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The misaligned condition in splines coupling brings more relative motion between the engaging tooth surface and subsequently a rise of wear phenomenon. The sliding friction between the spline surfaces and initial gap between the teeth are the key roles in wear behaviour in both crowned and straight splines. The paper aims to discuss these issues.

There is a design constraint to include fretting and wear damage of spline surface in design criteria. It becomes very essential to use a finite element tool to evaluate the wear behaviour of spline surface in order to design for severe environmental conditions. The fretting fatigue and fretting wear damage mechanisms on the spline surfaces are mainly dependent on the forces between the spline surfaces and relative movement between the teeth. This study focusses on the effect of sliding friction coefficients on the wear damage of the spline surfaces based on mating condition.

Analysis shows that the contact pressure and root stress increase with increasing friction coefficient and misalignment. This is irrelevant to the crowned type of splines. This case becomes worst when the spline has more misaligned condition.

The fretting wear damage of straight spline is essential criterial for the application in aero engines and the crowned spline under controlled misaligned condition provides better wear life compared to straight spline surfaces.

The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, and (iii) for the restricted models option Δ is preferred over the more often used strike relative to spot price as measure for moneyness.

During the operation of a wet clutch, there are fluctuations in speed and torque, which have an impact on the stability of the clutch and the strength of the friction plate and the spline pair of the dual steel plate. The purpose of this study is to investigate the vibration characteristics of the wet clutch and the dynamic load characteristics of the spline pairs.

The spline pair model is established by the piecewise linear function method, and on this basis, dynamic equations considering the spline pair of dual steel plates and friction plates are established. Considering that the wet clutch has multiple spline pairs, an equivalent model of the number of teeth and the equivalent model of the tooth width were proposed, and the Runge-Kutta numerical method was used for the wet clutch for these two models.

The research results show that the equal tooth number model has greater meshing stiffness and smaller fluctuation than the constant tooth width model, which shows that increasing the meshing stiffness of the system is beneficial to reduce system fluctuation and improve system stability.

The friction plate has the system that multiple splines are independent of each other, which is relatively complicated. Therefore, an equivalent calculation is performed on multiple pairs of steel plates (friction plates) to simplify the calculation of the spline pairs.

This paper provides a theoretical basis for further dynamic characteristics analysis of wet clutch and reducing fluctuation of speed and torque.

Dynamic equation considering the spline pair of the dual steel plates and the friction plates is established to study the vibration characteristics of the wet clutch and the dynamic load characteristics of the spline pair, etc.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2023-0078/

The purpose of this paper is to propose a smooth double-spline interpolation method for six-degree-of-freedom rotational robot manipulators, achieving the global C2 continuity of the robot trajectory.

This paper presents a smooth double-spline interpolation method, achieving the global C2 continuity of the robot trajectory. The tool center positions and quaternion orientations are first fitted by a cubic B-spline curve and a quartic-polynomial-based quaternion spline curve, respectively. Then, a parameter synchronization model is proposed to realize the synchronous and smooth movement of the robot along the double spline curves. Finally, an extra u-s function is used to record the relationship between the B-spline parameter and its arc length parameter, which may reduce the feed rate fluctuation in interpolation. The seven segments jerk-limited feed rate profile is used to generate motion commands for algorithm validation.

The simulation and experimental results demonstrate that the proposed method is effective and can generate the global C2-continuity robot trajectory.

The main contributions of this paper are as follows: guarantee the C2 continuity of the position path and quaternion orientation path simultaneously; provide a parameter synchronization model to realize the synchronous and smooth movement of the robot along the double spline curves; and add an extra u-s function to realize arc length parameterization of the B-spline path, which may reduce the feed rate fluctuation in interpolation.

The purpose of this paper is to analyse how London Interbank Offered Rate Index (LIBOR) and the spread between LIBOR and the base rate of interest as set by the Bank of England (BoE) influences the variation in house prices in the UK.

This paper uses monthly data over a long time series, since 1986, to investigate the relationships between house price and LIBOR. Data are drawn from several different sources to include housing, financial and macro-economic variables. The time series is sub-divided into a series of splines based on stages in the economic and property market cycle. Both value-based and percentage change models are developed.

The results show that BoE base/LIBOR margin variable has a strong positive and significant effect on house price; however, the percentage change model infers a weaker and inverse relationship. The spline analysis re-emphasised the significance of the BoE base/LIBOR margin variable. Where variation between base rates and LIBOR is reduced, a significant positive effect can be observed in the average house price; however, where significant variation exists, the BoE base/LIBOR margin has little effect and LIBOR itself becomes a significant driver.

The results highlight that the predictive qualities of the BoE base/LIBOR margin, as the contribution of this margin to the explanation of house price, exceeds both the base rate and LIBOR variables individually. Also highlighted is the contribution of unemployment to the explanation of house price. In both the value and percentage change models, unemployment is shown as a negative and highly significant contributor.

Previous papers have demonstrated the important linkage between house price and interest rates, the originality in this paper lies in examining the impact of LIBOR and the spreads between LIBOR and base rate as key variables influencing variation in UK house prices.

We have developed in this paper a morphological disambiguation hybrid system for the Arabic language that identifies the stem, lemma and root of a given sentence words. Following an out-of-context analysis performed by the morphological analyser Alkhalil Morpho Sys, the system first identifies all the potential tags of each word of the sentence. Then, a disambiguation phase is carried out to choose for each word the right solution among those obtained during the first phase. This problem has been solved by equating the disambiguation issue with a surface optimization problem of spline functions. Tests have shown the interest of this approach and the superiority of its performances compared to those of the state of the art.

T-spline is the latest powerful modeling tool in the field of computer-aided design. It has all the merits of non-uniform rational B-spline (NURBS) whilst resolving some flaws in it. This work applies T-spline surfaces to additive manufacturing (AM). Most current AM products are based on Stereolithograph models. It is a kind of discrete polyhedron model with huge amounts of data and some inherent defects. T-spline offers a better choice for the design and manufacture of complex models.

In this paper, a direct slicing algorithm of T-spline surfaces for AM is proposed. Initially, a T-spline surface is designed in commercial software and saved as a T-spline mesh file. Then, a numerical method is used to directly calculate all the slicing points on the surface. To achieve higher manufacturing efficiency, an adaptive slicing algorithm is applied according to the geometrical properties of the T-spline surface.

Experimental results indicate that this algorithm is effective and reliable. The quality of AM can be enhanced at both the designing and slicing stages.

The T-spline and direct slicing algorithm discussed here will be a powerful supplement to current technologies in AM.

This paper aims to propose a new boundary condition and a web-spline basis of finite element space approximation to remedy the problems of constraints due to homogeneous and non-homogeneous; Dirichlet boundary conditions. This paper considered the two-dimensional linear elasticity equation of Navier–Lamé with the condition CAB. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained; without using a numerical method as Lagrange multiplier. This study have developed mixed finite element; method using the B-splines Web-spline space. These provide an exact implementation of the homogeneous; Dirichlet boundary conditions, which removes the constraints caused by the standard; conditions. This paper showed the existence and the uniqueness of the weak solution, as well as the convergence of the numerical solution for the quadratic case are proved. The weighted extended B-spline; approach have become a much more workmanlike solution.

In this paper, this study used the implementation of weighted finite element methods to solve the Navier–Lamé system with a new boundary condition CA, B (Koubaiti et al., 2020), that generalises the well-known basis, especially the Dirichlet and the Neumann conditions. The novel proposed boundary condition permits to use a single Matlab code, which summarises all kind of boundary conditions encountered in the system. By using this model is possible to save time and programming recourses while reap several programs in a single directory.

The results have shown that the Web-spline-based quadratic-linear finite elements satisfy the inf–sup condition, which is necessary for existence and uniqueness of the solution. It was demonstrated by the existence of the discrete solution. A full convergence was established using the numerical solution for the quadratic case. Due to limited regularity of the Navier–Lamé problem, it will not change by increasing the degree of the Web-spline. The computed relative errors and their rates indicate that they are of order 1/H. Thus, it was provided their theoretical validity for the numerical solution stability. The advantage of this problem that uses the CA, B boundary condition is associated to reduce Matlab programming complexity.

The mixed finite element method is a robust technique to solve difficult challenges from engineering and physical sciences using the partial differential equations. Some of the important applications include structural mechanics, fluid flow, thermodynamics and electromagnetic fields (Zienkiewicz and Taylor, 2000) that are mainly based on the approximation of Lagrange. However, this type of approximation has experienced a great restriction in the level of domain modelling, especially in the case of complicated boundaries such as that in the form of curvilinear graphs. Recently, the research community tried to develop a new way of approximation based on the so-called B-spline that seems to have superior results in solving the engineering problems.

Majority of the existing direct slicing methods have generated precise slicing contours from different surface representations, they do not carry any interior information. Whereas, heterogeneous solids are highly preferable for designing and manufacturing sophisticated models. To directly slice heterogeneous solids for additive manufacturing (AM), this study aims to present an algorithm using octree-based subdivision and trivariate T-splines.

This paper presents a direct slicing algorithm for heterogeneous solids using T-splines, which can be applied to AM based on the fused deposition modeling (FDM) technology. First, trivariate T-splines are constructed using a harmonic field with the gradient direction aligning with the slicing direction. An octree-based subdivision algorithm is then used to directly generate the sliced layers with heterogeneous materials. For FDM-based AM applications, the heterogeneous materials of each sliced layer are discretized into a finite number of partitions. Finally, boundary contours of each separated partition are extracted and paired according to the rules of CuraEngine to generate the scan path for FDM machines equipped with multi-nozzles.

The experimental results demonstrate that the proposed algorithm is effective and reliable, especially for solid objects with multiple materials, which could maintain the model integrity throughout the process from the original representation to the final product in AM.

Directly slicing heterogeneous solid using trivariate T-splines will be a powerful supplement to current technologies in AM.

The purpose of this paper is to present a new approach of meshless local B-spline based finite difference (FD) method for solving two dimensional transient heat conduction problems.

In the present method, any governing equations are discretized by B-spline approximation which is implemented in the spirit of FD technique using a local B-spline collocation scheme. The key aspect of the method is that any derivative is stated as neighbouring nodal values based on B-spline interpolants. The set of neighbouring nodes are allowed to be randomly distributed thus enhanced flexibility in the numerical simulation can be obtained. The method requires no mesh connectivity at all for either field variable approximation or integration. Time integration is performed by using the Crank-Nicolson implicit time stepping technique.

Several heat conduction problems in complex domains which represent for extended surfaces in industrial applications are examined to demonstrate the effectiveness of the present approach. Comparison of the obtained results with solutions from other numerical method available in literature is given. Excellent agreement with reference numerical method has been found.

The method is presented for 2D problems. Nevertheless, it would be also applicable for 3D problems.

A transient two dimensional heat conduction in complex domains which represent for extended surfaces in industrial applications is presented.

The presented new meshless local method is simple and accurate, while it is also suitable for analysis in domains of arbitrary geometries.