The critical speed calculation and unbalanced response analysis of the shaft system of the 20MW-class high-speed variable frequency explosion-proof motor project for long-distance pipeline compressors were carried out using DyRoBeS rotor dynamics analysis software. This was done to prevent resonance of the shaft system during normal operation, thus providing a basis for the stability analysis and optimization design of the shaft system of ultra-high speed and high power motors.
0. Introduction
During operation, rotating machinery experiences vibrations due to various disturbance forces, making vibration one of the main causes of rotor failure. For the rotor system itself, lateral bending vibration caused by mass eccentricity is the most common, especially at certain speeds where the amplitude increases significantly, potentially leading to damage to the shaft and bearings. This phenomenon is usually caused by resonance. To avoid resonance in the shaft system during normal operation, the design of the shaft system requires that its critical speed be within a certain range, avoiding the operating frequency of the unit and the external excitation frequency.
This paper mainly relies on the 20MW high-speed variable frequency explosion-proof motor project of long-distance pipeline compressors. The DyRoBeS rotor dynamics analysis software is used to calculate the critical speed and analyze the unbalanced response of the entire shaft system (main unit and exciter). This unit has a three-bearing structure with a speed of 3120–5040 rpm. To ensure stable operation, the exciter end bearing needs to support 300 kg at its lower end. During installation, the bearing housing needs to be raised by a certain amount, which requires theoretical calculation.
1. Computational Model
1.1 Rotor Modeling
This calculation uses DyRoBeS software, simplifying the motor shaft into 48 elements (49 nodes). The fan, retaining ring, rotor windings, rectifier disk, etc., are added as additional mass to the nodes at their respective locations, and their rotational inertia are input. This motor is a two-pole motor, with 24 slots cut into the shaft section of the main body. This significantly affects the bending moments of inertia in the horizontal and vertical directions, easily causing vibration. To ensure consistent bending moments of inertia in the horizontal and vertical directions, crescent-shaped slots need to be cut into the large teeth to reduce the bending stiffness of the shaft in this direction. The rotor finite element model is shown in Figure 1.
1.2 Bearing Parameters
Bearing #1 (tilting pad, diameter 200mm) is installed on node 5, bearing #2 (tilting pad, diameter 200mm) is installed on node 22, and bearing #3 (ordinary sliding bearing, diameter 100mm) is installed on node 47. The oil film stiffness and oil film damping of bearings #1, #2, and #3 are calculated based on the bearing load and basic parameters. The calculation results are shown in Tables 1 and 2.
2. Calculation of critical speed of shaft system
Calculating the critical speed of the shaft system is a fundamental aspect of rotor dynamics analysis, and rationally designing the critical speed of the rotor system is an important prerequisite for the safe and reliable operation of the unit.
2.1 Calculation results of critical speed
Based on the simplified model of the shaft system and the oil film support stiffness and damping of the bearings, the first three critical speeds of the shaft system can be calculated, and the calculation results are shown in Table 3. The calculation results show that the first three critical speeds all avoid the motor's operating speed of 3120–5040 rpm, and have a certain safety margin.
2.2 Bearing Installation Position Calculation
This unit has a three-bearing structure. In order to ensure the stable operation of the exciter end bearing #3, the lower bearing shell needs to bear a support load of 300kg. Therefore, bearing #3 needs to be raised during installation. Based on the static deflection of the shaft system and the load, the raising amount of bearing #3 can be calculated to be 1.9mm.
3. Shaft Unbalance Response Analysis
Since there is always a mass eccentricity in the manufacturing and installation of the shaft, it is very important to calculate the shaft imbalance response during the design phase. By predicting the imbalance response, the rotor structure parameters can be adjusted to ensure that the vibration of the unit meets the specified standards during operation.
3.1 Calculation Model for Unbalanced Response of Rotor-Bearing System
The dynamic equation of the rotor-bearing system is:
In the formula, ω—rotational frequency; M1, K1, G1—overall mass matrix, stiffness matrix, and rotation matrix; cij, kij (i, j=1, 2)—overall oil film equivalent damping and stiffness matrices; U1, 2—system displacement vector, i.e.
We won't go into the rest of the complex formulas in the text. We'll focus on the parts that are more relevant to engineering applications.
3.2 Calculation of Unbalance
When adding unbalanced mass, according to the international standard "Balance Mass of Rigid Bodies of Rotation", the balance level is taken as G3.2.
e×ω=3.2
In the formula, e is the eccentricity of the rotating component; ω is the angular velocity of the rotating component. The maximum vibration response at the three bearing positions was calculated by applying corresponding unbalanced loads to the main body and exciter core. The calculation results are shown in Table 4.
4. Conclusion
This paper uses DyRoBeS rotor dynamics analysis software to calculate the critical speed and analyze the unbalanced response of the shaft system of a 20MW high-speed variable frequency explosion-proof motor for a long-distance pipeline compressor, and draws the following conclusions:
(1) To ensure the accuracy of the calculation results, the motor shaft system needs to be reasonably simplified. During the simplification process, the influence of the crescent groove of the shaft body and the lifting amount of bearing #3 needs to be considered.
(2) The critical speed of the shaft system was calculated using DyRoBeS rotor dynamics analysis software. The results were: first-order critical speed 1756 rpm, second-order critical speed 2232 rpm and third-order critical speed 5952 rpm. The operating speed of the motor 3120~5040 rpm was effectively avoided. Therefore, the structural design of the shaft system is reasonable.
(3) Based on the balance grade of the shaft system, the maximum response value of the bearing position when the shaft system passes the critical speed is calculated to be 0.048 mm, which is located at the position of bearing #3. This result meets the requirements of rotating machinery vibration.
