CN109766647A - Consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method - Google Patents
Consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method Download PDFInfo
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Abstract
The invention discloses determine method for a kind of high-performance electric main shaft timeparameter method for considering power thermal coupling effect, the present invention has fully considered the power thermal coupling effect during electro spindle runs at high speed, the size of the field distribution of electro spindle steady temperature and system support stiffness is obtained by numerical computation method, more accurate obtains the timeparameter method of electro spindle.
Description
Technical field:
The present invention relates to machinery field more particularly to a kind of high-performance electric main shaft heat dynamic for considering power thermal coupling effect are special
Property determines method.
Background technique:
With the development of the times, high-performance electric main shaft has become the core component of Modern High-Speed machining tool, for lathe plus
Work precision provides great guarantee.And electro spindle inevitably generates a large amount of heat during operation, makes electro spindle
System generates uneven thermal deformation, while also resulting in the softening of system support stiffness, to influence the processing quality of part, seriously
When also result in thrashing and can not work, this seriously inhibits the sustainable developments of high speed machining.Electro spindle heat dynamic
Characteristic mainly includes the distribution of Steady-State Thermal Field and the size of system support stiffness, it is effective predict electro spindle Steady-State Thermal Field and
The size of accurate computing system support stiffness is particularly important to the development of high speed machining.
Currently, the method for calculating electro spindle Steady-State Thermal Field mainly has numerical method and finite element stimulation method, number
Value calculating method is the ther mal network model by establishing electro spindle and finds out the electro spindle heat source calorific value under specified conditions, is then passed through
It crosses to solve equation and acquires electro spindle Steady-State Thermal Field, this method solves simple, computational efficiency height, but needs to consider heat source calorific value
Time variation.Finite element stimulation method is the finite element model by establishing system, then by the heat source calorific value acquired, change
Heat condition etc. is loaded on finite element model as boundary condition, and this method can accurately obtain the temperature of each part of electro spindle
Size, but solution efficiency is not often high, and has ignored the time variation of boundary condition.And calculate the method for electro spindle support stiffness then
Mainly analytic method, for mechanical electro spindle, the bearing rigidity calculation method of consideration fuel factor existing at present be then
Bearing thermal walking is added in bearing movable equation, calculates the support stiffness of main shaft-bearing system at present then mainly using this
Method, and to structure is complicated, for the high-performance electric main shaft more than number of bearings, this method could be improved.
And in the prior art, electro spindle thermal characteristic and dynamic characteristic are often used as two independent goals in research,
But in fact, electro spindle during running at high speed, power thermal coupling effect will inevitably occurs, i.e., produce when electro spindle operates
Raw heat can change the size of power inside electro spindle, and the distribution situation of power can change the size of heat source calorific value, only comprehensive
It closes and considers that more accurate the timeparameter method of electro spindle could be obtained.
Summary of the invention:
The purpose of the present invention is to provide a kind of high-performance electric main shaft timeparameter methods for considering power thermal coupling effect to determine
Method, the present invention have fully considered the power thermal coupling effect during electro spindle runs at high speed, have been obtained by numerical computation method
The size of the field distribution of electro spindle steady temperature and system support stiffness, more accurate obtains the timeparameter method of electro spindle.
To solve the above problems, the technical scheme is that
It is a kind of consider power thermal coupling effect high-performance electric main shaft timeparameter method determine method, which is characterized in that including
Following steps:
Step 1: establishing bearing thermal coupling model, analysis considers the compatible pass of Bearing inner geometry of power thermal coupling effect
It is and carries out shaft strength analysis and bearing heat production analysis；
Step 2: establishing the high-performance electric main shaft heat based on thermal resistance transmits network model, and analyze different type thermal resistance
Calculation expression；
Step 3: establishing loss model controller, motor heat production is analyzed；
Step 4: the bearing ring thermal walking situation of change under analysis different installation；
Step 5: the analytical calculation process for considering the high-performance electric main shaft timeparameter method of power thermal coupling effect is drafted, and
Selected algorithm is solved；
Step 6: output calculated result, obtains the hot dynamic parameter of electro spindle.
Further to improve, the hot dynamic parameter of electro spindle includes selected node temperature and each bearing stiffness of system
With the changing rule of the speed of mainshaft.
Further to improve, the step 1 includes the following steps: to establish bearing thermal coupling model, carries out bearing geometry
Analysis, force analysis and heat production analysis:
If the bearing outer ring center of curvature is fixed, bearing inner race is rotated with shaft, when bearing is by load F=
{Fx,Fy,Fz,Mx,MyWhen, bearing internal external circle generates relative displacement δ={ δx,δy,δz,θx,θy, wherein, Fx、Fy、Fz、Mx、My
The respectively moment of face of the external applied load in x, y, z direction and the direction x, y that is subject to of bearing, j is bearing sphere ordinal number, and Z is bearing ball
Body number；In view of bearing heat production and motor heat production, electric chief axis system will generate thermal deformation, so that bearing internal external circle can also produce
Heat displacement components u={ ua,ur, ua, urThe axially opposing thermal walking of bearing ring and diametrically thermal walking are respectively indicated, additionally
There is the centrifugation displacement of bearing inner racec, obtain Angle Position ψjThe bearing internal external circle at place axially and radially relative distance:
A1j=BDbsinα0+Δa
A2j=BDbcosα0+Δr+Δc
In formula, A1jFor the axially opposing distance of bearing internal external circle, A2jFor bearing internal external circle diametrically distance, B=fi+fo-
1, fi、foFor inside and outside raceway Curvature Radius Coefficient, DbFor sphere diameter, α0For bearing initial contact angle, ΔaFor bearing internal external circle
Axial total relative displacement, ΔrFor the radially total relative displacement of bearing internal external circle, ΔcIt is centrifuged and is displaced for bearing inner race；
Establish O-XYZ main shaft coordinate system, O1-X1Y1Z1For one coordinate system of bearing, O2-X2Y2Z2For two coordinate system of bearing；O point
It build shaft end face center in, O1 indicates the geometric center of bearing one, and O2 indicates the geometric center of bearing two；
Δa=δz+Riθxcosψj-Riθysinψj+ua
To bearing two:
Δa=-δz-Riθxcosψj+Riθysinψj+ua
In formula, δzFor the axially opposing displacement of bearing internal external circle, RiFor inner ring center of curvature radius of circle, θxFor bearing internal external circle x
To relative angular displacement, θyIt is bearing internal external circle y to relative angular displacement, ψjFor bearing roller position angle, uaFor bearing internal external circle axis
To opposite thermal walking；
The radially total relative displacement of bearing internal external circle:
In formula, δx、δyRespectively bearing internal external circle x to y to relative displacement, θrFor at maximum distortion rolling element and position
The angle between rolling element that angle setting is 0, andurFor the diametrically thermal walking of bearing internal external circle.
The centrifugation displacement of bearing inner racec:
In formula, ρiIndicate bearing inner race density, ωiIndicate bearing inner race revolving speed, EiIndicate bearing inner race elasticity modulus, μi
Indicate bearing inner race Poisson's ratio, d indicates bearing inner race diameter, diIndicate bear inner ring grooved railway diameter；
Obtain the deformation geometry compatible equations of contact ball bearing groove road contact are as follows:
(A1j-X1j)2+(A2j-X2j)2-[(fi-0.5)Db+δij]2=0
X1j 2+X2j 2-[(fo-0.5)Db+δoj]2=0
In formula, X1j、X2jThe respectively axial distance and radial distance of ball centre and the outer raceway groove center of curvature, δij、δojPoint
Inside and outside the flexible deformation approach amount contacted with sphere, D Wei not be enclosedbFor sphere diameter；
In the plane by ball centre and bearing axis, Angle Position ψjThe sphere institute at place is loaded, if λijAnd λojPoint
Inside and outside circle channel control coefrficient is not indicated, for high-speed case, if gyroscopic couple suffered by sphere is completely by sphere and outer ring raceway
Contact friction force offset, at this moment, take λij=0, λoj=2；It is closed according to Hertz point contact deformation relationship and sphere stress balance
System can obtain:
In formula, Kij、KojThe deformation under load coefficient that respectively inside and outside circle raceway is contacted with sphere, αij、αojRespectively bearing
Inside and outside circle and sphere contact angle, Mgj、FcjThe gyroscopic couple and centrifugal force that respectively j-th of sphere is subject to；
Bearing is each to shift value when in order to find out stable state, establishes bearing equilibrium equation loaded, it is assumed that axis
Afford connected load F={ Fx,Fy,Fz,Mx,MyAct under main shaft coordinate system, the relationship of bearing load and displacement is available
Following formula expression:
When level pressure pre-tightens:
To bearing one:
To bearing two:
In formula, Fx、Fy、Fz、Mx、MyThe respectively moment of face of the external applied load in x, y, z direction and the direction x, y that is subject to of bearing, j
For bearing sphere ordinal number, Z is bearing sphere number；
When positioning pre-tightens, bearing load equilibrium equation need to only remove the z in level pressure prefastening load equilibrium equation to equation i.e.
It can.
In the electro spindle course of work, due to the rubbing action of bearing roller and Internal and external cycle, bearing will generate heat, below
Provide the calculation method of bearing quantity of heat production:
For position angle ψjThe sphere at place has:
In formula, Mij、MojThe respectively moment of friction of sphere and inside and outside raceway, f0、f1It is and bearing type and lubrication, negative
Carry related coefficient, η0For the kinematic viscosity of lubricating oil, ωcjFor the revolution angular speed of j-th of sphere, Qij、QojRespectively sphere
With the contact stress of inside and outside raceway, Qimax、QomaxThe respectively maximum stress of sphere and inside and outside raceway contact；
Outer rollaway nest is controlled, it is only necessary to consider the spin friction torque of sphere and interior rollaway nest, it may be assumed that
In formula, MsijFor the spin friction torque of sphere and interior rollaway nest, μsiFor the coefficient of friction of sphere and interior rollaway nest, aijFor
The Hertz contact ellipse major semiaxis of sphere and interior rollaway nest, ΣijFor sphere and the elliptical second class complete product of interior rollaway nest Hertz contact
Point；
Therefore the frictional heating amount in inside and outside raceway contact area is respectively as follows:
Hij=ωcj.Mij+ωbj.Msij
Hoj=ωcj.Moj
In formula, Hij、HojThe respectively frictional heating amount of sphere and inside and outside raceway contact area, ωbjFor the spin angle of sphere
Speed.
It is further to improve, the step 2: electro spindle heat transmitting network model is established, the meter of different type thermal resistance is analyzed
Steps are as follows for operator expression formula:
During operation, there is two kinds of main thermaltransmission modes: heat transfer, thermal convection for electro spindle；
A. for heat transfer thermal resistance:
Heat transfer thermal resistance is divided into axial direction, radial direction thermal resistance；According to Fourier theorem, the axial thermally conductive heat of cylinder and cylinder
Hinder R1Are as follows:
In formula, L is cylinder or cylinder axial length, and k is cylinder or cylinder thermal conductivity, SaFor cylinder or cylinder axial cross section
Product；
Cylinder radial direction heat transfer thermal resistance R2Are as follows:
In formula, d2、d1Respectively outside diameter of cylinder and internal diameter；
Cylindrical radial heat transfer thermal resistance R3Are as follows:
Sphere heat transfer thermal resistance R4Are as follows:
In formula, kbFor sphere thermal conductivity；
The lubricating grease heat transfer resistance R of inside and outside raceway when grease lubrication5And R6It is respectively as follows:
In formula, kLFor lubricating grease thermal conductivity, DoFor bearing outer ring channel diameter, Bi、BoThe respectively inside and outside circle width of bearing；
B. convective heat transfer resistance
According to Fourier theorem, the axial direction of cylinder and cylinder, advection heat exchanged thermoresistance R7Are as follows:
In formula, h is convection transfer rate, and S is cylinder or cylinder and extraneous heat convection area；
The calculation method of the coefficient of heat transfer is as follows:
Heat transfer free convection and radiation heat transfer, composite heat-exchange coefficient h occur for bearing block and external environment1Are as follows:
In formula, Nu1For the nusselt number of bearing seating face and cross-ventilation heat exchange, λeFor surrounding medium thermal conductivity, DeTo change
Hot surface characteristic diameter.
Wherein,G is acceleration of gravity, βeIt is thermally expanded for surrounding medium and is
Number, ThFor bearing block surface temperature, TeFor ambient temperature, PrFor surrounding medium Prandtl number, ηeFor the movement of surrounding medium
Viscosity；
The coefficient of heat transfer h between fluid and peripheral wall surface in coolant jacket2Are as follows:
In formula, Nu2For the nusselt number of fluid and wall surface heat convection, λfFor fluid thermal conductivity, DfFor channel characteristics ruler
It is very little；
Wherein, Nu2=0.0225Re1 0.8Pr 0.3, Re1For Reynolds number, andufFor the movement velocity of fluid, ηf
For the kinematic viscosity of fluid；
Fluid motion speedQfFor fluid volume flow, AfFor channel cross-sectional area；
For cooling jacket, channel characteristics sizeCfFor channel cross-section perimeter；For rotor air gap, Df
For rotor gas length；
Electric chief axis system rotating part and surrounding ambient fluid convection transfer rate h3Are as follows:
In formula, deqFor rotating part equivalent diameter, Nu3For fluid and rotation wall surface heat convection nusselt number,λeFor surrounding medium thermal conductivity
Wherein, Re2For Reynolds number, andω is rotating part revolving speed；
The thermal contact resistance R of faying face8It indicates are as follows:
In formula, hcFor faying face contact conductane coefficient；A is faying face nominal contact area；
The heat transfer for considering dimpling peak, interface fluid media (medium), ignores the radiation heat transfer between air gap, contact conductane coefficient hcTable
It is shown as:
In formula, LgFor faying face gap thickness, k1、k2The thermal conductivity of respectively two mating parts, kfFor interfacial gap Jie
The thermal conductivity of matter, A*For faying face dimensionless real contact area, andAcFor real contact area.
Establish electro spindle ther mal network model:
Using bearing, motor radial geometric center plane as cut-off rule, a series of radially arranged nodes, wherein faying face
A node is respectively arranged at both ends, while guaranteeing that each radial node is in axial direction aligned, and establishes system heat balance equation.
It is further to improve, in the step 3: loss model controller is established, steps are as follows for analysis motor heat production:
In the course of work, stator loss includes copper loss and iron loss on stator winding, ignores rotor iron loss, considers rotor whirlpool
Stream loss；
Copper loss P on stator windingCu:
PCu=mI2R
In formula, m is the stator winding number of phases, and I is stator winding phase current, and R is stator winding resistance value；
P is lost in stator coreFeBy magnetic hystersis loss Ph, eddy-current loss PeAnd added losses PexcThe sum of three determines, it may be assumed that
PFe=Ph+Pe+Pexc
Wherein,
In formula, MsFor stator quality, khFor hysteresis loss coefficient, keFor eddy current loss factor, kexcFor added losses coefficient,
F is motor working frequency, BmFor peakflux density, α is dimensionless magnetic hystersis loss calculating parameter；
Rotor eddy current loss Pr:
Pr=ρ l ∫ ∫ J2dS
In formula, ρ is the mass density of permanent magnet, and l is permanent magnet guide passage length, and J is that the inductive loop electric current of permanent magnet is close
Degree, S are permanent magnet guide passage cross-sectional area.
Further to improve, the bearing ring thermal walking situation of change in the step 4 under analysis different installation is such as
Under:
According to heat transfer and thermal deformation basic theory, the one-dimensional alternating temperature of prismatic member is displaced differential equation are as follows:
In formula, u is axial displacement, and x is axial length, and T is temperature, and β indicates rod piece thermal expansion coefficient；
When rod piece is without inner heat source steady heat conduction, can obtain:
In formula, c1、c2、c3、c4For integral constant；
Bearing ring thermal walking calculation method under different installation:
Forward direction is installed, the axially opposing thermal walking u of bearing ringa:
ua=δs-δh-ub(sinαi+sinαo)
For reversely installing, the axially opposing thermal walking u of bearing ringa:
ua=δh-δs-ub(sinαi+sinαo)
In formula, δsFor the axial thermal walking at shaft and bearing fit, δhFor the axial thermal potential at bearing block and bearing fit
It moves, ubIt is displaced for bearing ball thermal expansion, and ub=βbΔTbDb, βbFor sphere thermal conductivity, Δ TbFor sphere temperature variation, αi
And αoThe respectively contact angle of sphere and bearing internal external circle；
The bearing ring diametrically thermal walking u of positive and negative dress bearingrCalculation method are as follows:
In formula, βiFor bearing inner race thermal conductivity, Δ TiFor bearing inner race temperature variation, βsFor shaft thermal conductivity, Δ TsFor
Temperature variation at shaft and bearing fit, μsFor shaft Poisson's ratio, βhFor bearing block thermal conductivity, Δ ThFor bearing block and axis
Hold the temperature variation at cooperation, μhFor bearing Poisson's ratio, DoFor outer ring raceway diameter.
Further to improve, the step 5 drafts analytical calculation process, and it includes following step that selected algorithm, which solve,
It is rapid:
Wherein, using Newton-Raphson solution by iterative method bearing quasi-static testing model and bearing thermal coupling model,
Electro spindle ther mal network model is solved using Kirchhoff's current law (KCL), i.e., in office one is instantaneous, flow to a certain node heat flow it
Be constantly equal to the sum of the heat flow flowed out by the node, for current ther mal network model, if system shares N number of temperature nodes,
And i-th of node has miA heat exchange approach then has using Kirchhoff's current law (KCL):
In formula, i, j=1,2 ..., N, TiIndicate the temperature of i-th of node, RijIndicate i-th of node and j-th node it
Between thermal resistance, QiIt indicates the heat flow that i-th of node itself generates, regards it as flowing into heat flow, and take and flow into heat flow direction
It is positive, outflow heat flow direction is negative；miIndicate heat exchange approach；The hot-fluid equilibrium equation of all nodes is assembled into just structure
At electric chief axis system hot-fluid equilibrium equation, it may be assumed that
{ Q }+[G] { T }=0
Above formula is electro spindle ther mal network mathematical model representation, wherein { Q } is system heat matrix, by bearing heat production
It is acquired with motor heat production calculating, [G] is the inverse of system thermal resistance matrix, i.e. thermal conductivity matrix, it is determined that { Q } and [G] can be obtained
System temperature distribution matrix { T }.
After inputting known parameters, first by solving bearing quasi-static testing model, the frictional heat generation of bearing contact zone is obtained
Amount, further according to loss model controller, is calculated motor quantity of heat production；By each section thermal resistance value being calculated and bearing heat production
Value, motor heat production value substitute into electro spindle ther mal network mathematical model, obtain electro spindle Temperature Distribution, bearing thus can be calculated
With the thermal walking at shaft and bearing block cooperation, obtained thermal walking value is substituted into bearing thermal coupling model and solved, if
It is convergence, then exports calculated result, is otherwise just closed according to the inner geometry that the thermal walking situation of each bearing corrects each bearing
System, later again solves bearing quasi-static testing model, repeatedly, after each model reaches the convergence precision of setting,
Final result can be exported.
Further to improve, the known parameters include each part material of electric chief axis system, structured data, bearing pre-tightened load
Lotus, the speed of mainshaft.
Advantages of the present invention and effective equity are:
(1) it specifies the inner geometry compatibility relation for considering the angular contact ball bearing of power thermal coupling effect, establishes difference
Bearing load equilibrium equation under mounting means；(2) thermal contact resistance for considering each near heating sources inside electro spindle, establishes base
Network model is transmitted in the high-performance electric main shaft heat of thermal resistance, model concept is clearly understandable；(3) loss model controller is established, point
Motor heat production has been analysed, it is more accurate compared to empirical equation calculating method；(4) the bearing ring heat of consideration system fuel factor is analyzed
Change in displacement situation gives relevant calculation formula；(5) the power thermal coupling effect in electro spindle operation process has been fully considered,
Accurate clearly calculation process has been drafted, this modeling method and couple solution thought are introduced into this Complex Assembly body of electro spindle
Hot dynamic property prediction field in.
Detailed description of the invention:
Fig. 1 is the angular contact ball bearing quasi-static testing model schematic established in the present invention
Fig. 2 is the angular contact ball bearing power thermal coupling model schematic established in the present invention
Fig. 3 is the angular contact ball bearing installation form figure established in the present invention
Fig. 4 is the position angle Ψ established in the present inventionjThe ball load schematic at place
Fig. 5 is the simplified electro spindle two-dimensional structure figure established in the present invention
Fig. 6 is the electro spindle ther mal network node diagram established in the present invention
Fig. 7 is the electro spindle ther mal network illustraton of model established in the present invention
Fig. 8 is the analytical calculation flow chart for the electro spindle timeparameter method established in the present invention
Fig. 9 a is bearing ball temperature
Fig. 9 b is motor temperature
Figure 10 a bearing axial direction support stiffness
Figure 10 b bearing radial support rigidity
Figure 10 c is the angular support stiffness of bearing.
Specific embodiment:
A kind of embodiment of the invention is further described in detail with reference to the accompanying drawing, comprising the following steps:
Step 1: establishing bearing thermal coupling model, carries out bearing geometrical analysis, force analysis and heat production analysis
Bearing quasi-static testing model as shown in Figure 1, the bearing thermal coupling model established on its basis as shown in Fig. 2,
Assuming that the bearing outer ring center of curvature is fixed, bearing inner race is rotated with shaft, when bearing is by load F={ Fx,Fy,
Fz,Mx,MyWhen, bearing internal external circle generates relative displacement δ={ δx,δy,δz,θx,θy, it is contemplated that bearing heat production and motor heat production,
Electric chief axis system will generate thermal deformation, so that bearing internal external circle can also generate certain thermal walking u={ ua,ur, in addition there are
The centrifugation displacement of bearing inner racec.Angle Position ψ is obtained by Fig. 2jThe bearing internal external circle at place axially and radially relative distance:
A1j=BDbsinα0+Δa
A2j=BDbcosα0+Δr+Δc
In formula, A1jFor the axially opposing distance of bearing internal external circle, A2jFor bearing internal external circle diametrically distance, B=fi+fo-
1, fi、foFor inside and outside raceway Curvature Radius Coefficient, DbFor sphere diameter, α0For bearing initial contact angle, ΔaFor bearing internal external circle
Axial total relative displacement, ΔrFor the radially total relative displacement of bearing internal external circle, ΔcIt is centrifuged and is displaced for bearing inner race.
As shown in figure 3, O-XYZ is main axis coordinate system, O1-X1Y1Z1For one coordinate system of bearing, O2-X2Y2Z2For the seat of bearing two
Mark system.
To bearing one:
Δa=δz+Riθxcosψj-Riθysinψj+ua
To bearing two:
Δa=-δz-Riθxcosψj+Riθysinψj+ua
In formula, δzFor the axially opposing displacement of bearing internal external circle, RiFor inner ring center of curvature radius of circle, θxFor bearing internal external circle x
To relative angular displacement, θyIt is bearing internal external circle y to relative angular displacement, ψjFor bearing roller position angle, uaFor bearing internal external circle axis
To opposite thermal walking.
The radially total relative displacement of bearing internal external circle:
In formula, δx、δyRespectively bearing internal external circle x to y to relative displacement, θrFor at maximum distortion rolling element and position
The angle between rolling element that angle setting is 0, andurFor the diametrically thermal walking of bearing internal external circle.
The centrifugation displacement of bearing inner racec:
In formula, ρiIndicate bearing inner race density, ωiIndicate bearing inner race revolving speed, EiIndicate bearing inner race elasticity modulus, μi
Indicate bearing inner race Poisson's ratio, d indicates bearing inner race diameter, diIndicate bear inner ring grooved railway diameter.
The deformation geometry compatible equations of contact ball bearing groove road contact can be obtained by Fig. 2 are as follows:
(A1j-X1j)2+(A2j-X2j)2-[(fi-0.5)Db+δij]2=0
X1j 2+X2j 2-[(fo-0.5)Db+δoj]2=0
In formula, X1j、X2jThe respectively axial distance and radial distance of ball centre and the outer raceway groove center of curvature, δij、δojPoint
Inside and outside the flexible deformation approach amount contacted with sphere, D Wei not be enclosedbFor sphere diameter.
In the plane by ball centre and bearing axis, Angle Position ψjPlace sphere institute it is loaded as shown in figure 4, its
Middle λijAnd λojInside and outside circle channel control coefrficient is respectively indicated, for high-speed case, it will be assumed that gyroscopic couple suffered by sphere is complete
It is offset by the contact friction force of sphere and outer ring raceway, at this moment, takes λij=0, λoj=2.According to Hertz point contact deformation relationship
And sphere stress balance relationship can obtain:
In formula, Kij、KojThe deformation under load coefficient that respectively inside and outside circle raceway is contacted with sphere, αij、αojRespectively bearing
Inside and outside circle and sphere contact angle, Mgj、FcjThe gyroscopic couple and centrifugal force that respectively j-th of sphere is subject to.
Bearing is each to shift value when in order to find out stable state, it is also necessary to bearing equilibrium equation loaded is established,
Assuming that bearing is by connected load F={ Fx,Fy,Fz,Mx,MyEffect, according to Fig.3, under main shaft coordinate system, bearing carry
The relationship of lotus and displacement can be expressed with following formula:
When level pressure pre-tightens:
To bearing one:
To bearing two:
In formula, Fx、Fy、Fz、Mx、MyThe respectively moment of face of the external applied load in x, y, z direction and the direction x, y that is subject to of bearing, j
For bearing sphere ordinal number, Z is bearing sphere number.
When positioning pre-tightens, bearing load equilibrium equation need to only remove the z in level pressure prefastening load equilibrium equation to equation i.e.
It can.
In the electro spindle course of work, due to the rubbing action of bearing roller and Internal and external cycle, bearing will generate certain heat
Amount, is given below the calculation method of bearing quantity of heat production.
For position angle ψjThe sphere at place has:
In formula, Mij、MojThe respectively moment of friction of sphere and inside and outside raceway, f0、f1It is and bearing type and lubrication, negative
Carry related coefficient, η0For the kinematic viscosity of lubricating oil, ωcjFor the revolution angular speed of j-th of sphere, Qij、QojRespectively sphere
With the contact stress of inside and outside raceway, Qimax、QomaxThe respectively maximum stress of sphere and inside and outside raceway contact.
Outer rollaway nest is controlled, it is only necessary to consider the spin friction torque of sphere and interior rollaway nest, it may be assumed that
In formula, MsijFor the spin friction torque of sphere and interior rollaway nest, μsiFor the coefficient of friction of sphere and interior rollaway nest, aijFor
The Hertz contact ellipse major semiaxis of sphere and interior rollaway nest, ΣijFor sphere and the elliptical second class complete product of interior rollaway nest Hertz contact
Point.
Therefore the frictional heating amount in inside and outside raceway contact area is respectively as follows:
Hij=ωcj.Mij+ωbj.Msij
Hoj=ωcj.Moj
In formula, Hij、HojThe respectively frictional heating amount of sphere and inside and outside raceway contact area, ωbjFor the spin angle of sphere
Speed.
Step 2: electro spindle heat transmitting network model is established, the calculation expression of different type thermal resistance is analyzed
During operation, there is three kinds of basic thermaltransmission modes: heat transfer, thermal convection, heat radiation for electro spindle.It is logical
Cooling system is often housed in electric chief axis system, therefore the heat radiation of internal system influences the distribution in entire electro spindle temperature field
Very little can be neglected.If electric chief axis system is connected with limited node by heat transfer resistance, a kind of base is constituted
In the electro spindle ther mal network model of thermal resistance.By the difference of system heat exchange mode, heat transfer resistance can be divided into heat transfer thermal resistance and right
Flow the thermal contact resistance between heat exchanged thermoresistance and components faying face.It, will be electric for the structure of electric chief axis system main parts size
Spindle bearing holder or hollow rotating shaft are reduced to several cylinders, and solid spindle is then reduced to several cylinders, bearing internal external circle, electricity
Machine rotor is reduced to cylinder, then calculates various types of heat transfer resistances with heat transfer theory, in this example simplified
Electro spindle two-dimensional structure figure is as shown in figure 5, be described below the calculation method of various types thermal resistance.
1. heat transfer thermal resistance
Heat transfer thermal resistance can be divided into axial direction, radial direction thermal resistance.According to Fourier theorem, the axial heat transfer of cylinder and cylinder
Thermal resistance R1Are as follows:
In formula, L is cylinder or cylinder axial length, and k is cylinder or cylinder thermal conductivity, SaFor cylinder or cylinder axial cross section
Product.
Cylinder radial direction heat transfer thermal resistance R2Are as follows:
In formula, d2、d1Respectively outside diameter of cylinder and internal diameter.
Cylindrical radial heat transfer thermal resistance R3Are as follows:
Sphere heat transfer thermal resistance R4Are as follows:
In formula, kbFor sphere thermal conductivity.
The lubricating grease heat transfer resistance R of inside and outside raceway when grease lubrication5And R6It is respectively as follows:
In formula, kLFor lubricating grease thermal conductivity, DoFor bearing outer ring channel diameter, Bi、BoThe respectively inside and outside circle width of bearing.
2. convective heat transfer resistance
Heat convection is mainly manifested in: bearing block, roller end and external environment, stator, rotor tip and ambient enviroment,
Stator and cooling water, stator inner surface, rotor outer surface and cooling air.According to Fourier theorem, the axis of cylinder and cylinder
To, advection heat exchanged thermoresistance R7Are as follows:
In formula, h is convection transfer rate, and S is cylinder or cylinder and extraneous heat convection area.
The calculation method of the system coefficient of heat transfer is described below.
Heat transfer free convection and radiation heat transfer, composite heat-exchange coefficient h occur for bearing block and external environment1Are as follows:
In formula, Nu1For the nusselt number of bearing seating face and cross-ventilation heat exchange, λeFor surrounding medium thermal conductivity, DeTo change
Hot surface characteristic diameter.
Wherein,G is acceleration of gravity, βeIt is thermally expanded for surrounding medium and is
Number, ThFor bearing block surface temperature, TeFor ambient temperature, PrFor surrounding medium Prandtl number, ηeFor the movement of surrounding medium
Viscosity.
Changing between the fluid and peripheral wall surface in coolant jacket and between rotor air gap cooling air and rotor wall surface
Hot coefficient h2Are as follows:
In formula, Nu2For the nusselt number of fluid and wall surface heat convection, λfFor fluid thermal conductivity, DfFor channel characteristics ruler
It is very little.
Wherein, Nu2=0.0225Re1 0.8Pr 0.3, Re1For Reynolds number, andufFor the movement velocity of fluid, ηf
For the kinematic viscosity of fluid.
Fluid motion speedQfFor fluid volume flow, AfFor channel cross-sectional area.
For cooling jacket, channel characteristics sizeCfFor channel cross-section perimeter；For rotor air gap, Df
For rotor gas length.
Electric chief axis system rotating part and surrounding ambient fluid convection transfer rate h3Are as follows:
In formula, deqFor rotating part equivalent diameter, Nu3For fluid and rotation wall surface heat convection nusselt number,
Wherein, Re2For Reynolds number, andω is rotating part revolving speed.
3. thermal contact resistance
Macroscopically, two mechanical structure surfaces be combineding with each other seem and are entirely incorporated in such as the mating surface of bearing and shaft
Together, but actual actual contact only occurs on limited dimpling peak of contact surface.When there is heat to pass through faying face, deposit
It is that the fluid in interfacial gap brings certain additional drag, referred to as thermal contact resistance to diabatic process, is examined in this example
The thermal contact resistance of bearing inner race and shaft, bearing outer ring and bearing block and the near heating sources faying face such as rotor and shaft is considered.Knot
The thermal contact resistance in conjunction face indicates are as follows:
In formula, hcFor faying face contact conductane coefficient；A is faying face nominal contact area.
The heat transfer for considering dimpling peak, interface fluid media (medium), ignores the radiation heat transfer between air gap, and contact conductane coefficient indicates
Are as follows:
In formula, LgFor faying face gap thickness, k1、k2The thermal conductivity of respectively two mating parts, kfFor interfacial gap Jie
The thermal conductivity of matter, A*For faying face dimensionless real contact area, andAcFor real contact area.
4. electro spindle ther mal network model
According to system node arrangement principle: radially arranged using the radial geometric center plane such as bearing, motor as cut-off rule
A series of nodes, wherein a node is respectively arranged at faying face both ends, while guaranteeing that each radial node is in axial direction aligned, with
Just system heat balance equation is established.Ready-portioned electro spindle ther mal network node is as shown in fig. 6, the electro spindle ther mal network model established
As shown in fig. 7, the T in Fig. 7eRepresent environment temperature, TcwRepresent cooling water temperature, TcaCooling air temperature is represented, remaining each temperature
Degree is then node temperature to be asked.
Step 3: establishing loss model controller, analyzes motor heat production
Electro spindle in this example is permanent magnet synchronous motor electro spindle, and in the course of work, stator loss includes stator winding
On copper loss and iron loss, rotor iron loss very little it is negligible, consider rotor eddy current loss.
Copper loss P on stator windingCu:
PCu=mI2R
In formula, m is the stator winding number of phases, and I is stator winding phase current, and R is stator winding resistance value.
According to classical iron core loss separation calculation method, P is lost in stator coreFeBy magnetic hystersis loss Ph, eddy-current loss PeWith
And added losses PexcThe sum of three determines, it may be assumed that
PFe=Ph+Pe+Pexc
Wherein,
In formula, MsFor stator quality, khFor hysteresis loss coefficient, keFor eddy current loss factor, kexcFor added losses coefficient,
F is motor working frequency, BmFor peakflux density, α is dimensionless magnetic hystersis loss calculating parameter.
Rotor eddy current loss Pr:
Pr=ρ l ∫ ∫ J2dS
In formula, ρ is the mass density of permanent magnet, and l is permanent magnet guide passage length, and J is that the inductive loop electric current of permanent magnet is close
Degree, S are permanent magnet guide passage cross-sectional area.
Step 4: the bearing ring thermal walking situation of change under analysis different installation
According to heat transfer and thermal deformation basic theory, the one-dimensional alternating temperature of prismatic member is displaced differential equation are as follows:
In formula, u is axial displacement, and x is axial length, and T is temperature.
When rod piece is without inner heat source steady heat conduction, can obtain:
In formula, c1、c2、c3、c4For integral constant, c3And c4It can be acquired by temperature boundary condition, c1And c2It can be by displacement boundary
Condition acquires.
As can be seen from FIG. 5, bearing one, bearing two and the positive installation of bearing six, bearing three, bearing four and bearing five are reversely pacified
Dress, is described below the bearing ring thermal walking calculation method under different installation.
Forward direction is installed, the axially opposing thermal walking u of bearing ringa:
ua=δs-δh-ub(sinαi+sinαo)
For reversely installing, the axially opposing thermal walking u of bearing ringa:
ua=δh-δs-ub(sinαi+sinαo)
In formula, δsFor the axial thermal walking at shaft and bearing fit, δhFor the axial thermal potential at bearing block and bearing fit
It moves, wherein δsAnd δhIt can be acquired according to previously described rod piece without inner heat source steady heat conduction calculation formula, ubFor bearing ball body heat
Expansion displacement, and ub=βbΔTbDb, βbFor sphere thermal conductivity, Δ TbFor sphere temperature variation, αiAnd αoRespectively sphere and axis
Hold the contact angle of Internal and external cycle.
The bearing ring diametrically thermal walking u of positive and negative dress bearingcCalculation method it is identical, are as follows:
In formula, βiFor bearing inner race thermal conductivity, Δ TiFor bearing inner race temperature variation, βsFor shaft thermal conductivity, Δ TsFor
Temperature variation at shaft and bearing fit, μsFor shaft Poisson's ratio, βhFor bearing block thermal conductivity, Δ ThFor bearing block and axis
Hold the temperature variation at cooperation, μhFor bearing Poisson's ratio, DoFor outer ring raceway diameter.
Step 5: drafting analytical calculation process, and selected algorithm is solved
For the changing rule for accurately grasping the hot dynamic parameter of high-performance electric main shaft, a consideration power thermal coupling effect is devised
High-performance electric main shaft timeparameter method analytical calculation process, as shown in Figure 8.Wherein, using Newton-Raphson iteration
Method solves bearing quasi-static testing model and bearing thermal coupling model, solves electro spindle using Kirchhoff's current law (KCL) (KCL)
Ther mal network model, i.e., in office one is instantaneous, the sum of the heat flow for flowing to a certain node be constantly equal to the heat flow that is flowed out by the node it
With for current ther mal network model, if system shares N number of temperature nodes, and i-th of node has miA heat exchange approach, is answered
With KCL, then have:
In formula, i, j=1,2 ..., N, TiIndicate the temperature of i-th of node, RijIndicate i-th of node and j-th node it
Between thermal resistance, QiIt indicates the heat flow that i-th of node itself generates, regards it as flowing into heat flow, and take and flow into heat flow direction
It is positive, outflow heat flow direction is negative.The hot-fluid equilibrium equation of all nodes is assembled and just constitutes electric chief axis system heat
Mobile equilibrium equation, it may be assumed that
{ Q }+[G] { T }=0
Above formula is electro spindle ther mal network mathematical model representation, wherein { Q } is system heat matrix, by bearing heat production
It is acquired with motor heat production calculating, [G] is the inverse of system thermal resistance matrix, i.e. thermal conductivity matrix, it is determined that { Q } and [G] can be obtained
System temperature distribution matrix { T }.
Entire calculating process is as follows: after input known parameters, first by solving bearing quasi-static testing model, obtaining bearing
Motor quantity of heat production is calculated further according to loss model controller in the frictional heat generation amount of contact zone.By each section being calculated heat
Resistance value and bearing heat production value, motor heat production value substitute into electro spindle ther mal network mathematical model, obtain electro spindle Temperature Distribution, thus
The thermal walking at bearing and shaft and bearing block cooperation can be calculated, obtained thermal walking value is substituted into the molding of bearing thermal coupling
It in type and solves, if convergence, then export calculated result, each bearing is just otherwise corrected according to the thermal walking situation of each bearing
Inner geometry relationship, bearing quasi-static testing model is solved again later, repeatedly, until each model reaches setting
After convergence precision, final result can be exported.
Step 6: solving according to calculation process and export calculated result, obtains the hot dynamic parameter of electro spindle with the speed of mainshaft
Changing rule.
The present invention is using a kind of permanent magnet synchronous motor electro spindle as example, and according to the calculation process drafted, solution obtains electric master
Each hot dynamic performance parameter of axis, including electro spindle node temperature and bearing stiffness etc. with the changing rule of revolving speed.This calculation
Selection of Bearings angular contact hybrid ceramic ball bearing in example, design parameter is shown in table 1, and bearing seat material is HT300, rotating shaft material
For 40Cr, fore bearing firmly beforehand means are that positioning pre-tightens, and rear bearing firmly beforehand means are level pressure preload, and prefastening load is 50N, environment
Temperature is 25 DEG C, and cooling water inlet temperature is 20 DEG C, and the cooling water volume flow in spiral cooling jacket is 4L/min, and motor is fixed
Axial cooling air volume flow between rotor airgap is 1.5L/min, and main shaft working speed is 1000~8000r/min.
Fig. 9 a and 9b show electric mainshaft bearing sphere and electricity of the revolving speed within the scope of 1000~8000r/min in this example
The temperature of machine rotor with revolving speed change curve, from the figure, it can be seen that rise with revolving speed, each bearing ball temperature gradually on
It rises, it is maximum in the range of speeds to rise about 3.2 DEG C, and fore bearing sphere temperature rate-of-rise is higher than rear bearing, and stator temperature
It is gradually reduced with temperature of rotor with revolving speed rising, this is because the cooling water flow in cooling jacket is constant, rotor calorific value
Also it is basically unchanged, and rotor and the coefficient of heat transfer of surrounding enviroment are gradually increased, so rotor temperature gradually decreases.
Figure 10 a-10c shows in this example electric mainshaft bearing of the revolving speed within the scope of 1000~8000r/min respectively to branch
Hold stiffness variation curve, from the figure, it can be seen that electro spindle fore bearing, that is, bearing one, 2,3,4 it is each to support stiffness with turn
Speed is increased and is gradually increased, and the rigidity of middle (center) bearing one, 2 increases trend obviously compared with bearing three, 4, this is because bearing one, 2
Sphere temperature rate-of-rise is greater than the sphere of bearing three, 4, so that the contact load increase of the Internal and external cycle and sphere of bearing one, 2 is more
Fastly, thus rigidity increase faster.The axial rigidity and angular stiffness of rear bearing, that is, bearing five, 6 are declined slightly with revolving speed rising, radial
Rigidity then slightly rises, this is because bearing internal external circle allows to have axial displacement, and inner ring contact load is basic under level pressure pre-tightens
It is constant, but contact angle increases, and outer ring contact load increases, so that outer ring normal contact stiffness increases, but the contact of inner ring normal direction is rigid
Degree is basically unchanged, and the series connection effect of rigidity increased bearing radial rigidity, but increasing degree is smaller, and outer ring contact angle
Reduce so that bearing axial rigidity and angular stiffness have the decline of certain amplitude.
1 bearing parameter of table
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (8)
1. a kind of high-performance electric main shaft timeparameter method for considering power thermal coupling effect determines method, which is characterized in that including such as
Lower step:
Step 1: establishing bearing thermal coupling model, analysis considers the Bearing inner geometry compatibility relation of power thermal coupling effect simultaneously
Carry out shaft strength analysis and bearing heat production analysis；
Step 2: establishing the high-performance electric main shaft heat based on thermal resistance transmits network model, and analyze the calculating of different type thermal resistance
Expression formula；
Step 3: establishing loss model controller, motor heat production is analyzed；
Step 4: the bearing ring thermal walking situation of change under analysis different installation；
Step 5: drafting the analytical calculation process for considering the high-performance electric main shaft timeparameter method of power thermal coupling effect, and select
Algorithm is solved；
Step 6: output calculated result, obtains the hot dynamic parameter of electro spindle.
2. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as described in claim 1, it is special
Sign is that the hot dynamic parameter of electro spindle includes the change of selected node temperature and each bearing stiffness of system with the speed of mainshaft
Law.
3. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as described in claim 1, it is special
Sign is that the step 1 includes the following steps: to establish bearing thermal coupling model, carries out bearing geometrical analysis, force analysis
It is analyzed with heat production:
If the bearing outer ring center of curvature is fixed, bearing inner race is rotated with shaft, when bearing is by load F={ Fx,Fy,
Fz,Mx,MyWhen, bearing internal external circle generates relative displacement δ={ δx,δy,δz,θx,θy, wherein, Fx、Fy、Fz、Mx、MyRespectively
The external applied load in the x, y, z direction that bearing is subject to and the moment of face in the direction x, y, it is contemplated that bearing heat production and motor heat production, electro spindle
System will generate thermal deformation, so that bearing internal external circle can also generate thermal walking u={ ua,ur, ua, urRespectively indicate bearing holder (housing, cover)
Axially opposing thermal walking and diametrically thermal walking are enclosed, in addition there are the centrifugation displacements of bearing inner racec, obtain Angle Position ψjPlace
Bearing internal external circle axially and radially relative distance:
A1j=BDbsinα0+Δa
A2j=BDbcosα0+Δr+Δc
In formula, A1jFor the axially opposing distance of bearing internal external circle, A2jFor bearing internal external circle diametrically distance, B=fi+fo- 1, fi、
foFor inside and outside raceway Curvature Radius Coefficient, DbFor sphere diameter, α0For bearing initial contact angle, ΔaIt is axial for bearing internal external circle
Total relative displacement, ΔrFor the radially total relative displacement of bearing internal external circle, ΔcIt is centrifuged and is displaced for bearing inner race；
Establish O-XYZ main shaft coordinate system, O1-X1Y1Z1For one coordinate system of bearing, O2-X2Y2Z2For two coordinate system of bearing；O point is built in
Shaft end face center, O1 indicate the geometric center of bearing one, and O2 indicates the geometric center of bearing two；
Δa=δz+Riθxcosψj-Riθysinψj+ua
To bearing two:
Δa=-δz-Riθxcosψj+Riθysinψj+ua
In formula, δzFor the axially opposing displacement of bearing internal external circle, RiFor inner ring center of curvature radius of circle, θxIt is bearing internal external circle x to phase
Diagonal displacement, θyIt is bearing internal external circle y to relative angular displacement, ψjFor bearing roller position angle, uaFor bearing internal external circle axial direction phase
To thermal walking；
The radially total relative displacement of bearing internal external circle:
In formula, δx、δyRespectively bearing internal external circle x to y to relative displacement, θrFor the rolling element and position angle at maximum distortion
For the angle between 0 rolling element, andurFor the diametrically thermal walking of bearing internal external circle.
The centrifugation displacement of bearing inner racec:
In formula, ρiIndicate bearing inner race density, ωiIndicate bearing inner race revolving speed, EiIndicate bearing inner race elasticity modulus, μiIndicate axis
Inner ring Poisson's ratio is held, d indicates bearing inner race diameter, diIndicate bear inner ring grooved railway diameter；
Obtain the deformation geometry compatible equations of contact ball bearing groove road contact are as follows:
(A1j-X1j)2+(A2j-X2j)2-[(fi-0.5)Db+δij]2=0
X1j 2+X2j 2-[(fo-0.5)Db+δoj]2=0
In formula, X1j、X2jThe respectively axial distance and radial distance of ball centre and the outer raceway groove center of curvature, δij、δojRespectively
It is inside and outside to enclose the flexible deformation approach amount contacted with sphere, DbFor sphere diameter；
In the plane by ball centre and bearing axis, Angle Position ψjThe sphere institute at place is loaded, if λijAnd λojTable respectively
Show inside and outside circle channel control coefrficient, for high-speed case, if the connecing by sphere and outer ring raceway completely of gyroscopic couple suffered by sphere
It touches frictional force to offset, at this moment, takes λij=0, λoj=2；It can according to Hertz point contact deformation relationship and sphere stress balance relationship
:
In formula, Kij、KojThe deformation under load coefficient that respectively inside and outside circle raceway is contacted with sphere, αij、αojRespectively bearing is inside and outside
Circle and sphere contact angle, Mgj、FcjThe gyroscopic couple and centrifugal force that respectively j-th of sphere is subject to；
Bearing is each to shift value when in order to find out stable state, establishes bearing equilibrium equation loaded, it is assumed that bearing by
To connected load F={ Fx,Fy,Fz,Mx,MyAct under main shaft coordinate system, the relationship of bearing load and displacement can use following formula
Expression:
When level pressure pre-tightens:
To bearing one:
To bearing two:
In formula, Fx、Fy、Fz、Mx、MyThe respectively moment of face of the external applied load in x, y, z direction and the direction x, y that is subject to of bearing, j is axis
Sphere ordinal number is held, Z is bearing sphere number；
When positioning pre-tightens, bearing load equilibrium equation need to only remove the z in level pressure prefastening load equilibrium equation to equation.
In the electro spindle course of work, due to the rubbing action of bearing roller and Internal and external cycle, bearing will generate heat, be given below
The calculation method of bearing quantity of heat production:
For position angle ψjThe sphere at place has:
In formula, Mij、MojThe respectively moment of friction of sphere and inside and outside raceway, f0、f1It is to have with bearing type and lubrication, load
The coefficient of pass, η0For the kinematic viscosity of lubricating oil, ωcjFor the revolution angular speed of j-th of sphere, Qij、QojRespectively sphere with
The contact stress of inside and outside raceway, Qimax、QomaxThe respectively maximum stress of sphere and inside and outside raceway contact；
Outer rollaway nest is controlled, it is only necessary to consider the spin friction torque of sphere and interior rollaway nest, it may be assumed that
In formula, MsijFor the spin friction torque of sphere and interior rollaway nest, μsiFor the coefficient of friction of sphere and interior rollaway nest, aijFor sphere
With the Hertz contact ellipse major semiaxis of interior rollaway nest, ΣijFor sphere and the elliptical second class complete integral of interior rollaway nest Hertz contact；
Therefore the frictional heating amount in inside and outside raceway contact area is respectively as follows:
Hij=ωcj.Mij+ωbj.Msij
Hoj=ωcj.Moj
In formula, Hij、HojThe respectively frictional heating amount of sphere and inside and outside raceway contact area, ωbjFor the spin angle velocity of sphere.
4. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as claimed in claim 3, it is special
Sign is, the step 2: establishes electro spindle heat transmitting network model, analyzes the calculation expression step of different type thermal resistance such as
Under:
During operation, there is two kinds of main thermaltransmission modes: heat transfer, thermal convection for electro spindle；
A. for heat transfer thermal resistance:
Heat transfer thermal resistance is divided into axial direction, radial direction thermal resistance；According to Fourier theorem, the Axial Thermal thermal-conduction resistance R of cylinder and cylinder1
Are as follows:
In formula, L is cylinder or cylinder axial length, and k is cylinder or cylinder thermal conductivity, SaFor cylinder or cylinder axial direction sectional area；
Cylinder radial direction heat transfer thermal resistance R2Are as follows:
In formula, d2、d1Respectively outside diameter of cylinder and internal diameter；
Cylindrical radial heat transfer thermal resistance R3Are as follows:
Sphere heat transfer thermal resistance R4Are as follows:
In formula, kbFor sphere thermal conductivity；
The lubricating grease heat transfer resistance R of inside and outside raceway when grease lubrication5And R6It is respectively as follows:
In formula, kLFor lubricating grease thermal conductivity, DoFor bearing outer ring channel diameter, Bi、BoThe respectively inside and outside circle width of bearing；
B. convective heat transfer resistance
According to Fourier theorem, the axial direction of cylinder and cylinder, advection heat exchanged thermoresistance R7Are as follows:
In formula, h is convection transfer rate, and S is cylinder or cylinder and extraneous heat convection area；
The calculation method of the coefficient of heat transfer is as follows:
Heat transfer free convection and radiation heat transfer, composite heat-exchange coefficient h occur for bearing block and external environment1Are as follows:
In formula, Nu1For the nusselt number of bearing seating face and cross-ventilation heat exchange, λeFor surrounding medium thermal conductivity, DeFor heat transfer sheet
Region feature diameter.
Wherein,G is acceleration of gravity, βeFor surrounding medium thermal expansion coefficient, ThFor
Bearing block surface temperature, TeFor ambient temperature, PrFor surrounding medium Prandtl number, ηeFor the kinematic viscosity of surrounding medium；
The coefficient of heat transfer h between fluid and peripheral wall surface in coolant jacket2Are as follows:
In formula, Nu2For the nusselt number of fluid and wall surface heat convection, λfFor fluid thermal conductivity, DfFor channel characteristics size；
Wherein, Nu2=0.0225Re1 0.8Pr 0.3, Re1For Reynolds number, andufFor the movement velocity of fluid, ηfFor stream
The kinematic viscosity of body；
Fluid motion speedQfFor fluid volume flow, AfFor channel cross-sectional area；
For cooling jacket, channel characteristics sizeCfFor channel cross-section perimeter；For rotor air gap, DfTo turn surely
Sub- gas length；
Electric chief axis system rotating part and surrounding ambient fluid convection transfer rate h3Are as follows:
In formula, deqFor rotating part equivalent diameter, Nu3For fluid and rotation wall surface heat convection nusselt number,λeFor surrounding medium thermal conductivity
Wherein, Re2For Reynolds number, andω is rotating part revolving speed；
The thermal contact resistance R of faying face8It indicates are as follows:
In formula, hcFor faying face contact conductane coefficient；A is faying face nominal contact area；
The heat transfer for considering dimpling peak, interface fluid media (medium), ignores the radiation heat transfer between air gap, contact conductane coefficient hcIt indicates are as follows:
In formula, LgFor faying face gap thickness, k1、k2The thermal conductivity of respectively two mating parts, kfFor interfacial gap medium
Thermal conductivity, A*For faying face dimensionless real contact area, andAcFor real contact area.
Establish electro spindle ther mal network model:
Using bearing, motor radial geometric center plane as cut-off rule, a series of radially arranged nodes, wherein faying face both ends
Respectively one node of arrangement, while guaranteeing that each radial node is in axial direction aligned, establish system heat balance equation.
5. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as claimed in claim 4, it is special
Sign is, in the step 3: loss model controller is established, steps are as follows for analysis motor heat production:
In the course of work, stator loss includes copper loss and iron loss on stator winding, ignores rotor iron loss, considers rotor vortex damage
Consumption；
Copper loss P on stator windingCu:
PCu=mI2R
In formula, m is the stator winding number of phases, and I is stator winding phase current, and R is stator winding resistance value；
P is lost in stator coreFeBy magnetic hystersis loss Ph, eddy-current loss PeAnd added losses PexcThe sum of three determines, it may be assumed that
PFe=Ph+Pe+Pexc
Wherein,
In formula, MsFor stator quality, khFor hysteresis loss coefficient, keFor eddy current loss factor, kexcFor added losses coefficient, f is
Motor working frequency, BmFor peakflux density, α is dimensionless magnetic hystersis loss calculating parameter；
Rotor eddy current loss Pr:
Pr=ρ l ∫ ∫ J2dS
In formula, ρ is the mass density of permanent magnet, and l is permanent magnet guide passage length, and J is the inductive loop current density of permanent magnet, S
For permanent magnet guide passage cross-sectional area.
6. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as claimed in claim 5, it is special
Sign is that the bearing ring thermal walking situation of change analyzed under different installation in the step 4 is as follows:
According to heat transfer and thermal deformation basic theory, the one-dimensional alternating temperature of prismatic member is displaced differential equation are as follows:
In formula, u is axial displacement, and x is axial length, and T is temperature, and β indicates rod piece thermal expansion coefficient；
When rod piece is without inner heat source steady heat conduction, can obtain:
In formula, c1、c2、c3、c4For integral constant；
Bearing ring thermal walking calculation method under different installation:
Forward direction is installed, the axially opposing thermal walking u of bearing ringa:
ua=δs-δh-ub(sinαi+sinαo)
For reversely installing, the axially opposing thermal walking u of bearing ringa:
ua=δh-δs-ub(sinαi+sinαo)
In formula, δsFor the axial thermal walking at shaft and bearing fit, δhFor the axial thermal walking at bearing block and bearing fit,
ubIt is displaced for bearing ball thermal expansion, and ub=βbΔTbDb, βbFor sphere thermal conductivity, Δ TbFor sphere temperature variation, αiAnd αo
The respectively contact angle of sphere and bearing internal external circle；
The bearing ring diametrically thermal walking u of positive and negative dress bearingrCalculation method are as follows:
In formula, βiFor bearing inner race thermal conductivity, Δ TiFor bearing inner race temperature variation, βsFor shaft thermal conductivity, Δ TsFor shaft
With the temperature variation at bearing fit, μsFor shaft Poisson's ratio, βhFor bearing block thermal conductivity, Δ ThMatch for bearing block and bearing
Temperature variation at conjunction, μhFor bearing Poisson's ratio, DoFor outer ring raceway diameter.
7. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as claimed in claim 6, it is special
Sign is that the step 5 drafts analytical calculation process, and selected algorithm, which solve, to be included the following steps:
Wherein, it using Newton-Raphson solution by iterative method bearing quasi-static testing model and bearing thermal coupling model, uses
Kirchhoff's current law (KCL) solves electro spindle ther mal network model, i.e., in office one is instantaneous, flows to the sum of the heat flow of a certain node perseverance
Equal to the sum of the heat flow flowed out by the node, for current ther mal network model, if system shares N number of temperature nodes, and i-th
A node has miA heat exchange approach then has using Kirchhoff's current law (KCL):
In formula, i, j=1,2 ..., N, TiIndicate the temperature of i-th of node, RijIt indicates between i-th of node and j-th of node
Thermal resistance, QiIt indicates the heat flow that i-th of node itself generates, regards it as flowing into heat flow, and inflow heat flow direction is taken to be positive,
Outflow heat flow direction is negative；miIndicate heat exchange approach；The hot-fluid equilibrium equation of all nodes is assembled and is just constituted
Electric chief axis system hot-fluid equilibrium equation, it may be assumed that
{ Q }+[G] { T }=0
Above formula is electro spindle ther mal network mathematical model representation, wherein { Q } is system heat matrix, by bearing heat production and electricity
Machine heat production calculating acquires, and [G] is the inverse of system thermal resistance matrix, i.e. thermal conductivity matrix, it is determined that { Q } and [G] can obtain system
Temperature Distribution matrix { T }.
After inputting known parameters, first by solution bearing quasi-static testing model, the frictional heat generation amount of bearing contact zone is obtained, then
According to loss model controller, motor quantity of heat production is calculated；By each section thermal resistance value being calculated and bearing heat production value, motor
Heat production value substitutes into electro spindle ther mal network mathematical model, obtains electro spindle Temperature Distribution, bearing and shaft thus can be calculated
With the thermal walking at bearing block cooperation, obtained thermal walking value is substituted into bearing thermal coupling model and solved, if convergence,
Calculated result is then exported, the inner geometry relationship of each bearing is otherwise just corrected according to the thermal walking situation of each bearing, later
Bearing quasi-static testing model is solved again, repeatedly, after each model reaches the convergence precision of setting, can be exported
Final result.
8. consider that the high-performance electric main shaft timeparameter method of power thermal coupling effect determines method as claimed in claim 7, it is special
Sign is that the known parameters include each part material of electric chief axis system, structured data, bearing pre-tightened load, the speed of mainshaft.
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| CN110555253A (en) * | 2019-08-26 | 2019-12-10 | 华南理工大学 | method for calculating temperature rise of solenoid valve coil in automobile braking system |
| CN111523212A (en) * | 2020-04-15 | 2020-08-11 | 吉林省北金机械科技有限公司 | Method for establishing electric spindle thermal error prediction model |
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| CN113343377A (en) * | 2021-05-22 | 2021-09-03 | 哈尔滨工业大学 | Method for predicting quenching residual stress of bearing steel |
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110555253A (en) * | 2019-08-26 | 2019-12-10 | 华南理工大学 | method for calculating temperature rise of solenoid valve coil in automobile braking system |
| CN111523212A (en) * | 2020-04-15 | 2020-08-11 | 吉林省北金机械科技有限公司 | Method for establishing electric spindle thermal error prediction model |
| CN111523212B (en) * | 2020-04-15 | 2023-05-26 | 长春科技学院 | Method for establishing electric spindle thermal error prediction model |
| CN112434452A (en) * | 2020-11-11 | 2021-03-02 | 西安交通大学 | Method and system equipment for determining shaft diameter fit tolerance of high-speed electric main shaft bearing |
| CN112434452B (en) * | 2020-11-11 | 2024-05-07 | 西安交通大学 | Method and system equipment for determining shaft diameter fit tolerance of high-speed motorized spindle bearing |
| CN112858865A (en) * | 2021-01-19 | 2021-05-28 | 元山(济南)电子科技有限公司 | Method and device for monitoring aging degree of silicon carbide power module |
| CN112858865B (en) * | 2021-01-19 | 2022-07-12 | 元山(济南)电子科技有限公司 | Method and device for monitoring aging degree of silicon carbide power module |
| CN113051686A (en) * | 2021-04-01 | 2021-06-29 | 重庆大学 | Spindle system thermal-structure coupling characteristic model creation method and thermal error model modeling method under inclined working condition |
| CN113051686B (en) * | 2021-04-01 | 2023-03-10 | 重庆大学 | Spindle system thermal-structure coupling characteristic model creation method and thermal error model modeling method under inclined working condition |
| CN113343377A (en) * | 2021-05-22 | 2021-09-03 | 哈尔滨工业大学 | Method for predicting quenching residual stress of bearing steel |
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