The use of ultrasonic vibration on milling has several benefits including reduction of the machining forces. However, the mechanism behind this phenomenon is unclear, and reported analytical studies are quite limited. An analytical predictive modeling work is presented in the current study. To describe the intermittent contact between tool and workpiece due to vibration, conditions of tool-workpiece separation are described by three types of criteria. The first criterion checks the instantaneous moving direction of cutting edge. The second criterion examines the radial displacement of cutting edge under vibration. The third criterion considers the smaller chip thickness due to extra displacement from previous tool path. If the material is being removed, the force prediction is performed through transformation of milling configuration, calculation of shear flow stress by mechanics of machining, and calculation of feed, cutting and axial force after coordinate transformation. The predicted forces are compared with experimental measurements on Aluminum alloy 2A12 for validation. The average percentage difference is 13.6% in feed direction and 13.8% in cutting direction. This is the first approach to mathematically describe the intermittent contact between tool and workpiece and combine the kinematic analysis with mechanics of machining to predict cutting forces.

Better surface finish is believed to be one of the most important benefits of ultrasonic vibration-assisted milling. Many studies have shown that this benefit is most significant during slot-milling of a part when the vibration is applied in feed direction. To explicitly explain this phenomenon, an analytical model is proposed to predict surface roughness based on the trajectory of tool and the response of machined surface. The overall machined surface profile under tool trajectory depends on the tool tip movement, in addition to the tool deformation under cutting force and tool tip geometry. The movement of tool tip is governed by feed, spindle rotation, and ultrasonic vibration. The tool deformation depends on the milling force and stiffness. The geometry of tool tip is characterized by the tip radius and angle. Besides surface profile under tool trajectory, the response of machined surface is considered by assuming pure elastic deformation when the actual instantaneous cutting thickness is smaller than a critical value. In that case, part of the material is recovered so the actual machined surface profile is different from the profile under tool trajectory only. Surface roughness is then calculated based on the actual surface profile. Experiments are conducted on Aluminum alloy in both conventional and ultrasonic vibration-assisted milling under different spindle speed, feed, and vibration amplitude. Through the comparison between the analytical predictions and experimental measurements, the proposed model has high accuracy in all cases with average percentage error of 15%.

Hydraulic fracturing of tight subsurface formations has mainly been conducted using water. Waterless hydraulic fracturing by CO₂ may have advantages over fracturing by water. The challenge has been numerical simulation of the process. In this work, we conduct a comprehensive study on 2D hydraulic fracturing simulation by water, CO₂, and nitrogen. The simulations are based on the phase‐field; the results are compared with the lab data. We first present advances in simulation of fluid exchange between the fractures and the rock matrix. The conventional nodal‐based finite element method may give rise to unphysical negative pressure around the tip and fracture notch. We demonstrate that the mixed hybrid finite element method gives non‐negative pressure distribution. Next, we examine the effect of inertial term on fracture configuration and observe branching by CO₂ under dynamic formulation with a low critical energy release rate. Lastly, we find from our simulations that in shale rocks, the critical energy release rate is the lowest for CO₂, followed by nitrogen, and then water. Consequently, CO₂ provides the highest fracture surface area and fracture intensity. In a sandstone sample we find nitrogen has a lower energy release rate than water. As a result, the fracture surface area is higher for nitrogen than water. Our simulation results confirm that the phase‐field method may incorporate fluid‐rock surface free energy without the need for various parameter adjustments.

In the current study, a predictive model on tool flank wear rate during ultrasonic vibration-assisted milling is proposed. One benefit of ultrasonic vibration is the frequent separation between tool and workpiece as the cutting time is reduced. In order to account for this effect, three types of tool–workpiece separation criteria are checked based on the tool center instantaneous position and velocity. Type I criterion examines the instantaneous velocity of tool center under feed movement and vibration. If the tool is moving away from workpiece, there is no contact. Type II criterion examines the position of tool center. If the tool center is far from the uncut workpiece surface, there is no contact even though the tool is getting closer. Type III criterion describes the smaller chip size due to the overlaps between current and previous tool paths as a result of vibration. If any criterion is satisfied, the tool flank wear rate is zero. Otherwise, the flank wear rate is predicted considering abrasion, adhesion and diffusion. The proposed predictive tool flank wear rate model is validated through comparison to experimental measurements on SKD 61 steel with uncoated carbide tool. The proposed predictive model is able to match the measured tool flank wear rate with high accuracy of 10.9% average percentage error. In addition, based on the sensitivity analysis, smaller axial depth of milling, larger feed per tooth or higher cutting speed will result in higher flank wear rate. And the effect of vibration parameters is less significant.