Flexible multibody approaches for simulating the deflection and contact mechanics of toothbrush bristles: modelling and testing

Brushing represents a specific procedure that aims to remove biofilms from the vertical and occlusal surfaces of the teeth, as well as from interdental spaces to the greatest extent possible. When developing toothbrushes, a common concern is determining the contact force required to assess cleaning performance, comfort and safety. This evaluation relies on the bristles, which serve as the contact elements of the toothbrush. Due to the significant deflection of the bristles, linear models or two-dimensional approaches may be inadequate for studying their deformation. On the other hand, nonlinear beam models are computationally intensive due to the lack of exact closed-form expressions for large complex deformations. Flexible multibody methodology emerges as a suitable approach to analyse this problem, offering insights into contact forces, sliding forces and bristle deformation. It proves to be a valuable tool for enhancing bristle design. The paper explores two multibody modelling approaches capable of accommodating large deflections. The first is a simplified model based on Howell’s PRB 3D model, employing a beam split into two segments connected by a spherical joint and three lumped spring elements. The second is the discrete flexible approach, utilising a larger number of rigid bodies connected with six-degrees-of-freedom elastic matrix elements. Both methods are compared with quantitative experimental results replicating toothbrush cleaning on reference surfaces along different directions.