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In five-axis flank milling operations, the intersecting surfaces of different cutting edges create roughness on the milled surfaces that cannot be ignored in situations with strict requirements, especially in aeronautical manufacturing. To focus on motion problems in milling operations, this paper presents a new model that utilizes elliptical paths as cutting edge trajectories on 3D surface topography machined by peripheral milling. First, the cutter parallel axis offset and location angle are considered, which change the location of the ellipse center and intersection point of the cutting edges. Then, through the proposed model, the predicted surface topography is obtained, and the factors that affect the development tendency of roughness are analyzed. Next, the effects of the cutter location position (CLP) geometric parameters, cutter parallel axis offset and curvature on the roughness are evaluated by a numerical simulation. Finally, machining tests are carried out to validate the model predictions, and the results show that the surface topography predictions correspond well with the experimental results.

Immobilized enzymes are better suited for industrial applications than free enzymes due to their favorable properties such as ease of separation and reuse, and enhanced stability and storage life. β-Galactosidases are an important class of glycosidases with hydrolysis and transglycosylation activities, which are applied in industries for lactose hydrolysis and prebiotics synthesis worldwide. The recent innovations in immobilized β-galactosidases have improved the performance of the immobilized enzymes and broadened their applications in the fields of food, energy, and medicine. Innovations in β-galactosidase immobilization methods include rational adsorption based on enzyme features, layer by layer adsorption for strengthened ionic bonding, 3-D printing for rapid and elaborate entrapment, modifications of either materials or enzymes for ingenious covalent binding, nontoxic crosslinking, carrier-free immobilization, and oriented immobilization either through protein engineering or enzyme display on cells, membranes, and phages, along with innovations in carrier materials involving the introduction of graphene derivatives, polyaniline nanomaterials, nanofibers, nucleotide molecules, Langmuir-Blodgett films, and so on. These innovations have partially solved the problems associated with traditional methods, resulting in enzymes with highly retained activity, excellent stability, reduced microbial contamination, enzyme leakage, and reagent toxicity. The immobilized β-galactosidases with potential economic and environmental benefits have been extendedly used for hydrolysis of prodrugs for disease treatment, assembly of biosensors for lactose detection, synthesis of bioactive carbohydrates, and even production of food additives and industrial products, such as tagatose and bioethanol. This review describes the innovations in β-galactosidases immobilization and the applications of these immobilized enzymes. It not only enables the fully understanding of β-galactosidases, but also provides a valuable reference for the immobilization of other industrially-important enzymes.

This work established an integrated utilization of dairy whey in β-galactosidase production from Lactobacillus bulgaricus and prebiotics synthesis by the probiotic enzyme. A cost-effective whey-based medium was newly developed for culturing Lactobacillus bulgaricus to produce β-galactosidase. The medium was optimized through response surface methodology (RSM) involving a series of statistical designs, such as the Plackett–Burman design, steepest ascent experiment, and central composite design. Under the optimized medium, the β-galactosidase activity of L. bulgaricus reached 2034 U/L, which was twice that produced from the traditional MRS medium. The cells of L. bulgaricus harvested from the whey-based medium were subsequently treated with lysozyme. The resulting crude enzyme was used as an efficient catalyst, which catalyzed the synthesis of the prebiotic galacto-oligosaccharides (GOS) in a high yield of 44.7% by using whey (200 g/L) as the substrate. The sugar mixture was further purified by activated charcoal adsorption, thereby yielding a high-purity level of 77.6% GOS.

α-Galacto-oligosaccharides (α-GOSs) have great functions as prebiotics and therapeutics. This work established the method of batch synthesis of α-GOSs by immobilized α-galactosidase for the first time, laying a foundation for industrial applications in the future. The α-galactosidase from Aspergillus niger L63 was immobilized as cross-linked enzyme aggregates (CLEAs) nano-biocatalyst through enzyme precipitating and cross-linking steps without using carriers. Among the tested agents, the ammonium sulfate showed high precipitation efficacy and induced regular structures of α-galactosidase CLEAs (Aga-CLEAs) that had been analyzed by scanning electron microscopy and Fourier-transform infrared spectroscopy. Through optimization by response surface methodology, the ammonium sulfate-induced Aga-CLEAs achieved a high activity recovery of around 90% at 0.55 U/mL of enzymes and 36.43 mM glutaraldehyde with cross-linking for 1.71 h. Aga-CLEAs showed increased thermal stability and organic solvent tolerance. The storage ability was also improved since it maintained 74.5% activity after storing at 4 °C for three months, significantly higher than that of the free enzyme (21.6%). Moreover, Aga-CLEAs exhibited excellent reusability in the α-GOSs synthesis from galactose, retaining above 66% of enzyme activity after 10 batch reactions, with product yields all above 30%.