Bending critical speed

When the intersection points lie below the 0.5 slope line, the system is said to have a bending critical speed. It is important to identify these points, since they indicate the increasing importance of bending stiffness over support stiffness. 

The determination of the first bending critical speed is well established however, there is also concern with regard to the rotor support system s sensitivity to exciting forces. These come from unbalance and/or gas dynamic forces arising during operation in service. Operation with dirty corrosive gas will soon cause rotor unbalance. The rotor dynamics verification test is concerned with synchronous excitaticm, namely unbalance. The test must also verify that the separation margins are to specification. 

The rotor of one- and two-stage pumps shall be designed so its first dry bending critical speed is at least 20 % above the pump s maximum continuous operating speed. 

The first or free-free rotor bending mode frequency (based on the required margin for operation below the critical speed)... 

Shaft wobble/vibration impeller speed too dose to the first critical speed/shaft runout at the impeller and impeller eccentridty too large/insufficient support. Excessive gear-reducer maintenance excessive load/high shock loads/excessive shaft bending/excessive temperature of gearbox lubricant/incorrect lube oil selection and oil changing. 

The transfer matrix (Pestel and Leckie, 1995) method can be used to calculate the critical speed and dynamic response of the shaft design. The matrix is composed of the mass and elastic characteristics of each span. The matrix is then multiplied by the deflection, slope, bending moment, and shear force at the position on one end of the span to calculate the deflection, slope, bending moment, and shear force at the position on the other end of the span. This calculation for each span is shown below in matrix form. Each span i has position i-1 on one end of the span and position i on the other end. 

The method for determining the deflection is very similar to calculating the critical speed. However, the hydraulic forces on the shaft are now taken into account. Also, the frequency is a known value. Hydraulic forces are determined based on the impeller torque. Because hydraulic forces used by mixer manufacturers already include the effect of dynamics, speed (frequency) is already included in the magnitnde. Consequently, a forced response at the shaft speed would not be appropriate because the results would reflect the effect of frequency twice. Therefore, determining the forced response for the static condition is necessary (frequency = 0). From the bending moment for each position along with the torque from the impeller(s), the tensile and shear stresses can be calculated for each position. The static condition can only be calcnlated where the forcing freqnency is effectively zero compared with the natnral frequency, and such an analysis requires a 4 x 5 matrix. 

Increase Sound- Transmission Loss. The only significant iacreases ia sound-transmission loss that can be achieved by the appHcation of dampiag treatments to a panel occur at and above the critical frequency, which is the frequency at which the speed of bending wave propagation ia the panel matches the speed of sound ia air. AppHcation of dampiag treatment to 16 ga metal panel can improve the TL at frequencies of about 2000 H2 and above. This may or may not be helpful, depending on the appHcation of the panel. 

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