Journal articles: 'Transition curves'

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Koc, Władysław, and Katarzyna Palikowska. "Modelling of joining route segments of different curvature." Baltic Journal of Road and Bridge Engineering 11, no. 1 (March 25, 2016): 1–10. http://dx.doi.org/10.3846/bjrbe.2016.01.

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The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.

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Brustad, Tanita Fossli, and Rune Dalmo. "Exploring Benefits of Using Blending Splines as Transition Curves." Applied Sciences 10, no. 12 (June 19, 2020): 4226. http://dx.doi.org/10.3390/app10124226.

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Track geometry is a fundamental subject in railway construction. With the demand for increased capacity in terms of load and speed, the need for suitable transitions between consecutive track sections is highly relevant. Properly constructed transition curves lead to improved travel comfort, increased safety, and reduced wear. The well known clothoid curve is widely used as a transition curve; however, the linear curvature is not sufficiently smooth to meet the requirements for railways carrying high speed trains or heavy hauls. Blending spline curves are flexible spline constructions possessing favourable smoothness properties at the end points, which makes them considerable for use as transition curves. This paper demonstrates some selected blending splines applied as transition curves between two existing circular arc segments selected from the Ofotbanen railway. The main results in this paper are related to the smoothness at the end points and the behaviour of the curvature of the curves, where the new transition curves were shown to be smoother than the original clothoid. Another new result is the observation that the proposed method allows for the improvement of existing railways without forcing extensive changes to the original track. Some representative examples are included to highlight the flexibility of this first instance of blending splines as transition curves.

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Chotěborský, R., D. Herák, V. Bezouška, P. Hrabě, and M. Müller. "Mathematical function for the transition curves description ." Research in Agricultural Engineering 51, No. 3 (February 7, 2012): 85–90. http://dx.doi.org/10.17221/4908-rae.

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Toughness is one of important material properties. At present steel is still the most used material. Owing to the temperature this material can fail both brittly and ductily. Therefore we look for the temperature above which the material will failur ductily. The Charpy impact test is one of methods how to determine the ductility by the temperature – transition access in the determined temperature range. The measured data file is large and it requires the interlay by a curve which presents the relation between the impact energy and the temperature.

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Kurhan, Mykola, Dmytro Kurhan, Marina Husak, and Nelya Hmelevska. "Determination of the type and the length for the transition curves on the directions of high-speed train operation." Acta Technica Jaurinensis 15, no. 2 (May 25, 2022): 117–24. http://dx.doi.org/10.14513/actatechjaur.00658.

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In many countries around the world, a cubic parabola is used as transition curves in a simplified form. Today, the properties of many mathematical curves are well studied, which can be used as transition curves. The object of research is the process of restructuring transition curves when organizing high-speed trains operation. The use of modern means of mathematical modelling allows to add a number of dynamic characteristics for evaluation parameters of motion in the curved sections of the tracks. Thus, with an increase in speed for transition curves, both the values of unbalanced acceleration and its change in time, and also the velocity attenuation of oscillations of rolling stock when moving from a transition curve to a circular curve or to a direct section. On the basis of the conducted research, it has been found that when increasing the speed of the vehicle movement in the range from 120 to 200 km/h, the length of the stabilization section increases at the output of the curvature by an average of 20 m for every 40 km/h. The analysis showed that with correctly set parameters of transition curves, which correspond to the maximum speed of movement and radius of a circular curve, the strength and reliability of the bearing elements in the structure of the permanent way and the travel comfort are fully ensured.

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Brustad, Tanita Fossli. "Preliminary Studies on Transition Curve Geometry: Reality and Virtual Reality." Emerging Science Journal 4, no. 1 (February 1, 2020): 1–10. http://dx.doi.org/10.28991/esj-2020-01204.

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The topic of transition curves is well known in track and road engineering. Over the years the need for easement between straight and curved sections in railway and road design has grown, with an important reason being increase in vehicle speed. Testing of transitions is often done with graph analysis where the property of lateral change of acceleration is compared between varieties of curves. However, graph analysis does not give a clear understanding of the behaviour of a vehicle in a transition phase the way, for instance, field or laboratory experiments might do. In this paper we present an initial study on the behaviour of a down-scaled vehicle model driving through three distinct transitions from straight to curved sections. In addition we show a comparison of the physical model against a virtual model.

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Koc, Władysław. "Smoothed transition curve for railways." Transportation Overview - Przeglad Komunikacyjny 2019, no. 7 (July 1, 2019): 19–31. http://dx.doi.org/10.35117/a_eng_19_07_03.

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The work draws attention to the existing situation in the area of transition curves used in the geometric layouts of the railway track. Difficulties in the practical implementation and maintenance of very small horizontal ordinates of the transition curve and the ordinates of the gradient due to cant in the initial section, appearing on smooth transition curves, were indicated. The main reason for this situation was the excessive smoothing of the curvature in their initial section. Employing the method of curvature identification by differential equations, a new form of the curve was obtained, which was referred to as the "smoothed transition curve". A definite advantage of this curve was shown, from the implementation point of view, over representing the smooth transition curves of the Bloss curve. . It seems that it could successfully compete with the commonly used clothoid, to which it is similar in the initial section, while it differs significantly along its further length, especially in the final section, where it provides a gentle entry from the transition curve into a circular arc.

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Red, Edward. "A dynamic optimal trajectory generator for Cartesian Path following." Robotica 18, no. 5 (September 2000): 451–58. http://dx.doi.org/10.1017/s0263574700002629.

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This paper considers a dynamic and adaptive trajectory generator for negotiating paths using S-curves. Applying constant jerk transitions between the constant acceleration and deceleration periods of the trajectory, the trajectory will optimally transition to the desired speed setting. Optimal is defined to be the minimum time to transition from the current speed to the set speed for the move segment when jerk and acceleration are limited. The S-curve equations will adapt to instantaneous changes in speed setting and path length. An integrated motion planner will determine allowable speeds and transitional profiles based on the remaining move distance.

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Lee, Tae-kyung, Seokmin Hong, Jongmin Kim, Min-Chul Kim, and Jae-il Jang. "Evaluation of Transition Temperature in Reactor Pressure Vessel Steels 6using the Fracture Energy Transition Curve from a Small Punch Test." Korean Journal of Metals and Materials 58, no. 8 (August 5, 2020): 522–32. http://dx.doi.org/10.3365/kjmm.2020.58.8.522.

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The small punch (SP) test is one of the small specimen test techniques, and standardization of the SP test method for evaluating the mechanical properties of metallic materials is in progress. In this study, the impact transition temperature of reactor pressure vessel steels (RPV) in nuclear power plants was estimated using the draft standard SP test method. The SP fracture energy (ESP) and normalized SP fracture energy (ENSP) of the RPV steels were evaluated at various temperatures, and their transition curves were derived and compared to the transition curve in the Charpy V notch (CVN) test. The SP transition region appeared at a much lower temperature range than that of the CVN owing to the size and notch effect. Ductile brittle transition temperature (DBTT) in the SP transition curve showed a linear relationship with DBTT and T41J in the CVN transition curve. The ductile to brittle transition behaviors of SP specimens were analyzed using fractographs and compared with the transition curves in ESP and ENSP. ENSP started to decrease at the temperature at which the SP ductile to brittle transition behavior occurred, and this means that the ENSP transition curves were in good agreement with transition behavior in the SP test. However, the ESP transition curves did not match transition behavior. Using DBTT in the ENSP transition curve is appropriate to estimate the CVNDBTT and T41J.

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Tari, Ergin, and Orhan Baykal. "A new transition curve with enhanced properties." Canadian Journal of Civil Engineering 32, no. 5 (October 1, 2005): 913–23. http://dx.doi.org/10.1139/l05-051.

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A new transition curve-3 (NTC-3), joining two straight lines by providing second-degree contact related to the properties of vehicle–road system without the necessity of a circular arc, is presented. The NTC-3 is offered by curvature and superelevation functions and is compared with the new generation transition curves-1 and -2 (NTC-1, NTC-2) and spiral curves. The properties of vehicle–road system, represented by function of lateral change of acceleration (LCA), are examined for these curves. Three criteria are taken into account to compare the curves. The NTC-3 and NTC-1 are compared in five-different motion models: model with constant velocity, model with positive acceleration, model with negative acceleration, model with negative acceleration – positive acceleration, and model with positive acceleration – negative acceleration. Examination of three criteria shows that NTC-3 is superior to the other curves on the basis of vehicle–road system.Key words: route design, transition curve, vehicle–road system, curvature, lateral change of acceleration, superelevation, motion model.

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Zboiński, Krzysztof, Piotr Woźnica, and Yaroslav Bolzhelarskyi. "Modelling of the shape of railway transition curves from the point of view of passenger comfort." Archives of Transport 60, no. 4 (December 31, 2021): 205–17. http://dx.doi.org/10.5604/01.3001.0015.6931.

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In the past, railway transition curves were not used. Instead of it, a simple connection of the straight track and circular arc was applied. Nowadays, such simplicity is not allowed due to the increasing vehicle operating velocities. It is mainly visible in the high-speed train lines, where long curves are used. The article aims to develop a new shape of railway transition curves for which passenger travel comfort will be as high as possible. Considerations in this paper concern the polynomials of 9th- and 11th-degrees, which were adopted to the mathematical model of the mentioned shape of curves. The study's authors applied a 2-axle rail vehicle model combined with mathematically understood optimisation methods. The advanced vehicle model can better assign the dynamical properties of railway transition curves to freight and passenger vehicles. The mentioned model was adopted to simulate rail vehicle movement in both cases of the shape of transition curves and the shape of circular arc (for comparison of the results). Passenger comfort, described by European Standard EN 12299, was used as the assessment criterion. The work showed that the method using the 2-axle railway vehicle model combined with mathematically understood optimisation works correctly, and the optimisation of the transition curve shape is possible. The current study showed that the 3rd-degree parabola (the shape of the curve traditionally used in railway engineering) is not always the optimum shape. In many cases (especially for the long curves), the optimum shape of curves is between the standard transition curves and the linear curvature of the 3rd-degree parabola. The new shapes of the railway transition curves obtained when the passenger comfort is taken into account result in new railway transition curves shapes. In the authors' opinion, the results presented in the current work are a novelty in optimisation and the properties assessment of railway transition curves.

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Zhusubaliyev, Zhanybai T., Viktor Avrutin, and Frank Bastian. "Transformations of Closed Invariant Curves and Closed-Invariant-Curve-Like Chaotic Attractors in Piecewise Smooth Systems." International Journal of Bifurcation and Chaos 31, no. 03 (March 15, 2021): 2130009. http://dx.doi.org/10.1142/s0218127421300093.

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The paper describes some aspects of sudden transformations of closed invariant curves in a 2D piecewise smooth map. In particular, using detailed numerically calculated phase portraits, we discuss transitions from smooth to piecewise smooth closed invariant curves. We show that such transitions may occur not only when a closed invariant curve collides with a border but also via a homoclinic bifurcation. Furthermore, we describe an unusual transformation from a closed invariant curve to a large amplitude chaotic attractor and demonstrate that this transition occurs in two steps, involving a small amplitude closed-invariant-curve-like chaotic attractor.

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12

Kobryń, Andrzej. "Polynomial Solutions of Transition Curves." Journal of Surveying Engineering 137, no. 3 (August 2011): 71–80. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000044.

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Kobryń, Andrzej. "Universal Solutions of Transition Curves." Journal of Surveying Engineering 142, no. 4 (November 2016): 04016010. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000179.

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Zboinski, Krzysztof, and Piotr Woznica. "Is the cubic parabola really the best railway transition curve?" Open Engineering 11, no. 1 (January 1, 2021): 1207–13. http://dx.doi.org/10.1515/eng-2021-0123.

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Abstract In the current study, the authors tested two railway transition curves in terms of their usefulness for railway practice. The first curve was a cubic parabola – the curve most popular in railway engineering. The second curve was a polynomial of ninth degree, and this curve was chosen due to the fact that this curve satisfies advanced geometrical demands. In this study, the model of a two-axle vehicle was applied. The study relied on the passage of the vehicle model through the route consisted of straight track, railway transition, and circular arc. Three different circular arc radii were used. The value – 0.6 m/s2 – of maximum lateral acceleration in the circular arc was applied. Three different vehicle velocities were also used. In this study, the authors simulated vehicle dynamics for different curves and ten lengths of the curves. As the main criterion, lateral acceleration of the vehicle body was applied. The results for these two mentioned curves were compared.

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Kobryń, Andrzej. "Transition curves in vertical alignment as a method for reducing fuel consumption." BALTIC JOURNAL OF ROAD AND BRIDGE ENGINEERING 9, no. 4 (February 20, 2014): 260–68. http://dx.doi.org/10.3846/bjrbe.2014.32.

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This paper presents a new approach to the fuel consumption reduction. This approach is based on vertical curve designs based on transition curves. The work presents selected curves, which are used for this purpose. Moreover, the results of comparative studies are shown for these curves, carried out in order to compare the possible reduction of fuel consumption in vertical curves designed using both conventional and proposed methods. Numerical studies were based on German engineering guidelines. In the case of vertical arcs formed by transition curves, fuel consumption indexes prove to be significantly lower than in curves based on a grade line consisting of straight lines with parabolic arcs. The obtained results indicate the advisability of forming vertical curves using transition curves.

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Zboinski, Krzysztof, and Piotr Woznica. "Optimum Railway Transition Curves—Method of the Assessment and Results." Energies 14, no. 13 (July 2, 2021): 3995. http://dx.doi.org/10.3390/en14133995.

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This article discusses the optimization of railway transition curves, through the application of polynomials of 9th and 11th degrees. In this work, the authors use a 2-axle rail vehicle model combined with mathematically understood optimization methods. This model is used to simulate rail vehicle movement negotiating both a transition curve and circular arc. Passenger comfort is applied as the criterion to assess which transition is actually is the best one. The 4-axle vehicle was also used to verify the results obtained using the 2-axle vehicle. Our results show that the traditionally used in a railway engineering transition—3rd degree parabola—which is not always the optimum curve. This fact is especially valid for the longest curves, with lengths greater than 150 m. For such cases, the transition curves similar to standard curves of 9th and 11th degrees is the optimum ones. This result is confirmed by the use of the 4-axle vehicle.

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Sedunov, Boris I. "Structural Transition in Supercritical Fluids." Journal of Thermodynamics 2011 (October 10, 2011): 1–5. http://dx.doi.org/10.1155/2011/194353.

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The extension of the saturation curve on the PT diagram in the supercritical region for a number of monocomponent supercritical fluids by peak values for different thermophysical properties, such as heat capacities and and compressibility has been studied. These peaks signal about some sort of fluid structural transition in the supercritical region. Different methods give similar but progressively diverging curves for this transition. The zone of temperatures and pressures near these curves can be named as the zone of the fluid structural transition. The outstanding properties of supercritical fluids in this zone help to understand the physical sense of the fluid structural transition.

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Kobryń, Andrzej, and Piotr Stachera. "S-Shaped Transition Curves as an Element of Reverse Curves in Road Design." Baltic Journal of Road and Bridge Engineering 14, no. 4 (December 27, 2019): 484–503. http://dx.doi.org/10.7250/bjrbe.2019-14.454.

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A road designing involves horizontal and vertical alignment. The horizontal geometry is formed by straight and curvilinear sections that are traditionally formed using circular and transition curves (mainly the clothoid). Different geometric systems that are designed using circular and transition curves are between others circular curves with symmetrical or unsymmetrical clothoids, combined curves, oval curves and reverse curves. Designing these systems is quite complex. Therefore, so-called S-shaped transition curves are an alternative to traditional approaches. These curves are known from literature and are modern geometric tools for the shaping of reverse curves. The paper analyses the basic geometric properties of these curves as well as compare to the geometry of the appropriate geometric systems, which are formed with clothoid or using S-shaped transition curves. In addition, a procedure for designing reverse curves using S-shaped transition curves was proposed. Another research topic was the comparison of the analysed reverse curves (created using polynomial transition curves) with traditional curves (created using the clothoid). The results of the studies, despite the noticeable differences in the geometry of the compared components, confirm the practical usefulness of the S-shaped transition curves for designing the geometry of the route.

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Arslan, Abdullah, Ergin Tari, Rushan Ziatdinov, and Rifkat I. Nabiyev. "Transition Curve Modeling with Kinematical Properties: Research on Log-Aesthetic Curves." Computer-Aided Design and Applications 11, no. 5 (April 16, 2014): 509–17. http://dx.doi.org/10.1080/16864360.2014.902680.

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Liu, Li, Chuan Ding, and Pengfei Wang. "Design and optimization of the transition curve in the novel profiled chamber metering pump." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 234, no. 3 (January 14, 2020): 435–46. http://dx.doi.org/10.1177/1464419319900755.

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To better understand the optimization of the stator profile to improve the dynamic performance of a novel profiled chamber metering pump, this paper presents a dynamic analysis method for transition curve design and optimization of the profiled chamber. The face-shaped curve of the inner chamber of the stator is formed of two quarter circular arcs and two quarter noncircular arcs, and the two quarter noncircular arcs are defined as transition curves, which directly affect the mechanical vibration, friction, and wear of the profiled chamber metering pump. The proposed design and optimization method combine a friction analysis with the motion control of the moving parts. The approach based on a new strategy mainly includes three steps. For the first step, based on motion analysis, the trigonometric function and polynomial function are adopted to derive the candidate transition curves that have different order of continuity. Secondly, a friction model between the slides and the stator is established, by means of kinematic and force analysis of the slides. Then, the model is used to examine the friction dissipated energy for different candidate transition curves. Finally, through a comparison analysis of motion parameters and energy losses, comprehensive optimal transition curves are obtained. This three-step analytical work is proved to be efficient in the design of the transition curves.

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Fischer, Szabolcs. "Comparison of railway track transition curves." Pollack Periodica 4, no. 3 (December 2009): 99–110. http://dx.doi.org/10.1556/pollack.4.2009.3.9.

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Long, X.-Y., Q.-C. Wei, and F.-Y. Zheng. "Dynamic analysis of railway transition curves." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 224, no. 1 (July 24, 2009): 1–14. http://dx.doi.org/10.1243/09544097jrrt287.

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Ulitsky, Alex, and David Shalloway. "Finding transition states using contangency curves." Journal of Chemical Physics 106, no. 24 (June 22, 1997): 10099–104. http://dx.doi.org/10.1063/1.474043.

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Kobryń, Andrzej. "New Solutions for General Transition Curves." Journal of Surveying Engineering 140, no. 1 (February 2014): 12–21. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000113.

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Yang, Xuefeng, and Youpeng You. "Linear Tool Path-Smoothing Method in High-Speed Machining Based on Error Feasible Area and Curvature Optimization." Applied Sciences 12, no. 19 (September 21, 2022): 9443. http://dx.doi.org/10.3390/app12199443.

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Linear tool path is widely used in high-speed NC machining. However, the geometrical discontinuity of the corner between the linear tool paths will lead to fluctuations in speed, acceleration and jerk, which can excite machinery vibration and reduce the machining efficiency and surface quality. To solve these problems, a novel corner smoothing method based on error feasible area and curvature optimization is proposed in this paper. Compared with most traditional corner smoothing methods using higher-order curves with all control points lying in the straight segment and inside of the tool path, the proposed method constructs B-spline transition curves with smaller curvatures to smooth the corners by reasonably distributing the curve control points inside and outside the straight line segment of the tool path (i.e., error feasible area). Furthermore, the corner transition curve is optimized by the minimum curve curvature extreme to improve the smoothness of the corner transition curve and reduce fluctuation in the kinematic profiles while respecting the G3 continuity (i.e., curvature-smooth), transition length limits and the uniqueness of curvature extremum. Finally, the simulation results show that the proposed method can reduce the curvature value and improve the smoothness of the curve and the minimum transitional velocity of the corner, which means that it can enhance machining efficiency and weaken machining vibration. The feasibility and effectiveness of the method are also verified.

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Bligh, Roger P., and King K. Mak. "Critical Impact Points for Transitions and Terminals." Transportation Research Record: Journal of the Transportation Research Board 1797, no. 1 (January 2002): 105–12. http://dx.doi.org/10.3141/1797-13.

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Guidelines for evaluating the safety performance of roadside safety features generally recommend that a worst case or critical impact point (CIP) be selected for crash testing. NCHRP Report 350 presents families of curves that can be used to determine the CIP for a transition section. However, these curves have been observed to overestimate the stiffness of a transition system and provide CIP values closer to the more rigid system of the transition (e.g., bridge rail end) than appropriate. New CIP selection curves for transitions are presented. A procedure is provided to aid in determining the CIP for transition sections with multiple rail elements or variations in post strength and post spacing. Various existing and theoretical transitions systems with wide-ranging combinations of beam and post strengths were used to validate the curves. The newly developed CIP relationships for transitions are recommended in lieu of the existing relationships contained in NCHRP Report 350. To facilitate the development of guidelines for the selection of a CIP for terminals, a new definition is proposed. The proposed definition for the CIP is the point along the terminal at which vehicle behavior transitions from gating to redirection. A methodology for determining the CIP using computer simulation techniques is investigated. The data clearly demonstrate that the selection of a single default impact location for all terminal configurations may not provide the CIP for many designs.

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Perren, Sonja, Roger Keller, Marco Passardi, and Urte Scholz. "Well-Being Curves Across Transitions." Swiss Journal of Psychology 69, no. 1 (January 2010): 15–29. http://dx.doi.org/10.1024/1421-0185/a000003.

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A newly developed instrument (retrospective well-being curves: WBC) was applied in two studies. In Study 1, a sample of 145 adults (M = 26.6 years) completed the WBC twice for different normative transitions. In Study 2, 151 university freshmen (M = 21.5 years) reported on their subjective well-being at 9 consecutive measurement points during their transition to university and completed the WBC at T10. In both studies, personality factors were assessed. Retest reliability of the individual growth parameters (intercept, linear, and quadratic change) was moderate to high (Study 1), whereas convergent validity of the growth parameters was moderate (Study 2). The results demonstrated distinct well-being trajectories for different transitions. Situational factors (e.g., timing) and personality factors (neuroticism and extraversion) were significantly associated with well-being. The results indicate that, although the use of the WBC may be limited by its retrospective design, the instrument provides a time-efficient way of measuring hedonic adaptation processes.

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Benková, Zuzana, Pavol Námer, and Peter Cifra. "Stripe to slab confinement for the linearization of macromolecules in nanochannels." Soft Matter 11, no. 11 (2015): 2279–89. http://dx.doi.org/10.1039/c4sm02382j.

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Brustad, Tanita Fossli, and Rune Dalmo. "Railway Transition Curves: A Review of the State-of-the-Art and Future Research." Infrastructures 5, no. 5 (May 18, 2020): 43. http://dx.doi.org/10.3390/infrastructures5050043.

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Transition curves are a useful tool for lateral alignment of railway segments. Their design is important to ensure safe and comfortable travel for passengers and cargo. Well designed transition curves can lead to reduced wear of tracks and vehicles, which is beneficial from a maintenance point of view. Extensive studies have been performed through decades to find transition curves that can replace existing railway segments for the purpose of enhancing certain properties. Those studies seek to form curves that satisfy desired evaluation criteria, which are often connected to geometric continuity between the curve segments, and vehicle dynamics, to secure a smooth ride. This research topic is still ongoing and active at present. Recent results and findings are in line with the developments on the topic of vehicle dynamics and within the railway industry. For this reason it is appropriate to collect and discuss the latest work, since there are no up-to-date detailed literature reviews available. This paper explores the present state-of-the-art of railway transition curves, and identifies some of the research challenges and future research opportunities in the field.

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Iwadate, T., Y. Tanaka, and H. Takemata. "Prediction of Fracture Toughness KIC Transition Curves of Pressure Vessel Steels From Charpy V-Notch Impact Test Results." Journal of Pressure Vessel Technology 116, no. 4 (November 1, 1994): 353–58. http://dx.doi.org/10.1115/1.2929601.

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A single and generalized prediction method of fracture toughness KIC transition curves of pressure vessel steels has been greatly desired by engineers in the petro-chemical and nuclear power industries, especially from the viewpoint of life extension of reactor pressure vessels. In this paper, the toughness degradation of Cr-Mo steels during long-term service was examined and the two prediction methods of fracture toughness KIC transition curves were studied using the data of 54 heats. 1) The toughness degradation of 2 1/4Cr-1Mo steels levels off within around 50,000 h service. 2) The FATT versus J-factor (=(Si+Mn)(P+Sn)×104) and/or X (=(10P+5Sb+4Sn+As)x10−2) relationships to estimate the maximum embrittlement of Cr-Mo steels were obtained. 3) A master curve method developed by authors et al.; that is, the method using a KIC/KIC−US versus excess temperature master curve of each material was presented for 2 1/4Cr-1Mo, 1 1/4Cr-1/2Mo, 1Cr and 1/2Mo chemical pressure vessel steels and ASTM A508 C1.1, A508 C1.2, A508 C1.3 and A533 Gr.B C1.1 nuclear pressure vessel steels, where KIC−US is the upper-shelf fracture toughness and excess temperature is test temperature minus FATT. 4) A generalized prediction method to predict the KIC transition curves of any low-alloy steels was developed. This method consists of KIC/KIC−US versus T–T0 master curve and temperature shift ΔT between fracture toughness and CVN impact transition curves versus yield strength relationship, where To is the temperature showing 50 percent KIC−US of the material. 5) The KIC transition curves predicted using both methods showed a good agreement with the lower bound of measured KJC values obtained from JC tests.

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Berthonnaud, E., R. Hilmi, and J. Dimnet. "Geometric Structure of 3D Spinal Curves: Plane Regions and Connecting Zones." ISRN Orthopedics 2012 (March 12, 2012): 1–10. http://dx.doi.org/10.5402/2012/840426.

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This paper presents a new study of the geometric structure of 3D spinal curves. The spine is considered as an heterogeneous beam, compound of vertebrae and intervertebral discs. The spine is modeled as a deformable wire along which vertebrae are beads rotating about the wire. 3D spinal curves are compound of plane regions connected together by zones of transition. The 3D spinal curve is uniquely flexed along the plane regions. The angular offsets between adjacent regions are concentrated at level of the middle zones of transition, so illustrating the heterogeneity of the spinal geometric structure. The plane regions along the 3D spinal curve must satisfy two criteria: (i) a criterion of minimum distance between the curve and the regional plane and (ii) a criterion controlling that the curve is continuously plane at the level of the region. The geometric structure of each 3D spinal curve is characterized by the sizes and orientations of regional planes, by the parameters representing flexed regions and by the sizes and functions of zones of transition. Spinal curves of asymptomatic subjects show three plane regions corresponding to spinal curvatures: lumbar, thoracic and cervical curvatures. In some scoliotic spines, four plane regions may be detected.

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Chrostowski, Piotr, Wladyslaw Koc, and Katarzyna Palikowska. "Prospects in elongation of railway transition curves." Proceedings of the Institution of Civil Engineers - Transport 173, no. 5 (October 2020): 309–20. http://dx.doi.org/10.1680/jtran.17.00097.

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Jadallah, H. T., J. Rubinstein, and P. Sternberg. "Phase Transition Curves for Mesoscopic Superconducting Samples." Physical Review Letters 82, no. 14 (April 5, 1999): 2935–38. http://dx.doi.org/10.1103/physrevlett.82.2935.

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Kobryń, Andrzej. "Vertical arcs design using polynomial transition curves." KSCE Journal of Civil Engineering 20, no. 1 (April 28, 2015): 376–84. http://dx.doi.org/10.1007/s12205-015-0492-z.

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Sánchez-Reyes, J., and J. M. Chacón. "Nonparametric Bézier Representation of Polynomial Transition Curves." Journal of Surveying Engineering 144, no. 2 (May 2018): 04018001. http://dx.doi.org/10.1061/(asce)su.1943-5428.0000251.

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Ciampa, Donato, and Saverio Olita. "The Use of Bloss Curve in The Exit Lanes of Road Intersections." Baltic Journal of Road and Bridge Engineering 15, no. 1 (March 17, 2020): 76–102. http://dx.doi.org/10.7250/bjrbe.2020-15.462.

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The paper proposes the use of the Bloss curve (also known as biparametric or bi-hyperclothoid) as a braking curve in the exit lanes of road intersections. The main international standards continue using the clohoid as the principal transitional geometric element, even though the limits of its use in driving regimes with non-uniform speeds are known. The proposal to use the Bloss curve is aimed at overcoming these limitations and opening a debate on the possible need to codify, even in the international standards, the use of more suitable alternative braking curves. In this context, a kinematic study was conducted by comparing the main parameters of the motion (lateral jerk, lateral acceleration, steering speed) between the Bloss curve and more traditional curves, such as clothoid and Generalized Cornu Spirals (GCS). Nine case studies were conducted, each case was characterized considering the type of transition curve used (clothoid, GCS and Bloss curve) and radius R of the exit curve (R = 60 m, 80 m, 100 m). The numerical values assumed by the kinematic variables along the transition curves were “locally” calculated, i.e. “pointby- point”, to take into account the non-uniform motion regime. The results obtained, limited to the cases studied, show that the Bloss curve better meets the kinematic conditions of the vehicle motion in non-uniform driving regimes. Therefore, the Bloss curve can be considered as a braking curve in the design of road intersections and be a candidate for further investigation to assess any additional benefits in terms of comfort, driving safety and visual perception of the geometric element.

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Torres, N. V., J. Sicilia, and E. Meléndez-Hevia. "Analysis and characterization of transition states in metabolic systems. Transition times and the passivity of the output flux." Biochemical Journal 276, no. 1 (May 15, 1991): 231–36. http://dx.doi.org/10.1042/bj2760231.

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In this paper we study the transitions between steady states in metabolic systems. In order to deal with this task we divided the total metabolite concentration at steady state, sigma, into two new fractions, delta (the Output Transition Time) and tau beta (Input Transition Time), which are related with the course of output and input mass to the system respectively. We show the equivalence time between these terms and the Total Transition Time, tau T, previously defined [Easterby (1986) Biochem. J. 233, 871-875]. Next, we define a new magnitude, the Output Passivity of a transition, rho, which quantifies a new aspect of the transition phase that we call the passivity of the output progress curve. With these magnitudes, all of them being experimentally accessible, several features of the transient state can be measured. We apply the present analysis to (a) the case of coupled enzyme assays, which allows us to reach conclusions about the progress curves in these particular transitions and the equivalence between tau sigma and tau delta, and (b) some experimental results that allow us to discuss the biological significance of the Output Passivity in the transition between steady states in metabolic systems.

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Ungar, E. K., and R. Eichhorn. "Transition Boiling Curves in Saturated Pool Boiling From Horizontal Cylinders." Journal of Heat Transfer 118, no. 3 (August 1, 1996): 654–61. http://dx.doi.org/10.1115/1.2822682.

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Pool boiling heat flux versus wall superheat boiling curves were obtained for horizontal 3.18-mm-dia thin-walled brass tubes heated by an internal high-speed flow of ethylene glycol. The boiling liquids were saturated n-pentane, R-113, acetone, methanol ethanol, benzene, and isopropanol. Boiling results include nucleate and transition boiling in all the test liquids, but film boiling was achieved only with methanol. The measured peak heat fluxes are well correlated by available predictions. The methanol experiments clearly display two transition boiling curves, one obtained on increasing the cylinder temperature from nucleate boiling, the other on decreasing the cylinder temperature from film boiling. For the cases in which the highest cylinder temperature reached only into the transition regime, a single transition boiling curve resulted.

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Habib, Zulfiqar, and Manabu Sakai. "FAIRING ARC SPLINE AND DESIGNING BY USING CUBIC BÉZIER SPIRAL SEGMENTS." Mathematical Modelling and Analysis 17, no. 2 (April 1, 2012): 141–60. http://dx.doi.org/10.3846/13926292.2012.655787.

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This paper considers how to smooth three kinds of G 1 biarc models, the C-, S-, and J-shaped transitions, by replacing their parts with spiral segments using a single cubic Bézier curve. Arc spline is smoothed to G 2continuity. Use of a single curve rather than two has the benefit because designers and implementers have fewer entities to be concerned. Arc spline is planar, tangent continuous, piecewise curves made of circular arcs and straight line segments. It is important in manufacturing industries because of its use in the cutting paths for numerically controlled cutting machinery. Main contribution of this paper is to minimize the number of curvature extrema in cubic transition curves for further use in industrial applications such as non-holonomic robot path planning, highways or railways, and spur gear tooth designing.

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Mauga, Timur. "New Spiral Curves for Appropriate Transition of Minimum Roadside Clearance on Simple Curves." Journal of Transportation Technologies 05, no. 03 (2015): 141–58. http://dx.doi.org/10.4236/jtts.2015.53014.

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Irving, R. E., M. Henderson, L. J. Curtis, I. Martinson, and P. Bengtsson. "Accurate transition probabilities for the 2s2 1S - 2s2p 1P transition in Be I and B II." Canadian Journal of Physics 77, no. 2 (June 1, 1999): 137–43. http://dx.doi.org/10.1139/p99-015.

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Transition probability determinations are reported for the 2s2 1S - 2s2p 1P transition in Be I and B II, based on lifetime measurements made by beam-foil excitation. The lifetimes were extracted by the ANDC method, which incorporates cascade-related decay curves into the analysis of the primary decay curve, thus accounting for the effects of cascade repopulation. The results are of higher precision than earlier measurements and improve the agreement with recent theoretical calculations. PACS No.: 32.70Cs

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Singh, L. Robindro, and S. Dorendrajit Singh. "Particle Size Effect on TL Emission of ZnS Nanoparticles and Determination of Its Kinetic Parameters." Journal of Nanomaterials 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/239182.

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Nanoparticles have large surface area, and most of the ions are lying on its surface. Could these surface ions be contributed in thermoluminescence emission or enhanced nonradiative transition? In view of this, we have prepared small sizes of ZnS nanoparticles at low temperature and made two samples, one as-prepared (size ~3 nm) and the other heat-treated at 1073 K (size ~32 nm). Characterization of the samples shows that the prepared phosphors are pure. Thermoluminescence (TL) glow curves could not be recorded in both samples without irradiation. Even for higher dose ofγ-radiation the as-prepared samples could not show TL signal, but 1073 K heat-treated sample shows the TL signal. This may be due to the fact that smaller particles have large surface area compared to bigger particles, the surface ions may produce the nonradiative transitions. The kinetic parameters of the TL glow curves are evaluated by the conventional methods and compared with curve fitting computerised glow curve deconvolution (CGCD) technique. The variations in both techniques are found only ±0.02. The shape factor of all the glow curves ~0.48, and these TL glow curves could be fitted with order of kinetics 1.5.

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Boryga, Marek, Paweł Kołodziej, and Krzysztof Gołacki. "Application of Polynomial Transition Curves for Trajectory Planning on the Headlands." Agriculture 10, no. 5 (May 1, 2020): 144. http://dx.doi.org/10.3390/agriculture10050144.

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This paper presents a method of polynomial transition curve application for making agricultural aggregate movement paths during headland turn drives as well as within the field. Four types of agricultural aggregate paths in five different variant designs are discussed. Each path is composed of only two curves, making the so-called transition bi-curve. The curvature described by the linear function as well as the third, fifth, seventh, and ninth degree polynomials was designated. Moreover, a trajectory planning algorithm in which the movement proceeds along two transition curves composing the so-called bi-curve was proposed. The simulation was carried out applying the MATLAB program in which the 4th order Runge–Kutta method was used. The results were presented by means of figures showing the proposed paths and kinematic quantity courses in the displacement function. The obtained trajectories were compared regarding the size and kinematic quantities. The trajectories, whose curvature is described by the 3° polynomial, were found to possess the smallest absolute values of maximal acceleration and jerk and to lack jerk discontinuity. The proposed solutions can be applied for planning trajectory of not only agriculture machines and aggregates but also autonomous vehicles or mobile robots.

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Shang, H. M., S. K. Shit, and C. J. Tay. "Relationship Between Workhardening Characteristics, Shape and Instability of Hydroformed Thin Shells." Journal of Engineering Materials and Technology 110, no. 3 (July 1, 1988): 253–57. http://dx.doi.org/10.1115/1.3226045.

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In this paper, a pattern is observed which relates the stress-strain curve of sheet materials to the shape and instability of hydroformed axisymmetrical thin shells. According to this pattern, prolate shells are obtained when the effective strain at the pole has a value within the linear (or almost linear) portion of the stress-strain curve; while oblate shells are obtained when the polar effective strain is at the curved portion of the stress-strain curve. With the aid of Ludwik and Hollomon equations, a family of stress-strain curves of various n-values is constructed and the curves are divided into four zones which indicate the shape of shells and its evolution with deformation, the transition point toward instability and the onset of instability. From the fracture strain of a given material during hydroforming, the observed pattern also indicates whether or not instability is present.

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45

Narayan, Ashutosh, Krishna Kumar Pandey, and Sandip Kumar Shrivastava. "Characteristics exponents of the triangular solution in the elliptical restricted three-body problem under radiating and triaxial primaries." International Journal of Advanced Astronomy 5, no. 1 (February 1, 2017): 12. http://dx.doi.org/10.14419/ijaa.v5i1.7114.

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This Paper deals with the effects of the radiation pressure and triaxiality of primaries on the stability of infinitesimal motion about triangular equilibrium points [ , ] in the elliptical restricted three body problem (ER3EB) around binary system. For determining the characteristic exponents of variational equations with periodic coefficient, we have used analytical method, described by Bennet in [3, 4]. This analytical method is based on Floquet’s theory. The stability of equilibrium points has been discussed under the assumption thatboth the primaries are radiating and triaxial. For this we have drawn transition cureves in μ-e plane. And it is seen that system is stable outside the transition curves, while system is Unstable within the transition curves.

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Koc, Władysław. "Extending transition curve in analytical design method." Transportation Overview - Przeglad Komunikacyjny 2016, no. 4 (April 1, 2016): 1–12. http://dx.doi.org/10.35117/a_eng_16_04_01.

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The paper presents the problem of extending the transitional curves, using for this purpose an analytical design method. The basis for the analysis of numerical calculations were carried out for a wide set of parameters characterizing the standard geometric system. We considered an importance of the size of radius of the circular arc and return angle of route on the obtained results after the formulation of appropriate theoretical dependence. It was found that the extension of the transition curve does not need cause large lateral displacements of the existing track at considerable length. It is only necessary to reduce the radius of the circular arc in a suitable way.

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Liu, Wei, Jian Hong Wang, Yang Li, and Wei Li. "Existing Railway Horizontal Alignment Reconstruction Algorithm Based on Line Segments Identification." Applied Mechanics and Materials 405-408 (September 2013): 1772–76. http://dx.doi.org/10.4028/www.scientific.net/amm.405-408.1772.

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A Line Segments Identification model is put forward to realize the existing railway horizontal alignment reconstruction. Firstly, Hough transform based on constraint adjustment quantity is introduced to reject the abnormal points that will affect the quality of the identification in latter steps. Then total least square method is used to get the linear segments, after which the circular curve segments and the transition curves segments will be got. At last, an evaluation function which has four arguments: circular curve radius , two transition curves length and length of straight line between curves was built and its function value is the sum of squares of all distances from measuring points to reconstruction alignment, based on the function , optimal alignment will be solved out by Powell method. Example shows that the reconstruction result is considerably superior to the traditional method and is feasible for the engineering practice.

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Basak, Agata, and Edward Nowak. "Dynamics of Railway Vehicles Movement on Transition Curves." Advances in Science and Technology Research Journal 15, no. 4 (December 1, 2021): 21–29. http://dx.doi.org/10.12913/22998624/142237.

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Farouki, Rida T. "Pythagorean-hodograph quintic transition curves of monotone curvature." Computer-Aided Design 29, no. 9 (September 1997): 601–6. http://dx.doi.org/10.1016/s0010-4485(97)00004-3.

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50

Kobryń, Andrzej. "Optimization of Vertical Alignment using General Transition Curves." KSCE Journal of Civil Engineering 22, no. 7 (September 25, 2017): 2549–59. http://dx.doi.org/10.1007/s12205-017-1937-3.

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Journal articles on the topic 'Transition curves'

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