Confirmation of the Critical Speed Stability Theory for Symmetrical Circular Saws

1975 ◽  
Vol 97 (3) ◽  
pp. 1112-1118 ◽  
Author(s):  
C. D. Mote ◽  
S. Holoyen
Keyword(s):  
Critical Speed ◽  
Radiation Thermometer ◽  
Optimal Operation ◽  
Direct Application ◽  
Experimental Program ◽  
Speed Prediction ◽  
Speed Stability ◽  
Product Thickness ◽  
Conditions Of Stability ◽  
Circular Saws

The critical speed theory for circular saws predicts conditions of stability when a saw remains plane and cuts a straight path, and conditions of instability when the saw is no longer plane and no longer produces accurate cuts. This paper presents results of an experimental program on a production process which shows near perfect correspondence between the theoretical critical speed prediction and the measured product accuracy. The critical speed computation required measurement of the production blade temperature with a radiation thermometer and the product accuracy was independently evaluated as the standard deviation of the product thickness. The critical speed theory has direct application to both optimal design and optimal operation of circular saws.

Circular Saw Vibration Control by Induction of Thermal Membrane Stresses

1981 ◽  
Vol 103 (1) ◽  
pp. 81-89 ◽  
Author(s):  
C. D. Mote ◽  
G. S. Schajer ◽  
S. Holo̸yen
Keyword(s):  
Vibration Control ◽  
Induction Heating ◽  
Transverse Vibration ◽  
Critical Speed ◽  
Dimensional Accuracy ◽  
Optimal Temperature ◽  
Blade Vibration ◽  
Circular Saw ◽  
Speed Stability ◽  
Circular Saws

Circular saw transverse vibration and product dimensional accuracy were measured during a series of production experiments in which sawblade vibration was controlled by the deliberate introduction of thermal membrane stresses. Induction heating near the saw collar was used to control the temperature difference between two concentric annular zones on the sawblade surface. Optimal temperature conditions were predicted using the critical speed stability theory for symmetrical circular saws and these predictions were verified through production experiments. Feedback control of sawblade temperature was successfully demonstrated in production as a means of reducing blade vibration and improving dimensional accuracy.

scholarly journals Risk index to monitor an anaerobic digester using a dynamic model based on dilution rate, temperature, and pH

2019 ◽  
Vol 9 (1) ◽  
pp. 35-50 ◽  
Author(s):  
Angélica M. Alzate-Ibañez ◽  
Carlos Ocampo-Martinez ◽  
Carlos A. Cardona Alzate ◽  
Víctor M. Trejos Montoya
Keyword(s):  
Dilution Rate ◽  
Risk Index ◽  
Optimal Operation ◽  
Operating Conditions ◽  
Dynamical Analysis ◽  
Optimum Operating ◽  
Behavior System ◽  
Fold Bifurcation ◽  
On Line ◽  
Conditions Of Stability

AbstractIn this work, a risk index to monitor an anaerobic digestion process is established. The index is derived from the dynamical analysis of the system and it is composed by two conditions ensuring an optimum operating conditions inside bioreactor. The analysis is performed using bifurcation theory in order to study the effects of dilution rate, temperature and pH parameters at behavior system. For these purpose an extended version of the mathematical model proposed by Bernard [1] involving the dependence of growth kinetics on temperature and pH is used. The analysis shows both microbial growth and the performance of the bioprocess, when is highly affected by these parameters, indeed the washout condition occurs by combining a fold bifurcation and a transcritical bifurcation. From bifurcation diagrams both safety and optimal operation regions of the bioreactor are defined. Consequently, based on two conditions of stability a risk index to monitor the bioprocess on-line is proposed. The index is evaluated via numerical simulations allowing to detect system destabilization. The results obtained in this work may provide a useful methodology to monitor an anaerobic process and to guarantee the optimal performance of the bioreactor given that the model is sufficiently accurate.

Thickness Profiles for Rotating Circular Disks That Maximize Critical Speed

1999 ◽  
Author(s):  
Anthony A. Renshaw ◽  
Grant M. Warner
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Critical Speed ◽  
Rotating Disks ◽  
Lower And Upper Bounds ◽  
Optimal Thickness ◽  
Minimum Thickness ◽  
Thickness Profile ◽  
Circular Saws ◽  
Circular Disks

Abstract Thickness profiles for rotating disks that maximize critical speed are determined for use by designers of industrial circular saws. The disk thickness is permitted to vary between fixed lower and upper bounds, the lower bound corresponding to the minimum thickness saw capable of supporting the in-plane stresses associated with cutting forces and rotation, the upper bound corresponding to the thickness of the saw teeth. The optimal thickness profile consists of two annuli, the inner one with thickness equal to the upper bound, the outer one with thickness equal to the lower bound. With the optimal thickness profile, the critical speed can be raised up to 24%, depending on the clamping ratio of the disk and the lower bound. Optimal thickness profiles and increases in critical speeds are described and compared to existing saw designs.

Critical Speeds of Turbomachinery: Computer Predictions vs. Experimental Measurements—Part II: Effect of Tilt-Pad Bearings and Foundation Dynamics

1987 ◽  
Vol 109 (1) ◽  
pp. 8-14 ◽  
Author(s):  
J. M. Vance ◽  
B. T. Murphy ◽  
H. A. Tripp
Keyword(s):  
Critical Speed ◽  
Natural Frequencies ◽  
State Of The Art ◽  
Dynamic Properties ◽  
Experimental Measurements ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Speed Prediction ◽  
Bearing Stiffness ◽  
Stiffness And Damping

This is the second of two papers describing results of a research project directed at verifying computer programs used to calculate critical speeds of turbomachinery. This part describes measurements made to determine the characteristics of tilt-pad bearings and foundation dynamics. Critical speeds of a 166 kg laboratory rotor on tilt-pad bearings are then compared with predictions from a state-of-the-art damped eigenvalue computer program. Measured natural frequencies of a steam turbine are also compared with computer predictions. Accuracy of critical speed prediction is shown to depend on accuracy of 1) the “free-free” rotor models, 2) the bearing stiffness and damping coefficients, and 3) the dynamic properties of the foundation, which can be represented by an impedance that must be determined by experimental measurements.

Hopf Bifurcation to Limit Cycles in Fluid Film Bearings

1986 ◽  
Vol 108 (2) ◽  
pp. 184-189 ◽  
Author(s):  
P. Hollis ◽  
D. L. Taylor
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Critical Speed ◽  
Stability Boundary ◽  
Linear Stability Theory ◽  
Stable Limit ◽  
Fluid Film Bearings ◽  
Speed Stability ◽  
Stable Limit Cycles ◽  
Range Of Values

The nonlinear response of a cylindrical journal bearing operating close to the critical speed stability boundary is studied in this paper. Using linear stability theory, the value of the critical variable (usually speed) at the point of loss of stability is obtained and shown to agree with results of previous researchers. Using Hopf bifurcation analysis, parameters for determining the behavior close to this point are obtained. Analytically, these parameters prove that the system can exhibit stable limit cycles for speeds above the critical speed. Such supercritical limit cycles only exist for a narrow range of values of modified Sommerfeld number. In other cases, subcritical limit cycles are predicted. The results are supported by numerical simulation. The results show why it may be difficult to observe supercritical limit cycles in test rigs.

The Effect of Bearing Support Flexibility on Critical Speed Prediction

1986 ◽  
Vol 29 (3) ◽  
pp. 329-338 ◽  
Author(s):  
J. C. Nicholas ◽  
L. E. Barrett
Keyword(s):  
Critical Speed ◽  
Speed Prediction

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.

A Study of the Modal Truncation Error in the Component Mode Analysis of a Dual-Rotor System

1982 ◽  
Vol 104 (3) ◽  
pp. 525-532 ◽  
Author(s):  
D. F. Li ◽  
E. J. Gunter
Keyword(s):  
Critical Speed ◽  
Truncation Error ◽  
Synthesis Method ◽  
Equation Of Motion ◽  
Mode Analysis ◽  
Turbine Engine ◽  
Generalized Coordinates ◽  
Acceptable Accuracy ◽  
Speed Stability ◽  
Modal Truncation

In the component mode synthesis method, the equation of motion in the generalized coordinates is built upon the undamped eigenvalue data of the component structures. Error is inevitable when truncated modes are used. In this paper, two model truncation schemes were evaluated with regard to the critical speed, stability, and unbalance response of a two-spool gas turbine engine. The numbers of modes required to yield acceptable accuracy in these cases were determined. Guidelines for modal truncation were derived from these results.

The 1-MeV Electron Microscope Installation at the University of Colorado

1973 ◽  
Vol 31 ◽  
pp. 8-9 ◽  
Author(s):  
Mircea Fotino
Keyword(s):  
Electron Microscopy ◽  
Developmental Biology ◽  
Transmission Electron Microscopy ◽  
Electron Microscope ◽  
National Institutes Of Health ◽  
Experimental Program ◽  
University Of Colorado ◽  
Transmission Electron ◽  
The University ◽  
Research Resources

A new 1-MeV transmission electron microscope (Model JEM-1000) was installed at the Department of Molecular, Cellular and Developmental Biology of the University of Colorado in Boulder during the summer and fall of 1972 under the sponsorship of the Division of Research Resources of the National Institutes of Health. The installation was completed in October, 1972. It is installed primarily for the study of biological materials without many of the limitations hitherto unavoidable in standard transmission electron microscopy. Only the technical characteristics of the installation are briefly reviewed here. A more detailed discussion of the experimental program under way is being published elsewhere.

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