Critical Speed Ratio Research Articles

Analysis of Mechanical Parameters in Multi-Pass Asymmetrical Rolling of Strip by Slab Method.

Mechanical parameters, time consumption and energy consumption are important considerations in the application of a certain rolling process. This study aims to investigate characteristics of the roll force, roll torque, roll power, rolling time and total work in multi-pass asymmetrical rolling of strip. Mathematic models were built using the slab method to calculate parameters in the asymmetrical rolling process, and the characteristics of these parameters were analyzed on the basis of simulation results. Mechanical parameters are affected by the change of deformation region type. When the speed ratio is less than the critical speed ratio, the roll force, absolute values of roll torque and roll power are found to increase with the increase in the speed ratio. After the speed ratio reaches the critical speed ratio, the roll force, roll torque and lower roll power keep constant, but the upper roll power continues increasing. The upper roll torque and upper roll power required by asymmetrical rolling are much greater than that by symmetrical rolling, which indicates that stronger drive shafts and more powerful drive motors are required by asymmetrical rolling. Compared with symmetrical rolling, asymmetrical rolling requires less roll force to obtain the same thickness reduction, especially for thin and hard strips. Rolling time can be saved at the cost of more energy consumption by using asymmetrical rolling with the same roll force to attain the same final thickness. The results and conclusions of this study can provide a reference for mill design and application of asymmetrical rolling in strip manufacturing.

Stress-deformation analysis of rail substructure under moving wheel load

A three-dimensional (3D) finite element (FE) analysis is developed to study the effect of moving wheel load on the dynamic response of track with the key objective of determining the accurate stress-deformation response of the substructure. The 3D FEM model is first calibrated and then validated with two independent set of field measurements. The computed transient displacements and vertical stresses corroborate well with the field data from the selected case studies, endorsing the reliability of the current numerical model. The changes attributed to dynamic stress paths and the angle of principal stress rotation are also analysed with respect to the train speed in the range, 60–450 km/h. The results show some limitations of the existing dynamic amplification factor in relation to the design of railway track. This traditional approach will only be appropriate when the train speeds are relatively low, but it will not be accurate at significantly higher speeds at which significant principal stress rotation occurs, resulting in correspondingly increased shear stresses. The current FEM model enables a limiting train speed to be determined to prevent shear failure of the ballast layer when the dynamic response in relation to ballast properties is interpreted based on the proposed R-wave speed /critical track speed ratio.

Study on minimum rollable thickness in asymmetrical rolling

A new model for the asymmetrical rolling is proposed to calculate the minimum rollable thickness simply and fast by the slab method. The calculation formulas of the rolling pressure, the rolling force, the critical roll speed ratio, and the critical front tension under different deformation zone configurations are proposed, and the deformation zone configuration-rolling parameter relationship diagram is given and analyzed. The results show that the minimum rollable thickness can be reached when the rolling parameters keep the deformation zone configuration as cross-shear zone + backward-slip zone (C + B) or all cross-shear zone (AC). The calculation formulas of the minimum rollable thickness and the required rolling parameters for different deformation zone configurations are proposed, respectively. The calculated value agrees well with the experimental result.

Experimental investigation on stall characteristics of contra-rotating compressor with variable speed ratios

By experiment at a low-speed large-scale axial contra-rotating compressor, the near stall points of 19 speed configurations were captured and the stall characteristics under different speed ratios were obtained successfully. The results show that the compressor with speed ratio greater than 1 are more likely to stall than the compressor with speed ratio less than 1 and the flow rate at the starting point of stall is at least 18% earlier, the pressurization capacity is at least 5.5% higher when speed values of the front and rear rotors are interchanged. At the same speed ratio, the dimensionless characteristic lines of pressure rise coefficient-flow coefficient almost coincide. With the decrease of speed ratio, the dimensionless characteristic line of contra-compressor moves upward. Through summing up all speed configurations' stall types and stall initial disturbance frequency, it can be found that: there is a critical speed ratio between 1.125 and 1.167 in the contra-rotating compressor studied in this paper. When the speed ratio is less than the critical value, the stall disturbance has the characteristic like spike stall. At this time, the initial stall disturbance frequency is higher with the speed ratio is smaller. And at the same speed ratio, the initial stall disturbance frequency increases with the increase of the average speed of the front and rear rotors. When the speed ratio is greater than the critical value, the stall disturbance doesn't rotate circumferentially.

Numerical Evaluation and High-Speed Rotating Test on Circular Arc Spring Dampers for Centrifugal Compressors

Abstract A circular arc spring damper (CASD) is a recently proposed fluid-film damper that has two or more arc-shaped centering springs and dual radial clearances formed by wire electric discharge machining (WEDM). CASD requires less space and weight than a conventional cage-centered squeeze-film damper (SFD). It provides linear stiffness and stable damping force in rotor-bearing systems to attenuate vibration due to imbalance or to improve rotordynamic stability. The authors have been investigated the dynamic characteristics of CASD in component-level experiments. However, their performance and applicability to real machines have not been confirmed in system-level experiments. Additionally, a theoretical means of evaluation for CASD should be established to predict its dynamic coefficients and to understand the mechanism of dynamic force generation. In the first part of this study, a numerical evaluation method using two-way fluid–structure interaction (FSI) analysis and its theoretical background is presented. Transient structural analysis and fluid-film flow analysis with a simple homogeneous cavitation model are coupled in the commercial multiphysics platform ansys. The accuracy of the method was validated by comparing the damping and added-mass coefficients with results from previous experiments. Furthermore, several aspects of the force generation mechanism and the difference from conventional SFD were studied numerically. The second part of the study addresses the application of CASD in a multistage centrifugal compressor. A combined 4-in. diameter, five-pad tilting pad journal bearing (TPJB) with four-arc type CASD was newly designed and manufactured. To prove the applicability of the developed damper bearing, a series of rotating tests were conducted at a high-speed balancing facility with a full-scale dummy rotor with a critical speed ratio (CSR) of approximately 3.1. The measured unbalance response showed a much lower amplification factor (AF) than that of the conventional TPJB without the damper, which infers a significant improvement in the stability. The measured responses agreed with the rotordynamic analysis, which uses the dynamic coefficients of CASD derived from the proposed numerical evaluation method.

Analysis of crack-free surface generation of photovoltaic polysilicon wafer cut by diamond wire saw

At present, diamond wire sawing technology has been widely used in slicing photovoltaic polysilicon. Improving the surface quality of the slices to obtain a sawn surface without microcrack damage can greatly increase the fracture strength of polycsilicon wafers and reduce the cost of wet black silicon texturing, which is beneficial to improve the final photoelectric conversion efficiency of solar cells. In this paper, a mathematical model of diamond wire sawing was established based on the machining mechanism of brittle material removal and surface generation, and the numerical calculation of the sawing process was carried out. The validity of the model was verified by sawing experiments. The critical ratio of workpiece feed speed to saw wire movement speed was obtained when generating a crack-free slice surface under the combination of different process parameters and saw wire parameters. Based on the established theoretical model of sawing, the influence of saw wire movement speed, abrasives density and abrasives size on the critical speed ratio was analyzed, and the critical speed ratio (CSR) corresponding to the finer diameter wire and the higher wire speed which will be gradually applied in industry in the future was analyzed. The research results show that it is more conducive to obtaining a crack-free sawn surface by reducing the workpiece feed speed or increasing the saw wire movement speed, and the workpiece feed speed has a greater impact on the sawn surface quality. The CSR will slightly decrease within a small change range when increasing the saw wire movement speed. Increasing the density of abrasives on the saw wire surface within a certain range or decreasing the abrasives size is more inclined to obtain a crack-free sawn surface. The CSR will decrease slightly in a small range when decreasing the abrasives density or increasing the abrasives average size.

Analysis of asymmetrical rolling of strip considering two deformation region types

Analytical models of two deformation region types considering the percentages of three regions in the plastic deformation zone are proposed for analyzing asymmetrical rolling of strip and used to calculate the critical speed ratio, three region percentages, roll force, and roll torque. The effective range of speed ratio on thickness reduction increases with increasing critical speed ratio. When the deformation region type is backward-slip zone + cross-shear zone + forward-slip zone (B+C+F), with increasing speed ratio, the thickness reduction in asymmetrical strip rolling increases evidently, but remains unchanged when the critical speed ratio is exceeded, where the deformation region type is backward-slip zone + cross-shear zone (B+C). It is achievable to increase thickness reduction by increasing the roll force and front tension, which can not only increase the reduction rate, but also increase the critical speed ratio. The effect of asymmetrical rolling on thickness reduction is enhanced with decreasing of the roll force and front and back tension because of the increasing cross-shear zone percentage.

Study on the relationship between asymmetrical rolling deformation zone configuration and rolling parameters

A new model for analyzing asymmetrical cold rolling process is proposed by the slab method, which solves the problem of insufficient applicability of existing models in the face of multiple asymmetric rolling conditions. In the new model, six configurations of the deformation zone are proposed as, forward-slip zone + cross-shear zone + backward-slip zone (F + C + B), cross-shear zone + backward-slip zone (C + B), all cross-shear zone (AC), forward-slip zone + cross-shear zone (F + C), all forward-slip zone (AF) and all backward-slip zone (AB). By analyzing the effects of rolling parameters such as reduction rate, roll speed ratio, tension and friction coefficient on the deformation zone configuration, the critical roll speed ratio and critical tension required for different deformation zone configurations are proposed. According to the variations of the critical roll speed ratio and critical tension with different rolling parameters, the deformation zone configuration - rolling parameters relationship diagram is obtained. Based on this diagram, the deformation zone configurations produced by different rolling parameter ranges can be determined, and the reasonable asymmetrical rolling technology can be selected for different production objectives. The proposed model can comprehensively and accurately calculate the rolling pressure, rolling force and torques under various rolling conditions, the calculated values agree well with the experimental results, the maximum error is 9.97%.

Analytical prediction of subsurface microcrack damage depth in diamond wire sawing silicon crystal

Subsurface microcrack damage depth (SSD) in silicon wafer processed by diamond wire sawing has a great influence on the subsequent processing process and fracture strength of silicon wafer. Based on the indentation fracture mechanics, a new numerical model for predicting the SSD of silicon wafer on the basis of half-penny crack system is proposed in this paper. In this model, effect of the random distribution characteristics of size, position and tip half angle of abrasives and different material removal modes to the contour of workpiece cutting groove are all considered. Median cracks and radial cracks are regarded that propagating into one body, that is half-penny crack system. Validity of this model is verified by comparing with experimental results in the literature. From this model, the relationship between SSD and feed rate, wire speed, size of abrasives and density of abrasives on the surface of saw wire is analyzed, the critical speed ratio of feed rate to wire speed that can achieve pure ductile processing is discussed as well. The results show that using the maximum extended length of half-penny crack system as the SSD of silicon wafer is more reasonable than using the maximum extended length of median cracks as the SSD of silicon wafer. As wire speed increases, feed rate decreases, or density of abrasives on the surface of saw wire increases, the SSD will decrease. Keeping other parameters of saw wire unchanged, the size of abrasives has no significant effect on the change of SSD. Keeping the ratio of feed rate to wire speed unchanged, the SSD varies within a small range. When the speed ratio is in the range of 10.43–16, the slice surface tends to be formed by pure ductile removal of material. The results can be used to guide the optimization of diamond wire sawing process.

Synergistic and interference effects in coaxial mixers: Numerical analysis of the power consumption

Abstract This paper is concerned with the design and application of coaxial mixers with the aid of analysis of interaction between each individual impeller. Two types of coaxial mixers pitched blade turbine (PBT)-helical ribbon (HR) and inner-outer HR operated in laminar regime were studied experimentally and numerically. The interaction implies synergistic and interference effects, which was revealed through the investigation of axial circulation rate, energy dissipation rate and power consumption. The influence factors including rotational speed ratio, rotating mode and impeller configuration were explored systematically. Quantitative analysis of power consumption involves three parameters: rate of variation in power consumption, interactive mode and ratio of power consumption. Analysis indicated that some important properties were embodied in the power curve. These properties are one-way and two-way interactions, critical speed ratio and dominant impeller. Finally, a new suggestion for power estimation was given.

Modeling of the effects of phase shift on cutting performance in elliptical vibration cutting

In the elliptical vibration cutting process, the elliptical locus is considered to be a vital factor that affects cutting performance. Besides the cutting speed and vibration amplitudes, the phase shift (i.e., the phase difference between the two-directional output harmonic vibrations forming the elliptical locus) is an intrinsic parameter that determines the shape and inclination of the elliptical locus with respect to the cutting direction. In this paper, a numerical recursive search method is proposed to investigate the effect of phase shift in elliptical vibration cutting. It has been shown that the critical speed ratio for considerably improving the cutting performance has a sinusoidal correlation with the phase shift. For elliptical loci with arbitrary shapes, the developed model theoretically predicts the maximal influential thickness of cut, surface roughness, and the tool-workpiece contact ratio as a function of phase shifts. Experiments were conducted to validate the developed model through the evaluation of the machined surface profile, roughness, and dynamic cutting force. The obtained results offer a method to determine the proper machining variables in cutting hard and brittle materials during the elliptical vibration cutting process with an arbitrary locus.

Compressibility effects on the flow past a rotating cylinder

In this paper, laminar flow past a rotating circular cylinder placed in a compressible uniform stream is investigated via a two-dimensional numerical simulation and the compressibility effects due to the combination of the free-stream and cylinder rotation on the flow pattern such as forming, shedding, and removing of vortices and also the lift and drag coefficients are studied. The numerical simulation of the flow is based on the discretization of convective fluxes of the unsteady Navier-Stokes equations by second-order Roe’s scheme and an explicit finite volume method. Because of the importance of the time dependent parameters in the solution, the second-order time accurate is applied by a dual time stepping approach. In order to validate the operation of a computer program, some results are compared with previous experimental and numerical data. The results of this study show that the effects due to flow compressibility such as normal shock wave caused the interesting variations on the flow around the cylinder even at a free-stream with a low Mach number. At incompressible flow around the rotating cylinder, increasing the speed ratio, α (ratio of the surface speed to free-stream velocity), causes the ongoing increase in the lift coefficient, but in compressible flow for each free-stream Mach number, increasing the speed ratio results in obtaining a limited lift coefficient (a maximum mean lift coefficient). In addition, results from the compressible flow indicate that by increasing the free-stream Mach number, the maximum mean lift coefficient is decreased, while the mean drag coefficient is increased. It is also found that by increasing the Reynolds number at low Mach numbers, the maximum mean lift coefficient and critical speed ratio are decreased and the mean drag coefficient and Strouhal number are increased. However at the higher Mach numbers, these parameters become independent of the Reynolds number.

Optimal design of protuberant blades for small variable-speed horizontal axis wind turbine-experiments and simulations

In our previous study, it has been shown that the use of protuberances covering the whole leading edges of B-blades will enhance the performance of horizontal axis wind turbine (HAWT) under low speed rotations. However, a great loss of performance shall occur after a critical tip speed ratio is reached. The research aims to optimize the protuberance design of HAWT blades for the system to gain optimal performance under low speed rotations, whereas no significant drop of performance happens at high tip speed ratios. The optimization study was performed not only for baseline blades but also for those designed by the blade element momentum theory. For verifications, wind tunnel experiments were carried out to provide comparative data; additionally, numerical simulations were also conducted to further visualize the flow fields. The results show that the optimal leading-edge protuberances would significantly increase the HAWT performance under low speed rotations, yet no serious performance payback occurs at high tip speed ratios.

Discussion of “Study of aerodynamic coefficients used to estimate critical wind speed for vehicle overturning” by Katsuhiro Kikuchi, Minoru Suzuki

The critical wind speed for vehicle overturning in railway lines is researched in the paper of “Study of aerodynamic coefficients used to estimate critical wind speed for vehicle overturning” by Katsuhiro Kikuchi, Minoru Suzuki, where the aerodynamic coefficients of vehicle are obtained by the wind tunnel tests (in the atmospheric boundary layer flow or in the uniform flow) and the full-scale field test. This is very meaningful for ensuring the running safety of the train under the crosswind. However, there are some definitions and conclusions are worth discussing, such as the minimum critical wind speed ratio.

Optimal design of a power-split hybrid hydraulic bus

The hydraulic power-split architecture, or the hydromechanical transmission, can exist in over 1000 configurations. Since a specific hydromechanical transmission configuration has a unique kinematic characteristic, the optimal hydromechanical transmission configuration for one application is different from the optimal hydromechanical transmission configurations for other applications. This study finds the optimal hydromechanical transmission configuration for a hybrid hydraulic city bus. Since a hydromechanical transmission uses at least one planetary gear set, the process of finding a suitable hydromechanical transmission configuration for a hybrid hydraulic city bus is very time consuming, but this study simplifies the procedure by utilizing the critical speed ratio ωcrit, where ωcrit is the missing link between the planetary gear set configuration, its gear ratio and its kinematic characteristic. This simplification also allows complex dual-stage hydromechanical transmission architecture configurations to be considered as candidates for the optimal drivetrain of the hybrid hydraulic city bus. The hydromechanical transmission configuration candidates are simulated over three city bus driving cycles and, to ensure that they operate at the optimal conditions for each driving cycle, dynamic programming is used. This study also establishes two power recirculation modes, one of which is useful because of its high efficiency. A single-stage power-split architecture configuration candidate is found to be the optimal drivetrain for a hydromechanical transmission bus.

Analysis of power consumption and gas holdup distribution for an aerated reactor equipped with a coaxial mixer: Novel correlations for the gas flow number and gassed power

The main objectives of this work were to study the gassed power consumption and the local gas holdup for an aerated coaxial mixer composed of a wall scraping anchor and a central impeller. The working fluids were viscous corn syrup solutions at different concentrations. The central impellers were downward pumping pitched blade turbine, upward pumping pitched blade turbine, and hydrofoil A310 impellers. A novel correlation was developed to estimate the gassed power drawn by the coaxial mixer as a function of the gas flow rate, central impeller type, rotational speeds of the anchor and central impeller, and the ungassed power consumption by the anchor and the central impeller. To obtain a master power curve, two new correlations were proposed for the generalized power number and gas flow number of the aerated reactor furnished with the coaxial mixer by incorporating the equivalent rotational speed for the coaxial mixer, speed ratio (central impeller speed/anchor speed), and the central impeller power fraction into these two correlations. The experimental data revealed that by increasing the gas flow rate, the aerated anchor power was increased whereas the gassed power uptake of the central impeller was decreased. It was found that at the higher fluid viscosity and beyond the critical speed ratio equal to 10, the anchor power was increased by increasing the speed ratio (i.e. reducing the anchor speed). To measure the distribution of the gas holdup throughout the aerated reactor, four electrical resistance tomography planes were installed around the reactor. The tomography data showed that the local gas holdup near the vessel wall was not improved by increasing the anchor speed.

The Analysis of the Flutter Region of Wind Turbine Blade

As the wind turbine blade is becoming larger and larger, the flutter of the wind turbine blade has been paid great attention by many fields. The flutter region of the wind turbine blade airfoil was focused on. The equation of motion for the flutter of blade airfoil was established, based on the simplified aerodynamic force and torque. The flutter analysis of wind turbine blade was carried out with the four-order Runge-Kutta methods, and so the flutter region of the blade airfoil can be obtained. The results show that, there are two critical tip speed ratios for the given blade airfoil. When the tip speed ratio is below the low critical speed ratio, the blade airfoil is convergent. At the low tip speed ratio, the blade airfoil system will become divergent from convergent condition. When the tip speed ratio is between the low critical tip speed ratio and the high one, the blade airfoil system will diverge. At the high tip speed ratio, the system will become convergent from divergent condition. When the tip speed ratio is above the high critical tip speed ratio, the blade airfoil system will converge again. In addition, the torsional angular displacement and velocity always keep convergent, the flap velocity is slightly divergent, because they are not sensible to the change of the tip speed ratio, and they are difficult to cause flutter, so the torsional motion will be more stable than flap motion for the given blade airfoil. It can provide one of references for the determination of the blade airfoil.

Using tomography to assess the efficiency of the coaxial mixers in agitation of yield-pseudoplastic fluids

The mixing performances of five anchor coaxial mixers (anchor-Scaba 6SRGT, anchor-Rushton, anchor-Spiral, anchor-ARI, and anchor-A200), utilized for the agitation of non-Newtonian fluids, were evaluated in the laminar and transitional regime. To achieve this goal, power consumption and mixing time were measured as a function of the design parameters. An electrical resistance tomography (ERT) system was used to measure the mixing time. The non-Newtonian fluid was 2.0% xanthan gum solution (pseudoplastic fluid possessing yield stress). It was found that for all five configurations there was a critical speed ratio (RN=central impeller speed/anchor speed), which beyond it the mixing time did not decrease anymore with an increase in the speed ratio. Prior to this critical speed ratio, mixing time was proportional to RN0.4 regardless of the coaxial mixer configurations. The new correlations developed for the generalized Reynolds and power numbers of the coaxial mixers were tested successfully for all studied configurations. The power consumption and the mixing time data revealed that the Scaba-anchor coaxial mixer in the co-rotating mode was the most efficient mixer among the coaxial mixers explored in this study.

Optimum revolution and rotational directions and their speeds in planetary ball milling

A grinding rate of a gibbsite powder sample was examined by using a planetary ball mill and it was well correlated with the specific impact energy, which was calculated by Discrete Element Method (DEM). This implies a fact showing the confidence of the simulation result. Based on this result, an optimum rotation-to-revolution speed ratio and rotational direction of the pot to the revolution disk were investigated by the simulation work. A significant large specific impact energy is obtained when the mill pot is rotated at around the critical speed ratio in the counter direction to the disk revolution at around the critical speed ratio.

Effects of rotational direction and rotation-to-revolution speed ratio in planetary ball milling

The rotational direction of a pot in a planetary ball mill and its speed ratio against revolution of a disk were studied in terms of their effects on the specific impact energy of balls calculated from the simulation on the basis of the Discrete Element Method (DEM) and structural change of talc during milling. The specific impact energy of balls is measured as a significantly large value, and the structure of talc is transferred into an amorphous state quickly when the mill pot is rotated in the counter direction against the revolution. In both rotation–revolution relationships, the specific impact energy increases with an increase in the rotation-to-revolution speed ratio in the initial stage and then falls around the critical speed ratio, which can be calculated by the balance equation based on the centrifugal forces acting on a ball due to the combination of the rotation and revolution. The highest value in the specific impact energy of balls during milling can be achieved effectively around this critical speed. This critical speed would, therefore, be a key condition in milling for designing suitable and optimum mechanical milling performance.