Maximum Critical Speed Research Articles

Study on Optimization of Pump Shaft Transmission System of Plastic Centrifugal Pump

At present, the design of the pump shaft transmission system mostly refers to the design method of the metal pump transmission system. The dynamic and static characteristics of the plastic centrifugal pump are not related to the structural parameters of the pump shaft. Aiming at the influence of the structural parameters of the pump shaft transmission system on the dynamic and static performance of the plastic centrifugal pump, the three-dimensional model of the impeller and volute chamber was drawn by Creo5.0. The CFD calculation of the load of the plastic centrifugal pump was carried out. The flow field of the plastic centrifugal pump under ideal working conditions was simulated by ANSYS FLUENT. Combined with the application principle of singular function in mechanics, the mathematical model of a deflection of the pump shaft transmission system was constructed. Considering the minimum deflection and the maximum critical speed of the first order as the objective function, an optimization model of the structural parameters of the pump transmission system was established. The NSGA-II multiobjective optimization method was used to solve the optimal structural parameters of the optimization model, and the optimization design of the pump shaft span, cantilever, front, and rear bearing clearance was completed. The optimal span cantilever ratio of the rotor model of the single span cantilever structure was 1:0.75. Compared with the traditional design model, the optimized pump shaft deflection is reduced by 52.35%, and the first-order critical speed is increased by 42.77%. Simultaneously, using polynomial fitting as a mathematical tool, the experimental data were analyzed, and the mathematical expression of the rotation speed deflection relationship of the pump shaft at the first critical rotation speed and the corresponding function curve was obtained.

Optimum Design of Journal Bearings Dimensions for Rotating Machines

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.

Frictionally-excited thermoelastic instability in functionally graded material

A transient finite element simulation is developed for the two-dimensional thermoelastic contact problem considering a stationary functionally graded material (FGM) between sliding layers, to investigate thermoelastic instability (TEI) due to frictional heating at the interface. The result shows that the critical speed of the FGM coating disk is larger than that of the conventional steel disk. The effect of the nonhomogeneity parameter in FGM is also investigated and it is implied that there is an optimal nonhomogeneity parameter which gives a maximum critical speed within a specific coating layer thickness. It is concluded that FGMs restrain the growth of perturbation and delay the contact separation.

Design of carbon fiber composite shafts for high speed air spindles

For the stable operation of high speed air spindles, the low rotational inertia and high damping ratio of spindle shafts as well as high fundamental natural frequency are indispensable. Conventional steel spindles are not appropriate for high speed operation because of their high rotational inertia and low damping ratio. In this study, a high-speed air spindle composed of a carbon fiber epoxy composite shaft and two steel flanges was designed for maximum critical speed considering both the deflection due to bending load and the radial expansion due to centrifugal force and temperature rise during high-speed rotation. The stacking angle and thickness of the composite shaft and the adherend dimensions of the steel flanges were selected through vibrational analysis as well as considering the bending stiffness and centrifugal characteristics.

Optimal Design of a High Speed Carbon Composite Air Spindle

For the stable operation of high speed air spindle, the low rotational inertia and high damping ratio of spindle shafts as well as high fundamental natural frequency are indispensable. Conventional steel spindles are net appropriate for very high speed operation because of their high rotational inertia and low damping ratio. In this study, a high speed spindle composed of carbon fiber epoxy composite shaft and steel flange was designed for maximum critical speed considering minimum static deflection and radial expansion due to bending load and centrifugal force during high speed relation. The stacking angle and the stacking thickness of the composite shaft and the adhesive bonding length of the 7teel flange were selected through vibrational analysis considering static and thermal loads due to temperature rise.

SUPERCRITICAL SPEED STABILITY OF THE TRIVIAL EQUILIBRIUM OF AN AXIALLY-MOVING STRING ON AN ELASTIC FOUNDATION

The stability of an axially-moving string supported by a discrete or distributed elastic foundation is examined analytically. Particular attention is directed at the distribution of the critical speeds and identifying the divergence instability of the trivial equilibrium. The elastically supported string shows unique stability behavior that is considerably different from unsupported axially-moving string. In particular, any elastic foundation (discrete or distributed) leads to multiple critical speeds and a single region of divergence instability above the first critical speed, whereas the unsupported string has one critical speed and is stable at all supercritical speeds. Additionally, the elastically supported string critical speeds are bounded above, and the maximum critical speed is the upper bound of the divergent speed region. The analysis draws on the self-adjoint eigenvalue problem for the critical speeds and a perturbation analysis about the critical speeds. Neither numerical solution nor spatial discretization, which can produce substantially incorrect results, are required. The system falls in the class of dispersive gyroscopic continua, and its behavior provides a useful comparison for general gyroscopic systems. The analytical findings also serve as a benchmark for approximate methods applied to gyroscopic continua.

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

SUMMARY The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values. It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.

Optimization of Rail Vehicle Operating Speed With Practical Constraints

A constrained optimization algorithm to maximize the operating speed of a fifteen degree-of-freedom lateral dynamic model for a passenger railcar subject to random alignment irregularities is presented in this paper. The constraints placed on the optimization problem limit the passenger discomfort, primary and secondary suspension clearance, the wheel slippage, and secondary suspension stroke to practical values while traversing a curve. The optimization results demonstrate that the primary suspension system and the wheel conicity have the most profound influence on maximizing the critical speed where “hunting” begins. The maximum critical speed is insensitive to large variations in secondary yaw stiffness. The secondary lateral stiffness has less effect on the maximum critical speed than the primary lateral stiffness. Thus, the secondary stiffness can be chosen primarily to satisfy passenger ride comfort specifications. The maximum critical speed is quite sensitive to whether the wheel is new, slightly worn, or severely worn.

On the Cutting by the Special Tool with a Land of Negative Relief Angle

The tear type roughness of the machined surface, which is considered to be produced by remains of fragments of falling-off built-up edge on the surface, can be diminished by using the specially designed tool with a land of negative relief angle. This paper deals with the outline of the specia1 tool design and, in comparison with the surface roughness of carbon-and chromium steels cut with the special-b and ordinary tools, the most suitable form of the land of negative relief angle was determined experimentally in the case of steel cutting associated with built-up edge. The cutting forces of this special tool are lower than those of the ordinary tool under the cutting speed lower than the maximum critical speed at which the built-up edge seems to disappear, and the cutting ratio is smaller. Moreover, the chip produced has the strong tendency to be discontinuous and the tool has the anti-chatter effect.