A Slicing Optimization Method of Manifold Model for 3D Printing Based on Dual Inclinations Probability

3D printing is widely used in modern medicine and high-end manufacturing fields. The existing 3D printing method is still difficult to meet precision and efficiency requirements for complex shape. Therefore, a slicing optimization method of manifold model for 3D printing based on dual inclinations probability (DIP) is proposed. Both the slicing inclinations and additive inclinations are synchronously considered. Uncertainty factors such as leadscrew nut screwing error, reverse engagement back clearance and heat effect of servo system are characterized. First, the Axis-aligned Bounding Boxes of the manifold model is constructed. The height-diameter ratio is obtained by minimum bounding cylinder. The projection area in Oxy, Oxz and Oyz plane is obtained by orthogonal projection of facets to determine the optimal direction (z direction) of 3D printing. A compound variable of the inclination angle of slicing plane is derived. The probability density function and probability model of generalized chi-squared distribution are built. The bounded coordinate equations of the non-horizontal worktable are deduced by a certain point and double angle method. Further, the maximum and minimum z value of the bounded slicing planes is determined according to the gradient rule of the slicing plane. The triangular facets that intersect with different slicing planes are found out by building interval partition blocks and layered intelligent screening facet. Based on the topological homomorphism of associated facet set and its orthogonal projection on the bounded slicing plane, the directed multi-connected domains of 3D printing model is finally obtained. According to Cavalieri principle, the volume of polyhedral prism in each layer is calculated, and the strategy of slicing is optimized iteratively according to the criterion of volume error and cusp height. Finally, the optimal robust slicing strategy is determined with the greatest tolerance to uncertainties according to the DIP model. 3D printing experiments are carried out on human second cervical vertebra. The Part's maximum cusp height is reduced by 10.12%. The stair effect is suppressed. It is proved that this DIP method can improve the forming accuracy of 3D printing for uncertain error factors. © 2019 Journal of Mechanical Engineering.