CN115242025A - Optimized design method for diameter of rotating shaft of submersible motor capable of avoiding resonance - Google Patents

Abstract

The invention discloses a method for optimally designing the diameter of a rotating shaft of a submersible motor for avoiding resonance, which simplifies a motor model, divides a pump system consisting of the submersible motor and a pump into three sections, comprises a rotor section, a shaft extension section and a pump section, respectively calculates the rotary inertia of each section, and selects a reasonable diameter of the rotating shaft by calculating the torsional vibration of a shaft system and comparing the torsional vibration with the rotating speed; the invention can effectively avoid resonance caused by locked rotor in the running process of the submersible motor and improve the stability of the system.

Description

Optimized design method for diameter of rotating shaft of submersible motor capable of avoiding resonance

Technical Field

The invention relates to a design method of a submersible motor, in particular to a design method for optimizing the diameter of a rotating shaft of the submersible motor, which avoids resonance.

Background

The submersible motor is commonly used in the aspects of urban water supply and drainage, emergency rescue, disaster relief and the like, and has high requirement on reliability. The rotating shaft is used as an important force transmission component, and the failure frequency is high. In the running process of the submersible motor, impurities such as silt in water can enter the pump and attach to the impeller, so that the load is increased instantly. When the load is increased, on one hand, the rotating speed of the rotating shaft is gradually increased, and on the other hand, the rotating shaft generates torsional vibration. When the inherent torsional vibration frequency of the rotating shaft of the pump system is close to or in a simple multiple relation with the angular speed of the rotating shaft, the system can resonate, and the stress borne by the rotating shaft is greatly increased, so that the pump system fails. The submersible motor is usually started with load, and the rotation blockage during the starting process can also cause the rotating shaft to vibrate in a torsional mode.

In the prior art, the mechanical strength of the rotating shaft is usually verified according to the comparison between the stress and the yield stress of the rotating shaft in overload, and when a pump system resonates, the stress of the rotating shaft is far greater than that in a common overload condition. Simply increasing the diameter of the shaft increases the volume of the submersible motor and pump. It is not practical to determine satisfactory shaft design parameters by producing a large number of prototypes and performing comparative experiments. Therefore, it is necessary to search an optimal design method for the diameter of the rotating shaft of the submersible motor, which can avoid shafting resonance, for the problem of torsional vibration of the rotating shaft of the submersible motor during load fluctuation.

Disclosure of Invention

The invention provides a method for optimally designing the diameter of a rotating shaft of a submersible motor, which avoids resonance and improves the reliability of the rotating shaft, aiming at the problem of torsional vibration when the load of the submersible motor fluctuates.

The invention realizes the aim through the following technical scheme, which comprises the following steps:

a diameter optimization design method for a rotating shaft of a submersible motor capable of avoiding resonance comprises the following steps:

step 1, dividing a rotating shaft structure into three sections, namely a rotor section, a shaft extension section and a pump section, wherein each section (namely the rotor section, the shaft extension section and the pump section) is equivalent to a continuous solid cylinder;

step 2, determining the initial diameter d of a rotating shaft of the shaft extension section;

step 3, calculating the torsional vibration natural angular frequency of the rotating shaft of the shaft extension section during normal work:

the stress equation of the rotating shaft of the shaft extension section is written according to the Dalnbel principle as follows:

in the formula: i is the rotational inertia of the unit length of the rotating shaft of the shaft extension section, theta (x, t) is the torsion angle of the rotating shaft of the shaft extension section, x is the axial distance of the rotating shaft of the shaft extension section, t is time, G is the shear modulus of the rotating shaft material, M (x, t) is the external moment borne by the rotating shaft of the shaft extension section, M (x, t) =0 is made, and the boundary conditions are as follows:

and

I ₁ including the moment of inertia of the rotor for the rotor section axis of rotation, I ₂ The rotational inertia of the shaft extension section including the impeller and water, L is the length of the shaft extension section, rho is the density of the material of the shaft, the torsional vibration natural angular frequency of the shaft extension section is obtained by solving the equation, and the formula is

Wherein: omega is the torsional vibration natural angular frequency of the rotating shaft of the shaft extension section, and I is the rotary inertia of the rotating shaft of the shaft extension section in unit length;

step 4, comparing the torsional vibration natural angular frequency omega of the rotating shaft at the shaft extension section with the rotating angular velocity omega of the rotating shaft in the step 3 ₁ Omega should avoid omega ₁ And 2 omega ₁ Plus or minus 10%, considering that the rotating speed of the rotating shaft will be reduced when the load is increased, therefore, when omega is more than or equal to 2.2 omega ₁ And (3) selecting the size of the rotating shaft of the current shaft extension section, or reselecting the value d which is larger than the value calculated in the step (2).

In some embodiments, the derivation process of the formula for selecting the initial value of the diameter of the rotating shaft of the axial extension section in step 2 is as follows:

when selected according to the maximum yield stress, there are

Wherein: m' _ef The resultant moment, M, borne by the shaft in the shaft extension section when calculated according to the yield stress _b For bending moment, take M _b K ' =0, k ' is yield overload coefficient, take k ' =2 _N Rated torque for submersible motors

Wherein sigma' _ef The yield limit of the material of the rotating shaft is 3.53 multiplied by 10 ⁸ Paa, W is a fracture-resistant system, and is derived to obtain the initial value of the diameter of the shaft extension section

As a further optimized scheme of the invention, the calculation formula of I in the step 3 is

Wherein m is the mass of the rotating shaft of the shaft extension section, d is the diameter of the rotating shaft of the shaft extension section, L is the length of the rotating shaft of the shaft extension section, I ₁ Is calculated by the formula

Wherein m is ₁ Including the mass of the rotor for the rotor section axis of rotation, D ₁ The outer diameter of the rotor is divided according to the structure of the submersible motor and the pump in the step 1,

wherein L is the length of the shaft at the shaft extension section, rho is the density of the material of the shaft, and L ₁ The length of the rotating shaft of the rotor section is obtained by substituting a calculation formula of the moment of inertia,

I ₂ is calculated by the formula

Wherein m is ₂₁ For the mass of the pump section shaft, D ₂₁ Is the diameter of the rotating shaft of the pump section, m ₂₂ For single impeller mass, D ₂₂ The outer diameter of the impeller, q the number of the impellers, and k the coefficient for reducing the rotational inertia of water and the resistance moment received by the impeller into the impeller.

As a further optimization scheme of the invention, in the step 3, when the starting process of the submersible motor is locked, the equation boundary condition is changed into

And

θ(x,t)| _x＝L ＝0

solving equation when the rotating shaft torsional vibration natural angular frequency of the shaft extension section is calculated according to the formula

Wherein G is the shear modulus of the material of the rotating shaft, I is the rotational inertia of the unit length of the rotating shaft of the shaft extension section, and I ₁ The rotor section rotating shaft comprises the rotational inertia of a rotor, rho is the density of a rotating shaft material, and L is the length of the shaft extension section.

In some embodiments, the initial diameter of the shaft extension section in step 2 can also be selected according to the fatigue stress, and the derivation process is as follows: resultant moment M borne by rotating shaft of shaft extension section in calculation according to fatigue stress _ef The calculation formula is as follows,

M _ef ＝0.4T _N

wherein, T _N Fatigue limit sigma of shaft material for rated torque of submersible motor _ef And the fracture resistance coefficient W is calculated as follows,

the derived initial diameter d is selected by the formula

Wherein, T _N Rated torque, σ, for submersible motors _ef Is the fatigue limit of the material of the rotating shaft.

As a further optimization scheme of the invention, in the step 4, when the diameter of the rotating shaft of the shaft extension section meets the requirement, 12 pi rf is judged ₁ Whether the natural angular frequency omega of the torsional vibration of the rotating shaft of the shaft extension section calculated in the claim 4 is equal to or not _locked Wherein r is a non-zero positive integer, f ₁ The power supply frequency for the submersible motor is controlled to avoid torsional resonance of a rotating shaft at a shaft extension section caused by fluctuation of starting torque during locked rotor.

In the step 3, k is 1.1-1.2 as a further optimized scheme of the invention.

Compared with the prior art, the invention has the beneficial effects that:

(1) Aiming at the extreme working conditions of the submersible motor, the influence of static stress on the mechanical performance of the rotating shaft is considered, the damage of torsional vibration on the rotating shaft is also considered, and the diameter optimization design method of the rotating shaft of the submersible motor for avoiding resonance is provided through the natural frequency of a reasonable computer pump system;

(2) When the rotational inertia of the impeller is calculated, the mass and the resistance of water are considered and are reduced into the rotational inertia of the impeller, so that the accuracy and the simplicity of the natural frequency calculation process are improved.

Drawings

FIG. 1 is a flow chart of the diameter optimization design method of the submersible motor shaft for avoiding resonance in the invention;

FIG. 2 is a schematic structural diagram of a submersible motor and an inner impeller of a pump;

FIG. 3 is a schematic view of a single impeller configuration;

FIG. 4 is a Campbell diagram of a shaft axis;

FIG. 5 is the torsional vibration natural frequency of the shaft system when the impeller is locked;

reference numbers in the figures: 1 rotor section, 2 shaft extension sections, 3 pump sections and 4 impellers.

Detailed Description

The embodiments of the present invention will be described in detail below, and the embodiments described by referring to the drawings are exemplary only for the purpose of illustrating the present invention and are not to be construed as limiting the present invention.

As shown in fig. 1, a method for optimally designing the diameter of a rotating shaft of a submersible motor for avoiding resonance comprises the following steps:

in this embodiment, a submersible motor is used, and the basic parameters of the motor are shown in the following table:

power of	150kW
		Number of pole pairs	2
Outer diameter of stator	445mm
		Stator bore	245mm
Inner diameter of rotor	100mm
		Length of iron core	440mm
Air gap	1.4mm
		Rated torque	900Nm

(1) The rotating shaft structure is divided into three sections, namely a rotor section 1, a shaft extension section 2 and a pump section 3, as shown in fig. 2, each section is equivalent to a continuous solid cylinder, the rotor section 1 comprises a rotor core and an internal rotating shaft thereof, the shaft extension section 2 is a part of the rotating shaft between the rotor core and the pump, and the pump section 3 comprises the rotating shaft inside the water pump and an impeller 4 on the shaft;

(2) According to rated data, determining the initial diameter of the rotating shaft of the shaft extension section

(3) As shown in fig. 2-3, the shear modulus G =8 × 10 of the material of the rotating shaft ¹⁰ Pa, density of the material of the rotating shaft rho =7800kg/m ³ The length L of the rotating shaft of the shaft extension section 2 is =0.64m, and the length L of the rotating shaft of the rotor section 1 is ₁ =0.44m, rotor segment 1 outer diameter D ₁ =0.225mm, mass m of pump segment 3 shaft ₂₁ =91.13kg, diameter D of the pump section 3 shaft ₂₂ =0.085mm, pump segment 3 single impeller 4 mass m ₂₂ =31.81kg, diameter D of impeller 4 in pump segment 3 ₂₂ =0.5m, the number q =6 of the impellers 4, a coefficient k =1.15 for calculating the rotational inertia of the water and the resisting moment received by the impellers 4 into the impellers 4, and the rotational inertia per unit length of the rotating shaft of the shaft extension section 2

Rotor segment 1 shaft including rotational inertia of rotor

The pump section rotating shaft comprises an impeller and water

Carry in data, calculate

(4) Rotation angular velocity ω of the rotating shaft ₁ =155rad/s, comparative 2.2 ω ₁ If the value of D is larger than omega, the value of D which is larger than the value of D calculated in the step (2) is selected, D =0.08m is selected (the value of D =0.08m is determined according to the installation size), omega =697.5deg/s is calculated again, the requirement is met, a finite element model is adopted for simulation, a 1D model is established, the model is subjected to line subdivision, the subdivision size is 20mm, the Poisson ratio of a rotating shaft material is 0.28, composite modal analysis is carried out, and a Campbell curve is drawn according to the finite element simulation result, and is shown in figure 4: in FIG. 4, the natural frequency 213.56rad/s at the intersection (1) of the broken line and the solid line corresponds to the rotation speed 1019.7rpm, which is a point pairThe response frequency is the resonance frequency, the simulation result is compared with the calculation result, the difference between the simulation result and the calculation result is 3%, the simulation result of the natural frequency of the rotating shaft is 679.3rad/s when d =80mm, the difference between the simulation result and the calculation result is 2.6%, and the frequency is not superposed with the angular frequency of the rotating speed of the rotating shaft, so that resonance is not caused;

in the step (3), the power supply frequency of the submersible motor is 50Hz, r is 1, and if the submersible motor is locked in the starting process, the torsional vibration angular frequency of the rotating shaft of the shaft extension section 2 is

Corresponding to a frequency of 102.4Hz, 12 pi rf by comparison ₁ And omega _locked And if the difference is different, meeting the requirements, establishing a 3D model by adopting 3D finite element simulation, carrying out tetrahedral subdivision on the model, taking the poisson of the rotating shaft material as 0.28, carrying out modal frequency response analysis, and comparing a figure 5 with a calculation result, wherein the difference between the finite element simulation result and the calculation result is 5.3 percent.

Claims (7)

1. The method for optimally designing the diameter of the rotating shaft of the submersible motor for avoiding resonance is characterized by comprising the following steps of:

step 1: dividing a rotating shaft structure into three sections, namely a rotor section, a shaft extension section and a pump section, wherein each section is equivalent to a continuous solid cylinder;

step 2: determining the initial diameter d of a rotating shaft of a shaft extension section;

and 3, step 3: calculating the torsional vibration natural angular frequency of the rotating shaft at the shaft extension section by the formula

Wherein: omega is the natural angular frequency of torsional vibration of the rotating shaft of the shaft extension section, i is the rotational inertia of the rotating shaft of the shaft extension section in unit length, i ₁ Including the moment of inertia of the rotor for the rotor section axis i ₂ The total rotational inertia of a rotating shaft, an impeller and water of the pump section, G is the shear modulus of a rotating shaft material, rho is the density of the rotating shaft material, and L is the length of the rotating shaft of the shaft extension section;

and 4, step 4: comparing the torsional vibration of the shaft extension section rotating shaft calculated in the step 3Angular frequency ω and rotational angular velocity ω of the rotating shaft ₁ ，ω≥2.2ω ₁ And selecting the size of the rotating shaft of the current shaft extension section, otherwise, reselecting a larger d value.

2. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 1, is characterized in that: step 2, the initial diameter of the rotating shaft at the shaft extension section is selected according to the formula

Wherein, T _N Is the rated torque of the submersible motor, sigma' _ef The yield limit of the material of the rotating shaft.

3. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 1, is characterized in that: in step 3, the formula of I is

I ₁ Is calculated by the formula

Where ρ is the density of the material of the rotating shaft, D ₁ Is the outer diameter of the rotor, L ₁ Is the length of the rotor section axis of rotation, I ₂ Is calculated by the formula

Wherein m is ₂₁ For the mass of the pump section shaft, D ₂₁ Is the diameter of the rotating shaft of the pump section, m ₂₂ For single impeller mass, D ₂₂ The outer diameter of the impeller, q the number of the impellers, and k the coefficient for integrating the rotational inertia of the water and the resisting moment received by the impeller into the impeller.

4. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 1, is characterized in that: in step 4, when the diameter of the rotating shaft of the shaft extension section meets the requirement, 12 pi rf is judged ₁ Whether to block rotation with the starting process of the submersible motorNatural angular frequency omega of torsional vibration of rotating shaft of time shaft extension section _locked If yes, the diameter of the rotating shaft of the shaft extension section is reselected, wherein r is a non-zero positive integer, f ₁ And supplying power frequency to the submersible motor.

5. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 4, is characterized in that: when the starting process of the submersible motor is locked, the calculation formula of the torsional vibration natural angular frequency of the rotating shaft at the shaft extension section is as follows

Wherein G is the shear modulus of the material of the rotating shaft, I is the rotational inertia of the unit length of the rotating shaft of the shaft extension section, and I ₁ The rotor section rotating shaft comprises the rotational inertia of a rotor, rho is the density of a rotating shaft material, and L is the length of the shaft extension section.

6. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 1, is characterized in that: in step 3, k is 1.1-1.2.

7. The optimal design method for the diameter of the rotating shaft of the submersible motor capable of avoiding resonance as claimed in claim 1, is characterized in that: the selection formula of the initial diameter of the rotating shaft of the shaft extension section in the step 2 can also be

Wherein, T _N Rated torque, σ, for submersible motors _ef Is the fatigue limit of the material of the rotating shaft.

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