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The whirling frequency of a symmetric cross section of a given length between two points is given by: N = 94.251 E I m L 3 RPM {\displaystyle N=94.251{\sqrt {EI \over mL^{3}}}\ {\text{RPM}}} where: E = Young's modulus, I = second moment of area , m = mass of the shaft, L = length of the shaft between points.
Stiffness of the shaft and its support; Total mass of shaft and attached parts; Unbalance of the mass with respect to the axis of rotation; The amount of damping in the system; In general, it is necessary to calculate the critical speed of a rotating shaft, such as a fan shaft, in order to avoid issues with noise and vibration.
The affinity laws (also known as the "Fan Laws" or "Pump Laws") for pumps/fans are used in hydraulics, hydronics and/or HVAC to express the relationship between variables involved in pump or fan performance (such as head, volumetric flow rate, shaft speed) and power. They apply to pumps, fans, and hydraulic turbines. In these rotary implements ...
Axial compressor performance is shown on a compressor map, also known as a characteristic, by plotting pressure ratio and efficiency against corrected mass flow at different values of corrected compressor speed. Axial compressors, particularly near their design point are usually amenable to analytical treatment, and a good estimate of their ...
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 ...
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. However, an alternative definition for S is used in some texts based on angular velocity: [2]
is a distributed load, in other words a force per unit length (analogous to pressure being a force per area); it may be a function of , , or other variables. E {\displaystyle E} is the elastic modulus and I {\displaystyle I} is the second moment of area of the beam's cross section.
In this case, the equation governing the beam's deflection can be approximated as: = () where the second derivative of its deflected shape with respect to (being the horizontal position along the length of the beam) is interpreted as its curvature, is the Young's modulus, is the area moment of inertia of the cross-section, and is the internal ...