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When an element of mass is offset from the axis of rotation, centrifugal force will tend to pull the mass outward. The elastic properties of the shaft will act to restore the “straightness”. If the frequency of rotation is equal to one of the resonant frequencies of the shaft, whirling will occur. In order to save the machine from failure ...
Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. The Rayleigh–Ritz method is discussed here. For a shaft that is divided into n segments, the first natural frequency for a given beam, in rad/s , can be approximated as:
In rotordynamical systems, the eigenfrequencies often depend on the rotation rates due to the induced gyroscopic effects or variable hydrodynamic conditions in fluid bearings. It might represent the following cases: Campbell Diagram of a steam turbine. Analysis shows that there are well-damped critical speed at lower speed range.
The critical speed of a rotating machine occurs when the rotational speed matches its natural frequency. The lowest speed at which the natural frequency is first encountered is called the first critical speed, but as the speed increases, additional critical speeds are seen which are the multiples of the natural frequency.
The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling. As the load is increased beyond the ...
S is the Sommerfeld Number or bearing characteristic number r is the shaft radius c is the radial clearance μ is the absolute viscosity of the lubricant N is the speed of the rotating shaft in rev/s P is the load per unit of projected bearing area. The second part of the equation is seen to be the Hersey number.
On a screw, the bearing area loosely refers to the underside of the head. [1] Strictly speaking, the bearing area refers to the area of the screw head that directly bears on the part being fastened. [2] For a cylindrical bearing, it is the projected area perpendicular to the applied force. [3]
The critical speed. This was defined as the speed at which the unbalanced reciprocating parts reversed the pull of the locomotive. At higher speeds this motion was damped by throttling oil flow in dashpots. The critical speed varied from 95 RPM for a Baldwin tandem compound to over 310 RPM for a Cole compound Atlantic.