3。1。2Experimental equipment and performance test

Our test equipment comprised a driver, a controller, and a fan unit, as shown in Fig。 9。 A torque meter was attached to the inner star component, and an angular meter was  attached to the outer star component。 The torsional torque and torsional angle were measured in real time during operation。

The experiment was carried out under the following condi- tions: velocity = 5cycle/sec, input torque = 1000N-m, number of cycles = 2000cycle。 Fig。 10 shows the torsional torque and stiffness values according to the number of cycles。 The per- formance test showed that abnormal values of torque were obtained until 1000 cycles, due to the low temperature of the oil, and that normal values of torque and stiffness were ob- tained after about 1500 cycles。 The maximum values over all regions, and the average values over 30 data obtained between 1500 cycles and 2000 cycles, are shown in Table 3。 Based on the values calculated using Eq。 (3), the test samples were deemed to be within an error of 3%。

Therefore we could confirm that the stiffness coefficient theory for a sleeve spring applied to a sleeve spring torsional vibration damper was in good agreement with the test results。

3。1。3Validation of finite element analysis (FEA) boundary conditions for two-roll bending

An FEA of the 90° bending process using DEFORM-2D Ver。 9。1 was performed to verify the validity of the boundary conditions in the elasto-plastic problem。 Fig。 11 shows the die modeling for the 90° bending process。 The punch, holder and die were assumed to be rigid bodies, and six layers of ele- ments were used in the thickness direction。 Fig。 12 shows the analysis  procedures  of  the  90°bending  process。  First,    the

Table 3。 Experimental results via theoretical results。 Table 4。 Comparison between design values and analysis results。

Fig。 10。 Results of performance test。

punch moves downward to bend the material to 90°, and then the punch moves to the right until it is separated from the ma- terial。

Table 4 shows the analysis results according to the thick- ness。 The results show an error of 3-6% compared with the design values。

3。1。4Finite element analysis (FEA) of two-roll bending

DEFORM-2D Ver。 9。1 was used for an FEA of the two-roll bending process。 Fig。 13 shows the analysis model, which is based on a two-roll bending process used in the actual field。 In the process, the bending roll is fixed, and a urethane-covered roll moves vertically while rotating。

However, in the analysis model, a urethane-covered roll with a deformed shape moved vertically to bend the material, and the bending roll rotated。

The main process parameters of two-roll bending are the material  thickness,  the diameter  of the bending  roll,  and the

Fig。 11。 Die modeling for 90° bending process。

Fig。 12。 Analysis procedures of 90° bending process。

compressed amount of urethane-covered roll。 The material thickness is determined based on the design value, and the diameter of the bending roll is determined by theoretical anal- ysis。

Fig。 13。 Analysis model representing 2-roll bending process in actual field。

Fig。 14。 Contact angle between bending roll and sheet。

Table 5。 Analysis results of 2-roll bending process。

Contact Angle [ ° ] Thickness [mm]

2。4 2。0 1。8 1。6 1。4 1。2