On the Segregation of Particles in a Horizontal Rotating Conical Vessel. Axial Segregation Mechanism of Particles in a Conical Vessel Rotating at Lower Critical Speed Ratio.

1991 ◽  
Vol 40 (459) ◽  
pp. 1591-1597 ◽  
Author(s):  
Masunori SUGIMOTO ◽  
Masaki SUGIHARA ◽  
Kenichi YAMAMOTO
Keyword(s):  
Critical Speed ◽  
Speed Ratio ◽  
Axial Segregation

Analysis on Sliding State of Ball in Rotated Dual-Plates Lapping Mode

2011 ◽  
Vol 317-319 ◽  
pp. 345-349
Author(s):  
Wei Yu ◽  
Ju Long Yuan ◽  
Bing Hai Lv ◽  
Qian Fa Deng ◽  
Dun Liu
Keyword(s):  
Friction Coefficient ◽  
Critical Speed ◽  
Sliding Friction ◽  
Lower Plate ◽  
Speed Ratio ◽  
Rotating Speed ◽  
Simulation Based ◽  
Simulation Results ◽  
Direct Processing

Abstract . The sliding states of precision ball is an important factor in lapping uniform. To study the sliding state of ball in Rotated Dual-Plates(RDP) Lapping Mode, this paper analyses several kinds of sliding states from theory to the simulation based on the kinematics and dynamic.It is assumed that the slide could occure between the ball and inner lower plate or between the ball and outer lower plate. The simulation results show that there are several numerical combination among the spin angle θ, the coefficient ratio of sliding friction and the rotating speed ratio of the outer lower plate and inner plate,which is beneficial or adverse to improve the lapping uniformity.The results also show Machining load and the friction coefficient is increased, the critical speed of lapping plate also is higher, the ball is more not easy slide,and the critical speed of slide could be obtained to direct processing.

scholarly journals Analysis of Gas-Liquid Flow in an Aerated Reactor Equipped with a Coaxial Mixer through Tomography and CFD

2021 ◽  
Author(s):  
Nasim Hashemi
Keyword(s):  
Power Consumption ◽  
Liquid Flow ◽  
Critical Speed ◽  
Gas Flow ◽  
Mixing Time ◽  
Gas Holdup ◽  
Bubble Size Distribution ◽  
Speed Ratio ◽  
Pitched Blade Turbine ◽  
Gas Liquid Flow

This doctoral thesis addresses the mixing of highly viscous Newtonian fluids (corn syrup solutions) in a novel aerated reactor equipped with a central impeller (a pitched blade turbine in upward or downward pumping mode) and a wall scraping anchor. The non-intrusive electrical resistance tomography (ERT), dynamic gas disengagement method (DGD), design of experiments (DOE), computational fluid dynamics (CFD), and population balance model (PBM) were employed to characterize the performance of this novel aerated system. The performance criteria to be examined were mixing time, power uptake, gas holdup, and bubble size distribution. In this study, novel correlations were developed to estimate the gassed power drawn by the coaxial mixer, mixing time, and gas holdup. In addition, to obtain a master power curve, two new dimensionless correlations were proposed for the generalized power number and gas flow number 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 demonstrated that gas flow affected the aerated anchor power consumption and central impeller power consumption in different manners. It was also found that at the higher fluid viscosity and beyond the critical speed ratio of 10, the anchor power consumption was increased by increasing the speed ratio (i.e. decreasing the anchor speed). It was shown that in the presence of gas, the anchor impeller in combination with the upward pumping pitched blade turbine in the co-rotating mode exhibited shorter mixing times and lower power consumption than the anchor-downward pumping pitched blade coaxial mixer. To enhance the efficiency of the aerated mixer, it is critical to investigate the influence of the gas-liquid flow within the vessel on the bubble size distribution (BSD) and the local and global gas holdup. To achieve this goal, the effects of the bubble breakup and coalescence on the BSD within the vessel were incorporated into the CFD model through the CFD-PBM coupling. The experimental and simulation results showed that beyond the critical speed ratio of 10, the volume fractions of the large bubbles decreased while the volume fractions of the small bubbles increased.

scholarly journals Operation Analysis of a SAG Mill under Different Conditions Based on DEM and Breakage Energy Method

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5247
Author(s):  
Qiyue Xie ◽  
Caifengyao Zhong ◽  
Daifei Liu ◽  
Qiang Fu ◽  
Xiaoli Wang ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Critical Speed ◽  
Optimal Operation ◽  
Steel Ball ◽  
Speed Ratio ◽  
Power Simulation ◽  
Sag Mill ◽  
Operation Parameters ◽  
Fill Level ◽  
Mill Speed

As one of the machines widely used in mining, a semi-autogenous grinding (SAG) mill can significantly improve the roughing efficiency of rock. But the SAG mill still faces the obstacles of significant energy consumption and empirical operation parameters. In order to obtain the optimal operation parameters of a SAG mill, in this paper, the discrete element method (DEM) is used to simulate the breakage process of the particles by controlling three parameters, i.e., the mill speed ratio, the mill fill level ratio, and the steel ball ratio. This method simulates the particles size, mill power, and qualified particles quality of crushed particle, which reveal the grinding strength and energy consumption of the SAG mill. In this paper, the grinding changes of a SAG mill under different parameter conditions are explored. Firstly, an experiment on the influence of a single parameter change on the mill’s operation is set up, and then the influence of three parameter changes on the mill’s operation is analyzed. These changes are characterized by particle size and mill power. Simulation results under the ∅5250 × 500 mm mill model show that the mill operates with the optimal effect when the mill is under the condition of 80% critical speed and 15% fill level; the power of the mill does not increase linearly with an increase in the mill speed ratio, but will decrease after 85% of the critical speed, and finally increase again; the optimal steel ball ratio in the SAG mill depends on the simulation time (mill actual working time) and the limitation of the rated power. The mill speed, fill level ratio, and steel ball ratio can significantly affect mill operation, and our conclusions can provide a reference for an actual situation.

scholarly journals Analysis of Gas-Liquid Flow in an Aerated Reactor Equipped with a Coaxial Mixer through Tomography and CFD

2021 ◽  
Author(s):  
Nasim Hashemi
Keyword(s):  
Power Consumption ◽  
Liquid Flow ◽  
Critical Speed ◽  
Gas Flow ◽  
Mixing Time ◽  
Gas Holdup ◽  
Bubble Size Distribution ◽  
Speed Ratio ◽  
Pitched Blade Turbine ◽  
Gas Liquid Flow

This doctoral thesis addresses the mixing of highly viscous Newtonian fluids (corn syrup solutions) in a novel aerated reactor equipped with a central impeller (a pitched blade turbine in upward or downward pumping mode) and a wall scraping anchor. The non-intrusive electrical resistance tomography (ERT), dynamic gas disengagement method (DGD), design of experiments (DOE), computational fluid dynamics (CFD), and population balance model (PBM) were employed to characterize the performance of this novel aerated system. The performance criteria to be examined were mixing time, power uptake, gas holdup, and bubble size distribution. In this study, novel correlations were developed to estimate the gassed power drawn by the coaxial mixer, mixing time, and gas holdup. In addition, to obtain a master power curve, two new dimensionless correlations were proposed for the generalized power number and gas flow number 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 demonstrated that gas flow affected the aerated anchor power consumption and central impeller power consumption in different manners. It was also found that at the higher fluid viscosity and beyond the critical speed ratio of 10, the anchor power consumption was increased by increasing the speed ratio (i.e. decreasing the anchor speed). It was shown that in the presence of gas, the anchor impeller in combination with the upward pumping pitched blade turbine in the co-rotating mode exhibited shorter mixing times and lower power consumption than the anchor-downward pumping pitched blade coaxial mixer. To enhance the efficiency of the aerated mixer, it is critical to investigate the influence of the gas-liquid flow within the vessel on the bubble size distribution (BSD) and the local and global gas holdup. To achieve this goal, the effects of the bubble breakup and coalescence on the BSD within the vessel were incorporated into the CFD model through the CFD-PBM coupling. The experimental and simulation results showed that beyond the critical speed ratio of 10, the volume fractions of the large bubbles decreased while the volume fractions of the small bubbles increased.

Critical Speeds Analysis for Dual Rotor Turbofan Engine Using Finite Element Method

2019 ◽  
Author(s):  
Kai Sun ◽  
Zhao Wan ◽  
Huiying Song ◽  
Shaohui Wang
Keyword(s):  
Finite Element ◽  
Rotational Speed ◽  
Critical Speed ◽  
Fixed Number ◽  
Rotor System ◽  
Speed Ratio ◽  
Aircraft Engines ◽  
Campbell Diagram ◽  
Critical Speeds ◽  
Rotor Model

Abstract Intershaft bearing is widely adopted in dual rotor turbofan aircraft engines. Since this kind of dual rotor system has two different rotor speeds and the intershaft bearing leads to the coupling between HP rotor and LP rotor, the calculation of the critical speeds is much more complicated than that of the rotor systems without intershaft bearing. Compared to a single rotor system, the dual rotor system has more critical speeds which can be classified as critical speeds excited by HP rotor and that by LP rotor. In the paper, a finite element rotor model of a high-bypass turbofan jet engine with intershaft bearing is established for the study of critical speeds analysis. The general axisymmetric element is used to model the shafts and disks, and the blades are simplified to mass points. The main bearings including the intershaft bearing are set up with spring element. Assuming that the rotational speed ratio of the two rotors for the dual rotor system is a fixed number, the critical speeds are calculated using three methods based on the finite element rotor model. For the first method, the system critical speeds are obtained directly by Campbell diagram based on QR damped solution method. Then the synchronous unbalance response analyses are carried out and the rotor critical speeds are derived from the amplitude-frequency curves. For the last method, multiple group Campbell diagram analyses are conducted. With one rotor speed fixed at constant rpm N, we can change the speed of the other rotor to obtain one group of critical speeds. By varying speed N of the two rotors, a critical speeds data set can be obtained and plotted as a dual rotor critical speed map. The critical speeds can be easily extracted from the critical speed map according to the rotational speed curve of the engine. The study shows that the dual rotor system critical speeds calculated from above three methods are identical. For the first two methods, the rotational speed ratio of two rotors must be a known and fixed number, which is impossible in reality. The third proposal has no rotation speed relation restriction for rotors, and therefore is recommended for analyzing the critical speeds of aircraft engines with intershaft bearing.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

Optimum Design of Journal Bearings Dimensions for Rotating Machines

2020 ◽  
Vol 38 (10A) ◽  
pp. 1481-1488
Author(s):  
Tariq M. Hammza ◽  
Ehab N. Abas ◽  
Nassear R. Hmoad
Keyword(s):  
Aspect Ratio ◽  
Dynamic Response ◽  
Numerical Solution ◽  
Critical Speed ◽  
Design Method ◽  
Considerable Effect ◽  
Journal Bearings ◽  
Rotating Machines ◽  
Bearing Clearance ◽  
Study Results

The values of Many parameters which involve in the design of fluid film journal bearings mainly depend on the bearing applied load when using the conventional design method to design the journal bearings, in this study, as well as applied bearing load, the dynamic response and critical speed have been used to calculate the dimensions of journal bearings. In the field of rotating machine, especially a heavy-duty rotating machines, the critical speed and response are the main parameters that specify bearing dimensions. The bearing aspect ratio (bearing length to bore diameter) and bearing clearance have been determined based on rotor maximum critical speed and minimum response displacement. The analytical solution of rotor Eq. of motion was verified by numerical solution via using ANSYS Mechanical APDL 18.0 and by comparing the numerical solution with the preceding study. The final study results clearly showed that the bearing aspect ratio has little effect on the critical speed, but it has a high effect on the dynamic response also the bearing clearance has little effect on the critical speed and considerable effect on the dynamic response. The study showed that the more accurate values of bearing aspect ratio to make the response of rotor as low as possible are about 0.65 - 1 and bearing percent clearance is about 0.15 - 0.2 for different rotor dimensions.

A pilot web former designed to study retention-formation relationships

2010 ◽  
Vol 25 (2) ◽  
pp. 185-194
Author(s):  
Anna Svedberg ◽  
Tom Lindström
Keyword(s):  
Pilot Scale ◽  
Operating Conditions ◽  
Montmorillonite Clay ◽  
Speed Ratio ◽  
Good Reproducibility ◽  
Total Solids ◽  
Retention Aids ◽  
Solids Content ◽  
Relationship Of ◽  
The Relationship

Abstract A pilot-scale fourdrinier former has been developed for the purpose of investigating the relationship between retention and paper formation (features, retention aids, dosage points, etc.). The main objective of this publication was to present the R-F (Retention and formation)-machine and demonstrate some of its fields of applications. For a fine paper stock (90% hardwood and 10% softwood) with addition of 25% filler (based on total solids content), the relationship between retention and formation was investigated for a microparticulate retention aid (cationic polyacrylamide together with anionic montmorillonite clay). The retention-formation relationship of the retention aid system was investigated after choosing standardized machine operating conditions (e.g. the jet-to-wire speed ratio). As expected, the formation was impaired when the retention was increased. Since good reproducibility was attained, the R-F (Retention and formation)-machine was found to be a useful tool for studying the relationship between retention and paper formation.

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