Fig。 1。 Sleeve spring-type torsional vibration damper。

(a)Sleeve spring pack

(b)Dimensions

Fig。 2。 Sleeve spring pack used in MT881 Ka-500 engine。

through an analysis of the 90°bending process。 In addition, we conducted durability tests to verify the wear resistance of the inner star and the outer star according to heat treatment speci- fications。

2。Theory

2。1Spring constant of sleeve spring and torsional character- istics of torsional vibration damper

The design parameters of the sleeve spring were determined as shown in Fig。 3。 The spring constant of the sleeve spring is expressed as [1]

Fig。 3。 Design parameters of sleeve spring。

Fig。 4。 Geometry of sleeve spring, whether inner star rotates or not。

Fig。 5。 Sleeve spring pack and damper assembly。

The sleeve spring pack used in the torsional vibration dam- per (Fig。 5) has a structure similar to leaf springs connected in

12D  ⎢  sin1⎜     GAP  ⎟⎥

(1)

parallel。  The  relation  between  the  torsional  torque  and the

⎣ ⎝D  ⎠⎦

rotation angle of the inner star of the torsional vibration dam- per is expressed as [1]

The dynamic  characteristics  of a torsional  vibration  damper

can be conceived as functions of the torsional torque versus

the torsional angle of the inner star。 Fig。 4 shows the geometry of a sleeve spring, whether the inner star rotates or not, when a sleeve spring pack is assembled in the damper。

The relation between the angle of the open gap in the sleeve spring and the rotation angle of the inner star is expressed

    2   RPitch    。 (2)

DA  RPitch 

2。2

Spring-back in the two-roll bending process

The coordinate system and nomenclatures describing the pure bending process are shown in Fig。 6。 [13, 14] The bend- ing moment needed to produce the bend results in stress in the X-direction, so the bending moment is expressed as

Fig。 6。 Coordinate system and nomenclatures in pure bending process。

Springback occurs upon removal of the bending moment。 The subscript ‘i’ represents the values before springback and the subscript ‘f’ represents the values after springback。 The stress deviation thus is expressed as

(a)Modeling

The deviation of the bending moment is expressed as

Boundary conditions

Fig。  7。 Modeling  and  boundary conditions  for obtaining  spring con-

stant of sleeve spring。

For nonlinear strain hardening material, flow stress, includ- ing the conditions of the plane-strain state and volume con- stancy is expressed as

After unloading, since the sum of the loading moment and unloading moment equals zero, we have

M M 0 。 (8)

Therefore, by Eqs。 (4), (6) and (7), the relationship between the radii of the sleeve spring before and after springback is expressed as

Fig。 8。 Results obtained from finite element analysis (FEA)。

Finite element analysis (FEA) and experiments on

core components

The forming radius is calculated by Eq。 (10), which is con- verted from Eq。 (9):

3。1

Sleeve spring

3。1。1Spring constant and torsional characteristics

A finite element analysis (FEA) using Ansys® Version 11。0