Centrifugal pump shafting critical speed calculation method

Abstract

The application discloses a kind of centrifugal pump shafting critical speed calculation method, including the finite element calculation of radial roller bearing and thrust roller bearing stiffness coefficient curve, the prestressed modal analysis and critical speed calculation of centrifugal pump shafting considering different bearing stiffness coefficient.The setting of constraint condition of this method is in line with actual situation, which can realize the accurate calculation of centrifugal pump shafting critical speed, and help to improve the reliability of safety check of centrifugal pump shafting in design stage, at the same time, the calculation steps are simple, and the engineering application range is wide.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rotating machinery, and relates to a centrifugal pump shafting critical speed calculation method, in particular to a centrifugal pump shafting critical speed calculation method considering the change of rolling bearing stiffness coefficient. BACKGROUND

[0002] As a general machine, centrifugal pumps are widely used in water conservancy, power, construction, mining, ocean and other industries, and play a key role in the transportation and pressurization of fluid media. Under the development trend of large-scale equipment, the requirements for the stability and safety of large-scale centrifugal pump units are increasing, especially in terms of shafting vibration characteristics. Accurate prediction of critical speed is a necessary condition for stable operation of the rotor, and it is necessary to propose a scientific calculation method for the critical speed of the centrifugal pump shafting in the design stage to prevent resonance damage.

[0003] The centrifugal pump shafting usually includes a pump shaft, an impeller and other rotating parts, and the pump shaft is usually supported and fixed by two radial roller bearings and one axial roller bearing. In the traditional calculation method of the critical speed of the centrifugal pump shafting, the bearing is usually regarded as a rigid support, or the bearing is set as an elastic support with a certain stiffness coefficient according to personal experience. The traditional rigid support assumption is not applicable to the bearings in large-scale shafting, and the existing bearing stiffness coefficient empirical value is not applicable to centrifugal pump units of different scales. The calculation method of the critical speed of the centrifugal pump shafting considering the change of the stiffness coefficient of different rolling bearings has not been reported in the currently published literature at home and abroad.

[0004] Therefore, it is necessary to propose a scientific calculation method for the critical speed of the centrifugal pump shafting considering the calculation of the stiffness coefficient of the rolling bearing, to improve the prediction accuracy of the critical speed of the shafting in the design stage, prevent resonance damage, and ensure the safe and stable operation of the unit. SUMMARY

[0005] To solve the above technical defects, a centrifugal pump shafting critical speed calculation method considering the change of the stiffness coefficient of the rolling bearing is provided. The method involves finite element calculation of the stiffness coefficient curves of the radial roller bearing and the thrust roller bearing, pre-stressed modal analysis of the centrifugal pump shafting considering different bearing stiffness coefficients, and critical speed calculation. The setting of the constraint conditions in this method is in line with the actual situation, and the accurate calculation of the critical speed of the centrifugal pump shafting can be realized, which helps to improve the reliability of the safety check of the centrifugal pump shafting in the design stage. At the same time, the calculation steps are simple, and the engineering application range is wide.

[0006] TECHNICAL SCHEME

[0007] A centrifugal pump shafting critical speed calculation method, characterized in that it specifically comprises the following steps:

[0008] S1: Rolling bearing stiffness coefficient calculation.

[0009] Specifically,

[0010] S1.1: Radial roller bearing stiffness coefficient calculation.

[0011] S1.1.1: Establish a three-dimensional finite element model of the radial roller bearing;

[0012] S1.1.2: Using static analysis method, apply radial support force F r on the support surface, calculate the average deformation δ r of the support surface;

[0013] S1.1.3: Calculate the stiffness coefficient k r according to formula (1),

[0014] S1.1.4: Apply different radial support forces respectively, calculate a series of stiffness coefficients, form the curve of radial roller bearing stiffness coefficient changing with radial support force, provide to S4.

[0015] S1.2: Thrust roller bearing stiffness coefficient calculation.

[0016] S1.2.1: Establish a three-dimensional finite element model of the thrust roller bearing;

[0017] S1.2.2: Using static analysis method, apply axial support force F a on the support surface, calculate the average deformation δ a of the support surface;

[0018] S1.2.3: Calculate the stiffness coefficient k a according to formula (2),

[0019] S1.2.4: Apply different axial support forces respectively, calculate a series of stiffness coefficients, form the curve of axial roller bearing stiffness coefficient changing with axial support force, provide to S4.

[0020] S2: Three-dimensional finite element modeling of centrifugal pump shafting:

[0021] A three-dimensional model of the shafting structure including the pump shaft, impeller and other rotor components is established, wherein the impeller should include the water body part within the base circle diameter of the volute, so as to consider the influence of water body additional mass and additional load, which is specifically represented by a disc entity with equivalent density. The three-dimensional entity model is meshed to form a three-dimensional finite element model.

[0022] S3: Material attribute assignment of each component of centrifugal pump shafting:

[0023] The density, elastic modulus, and Poisson's ratio of the pump shaft, impeller, and other rotor components are set according to the materials of the pump shaft, impeller, and other rotor components, respectively.

[0024] S4: Centrifugal pump shafting structure analysis constraint condition setting:

[0025] Comprise

[0026] S4.1 Set the shafting speed range,

[0027] S4.2 Apply a load at the center of gravity of the impeller,

[0028] S4.3 Set the elastic support stiffness coefficient at two radial roller bearings and one thrust roller bearing.

[0029] Specifically, in S4.2: the impeller hydraulic load is obtained by a centrifugal pump fluid unsteady simulation general technology, including hydraulic radial load F rh , axial load F a , torque T, F rh direction has the characteristics of periodic change, and the time average of the combined force of the impeller gravity is taken in the finite element calculation; F a , T take the calculation time average.

[0030] Specifically, in S4.3: the bearing stiffness coefficient needs to be determined according to the centrifugal pump impeller load. There are three bearings in the shafting, namely radial roller bearing 1 with a distance l1 from the impeller, radial roller bearing 2 with a distance l2 from the impeller, and one thrust roller bearing.

[0031] The radial bearing support force is obtained by theoretical calculation of shafting force analysis, and the specific formula is seen in (3), (4).

[0032] (F rh +m i g)+m s g+F r1 +F r2 =0 (3)

[0033]

[0034] In the formula, F r1 , F r2 are the radial support forces of radial roller bearing 1 and radial roller bearing 2, respectively, m i is the equivalent mass of the impeller containing the mass of the water body, and m s is the mass of the pump shaft and other rotor components.

[0035] S5: Rotor dynamics solving setting and calculation: select the first 12 order prestressed modal analysis, consider the gyroscopic effect, and the control equation is seen in the classical theoretical equation (5).

[0036]

[0037] In the formula, u is a displacement vector; M is a mass matrix, which is a positive definite real symmetric matrix; Omega is a rotation speed, G is a gyro matrix based on the rotation speed, K is a generalized stiffness matrix, and F is a hydraulic load vector of the impeller.

[0038] The rotor dynamics solving calculation is carried out by means of the commercial software ANSYS Mechanical APDL.

[0039] S6: centrifugal pump shaft system critical speed calculation: the Campbell curve diagram is obtained through the post-processing of the finite element calculation results, and each intersection point of the curve diagram and the 1 times frequency line is the critical speed of each order of the shaft system.

[0040] Compared with the prior art, the centrifugal pump shaft system critical speed calculation method has the following beneficial technical effects:

[0041] The centrifugal pump shaft system critical speed calculation method considering the stiffness coefficient change of the rolling bearing has the finite element calculation of the stiffness coefficient of the rolling bearing under different load conditions and takes the stiffness coefficient as a constraint condition for the shaft system critical speed calculation, so that the prediction of the critical speed is more scientific and reasonable and is practical, thereby guiding the unit to operate in a working condition far from the critical speed, avoiding resonance, and guaranteeing the safe and stable operation of the unit. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 The flowchart is designed for the method.

[0043] Figure 2 The three-dimensional finite element model of the centrifugal pump shaft system is for the embodiment.

[0044] Figure 3 The three-dimensional finite element model profile of the rolling bearing is for the embodiment, (a) radial roller bearing (b) thrust roller bearing.

[0045] Figure 4 The simply supported beam stress analysis principle in material mechanics is a stress analysis schematic diagram.

[0046] Figure 5 The stiffness coefficient-support load curve of the radial roller bearing is for the embodiment.

[0047] Figure 6 The stiffness coefficient-support load curve of the thrust roller bearing is for the embodiment.

[0048] Figure 7 The shaft system Campbell diagram is for the embodiment.

[0049] Figure 8 The curve of the shaft system critical speed calculation value changing with the bearing stiffness coefficient is for the embodiment.

[0050] Digital label:

[0051] 1-pump shaft, 2-equivalent impeller, 3-simplified model of radial roller bearing 1, 4-simplified model of radial roller bearing 2, 5-simplified model of thrust roller bearing, 6-wheel of disc DETAILED DESCRIPTION

[0052] The application will be further described in conjunction with specific examples, which are intended to explain but not limit the application.

[0053] Reference Figure 1 , a flow chart designed for the method of the application.

[0054] EXAMPLE

[0055] The critical speed calculation of a centrifugal pump shaft system considering the stiffness coefficient of rolling bearings is carried out.

[0056] The impeller suction diameter of the centrifugal pump in this example is 850 mm, the equivalent impeller outer diameter is 2240 mm, the equivalent mass of the impeller is 5132 kg, the design speed is 325 r / min (34 rad / s), and the pump shaft mass is 2300 kg.

[0057] A three-dimensional model of the shaft system structure including all rotor components such as the pump shaft, impeller, and disc wheel is established, wherein the impeller contains the water body part within the base circle diameter range of the volute. The three-dimensional entity model is meshed to form a three-dimensional finite element model, as shown in Figure 2 .

[0058] The stiffness coefficient curves of the radial roller bearing and the thrust roller bearing are calculated respectively. The three-dimensional finite element model of the radial roller bearing and the thrust roller bearing is established, as shown in Figure 3 . The bearing material properties are shown in Table 1. Different radial support forces are applied to the radial roller bearing in stages, and a series of stiffness coefficients are calculated according to formula (1) to form the variation curve of the radial roller bearing stiffness coefficient with the radial support force, as shown in Figure 5 . Different axial support forces are applied to the thrust roller bearing in stages, and a series of stiffness coefficients are calculated according to formula (2) to form the variation curve of the thrust roller bearing stiffness coefficient with the axial support force, as shown in Figure 6 .

[0059]

[0060]

[0061] According to Table 1, the material density, elastic modulus, and Poisson's ratio of each component of the centrifugal pump shaft system are assigned.

[0062] Table 1 Material properties of each component

[0063]

[0064] Constraints were set for the centrifugal pump shaft system structure analysis. The shaft rotation speed was set to 0–3000 rad / s. Using general simulation techniques for unsteady fluid flow in centrifugal pumps, the impeller hydraulic radial load F under the maximum flow condition was obtained. rh The average value of the resultant force with gravity is 3.8 × 10⁻⁶. 4 N, axial load F a The time average is 1.6 × 10 5 The time average value of N and torque T is 1.1 × 10⁻⁶. 5 N·m. Radial load, axial load, and torque are applied to the impeller body to calculate the prestress.

[0065] According to the principle of force analysis of simply supported beams in mechanics of materials, formula (3) indicates that the resultant force is 0, and formula (4) indicates that the moment about one end is 0. Figure 4 As shown. According to formulas (3) and (4), the absolute values ​​of the radial support forces of radial roller bearing 1 with a distance of l1 = 1.17m from the impeller and radial roller bearing 2 with a distance of l2 = 2.11m from the impeller are F respectively. r1 =1.1×10 5 N, F r2 =4.9×10 4 N. According to Figure 5 , Figure 6 Read the corresponding stiffness coefficient, k r1 =6.9×10 9 N / m, k r2 =5.2×10 9 N / m, k a =2.5×10 9 N / m, the calculated stiffness coefficient of each bearing is set at the corresponding bearing constraint.

[0066] (F rh +m i g)+m s g+F r1 +F r2 =0 (3)

[0067]

[0068] Rotor dynamics solution settings were performed, and the first 12 prestressed modal analyses were selected. Considering the gyro effect, the control equations were solved using the commercial software ANSYS Mechanical APDL, as shown in equation (5).

[0069]

[0070] In the formula, u is the displacement vector; M is the mass matrix, which is a positive definite real symmetric matrix; Ω is the rotational velocity; G is the gyroscope matrix based on the rotational velocity; K is the generalized stiffness matrix; and F is the impeller hydraulic load vector.

[0071] The Campbell curve is obtained through post-processing of the finite element calculation results, such as... Figure 7 Where FW represents the forward eddy mode, BW represents the reverse eddy mode, Axial represents the axial vibration mode, and Torsional represents the torsional vibration mode. The intersection of the first octave line with the curves of each forward eddy mode is the critical speed for each order. In this example, the frequency corresponding to the first intersection point calculated is 24Hz, that is, the first critical speed is 1440r / min, which is much greater than the pump shaft design speed of 325r / min. This means that there is no risk of resonance failure when this shaft system is operating normally.

[0072] To further illustrate the significance of accurately calculating the stiffness of rolling bearings, Figure 8 This demonstrates that three bearings are simultaneously taken at a rate of 1×10. 5 N, 5×10 5 N, 1×10 6 The first three critical speeds calculated at N show that the bearing stiffness coefficient has a significant impact on the calculated critical speed. In order to accurately assess the risk of shaft resonance, an appropriate bearing stiffness coefficient should be set according to the shaft load in the finite element calculation of the shaft system.

[0073] The above description is merely an embodiment of the present invention and is not intended to limit the present invention in any way. Any modifications, equivalent changes, or alterations made by those skilled in the art to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention. For example, the prediction of critical speed of other types of vane pump shaft systems still falls within the scope of the present invention.

Claims

1. A method for calculating the critical speed of a centrifugal pump shaft system, characterized in that, Specifically, the following steps are included: S1: Calculation of rolling bearing stiffness coefficient; S2: Three-dimensional finite element modeling of centrifugal pump shaft system: A three-dimensional model of the shaft system structure, including the pump shaft, impeller, and other rotor components, is established. The impeller should include the water body within the diameter of the volute base circle to account for the effects of the added mass and load of the water body. Specifically, it is represented by a disk solid with equivalent density. The three-dimensional solid model is meshed to form a three-dimensional finite element model. S3: Assigning material properties to each component of the centrifugal pump shaft system: Set the density, elastic modulus, and Poisson's ratio according to the materials of the pump shaft, impeller, and other rotor components; S4: Setting constraint conditions for centrifugal pump shaft system structure analysis; S5: Rotor Dynamics Solution Setup and Calculation: Select the first 12 prestressed modal analyses, consider gyroscopic effects, governing equations (5) In the formula, u It is the displacement vector; M Let be the mass matrix, and be a positive definite real symmetric matrix; Ω For rotational speed, G For the gyroscope matrix based on rotational speed, K For generalized stiffness matrix, F This is the impeller hydraulic load vector; Perform rotor dynamics calculations; S6: Calculation of critical speed of centrifugal pump shaft system: The Campbell curve is obtained by post-processing the finite element calculation results. The intersection points of the curve with the first octave line are the critical speeds of the shaft system. Step S4, setting constraint conditions for centrifugal pump shaft system structure analysis, includes... S4.1 Sets the shaft speed range; S4.2 Apply a load at the impeller's center of gravity; S4.3 sets the elastic support stiffness coefficient at the two radial roller bearings and one thrust roller bearing. In S4.2: the impeller hydraulic load is obtained by the general technique for unsteady simulation of centrifugal pump fluid, including the hydraulic radial load. F rh Axial load F a Torque T , F rh The direction has a periodic variation characteristic, and in the finite element calculation, the time average value of its resultant force with the impeller gravity is taken; F a , T Take the mean value used in the calculation; In S4.3: the bearing stiffness coefficient needs to be determined based on the centrifugal pump impeller load; there are three bearings in the shaft system, namely the bearings spaced from the impeller. l 1. Radial roller bearing (1), distance from impeller l 2 radial roller bearings (2) and a thrust roller bearing; The radial bearing support force is calculated using the shaft system force analysis theory, and the specific formulas are shown in (3) and (4): （3） （4） In the formula, F r1 , F r2 The radial support forces, m, are those of the radial roller bearing (1) and the radial roller bearing (2), respectively. i For the impeller's equivalent mass, including the mass of the water body, m s For the quality of the pump shaft and other rotor components.

2. The method for calculating the critical speed of a centrifugal pump shaft system as described in claim 1, characterized in that, Step S1, calculating the rolling bearing stiffness coefficient, includes: S1.1: Calculation of the radial roller bearing stiffness coefficient; S1.2: Calculation of the stiffness coefficient of the thrust roller bearing.

3. The method for calculating the critical speed of a centrifugal pump shaft system as described in claim 2, characterized in that, S1.1, the calculation of the radial roller bearing stiffness coefficient, includes: S1.1.1: Establish a three-dimensional finite element model of the radial roller bearing; S1.1.2: Apply radial support force to the support surface using static analysis method. F r The average deformation of the support surface was calculated. δ r ; S1.1.3: Calculate the stiffness coefficient according to formula (1) k r , (1); S1.1.4: Apply different radial support forces respectively, calculate a series of stiffness coefficients, form the curve of the change of radial roller bearing stiffness coefficient with radial support force, and provide it to S4.

4. The method for calculating the critical speed of a centrifugal pump shaft system as described in claim 2, characterized in that, S1.2, the calculation of the thrust roller bearing stiffness coefficient, includes: S1.2.1: Establish a three-dimensional finite element model of the thrust roller bearing; S1.2.2: Apply axial support force to the support surface using static analysis method. F a The average deformation of the support surface was calculated. δ a ; S1.2.3: Calculate the stiffness coefficient according to formula (2). k a , (2); S1.2.4: Apply different axial support forces respectively, calculate a series of stiffness coefficients, form the variation curve of axial roller bearing stiffness coefficient with axial support force, and provide it to S4.

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