Δημοσιεύσεις

A two DOF simulation of meshing in spur gear sets with modelling of the effect of individual tooth mass

Nikolaos Komitopoulos and Christos Vakouftsis

Abstract:

A Two-Degree Of Freedom analytical model of meshing in a single-stage spur gear set was developed and used for time-domain dynamic simulation. Apart from the time-varying tooth stiffness, the individual tooth mass, reduced to the meshing point, was also taken into consideration and modeled. The simulations that were performed by means of MatLab software using numerical methods highlight the effect of the individual tooth mass in the dynamic response of the gear stage.

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Benefits of crimped and prestressed CFRP’s over noncrimped fibres as reinforcement in machine elements.

Ioannis Kanellopoulos, Ioannis Vasileiou and Ioannis Kitsos

Abstract:

In this paper, a representative volume element consisted of a single wavy carbon fibre engulfed in a thermoplastic rectangular matrix is studied in order to examine the effect ofnon-crimpedcarbon fibre, and specifically its waviness, at the mechanical behavior. In order to quantify these influences and their nonlinear elastic behavior, a plane strain analysis of this model was simulated with finite elements.

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Sensitivity analysis of tip-thickness and slope on the tip strength of spur gear sets

Ioannis Kitsos, Ioannis Kanellopoulos and Ioannis Vasileiou

Abstract:

For gears working on a specific rotational direction it is possible to change coast side’s profile in order to increase strength on the root of the tooth. It is easily appreciated that increasing root’s thickness would result in increased strength for tooth’s root, but it would also result in decreased tip thickness. A highly decreased tip thickness would deteriorate the overall strength of the tooth. In this paper, in order to define the acceptable limits for tip thickness, a straight line approximation with variable slope was used as coast side tooth profile in order to cover a wide range of values as a first estimate.

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Two parametric parallel strand cables modelling of a socket-type termination for high tenacity

Christos Vakouftsis and Nikolaos Komitopoulos

Abstract:

The present study concerns the shape optimization of a socket-type cable termination, in order to define the optimum geometry which leads into a linearly decreasing axial stress along the cable. The goal of this paper is to prove that it is possible to create a single material termination which obtains the aforementioned distribution of stresses due to its geometry and at the same time eliminates the stress concentration effect at the cable entry. The importance of the casing’s geometry and its impact on the distribution of the stresses is revealed in the analysis of casings different geometry. An axisymmetric model with two design parameters was developed and analyzed.

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A three-point electrical potential difference method for in situ monitoring of propagating mixed-mode cracks at high temperature

V. Spitas,C. Spitas,P. Michelis

Abstract:

In this paper an electrical potential difference method for the real-time assessment of both the length and the direction of Mode II cracks is presented. Three measuring electrodes are placed in selected positions over the gauge area of a specially designed shear specimen and their readings are associated with the actual position of the crack tip using Finite Element Analysis (FEA). This information can be processed in real-time to provide continuous monitoring of the crack as it propagates either in pure Mode II (in-plane shear) or mixed Mode I (tension) and Mode II if the inclination of the crack exceeds 20°. In fatigue testing it is possible to produce dα/dN-ΔK_II (in pure-shear) and dα/dN-ΔK_I (in mixed-mode) plots on-line as the test is in execution. The method has been calibrated with optical measurements using a long-distance observation microscope on the nickel-based superalloy CMSX4 at high temperature. The main finding was that the central two sensing electrodes were sensitive to the length of the crack and insensitive to the crack angle, whereas the readings from the third electrode were sensitive to the crack angle and thus the exact position of the crack tip could be traced in real-time. Special techniques were implemented to rule-out thermoelectric effects and thermal stresses on the specimen.

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Effect of the stochastic nature of the constituents parameters on the predictability of the elastic properties of fibrous nano-composites

M.M.S. Dwaikat,C. Spitas,V. Spitas

Abstract:

The stochastic nature and the variability of the constituents of nano-composites materials affect the predictability of their properties. The few studies that dealt with the probabilistic nature of the micromechanics of fibrous nano-composites, focused on the effect of statistical variation of individual parameters. This study presents a systematic analysis of the influence of parameter randomness on the theoretical predictions of the elastic properties of nano-composites. To this end, Monte-Carlo simulations are performed using a modified version of the Mori–Tanaka Mean-Field theory under different combinations of parameter randomness. The results indicate that the randomness in interface imperfection, fibre orientation and length, and fibre stiffness have a significant influence on the variability of the composite properties. The analysis provided an insight into the sensitivity of the predictions of the elastic tensor to the probabilistic variations of the aforementioned parameters. A probabilistic model for the effective properties is called for in place of deterministic models.

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Predicting nonlinear stress–strain curves of unidirectional fibrous composites in consideration of stick–slip

M.M.S. Dwaikat,C. Spitas,V. Spitas

Abstract:

A simple and efficient methodology is developed for computing nonlinear stress–strain curve of unidirectional fibrous nano-composites loaded in the direction of the perfectly aligned fibers. The method, based on shear lag analysis and derived from basic principles of continuum micromechanics, incorporates shear stick–slip constitutive law at the fiber–matrix interface. The matrix is modeled as elastic–plastic with linear isotropic strain hardening. The approach thus predicts the nonlinear behavior of the composite stress–strain curve due to both interfacial shear slippage of reinforcement fibers within the matrix and due to spread of plasticity within the matrix. The proposed method is compared to experimental results on aligned fibrous nano-composites and very good agreement is obtained when low values of interfacial shear strength are used. The study shows that when the interfacial bond between the matrix and the fiber is strong, higher stress concentration leads to spread of plasticity in the composite at lower bulk strains. However, when the bond is weak, interfacial slippage causes a relief in the accumulation of stress in the matrix. Both factors seem to provide reasonable explanation for the observed nonlinearity and improved stiffness of the composite. A set of parametric studies is also performed and the proposed method is compared to existing models.

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Stochastic simulation of the power requirements of dry clinker pulverisation

V. Spitas,C. Spitas

Abstract:

Portland cement is obtained through mixing of gypsum with an intermediate product of the cement production line called ‘clinker’. This material is produced in the form of large nodules (lumps) and has to be pulverised in order to be suitable for mixing. In order to boost productivity by cutting down the excessive time needed for its pulverisation, fine grinding is preceded by dry grinding in a single stage roller press, which produces clinker wafers. In this paper the time-dependant torque and power requirements of such a press are calculated using stochastic simulation of the grinding process based on experimentally obtained clinker grain data from uniaxial compression tests. The methodology can be easily expanded to include other granular materials in similar fixed-geometry grinding systems.

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A model for elastic hysteresis of unidirectional fibrous nano composites incorporating stick-slip

M.M.S. Dwaikat,C. Spitas,V. Spitas

Abstract:

In fibrous nano-composites, slip of fillers within the matrix comprises a major mechanism through which energy is dissipated. In the current study, a simplified model for predicting the elastic hysteresis of perfectly aligned unidirectional nano-composites loaded in the direction of the fibers is developed. The model, based on shear lag analysis and derived from basic principles of continuum micromechanics, incorporates a shear stick-slip constitutive law at the matrix–fiber interface. Once calibrated by comparison to cyclic stress–strain curves on nano-composites, the model is used to conduct a set of parametric studies on the influence of various parameters on the energy dissipation. Simulation results reveal that the interfacial shear stick-slip constitutive law, the volume fraction andthe aspect ratio of the fibers, and the fiber-to-matrix stiffness ratio have a direct influence on the hysteresis of nano-composites. Also, it is demonstrated that it is possible to achieve an optimal set of parameters for which energy dissipation due to hysteresis is maximized. The proposed model provides a numerically efficient yet reasonably accurate alternative for use in design and analysis of fibrous composites when compared to existing complex models.

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Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations

C. Spitas,V. Spitas

Abstract:

Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.

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Numerical and experimental analysis of a triangular auxetic core made of CFR-PEEK using the Directionally Reinforced Integrated Single-yarn (DIRIS) architecture

Paul Michelis,Vasilios Spitas

Abstract:

The Directionally Reinforced Integrated Single-yarn (DIRIS) architecture is a novel, patented concept of creating directionally reinforced high-strength cores for sandwich panels developed at the Institute of Mechanics of Materials and Geostructures S.A. This technology using glass or carbon fibre-reinforced PEEK has been so far implemented on high-strength honeycomb cores of triangular isogrid geometry with impressive results in all constitutive parameters both in-plane and out-of-plane. In this paper the application of the DIRIS technology on creating high-strength auxetic triangular cores is presented. The mechanical behaviour of the resulting core and panel was numerically investigated using FEA and testing on manufactured prototypes confirmed the high strength of the proposed design. In fact the shear modulus of the DIRIS auxetic cores was found superior to that of existing mass-produced honeycomb cores despite the inherent complexity of the geometrical configuration and the non-standardized manufacturing method.

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Reduction of gear fillet stresses by using one-sided involute asymmetric teeth

Th. Costopoulos,V. Spitas

Abstract:

For increasing the load carrying capacity of geared power transmissions several tooth designs alternative to the standard involute have been proposed. The use of non-involute teeth has a number of disadvantages and for this reason asymmetric involute-type teeth have been studied as a promising alternative. In this paper the idea of one-sided involute asymmetric spur gear teeth is introduced to increase load carrying capacity and combine the good meshing properties of the driving involute and the increased strength of non-involute curves. These novel teeth are intended for constant direction of rotation although they can be used in a limited way for reverse rotation. Both flanks are fully generated by a hob, the design of which is also investigated. The increase in load carrying capacity can reach up to 28% compared to the standard 20° involute teeth.

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Direct analytical solution of a modified form of the meshing equations in two dimensions for non-conjugate gear contact

C. Spitas,V. Spitas

Abstract:

The current technological state-of-the-art utilises modified gear profiles, which are in part non-conjugate and therefore cannot be analysed using standard conjugate contact theory. Existing non-conjugate mathematical models require the solution of a system of implicit equations, typically with significant computational effort and need for careful monitoring of solution stability, convergence and selection of initial values. This paper derives a modified form for the fundamental gear meshing equations, which are reduced analytically to a single scalar equation, resulting in improved solution speed and stability. The solution is verified in benchmark tests using real gear geometries.

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Numerical and experimental comparative study of strength-optimised AGMA and FZG spur gears

V. Spitas,C. Spitas

Abstract:

In standard gear pairs there is typically a discrepancy between the bending strength of the pinion and the wheel, with the pinion being the weakest. Smaller pinion tooth numbers, typical of automotive gearing, further increase this problem and different optimised design solutions, based on long addendum modifications, have been proposed by the American Gear Manufacturers Association (AGMA) and the German organisation for gear research Forschungsstelle für Zahnräder und Getriebebau (FZG). AGMA favours a compromise between the strength of the pinion and the wheel (balanced bending strength), while FZG strengthens both pinion and wheel using bigger addendum modifications and a correspondingly bigger centre distance (maximum bending strength with balanced sliding velocities). A comprehensive comparison of the two methods does not exist in the literature because the shifting employed by the FZG recommendation exceeds the normal tabulated J-factor ranges and, because of the large number of design variables involved (i.e., number of teeth, pinion and wheel shift etc.). This paper uses non-dimensional modelling to decrease the number of independent design variables in conjunction with Boundary Element Analysis and photoelasticity measurements to compare the bending strength of all AGMA and FZG designs in the region of their intended use.

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Optimizing involute gear design for maximum bending strength and equivalent pitting resistance

V Spitas,C Spitas

Abstract:

Standard involute gear designs dominate high-power transmission applications because they combine sufficient bending strength with high pitting resistance, while retaining an adequate contact ratio. In this paper, a non-standard, optimal alternative involute gear design has been presented, which has the same pitting resistance as the standard involute gears but exhibits maximum resistance to bending. The optimization procedure is based on the complex algorithm, where the root stress, as calculated through tabulated boundary element analysis values, is the objective function and the active constraints include all of the kinematical, manufacturing and geometrical conditions, which must be satisfied by the optimal design, including the pitting resistance. The results indicate that optimal designs can achieve up to 8.5 per cent reduction of the fillet stress. Two-dimensional photoelasticity was used to verify the optimization results.

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Real-time measurement of shear fatigue crack propagation at high-temperature using the potential drop technique

V. Spitas,C. Spitas,P. Michelis

Abstract:

In this paper, a direct method for real-time measurement of the advancement closed cracks propagating in Mode II (in-plane shear) is presented. The method is based on a modified potential drop technique applied on a patented shear specimen, the geometry of which ensures that under certain loading conditions a uniform shear field is developed in its central region (gauge area). Therefore, by continuously measuring the change in the electrical resistance (potential drop) between the two electrodes attached on the specimen it is possible to correlate this change with the progression of the crack within the specimen and in turn correlate the crack length with the stress intensity factor at the crack tip. This information can be used to create dα/dN − ΔK_II plots as the experiment is progressing on-line from the acquired electrical data. The electrical field and the stress intensity factor in Mode II (K_II) have been calculated for the shear specimen using finite element analysis (FEA) for various crack lengths and graphs indicating the change in crack length versus the change of the resistance of the specimen have been plotted. The method has been calibrated with optical measurements using a long distance observation microscope and it can be used in high-temperature testing of electrically conductive materials (i.e. nickel-based superalloys).

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A FEM Study of the Bending Strength of Circular Fillet Gear Teeth Compared to Trochoidal Fillets Produced with Enlarged Cutter Tip Radius

C. Spitas & V. Spitas

Abstract:

Circular fillet (CF) gears have been proven to possess a higher bending strength than their standard trochoidal fillet (TF) counterparts. However, stronger nonstandard variants of the TF are already possible to produce by increasing the tip radius of the cutters used for gear generation (racks, hobs, pinion cutters), affording competitive results. In this paper a comparison of the bending strength is made between the CF and the nonstandard large tip radius TF designs spanning the entire usable tooth number range using FEA. The results suggest a systematic advantage of the CF over the stronger variants of the TF for numbers less than 17 teeth, which is the undercut limit for the 20° involute gear system.

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Fast modeling of conjugate gear tooth profiles using discrete presentation by involute segments

Vasilios Spitas,Theodore Costopoulos,Christos Spitas

Abstract:

This paper introduces the method of the discretization of the gear tooth flank in involute segments for the determination of conjugate gear tooth profiles. Instead of following a point-to-point analytical approach to the problem of determining the path of contact and the geometry of the generating rack and the mating wheel, the actual tooth flank is considered to be composed of infinitesimal local involutes and therefore a closed solution can be achieved. Due to its simplicity, the method is faster than the standard theory of gearing and this is particularly useful in problems requiring iterative calculations of the tooth geometry such as gear optimization. The method is implemented on modified involute as well as loboid gears used in lobe pumps and it is verified against existing theories.

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Increasing the Strength of Standard Involute Gear Teeth with Novel Circular Root Fillet Design

V. Spitas, Th. Costopoulos and C. Spitas

Abstract:

In this study the idea of spur gear teeth with circular instead of the standard trochoidal root fillet is introduced and investigated numerically using BEM. The strength of these new teeth is studied in comparison with the standard design by discretizing the tooth boundary using isoparametric Boundary Elements. In order to facilitate the analysis the teeth are treated as non-dimensional assuming unitary loading normal to the profile at their Highest Point of Single Tooth Contact (HPSTC), so that non-dimensional stress vs. Contact ratio diagrams are plotted. The analysis demonstrates that the novel teeth exhibit higher bending strength (up to 70%) in certain cases without affecting the pitting resistance since the geometry of the load carrying involute is not changed. The circular fillet design is particularly suitable in gear with a small number of teeth (pinions) and these novels gears can replace their existing counterparts in any mechanism without any alterations. Finally the geometry of the generating tool (i.e. rack) is determined in order to be able to cut these teeth using a generating method (i.e. hobbing).

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Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity

Abstract:

This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.

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