CN113051675A - Mechanical checking method for influence of working temperature rise on dynamic characteristics of high-speed motor rotor - Google Patents
Mechanical checking method for influence of working temperature rise on dynamic characteristics of high-speed motor rotor Download PDFInfo
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Abstract
The invention relates to a mechanical checking method for influence of working temperature rise on the dynamic characteristics of a high-speed motor rotor, which comprises the following steps: (1) establishing a rotor dynamics analysis model of the high-speed permanent magnet synchronous motor; determining a shaft section transmission model considering the material characteristic change of each part caused by the working temperature of the motor; (3) determining a disc transfer model under the influence of the thermal stress of the motor; (4) and integrating a mathematical model of the whole transfer matrix, solving the critical rotating speed under the condition of considering the working temperature rise, and finishing mechanical checking.
Description
Technical Field
The invention relates to the field of mechanical design of high-speed permanent magnet synchronous motors, in particular to a high-speed permanent magnet synchronous motor mechanical checking method considering the influence of temperature on the dynamic characteristics of a rotor.
Background
In recent years, a high-speed permanent magnet motor combines the overall advantages of the high-speed motor and the permanent magnet motor, has great application potential by virtue of the advantages of high speed, high power density, simple structure, quick dynamic response and the like, covers occasions with various power levels, becomes one of the research hotspots for the field of the motor in the modern times at home and abroad, and is widely applied to the fields of high-speed machine tools, blowers, compressors, turbine expanders, micro gas turbines and the like. Compared with the traditional motor, the working speed of the motor is far lower than the natural frequency, the rated rotating speed of the high-speed motor is higher, and resonance is easy to generate when the rated rotating speed is close to the critical rotating speed; and the compact rotor structure causes poor heat dissipation conditions of the rotor and the problem of easy occurrence of demagnetization of the permanent magnet due to temperature rise. The key technology of the design stage of the high-speed motor determined by the characteristics not only meets the requirement of electromagnetic performance, but also needs to emphatically examine the requirement of mechanical performance and the limitation of temperature rise.
For high speed motor designs, improper rotor design can produce severe vibration and noise, and even catastrophic destruction of the rotor and bearings. Therefore, the design is based on the limitation of mechanical characteristics. Generally, firstly, the mechanical strength is ensured to meet the limitation of centrifugal force on the outer diameter, sufficient torque and power can be output on the basis, and meanwhile, the working rotating speed of the motor is ensured to avoid the critical rotating speed of a rotor system and a certain safety margin is kept. The high-speed motor rotor is designed to be slim, which puts higher demands on the dynamic characteristics of the rotor.
At present, in order to simplify calculation, a single-degree-of-freedom simple shaft disc model is mostly adopted for checking the rigidity of a rotor, the rotating speed of a machine is calculated under the constant material property at normal temperature, and the influence of thermal stress and thermal deformation caused by operation temperature rise on the rotating speed is not considered. However, the problem of temperature rise of the rotor of the high-speed motor is one of the key design problems, the influence of temperature on the material property is aggravated due to the actually high working temperature rise, and in addition, due to the thermal deformation and the thermal stress generated by the thermal characteristics of each contact part, the accurate checking of the rigidity is further limited.
Disclosure of Invention
The invention aims to solve the technical problem that the accuracy of the rotor dynamics analysis of the existing high-speed permanent magnet motor is not enough, and provides a mechanical rigidity checking method of the high-speed permanent magnet motor, which comprehensively considers the effect of the working temperature rise effect, based on the modeling of a complex rotor shafting with an actual additional structure, so that the accuracy of the critical rotation speed calculation is effectively improved, and a reference is provided for the rotor dynamics design and optimization of the high-speed permanent magnet motor. The technical problem to be solved by the invention is mainly realized by the following technical scheme:
a mechanical checking method for influence of working temperature rise on dynamic characteristics of a high-speed motor rotor comprises the following steps:
(1) establishing a rotor dynamics analysis model of a high-speed permanent magnet synchronous motor
A transfer matrix method is adopted, a simplified model of a rotor system is dispersed into an equivalent disc shaft model with N nodes based on the principles of unchanged mass center and unchanged moment, and a rotor dynamics calculation model considering additional rotating parts including a thrust disc, a turbine and an impeller is established.
(2) Shaft section transmission model under condition of considering material characteristic change of each part caused by motor working temperature
Considering the change of the elastic modulus of the material caused by temperature according to the influence of the change of the material parameters along with the temperature on the critical speed, and calculating an approximate value E (t) of the elastic modulus along with the change of the temperature;
based on a transfer matrix method, according to the stress and deformation conditions of a shaft section or a disc of each node of the rotor dynamics analysis model, the change conditions of various state variables between the left side and the right side of the disc shaft model of each unit are described from left to right, and Z is setiIs a system state variable matrix comprising displacement y, cross section corner theta, shearing force Q and cross section bending moment M, so that the mathematical model of the shaft section transfer equation is
Wherein l is the length of the shaft section, I is the moment of inertia of the shaft section, FiIs a transfer equation for a rigid disk that does not count thickness but accounts for inertia; gamma is a shear-affecting factor and is,
ksis the cross-sectional shape coefficient, GiIs the shear modulus, the left side is represented by the upper label L and the right side is represented by the upper label R in the formula;
(3) determining a disc transfer model under the influence of thermal stress of a motor
Let α be the coefficient of thermal expansion of the material, and ν represents the poisson's ratio of the material, and the expression that the thermal stress is generated due to the differential expansion caused by the different materials of each component is:
according to the additional stress of the elastic shaft of the disc under the additional thermal stress caused by the temperature rise, a thermal stress term F is additionally arranged in the transmission matrix of the equivalent discth＝σthA, a is the area of the force-bearing surface, so the mathematical model of the disk transfer equation is:
wherein P isiIs the transfer equation for the elastic shaft, J, not counting mass but taking into account stiffnessdIs the moment of inertia of the disc at right angles, JpIs the polar moment of inertia; omega is the vortex frequency of the disc; omega is the rotation angular speed of the disc; fthFor additional thermal stress;
(4) integrating a mathematical model of the whole transmission matrix, solving the critical rotating speed under the consideration of the working temperature rise, and finishing mechanical checking, wherein the method comprises the following steps:
firstly, describing a transfer relation from an ith node to an (i + 1) th node by sorting transfer equations of discs and shaft segments of all nodes to obtain a complete transfer matrix of a unit disc-shaft model;
recursion of the transfer relationship among the units, and establishment of an overall transfer model reflecting the overall transfer relationship and considering the temperature influence;
taking the relation between the continuous condition and the state variable of the cross section at the end of the time as a boundary condition, substituting the boundary condition into an integral transfer model considering the temperature influence, and solving the characteristic value omega-omegacrObtaining the natural angular frequency to determine the calculated value n of the critical rotation speedcrAnd the standard is used as the rotor mechanical checking standard.
Preferably, in step (2), the approximate value of the elastic modulus with temperature change E (t) is calculated by the formula: e (t) ═ E0(1-c(ΔT)/100)，
Wherein E (t) is the elastic modulus at the working temperature t; e0The modulus of elasticity at normal temperature, Δ T is the actual working temperature rise; c is the magnitude of the decrease in elastic modulus per 100 ℃ increase in temperature.
Preferably, in the step (4), the maximum operation speed of the rotor is set as nmaxIf n is satisfiedmax＜0.75ncrAnd the mechanical limitation requirement of the rotor is met.
The invention provides a mechanical checking method suitable for a high-speed permanent magnet motor, which considers the influence of two action effects of working temperature on the critical rotating speed of a rotor: the contact stiffness of the rotor system can be influenced by the property change of the material property such as mass, elastic modulus and the like which changes with the temperature, and on the other hand, the stiffness of the rotor system can also be changed by the generation of thermal stress. Has the following beneficial effects:
(1) establishing a rotor system model for considering each additional rotating part by combining with actual operation conditions and application fields, and considering bending effects, contact behaviors and gyro effects under a rotating state among structures to meet the actual requirements of engineering so as to ensure that the dynamic performance of a rotor system is accurately pre-judged;
(2) the influence of actual working temperature rise on the dynamic characteristics of the rotor is fully considered, particularly for the high-speed permanent magnet motor with high rotating speed and closer to the critical rotating speed, the problem of the temperature rise of the rotor is more critical, the influence of the temperature rise on the mechanical characteristics is more obvious, and the higher requirement on accurate calculation of the critical rotating speed is met;
(3) the method is suitable for various motors, particularly for high-speed permanent magnet motors, and is beneficial to limiting the long diameter size of the rotor in the primary design stage; in the optimization design stage, the rigidity is checked through more accurate calculation, corresponding measures are taken in time to improve the rigidity of the rotor, and the running safety of the rotary machine is ensured.
Drawings
FIG. 1 is a schematic structural diagram of a rotor system of a high-speed permanent magnet synchronous motor;
FIG. 2 is a simplified model of a high-speed PMSM rotor system and a corresponding equivalent lumped mass model;
fig. 3 is a stress model of the elastic shaft of the rigid thin disk considering the effect of temperature rise.
In fig. 1 and 2:
1-cylindrical permanent magnet 2-sheath 3-left end cover 4-right end cover
5-left shaft head 6-right shaft head 7-thrust disc 8-air-cooled impeller
9-left turbine 10-right turbine 11-left nut 12-right nut
Detailed Description
The invention provides a mechanical checking method of a high-speed permanent magnet synchronous motor, which considers the influence of working temperature on the dynamic characteristics of a rotor. To more clearly explain the objects, technical solutions and advantages of the present invention, the following detailed description of the embodiments of the present invention is provided in conjunction with the examples and the accompanying drawings, and the exemplary embodiments and descriptions of the present invention are provided for the purpose of illustration only and are not intended to limit the present invention.
Referring to fig. 1, the high-speed permanent magnet synchronous motor of the present invention, which is applied to the field of compressors as an example, includes a cylindrical permanent magnet 1, a sheath 2, a left end cover 3, a right end cover 4, a left spindle nose 5, a right spindle nose 6, a thrust disk 7, an air-cooled impeller 8, a left turbine 9, a right turbine 10, a left nut 11, and a rotor system of an additional rotating component of a right nut 12.
The invention is based on a transfer matrix method, combines an actual complex rotor system to carry out modeling, and takes into account the influence of temperature on material characteristics and the effect of two temperature rise effects of thermal stress and thermal deformation caused by thermal expansion characteristics on the critical rotating speed, and the specific implementation steps are as follows:
(1) the method comprises the following steps of establishing a high-speed permanent magnet synchronous motor rotor dynamics analysis model based on the actual application field:
according to a complex rotor structure required by the practical application field, a transfer matrix method is adopted, a simplified model of a practical rotor system is dispersed into an equivalent concentrated mass model with N nodes (wherein N is more than or equal to 1+5.34r, and r is the highest order required to be researched) through equivalent mass, rotational inertia and equivalent bending stiffness based on the principles of constant mass center, constant moment and the like, and a rotor dynamics calculation model considering additional rotating parts such as a thrust disc, a turbine and an impeller is established, as shown in FIG. 2.
(2) Determining a shaft section transmission model considering the change of material characteristics of each part caused by the actual working temperature of the motor:
aiming at the influence of the material parameter changing along with the temperature on the critical speed, the invention considers the change of the elastic modulus of the material caused by the temperature, and replaces the value with an approximate relation formula changing along with the temperature according to the change rule of the elastic modulus along with the temperature as
E(t)＝E0(1-c(ΔT)/100) (1)
Wherein E (t) is the modulus of elasticity at the working temperature t; e0The modulus of elasticity at normal temperature, Δ T is the actual working temperature rise; c is the magnitude of the decrease in modulus for each 100 ℃ increase in temperature. When the rotor operates at the working temperature, the reduction of the elastic modulus leads to the reduction of the contact rigidity, so that the natural frequency of each step is reduced. According to the transfer matrix method, the change of each state variable between the left side and the right side of each unit disc axis model is described from left (indicated by L superscript) to right (indicated by R superscript) according to the stress and deformation conditions of the axis segment and the disc of each node of the analysis model, wherein Z isiThe system state variable matrix comprises displacement y, cross section rotation angle theta, shearing force Q and cross section bending moment M. The mathematical model of the axial section transfer equation is
Wherein l is the length of the shaft section, I is the moment of inertia of the shaft section, FiIs a transfer equation for a rigid disk that does not count thickness but accounts for inertia; gamma is a factor which affects the shear factor,
ksis the cross-sectional shape coefficient, GiIs the shear modulus.
(3) Determining a disc transfer model under the influence of thermal stress of a motor
When the rotor works in a high-temperature environment, thermal deformation is generated due to the thermal expansion property of materials, and the expression that thermal stress is generated due to uneven expansion caused by different materials of each part is as follows:
where α is the coefficient of thermal expansion of the material and υ represents the poisson's ratio of the material. According to the additional stress of the disc elastic shaft under the additional thermal stress caused by the temperature rise effect, a thermal stress term F is additionally arranged in the transmission matrix of the equivalent discth＝σthAnd A are the areas of the stress surfaces. The mathematical model of the disk transfer equation is therefore:
wherein P isiIs the transfer equation for the elastic shaft, J, not counting mass but taking into account stiffnessdIs the moment of inertia of the disc at right angles, JpIs the polar moment of inertia; omega is the vortex frequency of the disc; omega is the rotation angular speed of the disc; fthAdditional thermal stress.
(4) Integrating the mathematical model of the whole transmission matrix, solving the critical rotation speed under the consideration of the working temperature rise, and finishing the mechanical check
The transfer relation from the ith node to the (i + 1) th node can be expressed by arranging the transfer equations of the disks and the shaft segments of the nodes
Wherein the transfer matrix T of each disk axis unit modeliAnd combining the disc transfer equation (2) and the shaft section transfer equation (3) of each node unit to obtain a complete transfer matrix of the unit disc shaft model.
By analogy, the transfer relationship among the units is recurred, and a mathematical model reflecting the whole transfer relationship is established:
Zi＝Ai-1Zi-1＝TiTi-1…T2T1Z1 (7)
taking the relation between the continuous condition and the state variable of the cross section of the end all the time as a boundary condition, bringing the boundary condition into an integral transfer model considering the temperature influence, solving a characteristic value omega, and obtaining a critical rotating speed calculation value n considering the two temperature action effects through conversioncrr30 ω/pi. The reference value is used as the mechanical checking standard of the rotor, and the maximum operation rotating speed n of the rotormaxSatisfy nmax＜0.75ncrAnd the mechanical limitation requirement of the rotor is met.
In order to verify the necessity of the method, compared with a traditional method which does not consider the working temperature and adopts a temporary rotating speed calculation method, the calculation result shows that the calculated value of the critical rotating speed is 55160r/min under the condition of neglecting the temperature influence; the critical rotating speed is 52330r/min under the action of only considering the material property change along with the temperature rise; the critical rotating speed is 51813r/min only considering the effect of thermal stress generated by thermal expansion on the critical rotating speed; the critical rotating speed of the coupled change of the two temperature effect effects on the superposition of the natural frequency is 49151 r/min. The result shows that the actual critical rotating speed calculation value considering the two temperature action effects is lower than that of the existing calculation method, so that the influence of the working temperature rise on the dynamic characteristics of the high-speed motor rotor is considered, the rigidity checking error is favorably reduced, and the failure possibility is reduced.
The mechanical checking method of the high-speed permanent magnet synchronous motor, which considers the influence of the temperature on the dynamic characteristics of the rotor, can effectively improve the mechanical checking precision. Taking the present invention as an example, the present invention includes but is not limited to the above embodiments, and it should be noted that modifications and variations made without departing from the principle of the present invention are all considered to be the protection of the present invention.
Claims (3)
1. A mechanical checking method for influence of working temperature rise on dynamic characteristics of a high-speed motor rotor comprises the following steps:
(1) establishing a rotor dynamics analysis model of a high-speed permanent magnet synchronous motor
A transfer matrix method is adopted, a simplified model of a rotor system is dispersed into an equivalent disc shaft model with N nodes based on the principles of unchanged mass center and unchanged moment, and a rotor dynamics calculation model considering additional rotating parts including a thrust disc, a turbine and an impeller is established.
(2) Shaft section transmission model under condition of considering material characteristic change of each part caused by motor working temperature
Considering the change of the elastic modulus of the material caused by temperature according to the influence of the change of the material parameters along with the temperature on the critical speed, and calculating an approximate value E (t) of the elastic modulus along with the change of the temperature;
based on a transfer matrix method, according to the stress and deformation conditions of a shaft section or a disc of each node of the rotor dynamics analysis model, the change conditions of various state variables between the left side and the right side of the disc shaft model of each unit are described from left to right, and Z is setiIs a system state variable matrix comprising displacement y, cross section corner theta, shearing force Q and cross section bending moment M, so that the mathematical model of the shaft section transfer equation is
Wherein l is the length of the shaft section, I is the moment of inertia of the shaft section, FiIs a transfer equation for a rigid disk that does not count thickness but accounts for inertia; gamma is a factor which affects the shear factor,
ksis the cross-sectional shape coefficient, GiIs the shear modulus, the left side is indicated by the upper label L and the right side is indicated by the upper label R in the formula;
(3) determining a disc transfer model under the influence of thermal stress of a motor
Let α be the coefficient of thermal expansion of the material, and ν represents the poisson's ratio of the material, and the expression that thermal stress is generated due to uneven expansion caused by different materials of each component is:
according to the additional stress of the elastic shaft of the disc under the additional thermal stress caused by the temperature rise, a thermal stress term F is additionally arranged in the transmission matrix of the equivalent discth＝σthA, a is the area of the force-bearing surface, so the mathematical model of the disk transfer equation is:
wherein P isiIs the transfer equation for the elastic shaft, J, not counting mass but taking into account stiffnessdIs the moment of inertia of the disc at right angles, JpIs the polar moment of inertia; omega is the vortex frequency of the disc; omega is the rotation angular speed of the disc; fthFor additional thermal stress;
(4) integrating a mathematical model of the whole transmission matrix, solving the critical rotating speed under the consideration of the working temperature rise, and finishing mechanical checking, wherein the method comprises the following steps:
firstly, describing a transfer relation from an ith node to an (i + 1) th node by sorting transfer equations of discs and shaft sections of all nodes to obtain a complete transfer matrix of a unit disc shaft model;
recursion of the transfer relationship among the units, and establishment of an overall transfer model reflecting the overall transfer relationship and considering the temperature influence;
taking the relation between the continuous condition and the state variable of the cross section at the end of the time as a boundary condition, substituting the boundary condition into an integral transfer model considering the temperature influence, and solving the characteristic value omega-omegacrObtaining the natural angular frequency to determine the calculated value n of the critical rotation speedcrAnd the standard is used as the rotor mechanical checking standard.
2. The mechanical verification method of claim 1, wherein in the step (2), the approximate value e (t) of the elastic modulus with temperature change is calculated by the following formula: e (t) ═ E0(1-c(ΔT)/100)，
Wherein E (t) is the elastic modulus at the working temperature t; e0 is the elastic modulus at normal temperature, and delta T is the actual working temperature rise; c is the magnitude of the decrease in elastic modulus per 100 ℃ increase in temperature.
3. The mechanical checking method according to claim 1, wherein in step (4), the maximum operating speed of the rotor is set to nmaxIf n is satisfiedmax＜0.75ncrAnd the mechanical limitation requirement of the rotor is met.
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Cited By (2)
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| CN113569349A (en) * | 2021-07-08 | 2021-10-29 | 中国科学院工程热物理研究所 | Method for analyzing dynamic characteristics of pull rod rotor considering temperature effect |
| CN113704981A (en) * | 2021-08-11 | 2021-11-26 | 武汉理工大学 | Method for analyzing time-varying dynamic behavior of high-speed bearing in temperature rise process |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113569349A (en) * | 2021-07-08 | 2021-10-29 | 中国科学院工程热物理研究所 | Method for analyzing dynamic characteristics of pull rod rotor considering temperature effect |
| CN113569349B (en) * | 2021-07-08 | 2023-10-24 | 中国科学院工程热物理研究所 | Analysis method for dynamic characteristics of pull rod rotor in consideration of temperature effect |
| CN113704981A (en) * | 2021-08-11 | 2021-11-26 | 武汉理工大学 | Method for analyzing time-varying dynamic behavior of high-speed bearing in temperature rise process |
| CN113704981B (en) * | 2021-08-11 | 2024-04-09 | 武汉理工大学 | Analysis method for time-varying dynamic behavior of high-speed bearing in temperature rising process |
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