Structural analysis of rubber products with contact, friction, and large rotation

by Akihiko TOKUDA, "Salome-Meca Practice and Utilization Group" in Japan. Mr TOKUDA is a structural analysis engineer in a Japanese rubber products manufacturing company.

Salome-Meca Practice and Utilization Group

In order to precisely master the advanced functions of Code_Aster, Japanese beginners have a mandatory need of a Japanese speaking community around Salome-Meca for face-to-face exchanges and support. Thus, the Salome-Meca Practice and Utilization Group was introduced in Japan in 2011 by several engineers from different companies. This group is a sub-community of CAEKonwakai, a nonprofit organization structuring the CAE community in Japan. CAE Konwakai is working with The Open CAE Society of Japan whose mission is to promote the use of Salome-Meca and OpenFOAM.

Power transmission between two rollers with rubber band

The frictional force of the rubber strip transmits the movement of the left roller to the right one (fig. 1). The objective is to compute the stresses, the distribution of frictional forces and the deformation of the rubber strip. This case includes several nonlinearities: nonlinear material, large strain, large rotations. In addition, since the transmission between the two rollers is only produced by the frictional force, the problem is mechanically unstable.

However, despite these difficulties, Code_Aster can solve this problem thanks to its nonlinear features and its robustness.

Fig. 1: Power transmission between two rollers with rubber band

The calculation was carried out by chaining three calls to STAT_NON_LINE with plane strain finite element D_PLAN.

• Initial state : The initial shape of the rubber strip is a perfect circle. The rollers may be treated as rigid bodies, but LIAISON_SOLIDE is not applicable to large rotations. Thus, they are deformable bodies.

• Step 1 : Pulling the driven roller to the right, tension is generated in the rubber, which deforms. In the first steps of calculation, the roll and the rubber strip are unstable. Therefore, a small spring, of K_T_D_N type, is used to ensure stability. A spring too soft reduces the effect of stability, a spring too stiff has a visible effect on the deformation of the strip. To stabilize the initial contact, the use of SEUIL_INIT in DEFI_CONTACT is effective.

• Step 2 : The central point of the driven roller is fixed at the location of the deformed position in step 1 through TYPE_CHARGE = ’DIDI’. Then, the load assigned at the step 1 is released.

• Step 3 : The driving roller is rotated by imposing movement. On the other hand, a torque load is assigned to the driven roller. In order to maintain the torque constant despite the rotation of the driven roller, a following force TYPE_CHARGE = ’SUIV’ is assigned on the circumference of the drive roller. The stress and strain on the upper face of the rubber increases the torque load.

Contact of rubber plate and steel cam

A rotatable steel cam is in contact with a rubber sheet (Fig. 2). This calculation does not correspond to an actual product, but is used to evaluate the contact in Code_Aster. The friction is not taken into account.

Fig. 2: Contact of rubber plate and steel cam

The 3D analysis requires much more computing time than the 2D analysis, especially for contact problems. Therefore, to speed up the calculation, we use here the generalized Newton method for contact in the 11.2.0 version of Code_Aster. As a result, the computation time was reduced to 4897 sec. for version 11.2.0, compared to 13,141 sec. for version 10.5.