of an appropriate damper or by optimiza- tion of the combustion chamber stroke。 There are  several types of torsional vibration dampers, and they are selected according to engine speed: a viscous fluid type for low speed, a coil spring type for medium speed, and a sleeve spring type for high speed。 The sleeve spring torsional vibration damper is shown in Fig。 1, and the sleeve spring pack used in the MT881 Ka-500 Engine is shown in Fig。 2。

 Chul Kim et al。 [1] derived a spring constant formula for a sleeve spring and a torsional characteristic formula for  a sleeve spring torsional vibration damper。

The techniques for the production of cylindrical tubular sec- tions such as sleeve springs include roll-bending, stamp- bending, stretch-bending, and press-braking。 Roll-bending, compared with the other processes, can reduce set up time, reduce  costs  in tooling  investments,  minimize  the length of

† This paper was recommended for publication in revised form by Associate Editor Chang-Wan Kim

*Corresponding author。 Tel。: +82 51 510 2489, Fax: +82 51 512 9835

E-mail address: chulki@pusan。ac。kr

© KSME & Springer 2010

straight end-edges remaining in finished products, and achieve much better finished dimensional accuracy and better circular- ity of cylindrical sections。 Therefore, the roll-bending tech- nique is widely used in forming products with cylindrical tu- bular sections。 Various studies on three-roll bending [2-5] and four-roll bending [6-12] have been undertaken, but investiga- tions into two-roll bending do not appear to be available in the literature。 Roll bending is a complex process, and its forming mechanism is not yet fully understood。 Many factors can in- fluence  the  process:  material  properties,  the  geometry and

 configuration of the rolls, friction, temperature, and others。

In the present study, structural analyses of the inner star and the outer star, which are the core components of the torsional vibration damper, were performed, and a technique to manu- facture a sleeve spring was studied, in order to develop a sleeve spring torsional vibration damper。 The two-roll bending process is proposed here for the manufacture of the sleeve spring, because it is simpler than the three-roll and four-roll processes。 Also, the two-roll bending process is mainly ap- plied to the manufacture of small products, and therefore is more suitable for mass production than those other processes (three-roll bending and four-roll bending)。 We derived a closed-form equation to calculate the forming radius, taking account of the springback effect [13, 14], and we verified the FEA  method   used  to  analyze  the  elasto-plastic   problem,