Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness

This paper presents mechanisms studies of micro scale milling operation focusing on its characteristics, size effect, micro cutter edge radius and minimum chip thickness. Firstly, a modified Johnson–Cook constitutive equation is formulated to model the material strengthening behaviours at micron level using strain gradient plasticity. A finite element model for micro scale orthogonal machining process is developed considering the material strengthening behaviours, micro cutter edge radius and fracture behaviour of the work material. Then, an analytical micro scale milling force model is developed based on the FE simulations using the cutting principles and the slip-line theory. Extensive experiments of OFHC copper micro scale milling using 0.1 mm diameter micro tool were performed with miniaturized machine tool, and good agreements were achieved between the predicted and the experimental results. Finally, chip formation and size effect of micro scale milling are investigated using the proposed model, and the effects of material strengthening behaviours and minimum chip thickness are discussed as well. Some research findings can be drawn: (1) from the chip formation studies, minimum chip thickness is proposed to be 0.25 times of cutter edge radius for OFHC copper when rake angle is 10° and the cutting edge radius is 2 μm; (2) material strengthening behaviours are found to be the main cause of the size effect of micro scale machining, and the proposed constitutive equation can be used to explain it accurately. (3) That the specific shear energy increases greatly when the uncut chip thickness is smaller than minimum chip thickness is due to the ploughing phenomenon and the accumulation of the actual chip thickness.     

Estimation and experimental validation of cutting forces in ball-end milling of sculptured surfaces

Chip thickness calculation has a key important effect on the prediction accuracy of accompanied cutting forces in milling process. This paper presents a mechanistic method for estimating cutting force in ball-end milling of sculptured surfaces for any cases of toolpaths and varying feedrate by incorporation into a new chip thickness model. Based on the given cutter location path and feedrate scheduling strategy, the trace modeling of the cutting edge used to determine the undeformed chip area is resulted from the relative part-tool motion in milling. Issues, such as the selection of the tooth tip and the computation of the preceding cutting path for the tooth tip, are also discussed in detail to ensure the accuracy of chip thickness calculation. Under different chip thicknesses cutting coefficients are regressed with good agreements to calibrated values. Validation tests are carried out on a sculptured surface with curved toolpaths under practical cutting conditions. Comparisons of simulated and experimental results show the effectiveness of the proposed method.     

Thermomechanical modelling of oblique cutting and experimental validation

An analytical approach is used to model oblique cutting process. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within a thin band called primary shear zone. The analysis is limited to stationary flow and the material flow within the primary shear zone is modelled by using a one-dimensional approach. Thermomechanical coupling and inertia effects are accounted for. The chip flow angle is determined by the assumption that the friction force on the tool face is collinear to the chip flow direction. At the chip–tool interface, the friction condition can be affected by the important heating induced by the large values of pressure and sliding velocity. In spite of the complexity of phenomena governing the friction law in machining, a reasonable assumption is to consider that the mean friction coefficient is primarily function of the average temperature at the tool–chip interface. Comparisons between model predictions and experimental results are performed for different values of cutting speed, undeformed chip thickness, normal cutting angle and inclination angle. A critical study is presented in order to show the influences of the input parameters of the model including the normal shear angle, the thickness of the primary shear zone and the pressure distribution at the tool–chip interface. The model permits to predict the cutting forces, the chip flow direction, the contact length between the chip and the tool and the temperature distribution at the tool–chip interface which has an important effect on tool wear.     

Analytical predictions and experimental validation of cutting force ratio, chip thickness, and chip back-flow angle in restricted contact machining using the universal slip-line model

This paper presents analytical predictions and experimental validation of a recently developed universal slip-line model for machining with restricted contact cut-away tools. Three important machining parameters, i.e. the cutting force ratio, chip thickness, and chip back-flow angle, are predicted on the basis of: (1) the universal slip-line model; (2) a maximum value principle for determining the state of stresses in the plastic region in restricted contact machining; (3) Dewhurst and Collins’ matrix technique for numerically solving slip-line problems; and (4) Powell’s algorithm for non-linear optimizations. All predictions are based on purely theoretical calculations with no experimental/empirical data as input. The extensive comparisons between theory and experiments show a reasonable agreement. Major new research findings from this study include: (1) the applicable ranges of an extreme friction slip-line model and of Johnson’s and Usui and Hoshi’s slip-line models; and (2) the general rule of the variation of tool–chip friction conditions. Tool–chip contact in machining with restricted contact cut-away tools is categorized into three broad cases. A theoretical method is also presented in the paper to distinguish different tool–chip contact cases in practical machining situations.