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Based on a composited Newton–Cotes formula, this paper proposes a numerical method to predict milling stability considering regenerative chatter and focusing on rate and prediction accuracy. First, the dynamic model of milling motion is expressed as state-space equations considering regenerative chatter, with the tooth passing period divided into a set of time intervals. Second, a composited Newton–Cotes formula is introduced to calculate the transition function map for each time interval. Third, the state transition matrix is constructed based on the above-mentioned transition function, and the prediction stability boundary is determined by the Floquet theory. Finally, simulation analysis and experimental verification are conducted to verify the effectiveness of the proposed method. The simulation results demonstrate that, for the milling model with a single degree of freedom (DOF), the convergence rate and prediction accuracy of the proposed method are higher than those of the comparison method. The experimental results demonstrate that, for the milling model with two DOFs, the machining parameters below the prediction stability boundary can avoid the chatter as much as possible, ensuring the machined surface quality.

The integration of liquid exchange and microfluidic chips plays a critical role in the biomedical and biophysical fields as it enables the control of the extracellular environment and allows for the simultaneous stimulation and detection of single cells. In this study, we present a novel approach for measuring the transient response of single cells using a system integrated with a microfluidic chip and a probe with a dual pump. The system was composed of a probe with a dual pump system, a microfluidic chip, optical tweezers, an external manipulator, an external piezo actuator, etc. Particularly, we incorporated the probe with the dual pump to allow for high-speed liquid change, and the localized flow control enabled a low disturbance contact force detection of single cells on the chip. Using this system, we measured the transient response of the cell swelling against the osmotic shock with a very fine time resolution. To demonstrate the concept, we first designed the double-barreled pipette, which was assembled with two piezo pumps to achieve a probe with the dual pump system, allowing for simultaneous liquid injection and suction. The microfluidic chip with on-chip probes was fabricated, and the integrated force sensor was calibrated. Second, we characterized the performance of the probe with the dual pump system, and the effect of the analysis position and area of the liquid exchange time was investigated. In addition, we optimized the applied injection voltage to achieve a complete concentration change, and the average liquid exchange time was achieved at approximately 3.33 ms. Finally, we demonstrated that the force sensor was only subjected to minor disturbances during the liquid exchange. This system was utilized to measure the deformation and the reactive force of Synechocystis sp. strain PCC 6803 in osmotic shock, with an average response time of approximately 16.33 ms. This system reveals the transient response of compressed single cells under millisecond osmotic shock which has the potential to characterize the accurate physiological function of ion channels.

Avoiding chatter in milling processes is critical for obtaining machined parts with high surface quality. In this paper, we propose two methods for predicting the milling stability based on the composite Cotes and Simpson’s 3/8 formulas. First, a time-delay differential equation is established, wherein the regenerative effects are considered. Subsequently, it is discretized into a series of integral equations. Based on these integral equations, a transition matrix is determined using the composite Cotes formula. Finally, the system stability is analyzed according to the Floquet theory to obtain the milling stability lobe diagrams. The simulation results demonstrate that for the single degree of freedom (single-DOF) model, the convergence speed of the composite Cotes-based method is higher than that of the semi-discrete method and the Simpson’s equation method. In addition, the composite Cotes-based method demonstrates high computational efficiency. Moreover, to further improve the convergence speed, a second method based on the Simpson’s 3/8 formula is proposed. The simulation results show that the Simpson’s 3/8-based method has the fastest convergence speed when the radial immersion ratio is large; for the two degrees of freedom (two-DOF) model, it performs better in terms of calculation accuracy and efficiency.