A pre-bending design method for multistage centrifugal pumps

Abstract

This invention relates to the field of multistage centrifugal pump technology, and provides a pre-bending design method for multistage centrifugal pumps, comprising: Step 1, determining the clearance range between each intermediate section of the pump body and the impeller; Step 2, determining the weight of the rotating components of the multistage centrifugal pump; Step 3, calculating the pump shaft deflection at the intermediate section position; Step 4, based on the pump shaft deflection calculated in Step 3, determining whether the pump shaft deflection is within the clearance range between the intermediate section and the impeller; if the pump shaft deflection exceeds the clearance range between the intermediate section and the impeller, proceeding to Step 5; Step 5, calculating the cutting amount at both ends of the intermediate section; Step 6, determining whether each intermediate section needs cutting; if cutting is required, cutting the intermediate section according to the cutting amount of each intermediate section; assembling all intermediate sections to obtain a pre-bent pump body. This invention enables the design of an inclined intermediate section in a multistage pump to obtain a pre-bent pump body, avoiding the situation where the clearance between the impeller and the intermediate section is too small.

Description

Technical Field

[0001] This invention relates to the field of multistage centrifugal pump technology, and in particular to a pre-bending design method for multistage centrifugal pumps. Background Technology

[0002] In the design of horizontal multistage centrifugal pumps, theoretically, the axes of rotating components (such as the pump shaft and impeller) should coincide with the axes of the pump body and intermediate sections. However, due to slight deviations in machining or casting, as well as the influence of gravity on the rotating components between the pump shaft support points, the pump shaft deflects under its own weight and the weight of the mounted parts, causing the axes of the rotating components to no longer coincide with the pump body axis. Deviations caused by machining or casting can be resolved by improving manufacturing precision, but shaft deformation caused by deflection must be addressed in the pump design. Otherwise, when the pump shaft deflection exceeds the designed single-sided clearance between the impeller and the intermediate section, the pump's performance will degrade, and in severe cases, vibration, impeller-internal rubbing, and even pump damage may occur.

[0003] The primary function of the pump shaft in a multistage centrifugal pump is to support the impeller and other rotating components mounted on it, and to transmit torque during operation. During operation, the pump shaft deflects due to the rotor's own weight, causing the impeller to tilt accordingly. The more stages the pump has, and the larger the span between the shaft support points, the greater the deflection and the greater the impeller tilt. However, the intermediate section of the multistage centrifugal pump does not change with the pump shaft. This can lead to insufficient clearance between the impeller and the intermediate section, or even contact, causing the rotor to seize and the multistage centrifugal pump to malfunction. Centrifugal pumps must operate with a minimum clearance between rotating components and stationary components such as the pump body and intermediate section. Therefore, the maximum allowable deflection must be considered and calculated during bearing design.

[0004] Because of shaft deflection, the support points at both ends of the shaft are not a straight line, but an arc. To overcome the influence of deflection, most ordinary multistage pumps increase the gap between the intermediate section and the impeller, sealing ring, etc., to achieve normal pump operation. This will affect the pump performance, and the Lomakin effect will decrease as the gap between the impeller and the shaft increases. Summary of the Invention

[0005] This invention primarily addresses the technical problem of existing multistage centrifugal pumps where the pump shaft exhibits a certain degree of deflection, but the middle section of the pump does not change along with the pump shaft. This can lead to excessively small clearances or even contact between the impeller and the middle section, causing the rotor to jam and preventing the multistage centrifugal pump from functioning properly. The invention proposes a pre-bending design method for multistage centrifugal pumps to achieve a pre-bent pump body by designing the middle section of the multistage pump to avoid excessively small clearances between the impeller and the middle section, thus ensuring the normal operation of the multistage centrifugal pump.

[0006] This invention provides a pre-bending design method for a multi-stage centrifugal pump, comprising the following steps:

[0007] Step 1: Determine the clearance range between each section of the pump body and the impeller; the clearance range between the section and the impeller is f < CL < F, where F represents the maximum clearance between the section and the impeller, and f represents the minimum clearance between the section and the impeller.

[0008] Step 2: Determine the weight of the rotating parts of the multistage centrifugal pump;

[0009] Step 3: Calculate the pump shaft deflection at the mid-section based on the weight of the rotating component;

[0010] Calculate the pump shaft deflection using the following formula:

[0011]

[0012] In the formula, G represents the weight of the rotating component, S represents the sum of the lengths of the corresponding shaft diameters between bearings, and E represents the elastic modulus of the steel. For structural steel used in engineering, E = 2.1 × 10⁻⁶. 4 kgf / dm 2 J represents the average moment of inertia;

[0013]

[0014] In the formula, d i s represents the diameter of the i-th mid-section of the pump shaft. i This represents the length of the i-th middle section of the pump shaft;

[0015] Step 4: Based on the deflection of the pump shaft at the mid-section calculated in Step 3, determine whether the deflection of the pump shaft is within the range of the clearance between the mid-section and the impeller. If the deflection of the pump shaft is within the range of the clearance between the mid-section and the impeller, the pump shaft meets the design requirements and the mid-section does not need to be cut. If the deflection of the pump shaft exceeds the range of the clearance between the mid-section and the impeller, proceed to Step 5.

[0016] Step 5: Based on the positions of the two end supports of the pump shaft and the deflection of the pump shaft calculated in Step 3, calculate the cutting amount of the two end faces of the middle section, and cut the two end faces of the middle section according to the cutting amount.

[0017] Step 6: Following the methods in Steps 1 to 5, determine whether each middle section needs to be cut; if cutting is required, calculate the cutting amount of the middle section and cut the middle section according to the cutting amount of each middle section; assemble all middle sections to obtain the pre-bent pump body.

[0018] Furthermore, in step 1, F ≤ 0.40 mm, f ≥ 0.05 mm.

[0019] Furthermore, in step 2, the weight of the rotating parts of the multistage centrifugal pump is calculated according to the following formula:

[0020] G = G 轴 +G总叶轮 ;

[0021] G 轴 =Area of ​​each section of the variable diameter shaft × Length × Material specific gravity;

[0022] G 总叶轮 =NG 单叶轮 ;

[0023] Where N represents the number of impellers; the rotating parts include the pump shaft and multi-stage impellers, therefore, the weight of the rotating parts is the sum of the weights of the pump shaft and multi-stage impellers.

[0024] Furthermore, step 5 includes the following process:

[0025] The calculated maximum deflection is assumed to occur at the exact midpoint between the two support points of the pump shaft. The radius R of the circular arc is obtained by using the coordinates of the two support points of the pump shaft and the point where the maximum deflection occurs, as determined on the plane.

[0026] Based on the radius R of the circular arc, determine the point on the centerline of the newly formed shaft system after the maximum deflection. Given the standard mid-section thickness L and the aperture 2r, calculate the angle α between the vertical line of the mid-section and the inclined end face of the mid-section.

[0027]

[0028] In the formula, α represents the angle between the vertical line of the middle section and the inclined middle section that forms the pre-bending surface, R represents the radius of the axial arc after the deflection, r represents the design inner hole radius of the middle section, and L represents the thickness of the middle section.

[0029] Based on the angle α between the vertical line of the middle section and the end face of the inclined middle section, the width of the shorter side of the inclined middle section is calculated, and then the single-sided cutting amount ΔL is determined:

[0030]

[0031] In the formula, L1 represents the thickness of the short side of the inclined segment, L1=2tanα×(Rr), and ⊿L represents the single-sided cutting amount.

[0032] This invention provides a pre-bending design method for a multistage centrifugal pump. Based on the clearance range between the intermediate section and the impeller, and the weight of the rotating components, the deflection of the pump shaft at each intermediate section position is calculated. The intermediate section is pre-bent at appropriate locations, transforming the vertical end face into an inclined end face. This ensures that the clearance between the intermediate section and components such as the impeller remains within the designed clearance range during long-term operation, preventing significant changes in the Lomakin effect and achieving stable liquid film support. This guarantees normal operation of the multistage centrifugal pump and extends its service life. By designing the intermediate section of the multistage pump to be inclined, a pre-bent pump body is obtained, preventing excessively small clearances between the impeller and the intermediate section, thus ensuring the normal operation of the multistage centrifugal pump. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating the implementation of the pre-bending design method for multi-stage centrifugal pumps provided by the present invention.

[0034] Figure 2 This is a schematic diagram showing the range of gap amounts;

[0035] Figure 3a -c is a schematic cross-section of the impeller and middle section that generates deflection;

[0036] Figure 4 This is a schematic diagram of the shaft of a multistage centrifugal pump;

[0037] Figure 5 This is a diagram illustrating the deflection.

[0038] Figure 6 This is a schematic diagram for calculating cutting quantities;

[0039] Figure 7 This is a schematic diagram of the Lomakin effect. Detailed Implementation

[0040] To make the technical problems solved by this invention, the technical solutions adopted, and the technical effects achieved clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings, not all of them.

[0041] like Figure 1 As shown, the multi-stage centrifugal pump pre-bending design method provided in this embodiment of the invention includes the following process:

[0042] Step 1: Determine the range of clearance between each section 2 of the pump body and the impeller 1.

[0043] The horizontal multistage centrifugal pump has a pump shaft 3, on which multistage impellers 1 are installed. Each impeller 1 has a middle section 2. The pump body includes multistage middle sections 2 spliced ​​together.

[0044] In order to achieve the performance requirements, the design of multistage centrifugal pumps is similar to that of single-stage centrifugal pumps. First, the hydraulic model and performance curve are determined, and the clearance between each intermediate section 2 of the pump body and rotating components such as the impeller 1 is determined based on experience and theoretical calculations.

[0045] For multi-stage centrifugal pumps, the intermediate section 2 of each stage is part of the pump body. Typically, the clearance between intermediate section 2 and impeller 1 is controlled at a certain range. Figure 2 As shown, the gap between the pump body and the impeller is maintained within the envelope formed by F and f during pump operation.

[0046] In this invention, the gap between the middle section 2 and the impeller 1 is in the range of f < CL < F, where F represents the maximum gap between the middle section 2 and the impeller 1, and f represents the minimum gap between the middle section 2 and the impeller 1; wherein F ≤ 0.40 mm, f ≥ 0.05 mm.

[0047] Step 2: Determine the weight of the rotating parts of the multistage centrifugal pump.

[0048] The rotating components include, but are not limited to, the pump shaft and multi-stage impellers. Accessories such as sealing rings and bushings have been appropriately simplified in the calculation process.

[0049] Calculate the weight of the rotating parts of a multistage centrifugal pump using the following formula:

[0050] G = G 轴 +G 总叶轮 ;

[0051] G 轴 = Area of ​​each section of the variable diameter shaft × Length × Material specific gravity.

[0052] G 总叶轮 =NG 单叶轮 ;

[0053] Where N represents the number of impellers; the rotating parts include the pump shaft and multi-stage impellers, therefore, the weight of the rotating parts is the sum of the weights of the pump shaft and multi-stage impellers.

[0054] For example:

[0055] The pump shaft is made of 3Cr13 material with a specific gravity of 7.76 kg / dm³. 3 The impeller is made of 1Cr13Ni, and the actual weighing weight is 40kg each.

[0056] therefore,

[0057]

[0058] G 总叶轮 = 9 × 40 kg.

[0059] G = G 轴 +G 总叶轮 =655kg.

[0060] Step 3: Calculate the deflection of the pump shaft 3 at the middle section based on the weight of the rotating component.

[0061] In horizontal multistage centrifugal pumps, the pump shaft rotates horizontally, and the distance between the two end support points is relatively far. The weight of the suspended pump shaft, plus the weight of other rotating components mounted on it (such as impellers, isolation sleeves, etc.), will cause downward deflection in the suspended part of the pump shaft. When the deflection value y ≥ f, the multistage pump cannot work normally. Therefore, it is necessary to take measures to ensure y ≤ f in the design of horizontal multistage pumps based on known conditions. One method is to use a pre-bending design with an inclined middle section. The most crucial aspect of this design method is to pre-calculate the deflection value y and the single-sided cutting amount ΔL of the inclined middle section. The cross-section of the shaft that generates the deflection is then cut, such as... Figure 3a As shown, under normal circumstances, the pump shaft 3 does not deflect, and there is an ideal clearance between the impeller 1 and the middle section 2, with the clearance being evenly distributed; Figure 3b As shown, the pump shaft 3 deflects, and after bending downwards, the impeller 1 and the bottom of the middle section 2 make contact without gap, and the gap 4 is uneven. Figure 3c As shown, the middle section 2 is pre-bent. After the middle section 2 is tilted, the deflection deformation is corrected. The gap between the impeller 1 and the tilted middle section 2 is kept within the allowable design envelope, and the impeller 1 and the middle section 2 will not contact each other.

[0062] The influence of deflection on the design and operation of multistage centrifugal pumps, and the design dimensions of pump shaft 3 as follows: Figure 4 As shown; under the action of deflection, the simplified diagram of axial downward bending is as follows. Figure 5 Calculating the deflection y of a variable-diameter shaft is usually quite complex and is often done graphically. To illustrate this, this invention uses the formula for calculating the maximum deflection at mid-span under uniformly distributed load to calculate the static deflection of the pump shaft 3. Specifically:

[0063] Calculate the pump shaft deflection using the following formula:

[0064]

[0065] In the formula, G represents the weight of the rotating component, S represents the sum of the lengths of the corresponding shaft diameters between the bearings, and E represents the elastic modulus of the steel. For structural steel used in engineering, E = 2.1 × 10⁻⁶ is found in the material handbook. 4 kgf / dm 2 J represents the average moment of inertia;

[0066]

[0067] In the formula, di represents the diameter of the i-th middle section of pump shaft 3, and s i This represents the length of the i-th middle section of pump shaft 3.

[0068] Continuing from the example in step 2:

[0069]

[0070]

[0071]

[0072] Step 4: Based on the deflection of the pump shaft 3 at the middle section calculated in Step 3, determine whether the deflection of the pump shaft 3 is within the range of the clearance between the middle section and the impeller. If the deflection of the pump shaft 3 is within the range of the clearance between the middle section 2 and the impeller 1, then the pump shaft 3 meets the design requirements and the middle section 2 does not need to be cut; if the deflection of the pump shaft 3 exceeds the range of the clearance between the middle section 2 and the impeller 1, then proceed to Step 5.

[0073] If the deflection of pump shaft 3 is within the clearance range, the design of pump shaft 3 meets the requirements, and the intermediate section 2 does not need to be cut. If the deflection of pump shaft 3 exceeds the clearance range between intermediate section 2 and impeller 1, then pre-bending design is required at both ends of the intermediate section, the cutting amount is calculated, and cutting is performed.

[0074] Continuing with the example in step 3, since y = 0.1 mm > the minimum gap value of 0.05, a pre-bending design is required for the middle section.

[0075] Step 5: Based on the positions of the two end supports of the pump shaft 3 and the deflection of the pump shaft 3 calculated in Step 3, calculate the cutting amount of the two end faces of the middle section 2, and cut the two ends of the middle section 2 according to the cutting amount.

[0076] like Figure 6 As shown, the calculated maximum deflection is assumed to occur at the exact midpoint between the two support points of the pump shaft. The radius R of the circular arc is obtained by using the coordinates of the two support points of the pump shaft and the point where the maximum deflection occurs, as determined on the plane.

[0077] Based on the radius R of the circular arc, determine the point on the centerline of the newly formed shaft system after the maximum deflection. Given the standard mid-section thickness L and the aperture 2r, calculate the angle α between the vertical line of the mid-section and the inclined end face of the mid-section.

[0078]

[0079] In the formula, α represents the angle between the vertical line of the middle section and the inclined middle section that forms the pre-bending surface, R represents the radius of the axial arc after the deflection is generated, r represents the design inner hole radius of the middle section, and L represents the thickness of the middle section.

[0080] Based on the angle α between the vertical line of the middle section and the end face of the inclined middle section, the width of the shorter side of the inclined middle section is calculated, and then the single-sided cutting amount ΔL is determined:

[0081]

[0082] In the formula, L1 represents the thickness of the short side of the inclined segment, L1=2tanα×(Rr), and ⊿L represents the single-sided cutting amount.

[0083] After single-sided cutting on both sides of the middle section, the gap 4 between the outer diameter of the impeller 1 and the inner diameter of the middle section 2 is corrected to the position where it exceeds the envelope range, so as to obtain a pre-bent middle section that can meet the gap envelope, overcome the gap deviation caused by deflection, and limit the gap 3 between the impeller 1 and the middle section 2 to the gap range (0.05~0.40mm) envelope.

[0084] Step 6: Following the methods in Steps 1 to 5, determine whether each middle section 2 needs to be cut; if cutting is required, calculate the cutting amount of middle section 2 and cut the middle section 2 according to the cutting amount of each middle section 2; assemble all middle sections 2 to obtain the pre-bent pump body.

[0085] All the preceding discussion in this embodiment refers to the characteristics of the rotor and shaft in air. In actual operation of a horizontal multistage pump, the rotor is immersed in the pumped liquid, which flows through one or more small annular areas. These annular areas are formed by gaps that divide the pump into different pressure zones, such as at sealing rings, interstage bushings, or balancing devices. This liquid flow produces a hydrodynamic bearing effect, effectively transforming the rotor from being supported by two external pump bearings to being supported by multiple additional internal bearings lubricated by the pumped liquid. This phenomenon is commonly referred to as the Lomakin effect (e.g., ...). Figure 7 In the figure, reference numeral 5 indicates the direction of water flow, reference numeral 6 indicates the direction of fluid force, and reference numeral 7 indicates the formation of a certain force range. Due to the Lomakin effect, the critical speed of the shaft in liquid is higher than that in air. Maintaining the operating characteristics below the first critical speed ensures the safe operation of the horizontal multistage pump.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions for some or all of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of pre-bend design for a multi-stage centrifugal pump, characterized by, The method comprises the following steps: Step 1, determining the clearance range of each middle section (2) of the pump body and the impeller (1); the clearance range of the middle section (2) and the impeller (1) is f < CL < F, wherein F represents the maximum clearance of the middle section (2) and the impeller (1), and f represents the minimum clearance of the middle section (2) and the impeller (1); Step 2, determining the weight of the rotating part of the multi-stage centrifugal pump; Step 3, calculating the deflection of the pump shaft (3) at the position of the middle section (2) according to the weight of the rotating part; The deflection of the pump shaft (3) is calculated according to the following formula: ； In the formula, G represents the weight of the rotating member, S represents the length of each shaft diameter portion corresponding to the bearing, E represents the elastic modulus of steel, for engineering structural steel, E = 2.1 x 10 4 kgf / dm 2 , and J represents the average moment of inertia. In the formula, G represents the weight of the rotating member, S represents the length of each shaft diameter portion corresponding to the bearing, E represents the elastic modulus of steel, for engineering structural steel, E = 2.1 x 10 4 kgf / dm 2 , and J represents the average moment of inertia. ； wherein d i denotes the diameter of the i-th middle section of the pump shaft (3), s i denotes the length of the i-th middle section of the pump shaft (3); Step 4, judging whether the deflection of the pump shaft (3) is within the clearance range of the middle section (2) and the impeller (1) according to the deflection of the pump shaft (3) at the position of the middle section (2) calculated in step 3; if the deflection of the pump shaft (3) is within the clearance range of the middle section (2) and the impeller (1), the pump shaft (3) meets the design requirements, and the middle section (2) does not need to be cut; if the deflection of the pump shaft (3) exceeds the clearance range of the middle section (2) and the impeller (1), step 5 is performed; Step 5, calculating the cutting amount of the two end faces of the middle section (2) according to the positions of the two end supports of the pump shaft (3) and the deflection of the pump shaft (3) calculated in step 3, comprising the following steps: The maximum deflection is assumed to occur at the middle position of the two support points of the pump shaft, and the coordinates of the two end supports of the pump shaft and the point of maximum deflection determined on the plane are obtained to obtain the radius R of the circular arc curve; According to the radius R of the circular arc curve, the point position on the center line of the shaft system newly formed after the maximum deflection is determined, and the included angle α between the vertical line of the middle section and the inclined end face of the middle section is calculated under the known conditions of the design standard middle section thickness L and the hole diameter 2r: ； In the formula, α represents the included angle between the vertical line of the middle section and the inclined middle section forming the pre-bent face, R represents the radius of the shaft arc after the deflection, r represents the design inner hole radius of the middle section, and L represents the thickness of the middle section; According to the included angle α between the vertical line of the middle section and the inclined end face of the middle section, the short side width of the inclined middle section is calculated, and the single-side cutting amount ⊿L is determined: ； In the formula, L1 represents the short side thickness of the inclined section, L1 = 2tanα×(R-r), and ⊿L represents the single-side cutting amount; Step 6, judging whether each middle section (2) needs to be cut according to the method of steps 1 to 5; if cutting is needed, the cutting amount of the middle section (2) is calculated; and the middle section (2) is cut according to the cutting amount of each middle section (2); all middle sections (2) are assembled to obtain a pre-bent pump body.

2. The multi-stage centrifugal pump pre-bend design method of claim 1, wherein, In step 1, F≤0.40mm, and f≥0.05mm.

3. The multi-stage centrifugal pump pre-bend design method of claim 1 or 2, wherein, In step 2, the weight of the rotating part of the multi-stage centrifugal pump is calculated according to the following formula: G = G 轴 + G 总叶轮 ; G 轴 = area of each section of variable diameter shaft x length x specific gravity of material G 总叶轮 =NG 单叶轮； Wherein, N represents the number of impellers (1); the rotating part includes the pump shaft and the multi-stage impeller, and therefore the weight of the rotating part is the sum of the weights of the pump shaft (3) and the multi-stage impeller (1).

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