Quasi-static modelling of non-conjugate contact of tooth-modified spur and helical gears has been studied at length, but existing models are hindered by convergence problems and require a brute-force numerical approach. Here, a novel, computationally efficient, and stable and unconditionally convergent model is developed for non-conjugate tooth contact in three dimensions and applied to crowned spur and helical gears to assess parametrically the sensitivity of various in- and out-of-plane misalignments on the path of contact, transmission error, and contact pressure. Performance metrics are defined, and comparisons are made between three different crowning modification functions.

Coaxial magnetic gears have piqued the interest of researchers due to their numerous benefits over mechanical gears. These include reduced noise and vibration, enhanced efficiency, lower maintenance costs, and improved backdrivability. However, their adoption in industry has been limited by drawbacks like lower torque density and slippage at high torque levels. This work presents an analytical 2D model to compute the magnetic potential in Halbach array coaxial magnetic gears for every rotational angle, geometry configuration, and magnet specifications. This model calculates the induced torques and torque ripple in both rotors using the Maxwell Stress Tensor. The results were confirmed through Finite Element Analysis (FEA). Unlike FEA, this analytical model directly produces harmonics values, leading to faster computational times as it avoids torque calculations at each time step. In a case study, a standard coaxial magnetic gear was compared to one with a Halbach array, revealing a 14.3% improvement in torque density and a minor reduction in harmonics that cause torque ripple. Additionally, a case study was conducted to examine slippage in both standard and Halbach array gears during transient operations. The Halbach array coaxial magnetic gear demonstrated a 13.5% lower transmission error than its standard counterpart.

Involute gears have traditionally been the preferred choice for gear transmission systems due to their simplicity and interchangeability. However, there are applications where they do not provide the most durable and efficient solution. While the cost of implementing optimized non-involute gears in most applications often outweighs their comparative advantages, the advent of additive manufacturing has opened up possibilities for designers to explore alternative gear tooth profiles. This is particularly relevant in the realm of plastic gears, where optimized non-involute gears produced through 3D printing can address their primary drawbacks, such as surface durability and wear resistance. In this study, a comprehensive free-form optimization process was conducted to determine the optimal tooth profile that minimizes wear on 3D printed spur gears during operation. The tooth flank geometry was represented using a 4th order B-spline curve, and a genetic algorithm was employed to determine the optimum positions of the control points aiming to minimize wear depth across the tooth flanks. The spur gears were manufactured using Fused Deposition Modeling (FDM) with PLA material. The parameters of the additive manufacturing process were experimentally fine-tuned to achieve the best possible accuracy. To evaluate the performance of the optimized free-form gears, two case studies were implemented, demonstrating that the optimized gears achieved a remarkable reduction of average wear depth by more than 50% and a reduction of maximum wear depth by more than 69% compared to standard involute gears. To further validate the effectiveness of the optimization method, experiments were carried out using an FZG test rig. The profiles of the tooth flanks were measured on a Coordinate Measuring Machine (CMM) before and after the experiments to compare the wear depth against the standard involute gears. The results revealed a significant improvement in the wear resistance of the tooth flanks, with a reduction of wear depth of 44.1%.

Although steel involute gears are the standard solution for gear transmissions, they tend to suffer from poor pitting resistance. Pitting typically occurs when the gear tooth flanks have high equivalent curvature at the contact point and/or when the equivalent curvature is not constant across the contact path leading to high contact pressures and the development of surface fatigue. In this paper a new optimization method is presented to produce spur gear tooth flanks with improved pitting performance compared to involute ones. The tooth flanks are represented as B-spline curves, the control points of which are the variables for the optimization problem. The constraints were designed to ensure that all the examined profiles satisfy the law of gearing and do not contain any cusps or C¹ discontinuities. Deterministic and stochastic algorithms were implemented and both closed and open path of contact gear sets were examined to determine the optimum tooth profile. The optimization results show that the maximum equivalent curvature of the optimum profiles is reduced by 83% compared to the corresponding standard profiles, while the deviation from the mean value is reduced by 98%. Both the standard and the optimized gears where examined comparatively also through finite element analysis. For the case selected the maximum contact pressure developed on the optimized gear set was 77% of the respective maximum contact pressure on the standard gear set whereas the corresponding deviation from the mean value was 5%. At the same time, the bending stresses developed in the optimized gear are slightly lower than those in the standard one.

This work presents an analytical 2D model for estimating eddy current losses in the permanent magnets (PMs) of a coaxial magnetic gear (CMG), with a focus on loss minimization through magnet segmentation. The model is applied under various operating conditions, including different rotational speeds, load levels, and segmentation configurations, to derive empirical expressions for eddy current losses in both the inner and outer rotors. A 1D lumped-parameter thermal model is then used to predict the steady-state temperature of the PMs, incorporating empirical correlations for the thermal convection coefficient. Both models are validated against finite element analysis (FEA) simulations. The analytical eddy current loss model exhibits excellent agreement, with a maximum error of 2%, while the thermal model shows good consistency, with a maximum temperature deviation of 5%. The results confirm that eddy current losses increase with rotational speed but can be significantly reduced through magnet segmentation. However, achieving an acceptable thermal performance at high speeds may require a large number of segments, particularly in the outer rotor, which could influence the manufacturing cost and complexity. The proposed models offer a fast and accurate tool for the design and thermal analysis of CMGs, enabling early-stage optimization with minimal computational effort.

Background: Optimal porosity and surface area of additively manufactured Ti-6Al-4V scaffolds for early human mesenchymal stem cell (hMSC) retention remain unclear, despite their importance in reconstruction of critical-sized bone defects. This study evaluated scaffold architectures fulfilling biomechanical criteria for hMSC and osteocyte survival, proliferation, differentiation, cell cycle, and retention. Methods: Primary hMSCs from four healthy donors were characterized by flow cytometry, immunofluorescence, and Western blotting. Cells were seeded onto Ti-6Al-4V scaffolds with graded porosity (P50–P90, 50–90% porosity) and cultured for 120 h. Viability and retention were measured by trypan blue exclusion, apoptosis and cell cycle by flow cytometry, and osteogenic differentiation by collagen I, osteocalcin, and Akt phosphorylation analyses. Collagen-embedded hMSCs and osteoblasts were used to assess migration and phenotype maintenance. Results: The densest scaffold, P50, consistently retained significantly more viable hMSCs and differentiated osteoblasts than P60 and P70 (p < 0.005 in both cases, One-way ANOVA analysis, significance level a = 0.05 followed by Bonferroni correction). Among the scaffold architectures investigated, P50 demonstrated the most favorable early cellular retention under the present experimental conditions. No scaffold-induced apoptosis or proliferation changes were detected. Osteogenic differentiation and Akt phosphorylation increased during culture. In collagen-containing scaffolds, cells migrated from the matrix and preferentially coated titanium struts, with P50 supporting superior attachment. Conclusions: Among the scaffold architectures investigated, the low-porosity/high-surface-area P50 design provided the most favorable early microenvironment for hMSC and osteoblast retention without cytotoxic effects.