An approach on capturing the influence of the stochasticity of fibre distributions for modelling the variability of cutting forces in composite materials

The paper presents a novel model to evaluate the variation of orthogonal cutting forces for randomly distributed unidirectional fibres when cutting composite structures. The distribution analysis of fibre locations is first introduced into this topic, and has been experimentally validated, resulting in a Gaussian distribution based random method to simulate the stochastic fibre locations within composites. The dedicated cutting force model divides the resultant forces into fibre and matrix cutting forces, and for the first time is able to predict the force variations corresponding to the stochastic fibre distributions. The orthogonal cutting of unidirectional fibre composite is classified into three cases based on the relation between the tool feed direction and the fibre orientation, all these cases are taken into account to validate the proposed model. The validation shows that both cutting forces and fibre locations follow the Gaussian distribution with a standard error lower than one percent, and the simulated fibre locations show a satisfactory agreement with the real composite internal structure during distribution analysis. Furthermore, the predicted cutting forces coincide with the experimental data, especially their variations evaluated by probability density function and cumulative distribution function demonstrate the high degree of consistency between them. This work also indicates the proposed modelling framework could be of high relevance to other relevant applications, such as energy consumption and tool wear estimation, where the understanding of the dynamic cutting forces is crucial.