Rolling Radius Research Articles

An inverse design method for rail grinding profiles

ABSTRACTInspired by the optimisation design method for restoration of worn wheel profiles, an inverse design method based on optimal rail grinding profiles is presented in this paper. To improve grinding quality, vehicle dynamic performance is chosen as the main criteria and rolling radii difference function is selected as the key factor (also main target function) determining dynamic performance. Grinding material to be removed is chosen as the auxiliary target aimed at extending rail service life. Besides that, wheel–rail contact distribution is also taken into consideration as an auxiliary target preventing stress concentration and fatigue growth. By introducing certain presuppositions, all the design targets will form an inverse design problem. This problem can be solved using hybrid discrete numerical methods. Considering different grinding requirements, two examples of grinding profile design for straight and curved track will be discussed. Results show that the presented method is efficient and effective. Practical implementation has been carried out at several grinding sites in China.

A Study of the Rolling Load Calculation Models for Flat Cold Rolling Process

Abstract. In order to keep the rolling products free of defects, the calculation and constant assessment of the rolling load and torque are required. Many theories for rolling load calculation were developed and among them the most used nowadays still are the Bland and Ford ’s (1948) model and Alexander’s (1971) model in order to achieve a better online control for reversible and tandem cold rolling mills. In this work those models were implemented in a numerical calculation software. The elastic roll’s deformation was taken into account using the Hitchcock´s formula for the deformed roll radius in an iterative way. Those models state that the friction hill (or normal pressure) in the contact arc keeps circular after the elastic deformation. This hypothesis is analysed with a third offline model for calculating the rolling load, named Noncirc (Shigaki et al., 2015), that considers the real roll elastic deformation (not circular anymore). Two cold rolling cases were considered and the friction coefficient was varied in order to evaluate the influence of this parameter on the calculated rolling load/width, the contact arc length and profile and pressure distribution over the contact arc. It was found that both models present imprecise results for both cases analysed, as the thickness is very low and the strip is very work hardened. The noncircular model shows higher loads and larger arc of contacts, but has the drawback of being offline. Keywords: Rolling load, Cold rolling, Friction hill, Noncircular arc.

A theoretical model for the tread slip and the effective rolling radius of the tyres in free rolling

A rigid–elastic coupling theory for the rolling kinematics of tyres, by which the tread slip, the effective rolling radius and the ply steering of the tyres can be analysed, was formulated. The theory demonstrates that, during free-rolling motion, the coupling between the rotational velocity Ω along the wheel axis and the circumferential displacement gradient generates the longitudinal tread slip, and the coupling between the rotational velocity Ω along the wheel axis and the lateral displacement gradient generates the lateral tread slip and the ply steering. Revisiting the tread slip phenomenon using the newly proposed method numerically proves the kinematic mechanism of the rolling friction. It can be found that the effective rolling radius Re increases with increasing inflation pressure and decreases with increasing load; the sensitivity of Re to the inflation pressure is greater than the sensitivity of Re to the load. The good agreement between the theoretical predictions and the test results for the effective rolling radius of the radial tyres of a car is found. The coupling of the displacement gradient and the rigid rolling kinematics causes non-symmetry of the lateral tread slip which, in turn, leads to the ply steering and the residual aligning moment; these depend on the belt and tread design. The proposed theory and approach provide a quick and powerful tool for analysing the tread slip, the effective rolling radius and the ply steering of the tyres under free rolling.

Spinning Process Design Using Finite Element Analysis and Taguchi Method

Abstract Metal spinning process is widely used because of its low power requirement to producing complex symmetry components. Spinning process parameters influence the spinning force and wall breakage or wrinkling problems of finished parts. The experimental and numerical simulation of metal sheet spinning has been applied to investigate the effect of spinning process parameters in order to achieved lower force and large deformation without the wall breakage or wrinkling failure. In the study, Taguchi method is implemented in cooperate with finite element analysis to reduce the number of numerical simulation. The spinning experiments were carried out on a modified turning lathe to accommodate a Kreisler force transducer to measure spinning forces. The three dimensional finite element model of sheet metal spinning was developed using the same spinning experiment process parameters. The SPCC sheet metal workpiece is modelled as an isotropic elastic-plastic material. The average predicted spinning force was 853 N. There is an error of 6.25% in the FE model prediction. Furthermore, the predicted thicknesses of the deformed part were compared with the measured experimental parts thickness and the error was 6.06%. It is clear that the finite element model results agreed well with the spinning experimental results. The effect of eight process parameters, i.e. roller radius, spindle speed, feed rate and feed depth, friction coefficient, width of support roller, diameter of support roller and angel of mandrel slope, on spinning force and deformation were studied. Finite element analysis of Taguchi-L18 spinning experiment were carried out. Taguchi main effect analysis and ANOVA results show that the slope of mandrel, spinning depth and support roller width are the most important factors influencing the spinning force. The slopes of mandrel, spinning depth and roller radius are the most important factors influencing the thickness variation of deformed parts. The roller radius, spinning depth and support roller width are the most important factors influencing the severity of wrinkling failure.

Optimal design for an end face engagement worm gear with multiple worm-wheel meshing

To solve the problem for lacking a special mechanical transmission that could provide multiple outputs with high transmission efficiency and good lubrication in the modern industrial, a novel worm gear, named end face engagement worm gear, with multiple worm-wheel meshing is proposed for the first time. The essential parameters for the worm gear are optimized to enhance lubrication and meshing properties. Moreover, analysis of variance(ANOVA) is applied to determine the optimum levels and to determine the influence of parameters. The ANOVA results show that the novel end face engagement worm gear with multiple worm wheels provides high lubrication(the lubrication angle is more than 89°) and meshing performance(the induce normal curvature is less than 0.0002 mm−1). The interaction between center distance and roller slant distance most strongly influences the lubrication angle(contributed 51.6%), followed by the parameters of center distance(contributed 25.0%), roller slant distance(contributed 16.4%), tooth angle of gear, gear ratio, and roller radius. In addition, roller radius most strongly influences the induced normal curvature(contributed 39.4%), followed by roller slant distance(contributed 15.2%), tooth angle of the gear(contributed 9.0%), center distance, and gear ratio. The proposed worm gear helps to enrich the no-backlash high precision worm drive and the optimal design method can provide a useful reference on performance improvement of other worm gear.

Large Elasto-plastic Deflection of Thin Beams with Roller Support Contact

Here, an explicit numerical approach is presented to solve the problem of a three-point bending of a thin elasto-plastic beam undergoing large deflection supported on cylindrical rollers with radius comparable to the deflection. There are three sources of non-linearity in this problem: roller to beam contact, plastic deformations and large deflections. An incremental form of moment- curvature based constitutive law is derived from a uniaxial linearly hardening stress-strain material model. The governing boundary value problem in terms of its slope is transformed into an initial value problem, with the domain up-to the point of contact. The non-linear initial value problem is linearized about the current step and solution for the subsequent step is obtained by employing the classical Runge-Kutta fourth-order method. This solution procedure is repeated for a range of lengths and end angles of beam. Subsequently, a feasible data set is created from the solution space which satisfied the contact configuration condition. It is found that the increase in the radius of roller introduces a stiffening effect in the force response of the structure. A springback analysis is also performed for the beam data from a feasible set which satisfies plastic deformation condition. It is found that springback decreases with the increase in the radius of roller supports.

OPTIMIZACIÓN PARAMÉTRICA DEL PROCESO DE ENGATILLADO LINEAL POR ROLDANA PARA CHAPAS METÁLICAS

El presente trabajo, se enfoca en la optimizacion parametrica de las variables geometricas del engatillado, tales como: el radio de la roldana, el angulo de pre-engatillado y el radio del doblez del panel exterior para crear la ceja en funcion de generar una mejora en los parametros de calidad del proceso: enrollamiento de la pestana (Roll-in), desenrollamiento de la pestana (Roll-Out) y arruga. Adicionalmente, se muestra la comparacion de los resultados, iniciales (no optimos) y optimos, obtenidos tanto en simulacion numerica como en pruebas experimentales. Las simulaciones del proceso se llevaron a cabo implementando el software de analisis por elemento finito, ANSYS Workbench 15®. Para las pruebas experimentales se utilizo una estacion de trabajo consistente en un manipulador industrial de 6 grados de libertad (GDL) NACHI SRA210, sobre el que se monto un herramental de soporte para la roldana. A partir de los parametros determinados en simulacion, se fabricaron dos roldanas, uno con parametros optimos (10.18 mm de radio) y el otro con los parametros iniciales (25 mm de radio). Se realizaron pruebas de engatillado lineal sobre chapas de aluminio 6011, de 0.9 mm de espesor y dimensiones de 120 x 100 mm2. El analisis de los resultados experimentales obtenidos muestra que, al igual que en simulacion, la roldana con parametros de engatillado optimos genera una mejoria, en los tres parametros considerados de calidad de engatillado, en comparacion con la calidad obtenida con la roldana de parametros iniciales.

Optimization of the cold-rolling process to enhance service life of railway axles

Over the last years, deep rolling has been adopted to improve the fatigue strength of railway axles. In particular, recent researches between PoliMi and LucchiniRS have shown the possibility to greatly enhance the residual lifetime of axles in presence of defects from running in service by inhibiting the propagation of cracks under normal loading conditions and retarding the appearance of corrosion-fatigue phenomena. Therefore, the new automatic machining line for axles setup by LucchiniRS includes a modern cold-rolling machine as a finishing process for premium quality axles. This paper is devoted to discuss the optimization of the cold-rolling process considering all the relevant parameters (load, roller radius, pitch) through a novel model able to simulate the build-up of residual stresses. The model was validated by comparing the residual stress path with the experimental outcomes, showing a good agreement for the various combination of the adopted parameters. The exploitation of the model will enable the designer to optimize the cold-rolling process taking advantage of the increase of fatigue properties in the definition of a safe life maintenance plan.

Shear forming of 304L stainless steel – microstructural aspects

Shear forming is an incremental cold forming process. It transforms 2D plates into 3D structures commonly consisting of conical geometry. Roller(s) push the blank onto a cone-shaped mandrel, resulting in a decrease of the initial thickness. The shear forming process has diverse advantages, such as improved material utilisation, enhanced product characteristics, good surface finish, consistent geometric control and reduced production costs. Shear forming has potential applications in a wide range of conical geometries used within advanced aerospace structures, which are currently manufactured from bulk forgings with high associated machining costs. Research findings related to shear forming have been published over the past two decades, however, important remaining questions have still to be answered, with this paper addressing one such gap associated with the material deformation mechanism. Several studies have demonstrated the impact of key process variables on the final geometry and surface roughness, such as the feeds, roller nose radius and mandrel/roller offset. Although the material outputs are essential, as they link directly with the mechanical properties of the final components, the microstructure and texture of the material after shear forming have rarely been studied. Achieving a greater understanding in this area could reduce the reliance upon mechanical testing to validate the process and ease the exploitation route of the technology into advanced aerospace applications. Firstly, this paper presents the principle of shear forming and its related terminology. Then, a brief overview of the shear forming process including its history and origin is given. The areas of focus are a selection of the main variables encountered within this process which could impact the final properties. The generation of local stresses due to deviations from the sine law, the angle variations, and forces required during the forming operation are also considered. This is explored in the context of forming 304L stainless steel plates.

Examination of Vertical Dynamics of Passenger Car with Wheel Flat Considering Suspension Parameters

This paper describes the analysis of the vertical dynamics of the passenger car motion considering the vertical forces of wheel/rail interaction. The aim of this study is the assessment of the smoothness of passenger car running while one wheel is with a flat. The mathematical models of wheel flat impact on the rail and entire passenger car dynamic models are defined. In order to evaluate smoothness of rail vehicle movement by computer simulation means the software package Simpack was used. In this case, the wheel-flat was modelled considering the deviation of wheel rolling radius. On the base of the theoretical analysis, the vertical accelerations of passenger car with wheel flat running on the tangent track were evaluated. The analysis of passenger carbody oscillations was performed, while the vertical damping and stiffness of the car primary/secondary suspension changed within the specified range. The values of acceleration signals were measured and clarified. Finally, basic conclusions are given.

Utilizing 2-D and 3-D simulations in assisting tooling design in Chain-die forming threshold product

With the increasing demand of reducing the body weight of automobiles, the utilization of advanced high strength steel has increased dramatically in recent years. However, high residual stress and redundant strain caused by the traditional cold roll forming process is still an outstanding problem. Under such circumstances, the Chain-die forming method is developed as a novel sheet metal forming approach which combines roll forming and stamping processes. A Chain-die former employs discrete die blocks which run on a chain track with significant virtual roll radius, simulating a roll forming process. Meanwhile, individual pairs of die blocks deform the sheet metal gradually acting as a stamping process. Through the enlargement of virtual roll radius, the peak longitudinal strain developed during the forming process is dramatically decreased (contained in the elastic region), leading to significantly reduced residual stress and almost no redundant deformation. Due to low longitudinal strain, the cross-sections of the product can be considered as a plane strain state throughout the entire forming process, allowing utilization of 2-D plane strain simulations to represent for 3-D simulations. In this paper, using 2-D FE stamping simulations and 3-D FE Chain-die forming simulations in assisting die design for a Chain-die formed threshold product using AHSS material is discussed. The results show 2-D stamping simulations are able to predict the average forming angles of 3-D simulation results with high accuracy and much higher efficiency. In the initial tooling design process, 2-D stamping models should be employed to design the tooling geometry in order to compensate the springback effect, followed by 3-D Chain-die forming models validating the 2-D design and providing additional information such as variation of the flange angle along the longitudinal direction and the longitudinal bow condition. The findings can be applied in industrial practice which can significantly accelerate the tooling design process for the Chain-die forming method.

Improvement of formability of AZ31magnesium alloy by repeated roll bending process

Abstract Dispersion of the basal texture is effective to improve the formability. A repeated roll bending process (7 work rolls, work roll radius of 32 mm, roll pitch of 40 mm) was applied to AZ31 magnesium alloy sheets by activating the tensile twins. The larger applied bending strain per pass was effective to increase hardness at the surface of the sheet. The Erichsen value was slightly increased from 3.0 to 3.5 mm by subjected 2 passes repeated roll bending and subsequent at 180 °C for 12 hours annealing without decreasing the hardness of the sheet before bending (Hv=60). The Erichsen value of 3.3 and over hardness of Hv 65 through thickness were obtained by 2 passes bending and 160°C for 12 hours annealing. The tensile twins and texture randomizing were observed around center of thickness by electron backscatter diffraction (EBSD) analysis. It was possible to increase formability of AZ31 magnesium alloy by the repeated roll bending and subsequent low temperature annealing.

Optimization of Rail Profiles to Improve Vehicle Running Stability in Switch Panel of High-Speed Railway Turnouts

A method for optimizing rail profiles to improve vehicle running stability in switch panel of high-speed railway turnouts is proposed in this paper. The stock rail profiles are optimized to decrease the rolling radii difference (RRD). Such characteristics are defined through given rail profiles, and the target rolling radii difference is defined as a function of lateral displacements of wheel set. The improved sequential quadratic programming (SQP) method is used to generate a sequence of improving profiles leading to the optimum one. The wheel-rail contact geometry and train-turnout dynamic interaction of the optimized profiles and those of nominal profiles are calculated for comparison. Without lateral displacement of wheel set, the maximum RRD in relation to a nominal profile will be kept within 0.5 mm–1 mm, while that in relation to an optimized profile will be kept within 0.3 mm–0.5 mm. For the facing and trailing move of vehicle passing the switch panel in the through route, the lateral wheel-rail contact force is decreased by 34.0% and 29.9%, respectively, the lateral acceleration of car body is decreased by 41.9% and 40.7%, respectively, and the optimized profile will not greatly influence the vertical wheel-rail contact force. The proposed method works efficiently and the results prove to be quite reasonable.

A device to measure wheel slip to improve the fuel efficiency of off road vehicles

A hall sensor based simple technique was introduced to measure wheel slip and a microcontroller based embedded digital system was developed to display wheel slip data and warn the operator with audible and visible warnings if the optimum range is exceeds. Hall sensor slip measurement system was validated in controlled soil bin condition, tar macadam surface and actual field condition and compared with the commercial radar sensor. The developed system is simple in construction and can be mounted to any make and model of agricultural tractors by entering the appropriate rolling radius via the computer interface. Field trials were conducted to measure wheel slip and fuel consumption on farm use with and without activation of slip indicator; it was observed that, the amount of fuel saving during various agricultural operation was up 1.3l/h.

Analytical scrutiny of nonlinear equation of hypocycloid motion by AGM

The curve produced by fixed point on the circumference of a small circle of specified radius rolling around the inside of a large circle with bigger radius than the other one is named hypocycloid. In the present paper, a semi-hypocycloid motion of a cylinder has been simulated by extracting the governing nonlinear differential equation of this especial motion, and then, the obtained equation has been solved completely by a simple and innovative approach which we have named it Akbari---Ganji's method (AGM). On the basis of comparisons which have been made between the gained solutions by AGM, numerical method (Runge---Kutta 4th) and VIM, it is possible to indicate that AGM can be successfully applied for various differential equations. In this paper, a nonlinear vibrational equation has been solved by AGM, and afterward, the application of AGM will be shown in our own specified problem. It is noteworthy that this method has some valuable advantages, for instance in this approach, it is not necessary to utilize dimensionless parameters in order to simplify equation. So there is no need to convert the variables to new ones that heightens the complexity of the problem. Moreover by utilizing AGM, the shortage of boundary condition(s) for solving differential equation will be terminated by using derivatives of main differential equation(s). The results reveal that this method is very effective, simple, reliable and can be applied for many other nonlinear problems.

Tractor traction performance simulation on differently textured soils and validation: A basic study to make traction and energy requirements accessible to the practice

Several models exist to simulate traction performance of a tractor, however, for most of them a proper experimental validation is missing. Moreover, their possible application for a practical use in a wide range of vehicles, equipment and soil configurations has never been further developed. This study examines a semi-empirical model of soil-tyre interaction, adapted to simulate the traction performance of mechanical front wheel drive tractors, taking into account not only mechanical soil and tyre parameters and static vehicle load but also the multi-pass effect, the load transfer effect, and the theoretical speed ratio between front and rear axles. This model simulates drawbar pull, traction coefficient, traction efficiency, and motion resistance as a function of slip, wheel load, tyre size and pressure. Several traction tests were performed on four Swiss agricultural soils of different type (clay, clay loam, silty loam, and loamy sand) in order to validate the model experimentally. Three tractors of widely ranging power (from 40 to 132kW) and weight (from 24 to 68kN) were used. Tractor configurations were varied by changing tyre pressure and tractor weight. Slip normally ranged between 5 and 30%. In most of the cases the model simulated drawbar pull as well as its variations due to changes in tyre pressure, wheel load, and soil strength reliably for practical purposes. Only when high wheel load was combined with low inflation pressure the model did not give suitable results due to an overestimation of the rolling radius. Based on the presented model, a convenient Excel-application called TASCV3.0 was developed for the practice. Such a practical computer-tool supports farmers in decision making concerning the tractor configuration, oriented to save fuel during agricultural operations.

A New Method Predicting Contact Length and Flattening in Temper Rolling

The current trend in temper rolling is to make a small reduction to steel strip in order to achieve higher strength with good formability and toughness. In addition, very high strength steels can be cold rolled twice with very small reductions. This causes problems in setup values for cold rolling. Rolling models are usually overestimating roll flattening in the case of small reductions.In temper rolling thickness reduction is small (0.5 – 3%) and the elastic deformation of the work roll should be taken into account [3]. However, standard circular arc roll gap models (e.g. Bland Ford Ellis combined with Hitchcock model) fail to predict the roll flattening and thus the rolling force [4]. In this work, finite element method has been used to define a simplified model for work roll flattening and contact length. Model describes the effect of reduction, strength of steel strip and roll radius.

Analysis of snake rolling force and torque with changes of thickness depending on unequal roll radii based on pure aluminum experiments

An analytical model, in which unequal radii are replaced with an equivalent radius, is creatively proposed to predict the rolling force and roll torque in general case of snake rolling. With the model, the effects of roll radius ratio, roll speed ratio, offset distance between rolls, reduction and friction coefficient on rolling forces in hot snake rolling of aluminum alloy are obtained. Also, the thicknesses of slab are investigated in different zones, which firstly propose the changes of thickness during snake rolling. Owing to the good agreement with the results measured in experiments and calculated by finite element method and other traditional models, those calculated by the proposed model are verified. The proposed model can be used to predict more accurate theoretical results for snake rolling force and torque.

Effects of curve radius and rail profile on energy saving in heavy haul achieved by application of top of rail friction modifier

Energy saving achieved by application of top of rail (TOR) friction modifier (FM) in heavy haul are modeled, and the effects of curve radius and rail profile on the energy saving are discussed. A vehicle model for a C70 freight car running on the track of a heavy haul line was established. The coefficient of friction and Kalker coefficient were adjusted to simulate the creepage/force relationship when the TOR FM is applied to the wheel/rail interface. Friction work is used to represent the energy dissipation due to wheel/rail creepage. Energy saving achieved by applying TOR FM was calculated. The energy saving was studied under different operating conditions, and the effects of track curve radius and rail profile were studied. It is found that the curve radius of the track has significant influence on the energy saving. The energy saving was also found to behave differently on new and worn rails. The dramatic increase of lateral creepage on new rail when FM is applied and the decrease of the difference of wheel rolling radius when the rail profile changes from new to worn were found to be the main reasons that cause the difference.

Dynamic stability of cemented carbide circular saw blades for woodcutting

With increasing requests and applications for carbide circular saw blades in the wood industry for furniture manufacturing, dynamic stability becomes a critical problem that has a strong effect on cutting quality, noise, vibration, material waste and the lifetime of a saw blade. The dynamic stability of a circular saw blade is associated with its natural frequency and stress distribution, and roll tensioning is considered to be the most effective method to improve this dynamic stability. In this study, several roll tensioning methods have been investigated, and the results indicate that continuous roll tensioning along a fixed tracking groove on the surfaces of circular saw blade produces better dynamic stability compared with alternative roll tensioning along different tracking grooves. The effects of various roll-tensioning parameters, such as rolling force, rolling radius and rolling number, on the natural frequency and stress distribution of circular saw blades have also been investigated, thus, optimum parameters can be achieved. Results show that the influence of the rolling force is the strongest, while the effect of the rolling number is negligible. Radial slots can effectively increase the natural frequencies of a circular saw blade and reduce heat stress, particularly tangential heat stress, which is induced by cutting processes. The slot number and length also have strong effects on the natural frequencies. Additionally, the effects of geometric parameters, such as the thickness of the saw blade and the clamp diameter, on the natural frequencies are also examined using finite element analysis. The simulated results are validated by experimental tests, which exhibit good agreement with the experimental results.