Proceedings of the Institution of Mechanical Engineers,Part C: Journal of Mechanical Engineering Science

In this paper, an analytical solution of two-dimensional, isothermal, compressible, subsonic and rarefied gas flow in a microchannel with slowly varying cross-section is considered. In order to increase the accuracy of the solution for the slip flow regime as well as to obtain solution for the initial part of the transition regime, the second order boundary condition is applied along with governing system of equations. The analytical solution of the differential equation was achieved by expressing the pressure in terms of the local values of the Knudsen number and the channel height, which enable the separation of variables. Thus, the distribution of pressure and velocity field is obtained indirectly based on the distribution of the local value of the Knudsen number. This approach highlights the significance of the Knudsen number as the main characteristic of the rarefied gas flow. The obtained analytical solution is significant because it allows for the accurate calculation of gas flow through microchannels of variable cross-section and can serve as a benchmark for assessing the accuracy and reliability of numerical and experimental approaches to rarefied gas flow problems in microchannels.

Microscale fluid flow is a critical aspect of various biomedical applications, including lab-on-a-chip devices, microfluidic systems, and biomedical implants. Understanding the behavior of fluids at the microscale is essential for designing and optimizing these devices. However, the complex interactions between fluid flow, channel geometry, and surface properties at the microscale pose significant challenges. This study develops a mathematical model to investigate microscale fluid flow in an inclined microchannel, incorporating slip effects and Newtonian fluids. By simplifying the governing nonlinear equations using low Reynolds number and long wavelength approximations, the research provides an analytical solution to the dimensionless conservation equations. The results are validated using both the Shooting method and the bvp5c solver, ensuring the accuracy and reliability of the findings. The study offers comprehensive insights into various fluid characteristics, including: pressure gradients, velocity profiles, volumetric flow rates, skin friction, and stream function patterns. These were analyzed across a range of parameters, such as inclination angle ( α ), slip parameter ( β ), Froude number ( Fr ), and Reynolds number ( Re ). The inclination angle significantly influences fluid motion, particularly in gravity-driven flows and biomedical devices. Slip effects reduce friction at channel walls, enhancing pumping efficacy and optimizing microfluidic systems. This study provides valuable insights for biomedical applications, including controlled drug delivery, diagnostic devices, and organ-on-a-chip technologies. Additionally, understanding slip effects can improve industrial processes, such as lubricant coatings, heat exchangers, and filtration systems, by minimizing energy losses and optimizing performance.

Squeeze-swirling films are formed during the kiss-point filling phase of wet clutch engagement. These films play a critical role in enhancing torque transmission by enabling smooth engagement, reducing overshoots, improving cooling efficiency and minimising wear. Analytical studies have attempted to calculate the pressure and velocity distributions under these conditions, often relying on simplified assumptions based on the Reynolds equation. However, such assumptions are only valid under specific operating conditions and become inadequate when grooves are introduced into the system. To address these limitations, computational models have been used to solve the Reynolds equation, typically assuming a mixed lubrication regime at the beginning of the engagement, with film thicknesses below 30 µm. This study investigates the flow characteristics of squeeze-swirling films between grooved discs considering a hydrodynamic lubrication regime as the initial condition, using an initial film thickness of 150 µm. The Navier-Stokes equations are coupled with the dynamic force equilibrium equation to capture the transient nature of the process, instead of the quasi-static approaches commonly found in the literature. The results reveal significant differences in flow patterns between grooved and non-grooved regions, offering valuable insights into the filling phase and providing practical guidelines for improving the modelling and understanding of squeeze-swirling lubrication systems.

Reduction in mechanical stimulus due to space weightlessness, ageing and diseases can result in an imbalance between the remodelling processes, eventually leading to bone fracture. Bone reshapes their structure through physiological activities that is, bone modelling and bone remodelling to maintain its integrity and function. In vivo studies have reported that exogenous mechanical loading in the presence of a magnetic field on bone insinuates the remodelling process and enhances the fluid-induced shear stress inside the canaliculus, thus responsible for promoting new bone formation. Therefore, the present study develops a computer model to compute the mechanical loading-induced fluid flow in a complex canalicular channel having irregular wall and cell process in the presence of an exogenous magnetic field. The outcomes of the present study indicate that the loading frequency amplifies the fluid flow and wall shear stress at lower permeability. Moreover, the effect of non-dimensional frequency, Hartmann number and permeability on the fluid motion, shear stress and streamlines are examined. The result of this study encourages the use of an exogenous magnetic field alongside the mechanical loading to accelerate the fluid induced wall shear stress in the case of osteoporosis.

Immiscible fluids play a crucial role in various fluid dynamics applications, particularly in microfluidics, biomedical devices, and industrial transport systems, where their distinct properties enable controlled separation and flow dynamics. The present study investigates the behavior of two immiscible, incompressible fluids flow driven by membrane pumping with different dynamic viscosities in a circular tube. This research uniquely examines how variations in amplitude and diameter of a deformable membrane influence the interfaces of immiscible fluids, flow characteristics, and pumping characteristics providing insights under realistic conditions. Using axisymmetric cylindrical coordinates, the study analyses the impact of membrane deformation modeled through a spatial membrane function, on pressure gradients, velocity profiles, wall shear stress, and interface dynamics between the core and peripheral layers. The governing equations are simplified using the lubrication approximation, enabling a comprehensive numerical investigation via MATLAB. The results revealed that increasing the viscosity ratio reduces the core layer and expands the peripheral layer, shifting the interface downward with greater membrane amplitude and diameter. Higher viscosity ratio and membrane deformation enhance the pressure gradient, shear stress, and flow resistance. These outcomes provide critical insights for optimizing membrane-based systems in microfluidics, biomedical applications, and industrial fluid transport. The enhanced understanding of viscosity and geometric influences on flow dynamics offers a foundation for future studies to investigate non-Newtonian fluids and more complex geometries, paving the way for improved performance in practical applications.

Optimization of wind turbine aerodynamic performances implies solving the problem in the domains such as airfoil selection, blade rotation angle, number of blades, etc. The current article studies the effect of blade rotation angle ( β = 5 , 7 and 10 ° ) at the flow velocity in the wind tunnel ( V W = 5 . 8 ; 8 . 3 and 11 . 5 m s ) and a specific number of revolutions on the horizontal axis wind turbine –HAWT output power. The experiment involved two models of blades. Based on planning the experiment, mathematical models were created to be applied in practice. The highest number of revolutions ( n = 192 RPM ) and generator output ( P = 18 . 8 W ) were achieved at the velocity of V W = 11 . 5 m s

The gear tooth profile significantly influences the key operating parameters of gear pairs. By appropriately modifying the tooth profile, the vibration and noise of the gear system can be greatly reduced. In this study, four advanced optimization techniques are applied to determine the optimal geometric parameters of a cylindrical spur gear. The optimization problem is formulated with three mixed design variables: the profile shift coefficients and the normal pressure angle. The three objectives include minimizing the maximum specific sliding, sliding velocity, and nominal stresses at the pinion tooth root. Kinematic and geometric constraints, such as contact ratio, tooth thickness, and interference, are also considered to ensure an optimal spur gear design. The simulation results demonstrate that the algorithms employed are highly competitive for precision gear design optimization.

The Solid Isotropic Microstructure with Penalization (SIMP) model, a material interpolation model in the variable density method, has been widely applied in structural topology optimization. When combining the Sigmund sensitivity filtering method with the Optimality Criterion (OC) method for solving the SIMP model, numerical instabilities and relatively low optimization performance are often observed. To address these challenges, an improved scheme based on the variable density method is proposed. Firstly, an improved material interpolation model is proposed to overcome the deficiencies of the SIMP model in terms of penalty efficiency and convergence speed. Secondly, an improved sensitivity filtering method based on the Gaussian weight function is proposed, which not only successfully suppresses checkerboards and mesh-dependence but also contributes to a superior filtering effect. Furthermore, a new gray-scale suppression operator is designed to develop a function that suppresses gray-scale elements. This function is subsequently integrated into the iterative formula of the OC method, forming the improved OC method, which is capable of completely eliminating gray-scale elements. Finally, the feasibility and effectiveness of the improved scheme are verified through several typical numerical examples.

Hybrid rigid-flexible mechanisms are very current due to their good characteristics, but due to the complexity of the design process, they are less common than traditional ones, both in practice and in the literature. When designing hybrid mechanisms, the methods developed to design compliant mechanisms are most often practiced, while dimensional synthesis is applied sporadically. Therefore, this paper will focus on the problem of dimensional synthesis of a hybrid four-bar mechanism for open-path generation. The input link of the hybrid mechanism is flexible and represented as a fixed continuum rod of constant curvature. To solve the considered problem, four modern metaheuristic algorithms were applied: DE, MPA, SHADE-WOA and DE-MPA. The analysis of the efficiency of the applied algorithms was performed through four different examples of dimensional synthesis of the hybrid four-bar linkage for open-path generation. Similar to the case of the optimal synthesis of a traditional mechanism with rigid links, the application of metaheuristic algorithms in hybrid mechanisms achieved satisfactory results, which was confirmed by a corresponding comparative analysis.

The hydraulic-controlled blowout preventer ball valve shearing mechanism is a critical tool for cutting operation strings and sealing high-pressure underground oil and gas emissions during emergencies in offshore completion operations. This study aims to address the challenges faced by existing tools in shearing operation strings. First, a finite element numerical model of the ball valve shearing mechanism was established based on the Johnson-Cook model, and its accuracy was validated through shearing experiments. Next, a single-factor analysis was performed on key structural parameters of the ball valve shearing mechanism, including the blade edge rounding radius, valve seat angle, and shearing clearance. Finally, the response surface methodology was applied to determine the optimal structural parameters of the ball valve shearing mechanism. The results showed that the shearing torque of the ball valve shearing mechanism initially decreases and then increases with variations in the blade edge rounding radius, shearing clearance, and valve seat angle. The optimal structural parameters of the ball valve shearing mechanism were determined to be a blade edge rounding radius of 1.89 mm, a valve seat angle of 32.06°, and a shearing clearance of 1.91 mm. Under these conditions, the peak shearing torque obtained from the response surface analysis was 12.68 kN·m, while the peak shearing torque calculated from the finite element numerical model was 13.02 kN·m, with a relative error of 2.62%. Compared to the original design’s peak shearing torque of 16.92 kN·m, this optimization reduced the shearing torque by 22.34%, significantly enhancing the performance of the mechanism.

Unavoidable mechanical uncertainties in engineering structures significantly affect their crash performance. The mechanical uncertainty of Resistance Spot Welds (RSWs) and its effect on structure crashworthiness require a better understanding in vehicle safety and lightweight design. Therefore, this work proposed a feasible multi-objective optimization approach based on Hybrid Response Surface Method (HRSM) to explore the effect of RSWs mechanical uncertainty on B-pillar crashworthiness design. The mechanical uncertainty of RSWs was investigated experimentally and the variation range of RSWs strength under different loading conditions were quantified. Subsequently, a reasonable RSW modeling method and Body-In-White (BIW) subsystem collision simulation approach were demonstrated and validated with experimental results. A HRSM was proposed as surrogate model and the NSGA-III genetic algorithm was employed for multi-objective optimization. A multi-factor analysis based on HRSM was conducted to reveal effects of RSW strength uncertainty on structure crashworthiness design. The performance of HRSM was examined and results show that it can approximate the actual response between inputs and outputs of collision system. Compared with Kriging and Deep Neural Network (DNN), the HRSM can improve computational accuracy while ensuing efficiency. The machine-learning-based HRSM is an alternative for multiobjective optimization and subsequent robustness optimization design for vehicle crashworthiness safety. The numerical modeling method and control mechanisms of RSWs’ mechanical uncertainty on B-pillar crashworthiness can provide reference for BIW safety design.

This research focuses on nonlinear modeling techniques for direct current (DC) motor, with permanent magnets in the stator, using optimized adaptive neuro-fuzzy inference systems (ANFIS). The traditional linear model fails to accurately represent the dynamics of a DC motor due to nonlinear friction effects. To address this limitation, a nonlinear model incorporating Tustin’s friction model is proposed and evaluated against experimental data. Despite improvements over the linear model, challenges remain due to the discontinuity introduced by the signum function in friction representation, necessitating smoother approximations like hyperbolic tangent for control applications. The nonlinear modeling approach also does not fully capture the dynamics of the real-world behavior of the object. To achieve a robust and accurate model across all operational conditions without approximations, three ANFIS variants are developed. These models employ diverse approaches to generate fuzzy rules, such as grid partitioning and fuzzy C-Means clustering. The second and third models undergo optimization using two different nature inspired optimization algorithms. Comparative analysis reveals that all ANFIS models yield superior performance, with GA-ANFIS on top, accurately predicting DC motor velocity under varying input conditions such as step, sinusoidal, and chirp signals. Experimental validation demonstrates that the optimized ANFIS model closely tracks the real-world behavior of the DC motor, offering promising prospects in every type of control, especially in direct inverse control in which the system model is inverted and used as a controller. This approach enables precise control actions based solely on observed system dynamics, avoiding the pitfalls of approximation-based methods.

The ISO 6336 Standard provides widely accepted analytical methods for calculating load distribution factors in helical gears, particularly the face load factor. However, these methods rely on simplifications that may not accurately capture real-world operating conditions, potentially leading to non-conservative results. This study critically assesses the ISO 6336 Standard approach by comparing its predictions to those obtained from an advanced finite element model (FEM) of a helical gear transmission, which incorporates a complete gear-shaft-support system. The numerical results reveal that the methods in ISO 6336 Standard systematically overestimate the face load factor in most cases, though its predictions remain close to FEM calculations for certain configurations. Additionally, the study highlights the influence of helix angle direction and power input/output configuration on load distribution, factors not explicitly considered in the standard. The findings suggest potential refinements to the ISO 6336 Standard to improve its accuracy in engineering applications.

The use of polymer gears is increasingly becoming popular due to their lightweight, low noise, and low manufacturing cost. However, wear is a critical issue affecting their durability and reliability. This study aims to investigate the wear behavior of asymmetric polymer gears using experimental and numerical methods. The experiments involve conducting wear tests under varying load, speed, and temperature conditions. The numerical method involved an explicit dynamic algorithm to simulate the gear contact and wear behavior. In the current approach of the dynamic contact of gears, the contact forces generated are highly non-linear and time dependent in nature. Also, stress concentration is observed only at the point/line of contact, which accelerates the wear rate. Hence, in order to effectively capture these phenomena, explicit dynamic analysis is best suited for capturing the wear behavior of gear pairs under a given operating domain. While Implicit methods are best suited for static analysis where the response of the system is not time dependent. The simulation model is validated using experimental data, and the wear behavior is analyzed using wear rate, contact pressure, and contact stress. The weight loss percentage method has been used to analyze the wear amount on the gears. The results show that the wear rate increases with increasing load and speed, while decreasing with increasing temperature. A temperature rise of 4°C–5°C has been observed for a running time of 6 h. Thus, temperature rise may not lead to a major wear in Nylon 6 gears. The numerical results show good agreement with the experimental data, with around 5% variation, indicating that finite element analysis can be a reliable method for predicting the wear behavior of polymer gears.

This research work presents a methodology for the determination of the required manufacturing accuracy of custom, high-pressure angle gears. The gears examined throughout the present work are constructed using involute segments beyond the 25° limit specified in the ISO/TC 60/SC 2 and custom root filet geometries produced with the employment of fourth order Bezier curves. Due to the existence of extensive undercuts in the root region, production of these geometries cannot be practically achieved by conventional machining, for example, hobbing; therefore, production methods such as additive manufacturing or powder metallurgy are required. The root geometry incorporating the fourth order Bezier curves is optimized and described in closed form in terms of the coordinates of the control points. In the context of this study finite element analyses are performed to determine the sensitivity of strength (maximum principal stresses) and functional characteristics (static transmission error—STE) on the surface profile deviations focusing on the root area. Tolerancing of the tooth profile is performed as per ISO 1660:2017, by specifying an unequally disposed tolerance zone with an offset that takes into account the maximum material condition of the theoretically exact feature (TEF) in order to avoid interference at zero backlash nominal tooth geometries and considering nominal center distances. The surface profile tolerance values are calculated using appropriate thresholds for the strength and STE values and can be used as design guidelines for both the production and quality inspection of the gear geometries presented herein. The presented methodology can be applied to any gear pair regardless of the root or flank geometry used. The case studies shown in this work demonstrate very small STE variations (in the order of 5%) for a 10% increase of the resulting maximum principal stress at the tooth root area. At the same time, the asymmetric tolerance zone for the same stress increase threshold is calculated in the order of 0.1 times the normal module.

The present work dwells with the dynamic modeling of high-pressure angle spur gears ranging from 30 to 35 degrees. The benefits and potential of such gears in terms of dynamic performance is explored. A custom optimized spur gear tooth root geometry is used to construct the root area of the case studies presented and compared versus standardized ISO geometries. An extension of the closed-form load and position-dependent mesh stiffness previously developed by the authors is introduced to accommodate the hereby studied non-standard gear geometries. The non-linear load and position-dependent mesh stiffness is formulated in closed form using a hybrid polynomial/ logarithmic approximation and validated versus finite element results. The non-implicit single degree of freedom (DOF) dynamic model employed is discussed in detail and manages to successfully predict the dynamic transmission error of a gear pair as well as meshing nonlinearities including contact reversal and loss of contact. We present an extensive comparison of the dynamic behavior between standard 20-degre and high-pressure angle gears, for a wide range of rotational speed and transmitted torque values. A colormap with the peak-to-peak transmission error values indicates significant regions of gear operation where high-pressure angle geometries result to a favorable dynamic response. We further examine the transmission error response limit cycle by comparing phase diagrams of different geometries under specific rotational speed and torque conditions. Clear improvement of the transmission error values is demonstrated for the majority of the tested scenarios suggesting increased performance of high pressure angle gears versus conventional geometries.

One-and-a-half-stage counter-rotating turbines (CRTs) consist of one stator and two rotors; the blade rows rotate in opposite directions. The aerodynamic design process typically involves primary aerodynamic design, throughflow design, and three-dimensional geometry optimization. However, the process lacks an inversion model for propagating information in the opposite direction—from the throughflow design results back to the primary aerodynamic parameters, which is important for improving the accuracy of selecting the primary design parameters. This paper proposes a mathematical model based on Euler’s equation and the first law of thermodynamics, which establishes a connection between the primary design and throughflow design steps. This linkage enables reverse iteration from the throughflow design back to the primary aerodynamic design step to correct the primary design parameters, such as blade load coefficient, degree of reaction, and other input parameters of the throughflow design. The model was validated by using Reynolds-averaged Navier-Stokes (RANS) equations simulations with the Spalart-Allmaras (S-A) one-equation turbulence model, demonstrating a relative error ranging from 0.36% to 4.86%.

Skew plates have wide applications across various industries. Consequently, their mechanical behavior has attracted considerable attention from researchers. However, most prior studies on the vibration characteristics of these plates have predominantly focused on thin plates with gradual material property variations along the thickness direction, while the investigation of thick skew plates and the effects of porosity remain limited. This study examines the free vibration response of thick functionally graded porous skew plates resting on an elastic foundation. The governing equations of motion are initially formulated within the framework of three-dimensional elasticity theory using Cartesian coordinates and subsequently transformed into oblique coordinates via an appropriate coordinate transformation. The differential quadrature method is employed to discretize the resulting equations and assemble the necessary matrices. Modal analysis is conducted to extract the natural frequencies, which are validated against existing cases reported in the literature. The influence of gradual material property gradients along the three spatial directions, elastic foundation stiffness, plate thickness, porosity parameters, skew angle, and boundary conditions on the natural frequencies is investigated. The results provide valuable insights for optimizing the design of such plates to achieve desired natural frequency characteristics under operational conditions.

Metro trains are a type of electrical multiple unit (EMU) that obtain energy through electrical contact between the pantograph strip and the contact wire. When a metro train arrives at a station or temporarily halts on the track, the catenary system must maintain the supply of electrical current to support for essential functions such as air conditioning, illumination, door operation, braking, startup, and other onboard devices. However, due to the presence of contact resistance, concentrated Joule heating is generated the interface of the pantograph-catenary system when electrical current flows through it. This static contact condition can lead to overheating, which may result in thermal damage to the pantograph strip and potentially cause wire breakage accidents. Therefore, investigating the temperature rise at the pantograph-catenary contact when the train halts is crucial. The characteristics of the contact force, contact resistance, and thermal conductivity within the pantograph-catenary system indicate that this contact represents a complex interaction involving thermal, mechanical, and electrical behaviors. Consequently, a multi-field coupled model is required. In this study, a three-dimensional finite element model that incorporates the thermal-mechanical-electrical interactions of the pantograph-catenary contact is proposed. Based on this model, simulations of the temperature rise during static contact between the pantograph strip and the contact wire is simulated to examine, examining the effects of contact force, contact resistance, thermal conductivity, and the wear condition of the contact wire. The model and analytical results presented in this paper provide valuable insights for the parameter design and optimization of the pantograph-catenary system.