The Sealing Effect Improvement Prediction of Flat Rubber Ring in Roller Bit Based on Yeoh_Revised Model

Abstract

In a roller bit, the flat rubber ring (FRR) often needs to apply a certain amount of compression to ensure that its rotation and static sealing surfaces can be stably sealed. For the predicted Mises stress, values smaller than the actual Mises stress due to soft single-axis compression (SAC) stress are predicted by the Yeoh (N = 3) model. To more reasonably predict stress under the static compression of the FRR in the roller bit, the sealing effect of the FRR based on the SAC contact stress and the calculated Mises stress was evaluated by the Yeoh_revised model. Based on the assumption that hydrogenated nitrile-butadiene rubber (HNBR) is isotropic and incompressible, first, we derived the fitting formulas for three types of constitutive models and the Jacobi matrix of the Yeoh_revised model and developed hyperelastic constitutive subroutines. Simultaneously, the accuracy of three models (Yeoh, Yeoh_revised and Ogden) was evaluated by the goodness of fit (R²) to data from three kinds of tensile experiment tests. The highest R² is 0.9771 with the Yeoh_revised model, which merges the advantages of the other two fitting models and effectively improves the Yeoh model's soft property of SAC contact stress. Additionally, by measuring on-site FRR wear, the maximum Mises stress on the sealing surface calculated based on the Yeoh_revised model is about twice that of the Yeoh model, and the maximum Mises stress on the rotation contact sealing surface is higher than that on the outside (static sealing) surface, which makes the aging of the rotation surface more severe. Thus, it was demonstrated that, on the premise of ensuring FRR sealing contact stress, the Yeoh_revised model can more reasonably predict the sealing effect of the FRR to more precisely calculate Mises stress than the Yeoh model. This also contributes to FRR structure optimization to prolong the service life of the FRR in the roller bit.

Keywords: FRR; Mises stress; Yeoh_revised; incompressible.

Figure 1

Schematic diagram of the cross-sectional structure (a) and contact deformation of FRR (b) in a roller bit. In the contact path (green dotted line in Figure 1b), the critical point on the rotation surface contact with the outer and inner fluid zone is A and B, point C is the middle point in the contact path and the critical point on the outside surface contact with the outer and inner fluid zone is D and E.

Figure 2

Three tensile test devices (a1–c1), test section magnification (a2–c2) and test samples’ extrinsic features (a3–c3) after tests.

Figure 3

Schematic representation of uniaxial tensile (a), equivalent tensile (b), planar tensile (c) of stretched samples and deformation directions (d).

Figure 4

Multiplicative decomposition of deformation.

Figure 5

The FEM schematic diagram for rubber SAC.

Figure 6

The results of three models fitted to HNBR stretching experiments at 120 °C: Yeoh model (a), Yeoh_revised model (b) and Ogden model (c).

Figure 7

Residual analysis of three models for fitting results of HNBR tensile experiment at 120 °C: UT tensile (a), ET tensile (b) and PT tensile (c) results.

Figure 8

The SAC stress compared with FEM calculations at 120 °C.

Figure 9

Contact stress cloud diagram of FRR in a roller bit: (a) pre-compression contact stress based on Yeoh model; (b) contact stress after fluid extrusion based on Yeoh model; (c) pre-compression contact stress based on Yeoh_revised model; (d) contact stress after fluid extrusion based on Yeoh_revised model.

Figure 10

Contact stress on the contact path of FRR in a roller bit. In the contact path (green dotted line in Figure 1b), the critical point on the rotation surface contact with the outer and inner fluid zone is A and B, point C is the middle point in the contact path and the critical point on the outside surface contact with the outer and inner fluid zone is D and E.

Figure 11

Mises stress cloud diagram of FRR in a roller bit: (a) pre-compression Mises stress based on Yeoh model; (b) Mises stress after fluid extrusion based on Yeoh model; (c) pre-compression Mises stress based on Yeoh_revised model; (d) Mises stress after fluid extrusion based on Yeoh_revised model. In the contact path (green dotted line in Figure 1b), the critical point on the rotation surface contact with the outer and inner fluid zone is A and B, point C is the middle point in the contact path and the critical point on the outside surface contact with the outer and inner fluid zone is D and E.

Figure 12

Mises stress on the contact path of FRR in roller bit. In the contact path (green dotted line in Figure 1b), the critical point on the rotation surface contact with the outer and inner fluid zone is A and B, point C is the middle point in the contact path and the critical point on the outside surface contact with the outer and inner fluid zone is D and E.

Figure 13

The on-site wear effect on FRR in a roller bit. The wear effect on the outside and rotation surfaces of FRR before and after use is shown in (a) and (c), respectively. The magnification of the outside and rotation surfaces’ wear effect is shown in (b) and (d), respectively. In the contact path (green dotted line in Figure 1b), the critical point on the rotation surface contact with the outer and inner fluid zone is A and B, the critical point on the outside surface contact with the outer and inner fluid zone is D and E.

Figure 14

Schematic diagram of wear measurement of FRR in a roller bit.