CN107590311A - A kind of planetary drive gear-box Strength co-mputation integrated system - Google Patents

A kind of planetary drive gear-box Strength co-mputation integrated system Download PDF

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CN107590311A
CN107590311A CN201710670962.1A CN201710670962A CN107590311A CN 107590311 A CN107590311 A CN 107590311A CN 201710670962 A CN201710670962 A CN 201710670962A CN 107590311 A CN107590311 A CN 107590311A
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msub
coefficient
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bearing
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CN107590311B (en
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段博志
卢军
杨明川
黄翀
邹荔兵
曹奇
赵春雨
李学旺
刘凡鹰
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MingYang Smart Energy Group Co Ltd
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Abstract

The invention discloses a kind of planetary drive gear-box Strength co-mputation integrated system, the system is the planetary drive gear-box strength check instrument based on Matlab exploitations, the specific factory site structural strength for being mainly used in wind-driven generator type selecting at initial stage, certification and later stage is assessed, the instrument, which is distinguished, six big modules, and respectively planetary gear strength check module, bolt strength check module, cylinder roller bearing strength check module, spline strength check module, trundle strength check module and power loss and efficiency calculation module.What the platform of so systematization provided components ' load automatically processes conversion, the intensive analysis of key components and parts and the function of automatically generating report so that whole design is completed under a platform, is advantageous to the adjustment of overall design scheme, improves design efficiency.In a word, the present invention can not only design each component in parallel of gear-box, while advantageously improve design efficiency in the adjustment of overall design scheme.

Description

A kind of planetary drive gear-box Strength co-mputation integrated system
Technical field
The present invention relates to wind power generating set strength of parts analysis field, refers in particular to a kind of planetary drive gear-box intensity Calculate integrated system.
Background technology
For gear-box as driving chain of wind generating set core component, its reliability of structure determines whole transmission linkwork The reliability of system.The primary intensity of gear-box, which calculates, includes planetary gear strength check, bolt strength is checked, cylinder roller bearing Strength check, spline strength check, trundle strength check and power loss and efficiency calculation module.
Wind-powered electricity generation industry at present, for big megawatt of half-direct-drive wind driven generator group generally use planetary drive gear-box, and mesh The preceding intensive analysis to so a gear-box does not have a integrated system to analyze, therefore the analysis of integrated system level is not Each component in parallel of gear-box can only be designed, while advantageously improve design efficiency in the adjustment of overall design scheme.
The content of the invention
The purpose of the present invention is the drawbacks of overcoming during existing planetary drive gear-box Strength co-mputation, there is provided Yi Zhonggao Effect, efficiently planetary drive gear-box Strength co-mputation integrated system, system integration components ' load processing and intensity are efficiently commented Estimate, highly effective can shorten complete machine and start the design cycle, better services improve wind in wind generator design, certification and assessment The reliability of machine generating set design, it is cost-effective.
To achieve the above object, technical scheme provided by the present invention is：A kind of planetary drive gear-box Strength co-mputation collection Into system, the system is the planetary drive gear-box strength check instrument based on Matlab exploitations, is mainly used in wind-power electricity generation Machine type selecting at initial stage, certification and the specific factory site structural strength in later stage are assessed, and the instrument, which is distinguished, six big modules, respectively planet The strength of gear teeth check module, bolt strength check module, cylinder roller bearing strength check module, spline strength check module, Trundle strength check module and power loss and efficiency calculation module.
The planetary gear strength check module, miner defect theories are incorporated, by importing LDD loading spectrums and other are defeated Enter damage and durability analysis that required basic parameter carries out gear, solution face fatigue safety coefficient, tooth root bending are tired Labor safety coefficient, and can be solved by the proportionality coefficient of accommodation limit load and rated load face Jing'an overall coefficient, Tooth root bends Jing'an overall coefficient.
The bolt strength checks module, by the basic parameter needed for inputting, can be directed to standard bolt and nonstandard Bolt accurately calculates the anti-yield factor of safety of bolt, resistant slide safety coefficient, safety factor for compressive stress, fracture-damage, together When for production tightening torque is provided.
The cylinder roller bearing strength check module, loading spectrum import feature is incorporated, loading spectrum is carried out automatically equivalent Processing, while the load balance coefficient of planetary system is also incorporated in the module, it can preferably react the life-span of bearing；In addition, according to The defeated basic parameter of institute, the module can export the static strength knot of primary planet bearing, secondary planet bearing, planet carrier bearing simultaneously Fruit and fatigue life result.
The spline strength check module, passes through the concrete structure of spline, stress, material heat treatment and hardness, essence Grade these situations are spent, check the contact strength of tooth surface of spline, teeth bending strength, tooth root shear strength, the flank of tooth is wear-resistant energy Power.
The trundle strength check module, can be to the shear resistance of trundle by inputting required basic parameter Extruding with relatively weak part is checked, while the model can be checked using different yield conditions, including meter Sai This yield condition and Leix in the wrong add yield condition.
The power loss and efficiency calculation module, for calculating the power loss of bearing, in combination with gear Power loss come calculate gear-box capacity loss and gear-box efficiency.
The situation of the planetary gear strength check module is as follows：
1) planetary gear strength check module is 1997 national standards, in combination with ISO6336-2006 states according to GB3480 The middle renewal part of border standard is worked out, and calculating process is defined by national standard；
The contact stress of the gear teeth is as follows：
The allowable contact stress of the gear teeth：
σHP=σHlimZNTZLZVZRZWZX (1.2)
Load is in the extraneous point in single pair tooth region of engagement, the bending stress of the gear teeth：
When load acts on tooth top, the bending stress of the gear teeth：
Gear teeth permissible bending stress：
σFP=σFlimYSTYNTYδrelTYRrelTYX (1.5)
In formula 1.1 to 1.5, KγFor load balance coefficient, KAFor coefficient of utilization, KVDynamic load factor, KHβCarried for face teeth directional Lotus breadth coefficient, KHαFor face load distribution among gear teeth coefficient, ZEFor coefficient of elasticity, ZHFor node region coefficient, ZεFor the flank of tooth Contact Superposition degree modulus, ZβFor face spiral ascent, Z(B/D)It is little gear and gear wheel respectively at meshing point B, D Single pair tooth contact ratio, for planetary gear and internal gear, Z(B/D)Take 1, ZNTFor face life factor, circulation is considered Number is to intensity, ZLFor lubricating coefficient, ZVVelocity coeffficient, ZRRoughness value, ZWFlank of tooth work hardening coefficient, ZXFor face Size factor, KFβLongitudinal Load Distribution Factors, K are bent for tooth rootFαLoad distribution among gear teeth coefficient, Y are bent for tooth rootFShould for bending Power form factor, YFaFor bending stress form factor, YSFor Stress Correction Coefficient, YSaFor Stress Correction Coefficient, YβIt is curved for tooth root Bent spiral ascent, YDTFor tooth depth coefficient, YSTThe Stress Correction Coefficient of the experiment gear calculated for bending strength, YNTFor for tooth Root flex life coefficient, YδrelTFor relative root fillet sensitivity coefficient, YRrelTWith respect to root surface situation coefficient, YXIt is curved for tooth root Bent size factor, FtFor engagement force, b is effective facewidth, d1For pitch diameter, u is gear ratio, mnFor normal module, σHlimFor tooth Face contacts nominal stress, σFlimNominal stress is bent for tooth root；
For contact fatigue strength, initial factor of safety, i.e., using the face fatigue safety system under rated load Number：
In formula, σHPeFor initial Contact Stress of Gear, σHeFor initial flank of tooth allowable contact stress, SHeFor initial face Safety coefficient；
Each the life factor under operating mode is：
In formula, σHiFor the Contact Stress of Gear under i-th of operating mode in loading spectrum, σHPiFor under i-th of operating mode in loading spectrum Contact Stress of Gear allowable, ZNTiFor the life factor under i-th of operating mode in loading spectrum；
The cycle-index of fatigue failure under each operating mode：
Ni=(ZNTi)exp2×NLref2 ZNTi≤1 (1.9)
In formula, NLref1Reference cycle-index during for life factor more than 1, NLref2Reference during for life factor less than 1 Cycle-index, exp1 are index when life factor is more than 1, and exp2 is index when life factor is less than 1, these values and material Selection it is relevant；
The damage ratio of each operating mode：
In formula, niFor the cycle-index under each operating mode
Total damage：
2) input and output of module parameter are as follows：
Module interfaces are divided into six parts：Basic parameter input, strength check coefficient, service condition, other requirements, calculating knot Fruit and result output.Modulus, pressure angle, centre-to-centre spacing, helical angle, the planetary gear of input gear are needed in basic parameter input Number, the number of teeth, addendum coefficient, top coefficient, the facewidth, wheel rim intracavity diameter, web thickness, accuracy class, contact fatigue pole Limit, bending fatigue limit, tooth top profiling quantity, tooth-face roughness, tooth root roughness, boss height, cutter outside circle angle, the flank of tooth are hard Degree, end relief and pinion cutter these parameter informations.Need to input dynamic load factor, teeth directional load in strength check coefficient Breadth coefficient, load distribution among gear teeth coefficient, coefficient of utilization and load balance coefficient.Needed in service condition input rated speed, Nominal torque, life requirements, dead load and rated load ratio and lubricant movement viscosity, while import loading spectrum.At other Need to be defined the selection principle for being changed into coefficient, the selection principle of sideshake, effective hardness layer meter by following menu in it is required that Calculation method, the connected mode of gear, the type of belt drive of gear, root stress computational methods, lubricating oil, whether consider flange thickness Influence, dynamic load factor whether from host computer, whether consider the selection of Superposition degree modulus and corresponding material heat treatment.Counting Calculate in result and export final calculation result, including face fatigue safety coefficient, tooth root flexural fatigue safety coefficient, the flank of tooth connect Touch static strength safety coefficient and tooth root static bending strength safety coefficient.The text of detailed result of calculation is shown in result output Part path.
The situation that the bolt strength checks module is as follows：
1) for standard bolt, by selecting bolt model to select bolt；It is straight by inputting nominal for nonstandard bolt The aperture of external diameter, pitch diameter, bolt rostral at footpath, Minor diameter of screw, bolt head and work piece interface determines bolt and company The physical dimension of fitting；
2) calculating process is as follows：
2.1) moment of torsion M is born by bolt connectionTmaxAnd the force of periphery F on caused each boltQmax：
In formula, i is bolt number, DtFor bolt circle diameter；
2.2) determine to tighten factor alphaA, the selection for tightening coefficient is relevant with the installation tool of bolt；
2.3) minimum fastening force F is determinedkerf：
Fkerf=FQmax/u (2.2)
In formula, u is coefficient of friction；
2.4) loss of pretightning force caused by insertion is determined, including：
The resilience δ of boltS：
δS=δSK+δ1+δGew+δGm (2.7)
In formula, d is nominal diameter, EsFor bolt modulus of elasticity, EMFor the connected piece modulus of elasticity with blind hole, ANFor work Journey area,Path area, l1For the length of screw rod, lGewReach, δ can be loaded for residueSKFor the resilience on head, δ1For The resilience of screw parts, δGewFor the resilience of zero load place's screw thread, δGAt bolt thread path, δMFor nut or workpiece blind hole Locate resilience, δGmFor total resilience at nut or screw thread；
Determine the resilience of workpiece：
In formula, dwFor the external diameter at bolt head and work piece interface, dhFor the aperture of connected piece, lkTo be clamped length,For bolted cone angle, EpFor connected piece modulus of elasticity；
Embedded quantity fzIt is relevant with material, connector quantity；
The loss F of pretightning forcez：
Fz=fz/(δs+δp) (2.9)
2.5) minimum installation pretightening force F is determinedMmin：
FMmin=Fkerf+FZ (2.10)
2.6) maximum installation pretightening force F is determinedMmax：
FMmax=αA·FMmin (2.11)
2.7) erection stress σ is determinedrde,Mzul：
σrde,Mzul=vRp0.2 (2.12)
In formula, v accounts for the percentage of yield limit stress, R for pretightning forcep0.2For yield limit stress；
Determine assembly pretightening power：
FMzul=As·v·Rp0.2 (2.13)
In formula, AsFor stress area of section；
2.8) service load FSmax：
FSmax=FMzul (2.14)
Maximum tensile stress σzmax：
σzmax=FSmax/As (2.15)
Working stress σred,B：
σred,B=σzmax (2.16)
Anti- yield factor of safety SF：
SF=Rp0.2/σred,B (2.17)
2.9) minimum bearing-surface area Apmin：
Bearing stress pMmax：
Safety factor for compressive stress Sp：
2.10) minimum pretightning force FVmin：
Resistant slide safety coefficient SG：
The maximum shear stress τ caused by slidingmax：
Fracture-damage SA：
2.11) screw-down torque M is determinedA：
In formula, P is pitch, uGFor thread friction coefficient, ukRubbed for pressure-bearing surface is DkmFor in bolt head or nut carrying The effective diameter of region moment of friction, d2Screw thread pitch diameter；
3) input and output of module parameter are as follows：
Module interfaces are divided into six parts：Boundary condition, bolt arrangement size, material properties, connected piece structure, calculating knot Fruit and result output.Needed in boundary condition input torque, bolt performance rate, tighten coefficient, yield limit stress ratio, It is combined material coefficient of friction, bolt number, thread friction coefficient, pressure-bearing surface coefficient of friction, nut pressure-bearing surface coefficient of friction, allowable Compression, shear stress allowable, yield limit and strength degree, while need to select bolt result formats.In bolt arrangement Need to input bolt diameter, path, bolt head diameter, central diameter, spiro rod length and pitch in size, while need to select Select bolt head form.Need to input bolt modulus of elasticity, nut or elasticity modulus of materials respectively in material properties and connected Fitting modulus of elasticity.Need to input clamping length, bolt distribution pitch diameter, two connector contacts in connected piece structure Partial internal-and external diameter and embedded quantity.Final calculation result, including the anti-yield factor of safety, resistant slide are exported in result of calculation Safety coefficient, safety factor for compressive stress, fracture-damage and screw-down torque value.Detailed meter is shown in result output module Calculate the storage path of result report.
The situation of the cylinder roller bearing strength check module is as follows：
According to ISO76/ISO281 standards, the static strength and life-span for carrying out cylinder roller bearing calculate；
1) LDD loading spectrums are processed into equivalent load TeqIt is as follows：
In formula, riFor the revolution under each operating mode, TiFor moment of torsion under each operating mode；
2) derivation of equation is as follows：
2.1) system checks static strength safely
In formula, C0rFor the basic rated static load of bearing, PorFor bearing Equivalent static load；
2.2) Life-span checking of bearing
In formula, a is fatigue exponent, CrFor basic dynamic load rating, PrFor equivalent radial load, n mean speeds；
3) input and output of module parameter are as follows：
Module interfaces are divided into eight parts：Service data, planet carrier bearing, gear, primary planet bearing, secondary planet axle Hold, dead load, calculation of dynamic load foundation, result of calculation and result output.Defeated ultimate torque, specified is needed in service data Moment of torsion, rated speed, while import loading spectrum.The basic rated static load, basic of input shaft bearing is needed in planet carrier bearing Rated static load, secondary planet system weight, bearing pitch diameter, single roller quantity, columns, roller effective length, roller The contact angle of diameter, roller.Need to input one-level, the number of teeth of secondary gear respectively in gear.Needed in primary planet bearing Want basic rated static load, basic rated static load, primary planet the system centre distance of input shaft bearing, planetary gear number, every The number of individual planetary gear upper bearing (metal), load balance coefficient, bearing pitch diameter, single roller quantity, columns, roller effective length, rolling The contact angle of sub- diameter, roller.The basic rated static load of input shaft bearing, substantially specified static load are needed in secondary planet bearing Lotus, secondary planet system centre distance, planetary gear number, the number of each planetary gear upper bearing (metal), load balance coefficient, bearing pitch circle are straight Footpath, single roller quantity, columns, roller effective length, roller diameter, the contact angle of roller.Dead load, calculation of dynamic load according to There is provided according to middle selection supplier or iso standard calculates.Export final calculation result in result of calculation, including ultimate load is quiet Safety coefficient, contact stress, the contact stress of rated load, mathematic(al) expectation, the contact stress of equivalent load, mathematic(al) expectation. As a result the storage path of detailed result of calculation report is shown in output module.
The situation of the spline strength check module is as follows：
According to GBT17855-1999 standards, the bearing capacity of spline is calculated as follows；
1) bearing capacity calculates
1.1) contact strength of tooth surface calculates
[σH]=σ0.2/(SH·K1K2K3K4) (4.2)
1.2) teeth bending strength calculates
Involute spline：
Rectangular spline：
[σF]=σb/(SF·K1K2K3K4) (4.5)
1.3) tooth root shear strength calculates
τFmax=τtn·αtn (4.6)
[τF]=[σF]/2 (4.7)
1.4) flank of tooth wear resistance calculates
Permissible compression stress：
[σH1] for spline pair 108Permissible compression stress when being worked under secondary period is averagely hard according to heat treatment and the flank of tooth Degree selection；
[σH2]=n × ball hardness number (4.8)
1.5) torsion of external splines calculates with bending strength
[σV]=σ0.2/(SF·K1K2K3K4) (4.10)
In formula 4.1-4.10, σHFor face pressure, W is position specific loading, hwFor the wokring depth of tooth, σ0.2For bending for material Take intensity, SHFor the calculating safety coefficient of contact strength of tooth surface, K1For coefficient of utilization, K2For backlash coefficient, K3Distribution system Number, K4For axial load unbalance loading coefficient, [σH] it is flank of tooth permissible compression stress, αDFor normal pressure angle, SFnFor chordal tooth thickness, h is full tooth Height, σFFor face pressure angle, [σF] it is Dedenda's bending stress allowable, SFSafety coefficient, σ are calculated for bending strengthbFor the drawing of material Stretch intensity, τFmaxFor tooth root the maximum shear stress, τtnShear stress, αtnFor the factor of stress concentration, [τF] it is shear stress allowable, [σH2] permissible compression stress of the spline pair long-term work without abrasion, n is the coefficient related to heat treatment, σvFor equivalent stress σFnTo be curved Transverse stress, τtnFor shear stress, [σV] reversed and allowable stress during bending strength to calculate spline；
2) input and output of module parameter are as follows：
Module interfaces divide quinquepartite：Basic parameter, material characteristics, service condition and loading coefficient, result of calculation and As a result export.Needed in basic parameter defeated axle and hub modulus, pressure angle, helical angle, height of teeth root coefficient, root fillet coefficient, Addendum coefficient, the grade of tolerance, accuracy class.The yield strength, tensile strength, the flank of tooth of input material are needed in material characteristics Wear permissible compression stress, flank of tooth permissible compression stress.Input torque, coefficient of utilization, tooth are needed in service condition and loading coefficient Side clearance coefficient, distribution coefficient, axial unbalance loading coefficient.Export final calculation result in result of calculation, including flank of tooth compression, Root stress, tooth root shear stress, tooth surface abrasion compression.Detailed result of calculation report is shown in result output module Deposit path.
The situation of the trundle strength check module is as follows：
1) derivation of equation is as follows
Because trundle is subjected only to moment of torsion effect, therefore the cross force suffered by single trundle is：
In formula, F is single bolt cross force, and T is ultimate torque, DiThe central diameter where pin, Z is pin number；
Secondary planet frame shears safety coefficient：
In formula 5.2-5.4, τpFor the shear stress allowable of determination, σsFor the yield limit of bearing pin material, a is according to different Yield condition criterion value differs, meter Sai Si yield conditions a=30.5, Leix in the wrong adds yield condition a=2, τ to be in horizontal masterpiece Shear stress under, D are pin external diameter, and d is pin internal diameter, K1For dynamic load factor, K2For load balance coefficient；
The extruding safety coefficient of most weak connected piece：
σR0.2=1.15* τp' (5.6)
In formula 5.5-5.8, σ 'sFor the yield limit of relatively weak connected piece, i.e., shear stress allowable, σR0.2For phase To the extrusion stress allowable of the connected piece of weakness, PsTo act on the compression on relatively weak connected piece, lsFor effect In the effective length of relatively weak connected piece endoporus, SσFor the extruding safety coefficient of most weak connected piece；
2) input and output of module parameter are as follows：
Module interfaces are divided into three parts：Basic parameter, result of calculation and result output.In basic parameter, Yong Huxu Self-defined basic parameter, main input parameter have input limits moment of torsion, loading coefficient, load balance coefficient, pin number, planet frame aperture Depth, flange hole depth, pin external diameter, pin internal diameter, pin pitch circle diameter, planet carrier yield limit, spline flange yield limit and transmission Yield limit is sold, while yield condition needs to carry out the definition of relevant parameter by following menu.Exported most in result of calculation Whole result of calculation, including the anti-shearing safety coefficient of pin and the extruding safety coefficient of relatively weak part.In result output module The storage path of the detailed result of calculation report of middle display.
The situation of the power loss and efficiency calculation module is as follows：
1) derivation of equation is as follows：
Planetary bearing no-load torque is lost：
In formula, TVLFor the system bearing no-load torque loss of planet single-planetary gear train, f0For the profit with bearing type and bearing Sliding relevant coefficient, voilFor the lubricant movement viscosity under running temperature, n1For planet wheel speed, dmBearing central diameter, k are single-stage Planet gear transmission system planetary gear number, x are single planetary gear upper planet bearing number；
Planetary bearing load torque is lost：
For the roller bearing of radial load：
TVLP2=0 (6.4)
For the roller bearing of the additional axial thrust of band：
In formula 6.3-6.5, f1The coefficient chosen for reference standard, P1For single planet bearing load, a, b are and bearing The relevant index of mechanism, TVLP1The power attenuation of radial load bearing, TVLP2The power attenuation of axial load bearings, FaFor additional shaft To thrust；
Because planet carrier bearing calculates no k, x value, remaining method is consistent with planetary bearing computational methods；
2) input and output of module parameter are as follows：
Module interfaces are divided into four parts：Basic parameter, service condition, result of calculation and result output.In basic parameter In, user needs to input one-level, the engagement monodentate power loss of secondary planet system, internal messing monodentate power loss, planet axis Hold internal diameter, planetary bearing external diameter, the ring gear number of teeth, the sun gear number of teeth, centre-to-centre spacing, planetary gear number, single planet wheel bearing Number, coefficient f0、f1、f2, index a, b, planet carrier bearing bore diameter, planet carrier bearing outside diameter.Input speed, volume in service condition Determine power, kinematic viscosity.Final calculation result, including the total-power loss of primary planet bearing, two level are exported in result of calculation Planetary bearing total-power loss, the total-power loss of planet carrier bearing, gear-box total-power loss, gear-box efficiency.It is defeated in result Go out in module and show the storage path of detailed result of calculation report.
The present invention compared with prior art, has the following advantages that and beneficial effect：
1st, from functional perspective：The system, which is distinguished, six big modules, respectively planetary gear strength check module, bolt strength Check module, cylinder roller bearing strength check module, spline strength check module, trundle strength check module and power Loss and efficiency calculation module, what the platform of such systematization provided components ' load automatically processes conversion, key components and parts Intensive analysis and the function of automatically generating report so that whole design is completed under a platform, is advantageous to overall design scheme Adjustment, improve design efficiency.
2nd, from interface angle：Each module of the system is single interface, embodies the friendly at interface.
3rd, from design angle：Integrated system causes each component in parallel design of epicyclic gearbox, reasonably controls intensity The superfluous design un-reasonable phenomenon brought with intensity deficiency, it ensure that the reasonability of the reliability and design of unit.
4th, from certification angle：Processing from load, to calculating process, again to the establishment of report calculated comply fully with certification mark Standard, fully meet authentication requesting.
5th, from evaluation perspective：Substantially reduce gear-box parts to check the cycle, original supplier's check result needs 1 The moon (containing report), it can ideally be foreshortened to 1~2 day using the system and report calculated can be exported automatically, it is very effective Shorten the assessment cycle of blower fan.
6th, from the angle of user：Software also exports detailed intermediate variable while output result, for entirely setting Meter process can comprehensive control.
Brief description of the drawings
The loading spectrum that Fig. 1 is the present invention calculates gear fatigue life flow chart.
Fig. 2 is the software main interface of the present invention.
Fig. 3 is the planetary gear strength check module interfaces figure of the present invention.
The gear ring bolt that Fig. 4 is the present invention checks module interfaces figure.
Fig. 5 is that the cylinder roller bearing of the present invention checks the surface chart of module.
Fig. 6 is the surface chart of the spline strength check module of the present invention.
Fig. 7 is the surface chart of the trundle strength check module of the present invention.
Fig. 8 is the power loss of the present invention and the surface chart of efficiency calculation module.
Embodiment
With reference to specific embodiment, the invention will be further described.
Planetary drive gear-box Strength co-mputation integrated system described in the present embodiment, the planet to be developed based on Matlab are passed Moving teeth roller box strength check instrument, the specific factory site structure for being mainly used in wind-driven generator type selecting at initial stage, certification and later stage are strong Degree is assessed, as shown in Fig. 2 the instrument, which is distinguished, following six big modules：
1st, planetary gear strength check module
1) function describes：In module incorporate miner defect theories, by import LDD loading spectrums and other input needed for Basic parameter carries out the damage of gear and durability analysis, solves face fatigue safety coefficient, tooth root flexural fatigue safety Coefficient while module can be solved by the proportionality coefficient of accommodation limit load and rated load face Jing'an overall coefficient, Tooth root bends Jing'an overall coefficient；
2) principles illustrated
2.1) planetary gear strength check module according to GB3480 be 1997 national standards (quote ISO6336-1996), it is same When worked out with reference to the middle renewal parts of ISO6336-2006 international standards, calculating process is defined by national standard.
The contact stress of the gear teeth is as follows：
The allowable contact stress of the gear teeth：
σHP=σHlimZNTZLZVZRZWZX (1.2)
Load is in the extraneous point in single pair tooth region of engagement, the bending stress of the gear teeth：
When load acts on tooth top, the bending stress of the gear teeth：
Gear teeth permissible bending stress：
σFP=σFlimYSTYNTYδrelTYRrelTYX (1.5)
In formula 1.1-1.5, KγFor load balance coefficient, KAFor coefficient of utilization, KVDynamic load factor, KHβFor face teeth directional load Breadth coefficient, KHαFor face load distribution among gear teeth coefficient, ZEFor coefficient of elasticity, ZHFor node region coefficient, ZεConnect for the flank of tooth Touch Superposition degree modulus, ZβFor face spiral ascent, Z(B/D)For little gear and the gear wheel list at meshing point B, D respectively To tooth contact ratio, for planetary gear and internal gear, Z(B/D)Take 1, ZNTFor face life factor, circulation time is considered It is several to intensity, ZLFor lubricating coefficient, ZVVelocity coeffficient, ZRRoughness value, ZWFlank of tooth work hardening coefficient, ZXFor face chi Very little coefficient, KFβLongitudinal Load Distribution Factors, K are bent for tooth rootFαLoad distribution among gear teeth coefficient, Y are bent for tooth rootFFor bending stress Form factor (load acts on single pair region of engagement external world point), YFaFor bending stress form factor (load acts on tooth top), YS For Stress Correction Coefficient (load acts on single pair region of engagement external world point), YSaFor Stress Correction Coefficient (load acts on tooth top), YβSpiral ascent, Y are bent for tooth rootDTFor tooth depth coefficient, YSTThe Stress Correction Coefficient of the experiment gear calculated for bending strength, YNTFor for tooth root flex life coefficient, YδrelTFor relative root fillet sensitivity coefficient, YRrelTWith respect to root surface situation coefficient, YXSize factor, F are bent for tooth roottFor engagement force, b is effective facewidth, d1For pitch diameter, u is gear ratio, mnFor normal direction mould Number, σHlimFor face nominal stress, σFlimNominal stress is bent for tooth root.
For contact fatigue strength
Initial factor of safety (uses the face fatigue safety coefficient under rated load)
σHPeInitial Contact Stress of Gear, σHeInitial flank of tooth allowable contact stress, SHeInitial flank of tooth touch-safe coefficient.
Each the life factor under operating mode is
In formula, σHiFor the Contact Stress of Gear under i-th of operating mode in loading spectrum, σHPiFor under i-th of operating mode in loading spectrum Contact Stress of Gear allowable, ZNTiFor the life factor under i-th of operating mode in loading spectrum；
The cycle-index of fatigue failure under each operating mode
Ni=(ZNTi)exp2×NLref2 ZNTi≤1 (1.9)
In formula, NLref1Reference cycle-index during for life factor more than 1, NLref2Reference during for life factor less than 1 Cycle-index exp1 is index when life factor is more than 1, and exp2 is index when life factor is less than 1, these values and material Selection it is relevant.
The damage ratio of each operating mode
niFor the cycle-index under each operating mode
Total damage
It is shown in Figure 1 that maneuvering load spectrum calculates gear fatigue life flow.
2.2) as shown in figure 3, the input and output of module parameter are as follows：
Module interfaces are divided into six parts：Basic parameter input, strength check coefficient, service condition, other requirements, calculating knot Fruit and result output.
Modulus, pressure angle, centre-to-centre spacing, helical angle, planetary gear number, the tooth of input gear are needed in basic parameter input Number (inputting negative value for ring gear), addendum coefficient, top coefficient, the facewidth, wheel rim intracavity diameter, web thickness, precision etc. Level, contact fatigue strength limit, bending fatigue limit, tooth top profiling quantity (as do not determined that profiling quantity can input 0), tooth-face roughness, tooth The parameter informations such as root roughness, boss height, cutter outside circle angle, tooth face hardness, end relief and pinion cutter.
Need to input dynamic load factor, Longitudinal Load Distribution Factors in strength check coefficient, load distribution among gear teeth coefficient, make With coefficient and load balance coefficient.
Need to input rated speed, nominal torque, life requirements, dead load and rated load ratio (use in service condition In the static strength for calculating gear) and lubricant movement viscosity, while import loading spectrum.
Need to be defined the selection principle for being changed into coefficient, the selection original of sideshake by following menu in other requirements Then, effective hardness layer computational methods, the connected mode of gear, the type of belt drive of gear, root stress computational methods, lubricating oil, Whether consider the influence of flange thickness, dynamic load factor whether from host computer, whether consider Superposition degree modulus and corresponding material The selection of heat treatment.
Final calculation result is exported in result of calculation, it is tired including face fatigue safety coefficient, tooth root bending Labor safety coefficient, face static strength safety coefficient and tooth root static bending strength safety coefficient
The file path of detailed result of calculation is shown in result output.
2nd, bolt strength checks module
1) function describes：By inputting required basic parameter, standard bolt can be directed to and nonstandard bolt is accurate Calculate the anti-yield factor of safety of bolt, resistant slide safety coefficient, safety factor for compressive stress, fracture-damage.Carried simultaneously for production For tightening torque.
2) principles illustrated：
2.1), can be by selecting bolt model to select bolt for standard bolt, can be public by inputting for nonstandard bolt The aperture of diameter, Minor diameter of screw, external diameter at bolt head and work piece interface, pitch diameter, bolt rostral is claimed to determine bolt With the physical dimension of connector.
2.2) calculating process is as follows：
Moment of torsion M is born by bolt connectionTmaxAnd the force of periphery F on caused each boltQmax
In formula, i is bolt number, DtFor bolt circle diameter
It is determined that tighten factor alphaA
The selection for tightening coefficient is relevant with the installation tool of bolt.
It is determined that minimum fastening force Fkerf
Fkerf=FQmax/u (2.2)
In formula, u is coefficient of friction.
It is determined that the loss of pretightning force caused by embedded
The resilience δ of boltS
δS=δSK+δ1+δGew+δGm (2.7)
In formula, d is nominal diameter, EsFor bolt modulus of elasticity, EMFor the connected piece modulus of elasticity with blind hole, ANFor work Journey area,Path area, l1For the length of screw rod, lGewReach, δ can be loaded for residueSKFor the resilience on head, δ1For The resilience of screw parts, δGewFor the resilience of zero load place's screw thread, δGAt bolt thread path, δMFor nut or workpiece blind hole Locate resilience, δGmFor total resilience at nut or screw thread.
Determine the resilience of workpiece：
In formula, dwFor the external diameter at bolt head and work piece interface, dhFor the aperture of connected piece, lkTo be clamped length,For bolted cone angle, EpFor connected piece (casing) modulus of elasticity；
Embedded quantity fzIt is relevant with material, connector quantity.
The loss F of pretightning forcez
Fz=fz/(δs+δp) (2.9)
It is determined that minimum installation pretightening force FMmin
FMmin=Fkerf+FZ (2.10)
It is determined that maximum installation pretightening force FMmax
FMmax=αA·FMmin (2.11)
Determine erection stress σrde,Mzul
σrde,Mzul=vRp0.2 (2.12)
In formula, v accounts for the percentage of yield limit stress, R for pretightning forcep0.2For yield limit stress；
Determine assembly pretightening power
FMzul=As·v·Rp0.2 (2.13)
In formula, AsFor stress area of section；
Service load FSmax：
FSmax=FMzul (2.14)
Maximum tensile stress σzmax：
σzmax=FSmax/As (2.15)
Working stress σred,B：
σred,B=σzmax (2.16)
Anti- yield factor of safety SF：
SF=Rp0.2/σred,B (2.17)
Minimum bearing-surface area Apmin：
Bearing stress pMmax：
Safety factor for compressive stress Sp：
Minimum pretightning force FVmin：
Resistant slide safety coefficient SG：
The maximum shear stress τ caused by slidingmax：
Fracture-damage SA：
Determine screw-down torque MA：
In formula, P is pitch, uGFor thread friction coefficient, ukRubbed for pressure-bearing surface is DkmFor in bolt head or nut carrying The effective diameter of region moment of friction, d2Screw thread pitch diameter.
2.3) shown in Figure 4, the input and output of module parameter are as follows：
Module interfaces are divided into six parts：Boundary condition, bolt arrangement size, material properties, connected piece structure, calculating knot Fruit and result output.
Input torque, bolt performance rate are needed in boundary condition, tightens coefficient, yield limit stress ratio, combination material Expect that coefficient of friction, bolt number, thread friction coefficient, pressure-bearing surface coefficient of friction, nut pressure-bearing surface coefficient of friction, pressure allowable should Power, shear stress allowable, yield limit and strength degree, while need to select bolt result formats.
Need to input bolt diameter, path, bolt head diameter, central diameter, spiro rod length in bolt arrangement size And pitch, while need to select bolt head form.
Need to input respectively in material properties bolt modulus of elasticity, nut or material (blind bored member) modulus of elasticity and by Connector modulus of elasticity.
Need to input clamping length, bolt distribution pitch diameter, two connector contact portions in connected piece structure Internal-and external diameter and embedded quantity.
Final calculation result is exported in result of calculation, including the anti-yield factor of safety, resistant slide safety coefficient, is resisted Press safety coefficient, fracture-damage and screw-down torque value.
The storage path of detailed result of calculation report is shown in result output module.
3rd, cylinder roller bearing strength check module
1) function describes：Loading spectrum import feature is incorporated in module, carries out equivalent process, while module to loading spectrum automatically Load balance coefficient in middle involvement planetary system, the life-span of reaction bearing that can be genuiner；According to the defeated basic parameter of institute, module Primary planet bearing, secondary planet bearing, the static strength results of planet carrier bearing and fatigue life result can be exported simultaneously.
2) principles illustrated：
According to ISO76/ISO281 standards, the static strength and life-span for carrying out cylinder roller bearing calculate；
2.1) LDD loading spectrums are processed into equivalent load TeqIt is as follows：
In formula, riFor the revolution under each operating mode, TiFor moment of torsion under each operating mode.
2.2) derivation of equation is as follows：
2.2.1) system checks static strength safely
In formula, C0rFor the basic rated static load of bearing, PorFor bearing Equivalent static load
2.2.2) the Life-span checking of bearing
In formula, a is fatigue exponent, CrFor basic dynamic load rating, PrFor equivalent radial load, n mean speeds；
2.3) as shown in figure 5, the input and output of module parameter are as follows：
Module interfaces are divided into eight parts：Service data, planet carrier bearing, gear, primary planet bearing, secondary planet axle Hold, dead load, calculation of dynamic load foundation, result of calculation and result output.
Defeated ultimate torque, nominal torque, rated speed are needed in service data, while imports loading spectrum.
The basic rated static load, basic rated static load, secondary planet system of input shaft bearing are needed in planet carrier bearing System weight, bearing pitch diameter, single roller quantity, columns, roller effective length, roller diameter, the contact angle of roller.
Need to input one-level, the number of teeth of secondary gear respectively in gear.
The basic rated static load, basic rated static load, primary planet of input shaft bearing are needed in primary planet bearing System centre distance, planetary gear number, the number of each planetary gear upper bearing (metal), load balance coefficient, bearing pitch diameter, single roller Quantity, columns, roller effective length, roller diameter, the contact angle of roller.
The basic rated static load, basic rated static load, secondary planet of input shaft bearing are needed in secondary planet bearing System centre distance, planetary gear number, the number of each planetary gear upper bearing (metal), load balance coefficient, bearing pitch diameter, single roller Quantity, columns, roller effective length, roller diameter, the contact angle of roller.
Supplier is selected to provide as supplier position provides or iso standard calculates according in dead load, calculation of dynamic load.
Final calculation result is exported in result of calculation, including Jing'an overall coefficient of ultimate load, contact stress, volume Determine contact stress, the mathematic(al) expectation of load, the contact stress of equivalent load, mathematic(al) expectation.
The storage path of detailed result of calculation report is shown in result output module.
4th, spline strength check module
1) function describes：Pass through the feelings such as the concrete structure of spline, stress, material heat treatment and hardness, accuracy class Condition, check the contact strength of tooth surface of spline, teeth bending strength, tooth root shear strength, flank of tooth wear resistance etc..
2) principles illustrated：
According to GBT17855-1999 standards, the bearing capacity of spline is calculated as follows；
2.1) bearing capacity calculates
Contact strength of tooth surface calculates：
[σH]=σ0.2/(SH·K1K2K3K4) (4.2)
Teeth bending strength calculates：
Involute spline：
Rectangular spline：
[σF]=σb/(SF·K1K2K3K4) (4.5)
Tooth root shear strength calculates：
τFmax=τtn·αtn (4.6)
[τF]=[σF]/2 (4.7)
Flank of tooth wear resistance calculates：
Permissible compression stress：
[σH1] for spline pair 108Permissible compression stress when being worked under secondary period is averagely hard according to heat treatment and the flank of tooth Degree selection；
[σH2]=n × ball hardness number (4.8)
1.5) torsion of external splines calculates with bending strength
[σV]=σ0.2/(SF·K1K2K3K4) (4.10)
In formula 4.1-4.10, σHFor face pressure, W is position specific loading, hwFor the wokring depth of tooth, σ0.2For bending for material Take intensity, SHFor the calculating safety coefficient of contact strength of tooth surface, K1For coefficient of utilization, K2For backlash coefficient, K3Distribution system Number, K4For axial load unbalance loading coefficient, [σH] it is flank of tooth permissible compression stress, αDFor normal pressure angle, SFnFor chordal tooth thickness, h is full tooth Height, σFFor face pressure angle, [σF] it is Dedenda's bending stress allowable, SFSafety coefficient, σ are calculated for bending strengthbFor the drawing of material Stretch intensity, τFmaxFor tooth root the maximum shear stress, τtnShear stress, αtnFor the factor of stress concentration, [τF] it is shear stress allowable, [σH2] permissible compression stress of the spline pair long-term work without abrasion, n is the coefficient related to heat treatment, σvFor equivalent stress σFnTo be curved Transverse stress, τtnFor shear stress, [σV] reversed and allowable stress during bending strength to calculate spline；
2.2) as shown in fig. 6, the input and output of module parameter are as follows：
Module interfaces divide quinquepartite：Basic parameter, material characteristics, service condition and loading coefficient, result of calculation and As a result export.
Defeated axle and hub modulus, pressure angle, helical angle, height of teeth root coefficient, root fillet coefficient, tooth are needed in basic parameter Rise coefficient, the grade of tolerance, accuracy class.
The yield strength of input material, tensile strength, tooth surface abrasion permissible compression stress, the flank of tooth is needed to be permitted in material characteristics Use compression.
Input torque, coefficient of utilization, backlash coefficient, distribution coefficient, axle are needed in service condition and loading coefficient To unbalance loading coefficient.
Final calculation result is exported in result of calculation, is answered including flank of tooth compression, root stress, tooth root shearing Power, tooth surface abrasion compression.
The storage path of detailed result of calculation report is shown in result output module.
5th, trundle strength check module
1) function describes：By inputting required basic parameter, module can be to the shear resistance and weakness relatively of trundle The extruding of part is checked, and model can be checked using different yield conditions, and (meter Sai Si yield conditions and Leix in the wrong add Yield condition).
2) principles illustrated：
Trundle strength check module is worked out according to mechanical design handbook.
2.1) derivation of equation is as follows
Because trundle is subjected only to moment of torsion effect, therefore the cross force suffered by single trundle is
In formula, F is single bolt cross force, and T is ultimate torque, DiThe central diameter where pin, Z is pin number
Secondary planet frame shears safety coefficient：
In formula 5.2-5.4, τpFor the shear stress allowable of determination, σsFor the yield limit of bearing pin material, a is according to different Yield condition criterion value differs, meter Sai Si yield conditions a=30.5, Leix in the wrong adds yield condition a=2, τ to be in horizontal masterpiece Shear stress under, D are pin external diameter, and d is pin internal diameter, K1For dynamic load factor, K2For load balance coefficient；
The extruding safety coefficient of most weak connected piece：
σR0.2=1.15* τp' (5.6)
In formula 5.5-5.8, σ 'sFor the yield limit of relatively weak connected piece (planet carrier), (planet carrier) it is allowable Shear stress, σR0.2For the extrusion stress allowable of relatively weak connected piece (planet carrier), PsTo act on relatively weak quilt Compression on connector (planet carrier), lsTo act on the effective length of relatively weak connected piece (planet carrier) endoporus, Sσ For the extruding safety coefficient of most weak connected piece；
2.2) as shown in fig. 7, the input and output of module parameter are as follows：
Module interfaces are divided into three parts：Basic parameter, result of calculation and result output.
In basic parameter, user needs self-defined basic parameter, and main input parameter has input limits moment of torsion, system of load Number, load balance coefficient, pin number, planet carrier hole depth, flange hole depth, pin external diameter, pin internal diameter, pin pitch circle diameter, planet carrier are bent The limit, spline flange yield limit and trundle yield limit are taken, while yield condition needs to carry out correlation by following menu The definition of parameter.
Final calculation result is exported in result of calculation, including anti-shearing safety coefficient and the relatively weak part of pin Extruding safety coefficient.
The storage path of detailed result of calculation report is shown in result output module.
6th, trundle strength check module
1) function describes：Module can be calculated the power loss of bearing, in combination with gear power loss, calculate tooth Roller box power loss and gear-box efficiency.
2) principles illustrated：
Power loss is worked out with efficiency calculation module according to GB/Z 22559 (ISO/TR1479-2).In combination with big The operating experience of megawatt unit.
2.1) derivation of equation is as follows
Planetary bearing no-load torque is lost
In formula, TVLFor the system bearing no-load torque loss of planet single-planetary gear train, f0It is coefficient (with bearing type and bearing Lubrication it is relevant), voilFor the lubricant movement viscosity under running temperature, n1For planet wheel speed, dmBearing central diameter (internal-and external diameter and Two points one), k be single-planetary gear train system planetary gear number x be single planetary gear upper planet bearing number；
Planetary bearing load torque is lost：
For the roller bearing of radial load：
TVLP2=0 (6.4)
For the roller bearing of the additional axial thrust of band：
In formula 6.3-6.5, f1For coefficient (reference standard selection), P1For single planet bearing load, a, b are index (with axle The mechanism held is relevant).TVLP1The power attenuation of radial load bearing, TVLP2The power attenuation of axial load bearings, FaFor additional shaft To thrust.
Because planet carrier bearing calculates no k, x value, remaining method is consistent with planetary bearing computational methods.
2.2) as shown in figure 8, the input and output of module parameter are as follows：
Module interfaces are divided into four parts：Basic parameter, service condition, result of calculation and result output.
In basic parameter, user needs to input one-level, the engagement monodentate power loss of secondary planet system, internal messing list Tooth power loss, planetary bearing internal diameter, planetary bearing external diameter, the ring gear number of teeth, the sun gear number of teeth, centre-to-centre spacing, planetary gear number, Single planet wheel bearing number, coefficient f0、f1、f2, index a, b, planet carrier bearing bore diameter, planet carrier bearing outside diameter.
Input speed, rated power, kinematic viscosity in service condition.
Final calculation result, including the total-power loss of primary planet bearing, secondary planet bearing are exported in result of calculation Total-power loss, the total-power loss of planet carrier bearing, gear-box total-power loss, gear-box efficiency.
The storage path of detailed result of calculation report is shown in result output module.
Examples of implementation described above are only the preferred embodiments of the invention, and the implementation model of the present invention is not limited with this Enclose, therefore the change that all shape, principles according to the present invention are made, it all should cover within the scope of the present invention.

Claims (7)

  1. A kind of 1. planetary drive gear-box Strength co-mputation integrated system, it is characterised in that：The system is to be developed based on Matlab Planetary drive gear-box strength check instrument, be mainly used in wind-driven generator type selecting at initial stage, certification and the specific factory in later stage Location structural strength is assessed, and the instrument, which is distinguished, six big modules, and respectively planetary gear strength check module, bolt strength check mould Block, cylinder roller bearing strength check module, spline strength check module, trundle strength check module and power loss with Efficiency calculation module；Wherein：
    The planetary gear strength check module, miner defect theories are incorporated, by importing LDD loading spectrums and other input institutes The basic parameter needed carries out damage and the durability analysis of gear, solves face fatigue safety coefficient, tooth root flexural fatigue peace Overall coefficient, and face Jing'an overall coefficient, tooth root can be solved by the proportionality coefficient of accommodation limit load and rated load Bend Jing'an overall coefficient；
    The bolt strength checks module, by inputting required basic parameter, can be directed to standard bolt and nonstandard bolt It is accurate to calculate the anti-yield factor of safety of bolt, resistant slide safety coefficient, safety factor for compressive stress, fracture-damage, be simultaneously Production provides tightening torque；
    The cylinder roller bearing strength check module, loading spectrum import feature is incorporated, equivalent process is carried out to loading spectrum automatically, The load balance coefficient of planetary system is also incorporated in the module simultaneously, can preferably react the life-span of bearing；In addition, according to the defeated base of institute This parameter, the module can export simultaneously primary planet bearing, secondary planet bearing, planet carrier bearing static strength results with it is tired Labor lifetime results；
    The spline strength check module, passes through the concrete structure of spline, stress, material heat treatment and hardness, precision etc. These situations of level, check contact strength of tooth surface, teeth bending strength, tooth root shear strength, the flank of tooth wear resistance of spline；
    The trundle strength check module, can be to the shear resistance and phase of trundle by inputting required basic parameter Extruding to weak part is checked, while the model can be checked using different yield conditions, including meter Sai Si is bent Take condition and Leix in the wrong adds yield condition；
    The power loss and efficiency calculation module, for calculating the power loss of bearing, in combination with gear power Lose to calculate gear-box capacity loss and gear-box efficiency.
  2. A kind of 2. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the row The situation that the star strength of gear teeth checks module is as follows：
    1) planetary gear strength check module is 1997 national standards, in combination with the international marks of ISO6336-2006 according to GB3480 Accurate middle renewal part is worked out, and calculating process is defined by national standard；
    The contact stress of the gear teeth is as follows：
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>H</mi> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mi>E</mi> </msub> <msub> <mi>Z</mi> <mi>H</mi> </msub> <msub> <mi>Z</mi> <mi>&amp;epsiv;</mi> </msub> <msub> <mi>Z</mi> <mi>&amp;beta;</mi> </msub> <msub> <mi>Z</mi> <mrow> <mo>(</mo> <mi>B</mi> <mo>/</mo> <mi>D</mi> <mo>)</mo> </mrow> </msub> <msqrt> <mrow> <mfrac> <mrow> <msub> <mi>K</mi> <mi>&amp;gamma;</mi> </msub> <msub> <mi>K</mi> <mi>A</mi> </msub> <msub> <mi>K</mi> <mi>V</mi> </msub> <msub> <mi>K</mi> <mrow> <mi>H</mi> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>H</mi> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>bd</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mfrac> <mrow> <mo>(</mo> <mi>u</mi> <mo>&amp;PlusMinus;</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>u</mi> </mfrac> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.1</mn> <mo>)</mo> </mrow> </mrow>
    The allowable contact stress of the gear teeth：
    σHP=σHlimZNTZLZVZRZWZX (1.2)
    Load is in the extraneous point in single pair tooth region of engagement, the bending stress of the gear teeth：
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>F</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mi>&amp;gamma;</mi> </msub> <msub> <mi>K</mi> <mi>A</mi> </msub> <msub> <mi>K</mi> <mi>V</mi> </msub> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>bm</mi> <mi>n</mi> </msub> </mrow> </mfrac> <msub> <mi>Y</mi> <mi>F</mi> </msub> <msub> <mi>Y</mi> <mi>S</mi> </msub> <msub> <mi>Y</mi> <mi>&amp;beta;</mi> </msub> <msub> <mi>Y</mi> <mrow> <mi>D</mi> <mi>T</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.3</mn> <mo>)</mo> </mrow> </mrow>
    When load acts on tooth top, the bending stress of the gear teeth：
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>F</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mi>&amp;gamma;</mi> </msub> <msub> <mi>K</mi> <mi>A</mi> </msub> <msub> <mi>K</mi> <mi>V</mi> </msub> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mi>&amp;beta;</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow> <mi>F</mi> <mi>&amp;alpha;</mi> </mrow> </msub> <msub> <mi>F</mi> <mi>t</mi> </msub> </mrow> <mrow> <msub> <mi>bm</mi> <mi>n</mi> </msub> </mrow> </mfrac> <msub> <mi>Y</mi> <mrow> <mi>F</mi> <mi>L</mi> </mrow> </msub> <msub> <mi>Y</mi> <mi>&amp;epsiv;</mi> </msub> <msub> <mi>Y</mi> <mrow> <mi>S</mi> <mi>a</mi> </mrow> </msub> <msub> <mi>Y</mi> <mi>&amp;beta;</mi> </msub> <msub> <mi>Y</mi> <mrow> <mi>D</mi> <mi>T</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.4</mn> <mo>)</mo> </mrow> </mrow>
    Gear teeth permissible bending stress：
    σFP=σFlimYSTYNTYδrelTYRrelTYX (1.5)
    In formula 1.1 to 1.5, KγFor load balance coefficient, KAFor coefficient of utilization, KVDynamic load factor, KHβFor face load distribution along width Coefficient, KHαFor face load distribution among gear teeth coefficient, ZEFor coefficient of elasticity, ZHFor node region coefficient, ZεFor face weight Right coefficient, ZβFor face spiral ascent, Z(B/D)For little gear and gear wheel the single pair tooth at meshing point B, D respectively Contact ratio, for planetary gear and internal gear, Z(B/D)Take 1, ZNTFor face life factor, cycle-index pair is considered Intensity, ZLFor lubricating coefficient, ZVVelocity coeffficient, ZRRoughness value, ZWFlank of tooth work hardening coefficient, ZXFor face size system Number, KFβLongitudinal Load Distribution Factors, K are bent for tooth rootFαLoad distribution among gear teeth coefficient, Y are bent for tooth rootFFor bending stress tooth form Coefficient, YFaFor bending stress form factor, YSFor Stress Correction Coefficient, YSaFor Stress Correction Coefficient, YβSpiral is bent for tooth root Ascent, YDTFor tooth depth coefficient, YSTThe Stress Correction Coefficient of the experiment gear calculated for bending strength, YNTTo be bent for tooth root Life factor, YδrelTFor relative root fillet sensitivity coefficient, YRrelTWith respect to root surface situation coefficient, YXSize is bent for tooth root Coefficient, FtFor engagement force, b is effective facewidth, d1For pitch diameter, u is gear ratio, mnFor normal module, σHlimFor face Nominal stress, σFlimNominal stress is bent for tooth root；
    For contact fatigue strength, initial factor of safety, i.e., using the face fatigue safety coefficient under rated load：
    <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>e</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>H</mi> <mi>P</mi> <mi>e</mi> </mrow> </msub> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>H</mi> <mi>e</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.6</mn> <mo>)</mo> </mrow> </mrow>
    In formula, σHPeFor initial Contact Stress of Gear, σHeFor initial flank of tooth allowable contact stress, SHeFor initial flank of tooth touch-safe Coefficient；
    Each the life factor under operating mode is：
    <mrow> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>H</mi> <mi>i</mi> </mrow> </msub> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>H</mi> <mi>P</mi> <mi>i</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.7</mn> <mo>)</mo> </mrow> </mrow>
    In formula, σHiFor the Contact Stress of Gear under i-th of operating mode in loading spectrum, σHPiTo be allowable under i-th of operating mode in loading spectrum Contact Stress of Gear, ZNTiFor the life factor under i-th of operating mode in loading spectrum；
    The cycle-index of fatigue failure under each operating mode：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mn>1.6</mn> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>exp</mi> <mn>1</mn> </mrow> </msup> <mo>&amp;times;</mo> <msub> <mi>N</mi> <mrow> <mi>L</mi> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mn>1</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>Z</mi> <mrow> <mi>N</mi> <mi>T</mi> <mi>i</mi> </mrow> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.8</mn> <mo>)</mo> </mrow> </mrow>
    Ni=(ZNTi)exp2×NLref2 ZNTi≤1 (1.9)
    In formula, NLref1Reference cycle-index during for life factor more than 1, NLref2Reference when being less than 1 for life factor circulates Number, exp1 be life factor be more than 1 when index, exp2 be life factor be less than 1 when index, the choosing of these values and material Take relevant；
    The damage ratio of each operating mode：
    <mrow> <msub> <mi>U</mi> <mi>i</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>n</mi> <mi>i</mi> </msub> <msub> <mi>N</mi> <mi>i</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.10</mn> <mo>)</mo> </mrow> </mrow>
    In formula, niFor the cycle-index under each operating mode
    Total damage：
    <mrow> <mi>U</mi> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mi>i</mi> </munder> <msub> <mi>U</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1.11</mn> <mo>)</mo> </mrow> </mrow>
    2) input and output of module parameter are as follows：
    Module interfaces are divided into six parts：Basic parameter input, strength check coefficient, service condition, other require, result of calculation with And result output；
    Needed in basic parameter input the modulus of input gear, pressure angle, centre-to-centre spacing, helical angle, planetary gear number, the number of teeth, Addendum coefficient, top coefficient, the facewidth, wheel rim intracavity diameter, web thickness, accuracy class, contact fatigue strength limit, flexural fatigue The limit, tooth top profiling quantity, tooth-face roughness, tooth root roughness, boss height, cutter outside circle angle, tooth face hardness, end relief with And pinion cutter these parameter informations；
    Needed in strength check coefficient input dynamic load factor, Longitudinal Load Distribution Factors, load distribution among gear teeth coefficient, using system Number and load balance coefficient；
    Need to input rated speed, nominal torque, life requirements, dead load and rated load ratio and lubrication in service condition Oily kinematic viscosity, while import loading spectrum；
    Need to be defined the selection principle for being changed into coefficient, the selection principle of sideshake by following menu in other requirements, have Effect hardened layer computational methods, the connected mode of gear, the type of belt drive of gear, root stress computational methods, lubricating oil, whether examine Consider the influence of flange thickness, dynamic load factor whether from host computer, whether consider Superposition degree modulus and corresponding material heat treatment Selection；
    Final calculation result is exported in result of calculation, including face fatigue safety coefficient, tooth root flexural fatigue are safely Number, face static strength safety coefficient and tooth root static bending strength safety coefficient；
    The file path of detailed result of calculation is shown in result output.
  3. A kind of 3. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the spiral shell The situation of bolt strength check module is as follows：
    1) for standard bolt, by selecting bolt model to select bolt；For nonstandard bolt, by inputting nominal diameter, spiral shell The aperture of external diameter, pitch diameter, bolt rostral at bolt path, bolt head and work piece interface determines bolt and connector Physical dimension；
    2) calculating process is as follows：
    2.1) moment of torsion M is born by bolt connectionTmaxAnd the force of periphery F on caused each boltQmax：
    <mrow> <msub> <mi>F</mi> <mrow> <mi>Q</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <msub> <mi>M</mi> <mrow> <mi>T</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi>i</mi> <mo>*</mo> <msub> <mi>D</mi> <mi>t</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.1</mn> <mo>)</mo> </mrow> </mrow>
    In formula, i is bolt number, DtFor bolt circle diameter；
    2.2) determine to tighten factor alphaA, the selection for tightening coefficient is relevant with the installation tool of bolt；
    2.3) minimum fastening force F is determinedkerf：
    Fkerf=FQmax/u (2.2)
    In formula, u is coefficient of friction；
    2.4) loss of pretightning force caused by insertion is determined, including：
    The resilience δ of boltS：
    <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>S</mi> <mi>K</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.5</mn> <mi>d</mi> </mrow> <mrow> <msub> <mi>E</mi> <mi>s</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <mi>N</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.3</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;delta;</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <msub> <mi>l</mi> <mn>1</mn> </msub> <mrow> <msub> <mi>E</mi> <mi>s</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <mi>N</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.4</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>G</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>l</mi> <mrow> <mi>G</mi> <mi>e</mi> <mi>w</mi> </mrow> </msub> <mrow> <msub> <mi>E</mi> <mi>s</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <msub> <mi>d</mi> <mn>3</mn> </msub> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.5</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;delta;</mi> <mrow> <mi>G</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;delta;</mi> <mi>G</mi> </msub> <mo>+</mo> <msub> <mi>&amp;delta;</mi> <mi>M</mi> </msub> <mo>=</mo> <mfrac> <mrow> <mn>0.5</mn> <mi>d</mi> </mrow> <mrow> <msub> <mi>E</mi> <mi>s</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <msub> <mi>d</mi> <mn>3</mn> </msub> </msub> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>0.33</mn> <mi>d</mi> </mrow> <mrow> <msub> <mi>E</mi> <mi>M</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <mi>N</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.6</mn> <mo>)</mo> </mrow> </mrow>
    δS=δSK+δ1+δGew+δGm (2.7)
    In formula, d is nominal diameter, EsFor bolt modulus of elasticity, EMFor the connected piece modulus of elasticity with blind hole, ANFor engineering face Product,Path area, l1For the length of screw rod, lGewReach, δ can be loaded for residueSKFor the resilience on head, δ1For screw rod The resilience at position, δGewFor the resilience of zero load place's screw thread, δGAt bolt thread path, δMTo be returned at nut or workpiece blind hole Bullet, δGmFor total resilience at nut or screw thread；
    Determine the resilience of workpiece：
    In formula, dwFor the external diameter at bolt head and work piece interface, dhFor the aperture of connected piece, lkTo be clamped length,For Bolted cone angle, EpFor connected piece modulus of elasticity；
    Embedded quantity fzIt is relevant with material, connector quantity；
    The loss F of pretightning forcez：
    Fz=fz/(δs+δp) (2.9)
    2.5) minimum installation pretightening force F is determinedMmin：
    FMmin=Fkerf+FZ (2.10)
    2.6) maximum installation pretightening force F is determinedMmax：
    FMmax=αA·FMmin(2.11)
    2.7) erection stress σ is determinedrde,Mzul：
    σrde,Mzul=vRp0.2 (2.12)
    In formula, v accounts for the percentage of yield limit stress, R for pretightning forcep0.2For yield limit stress；
    Determine assembly pretightening power：
    FMzul=As·v·Rp0.2 (2.13)
    In formula, AsFor stress area of section；
    2.8) service load FSmax：
    FSmax=FMzul (2.14)
    Maximum tensile stress σzmax：
    σzmax=FSmax/As (2.15)
    Working stress σred,B：
    σred,B=σzmax (2.16)
    Anti- yield factor of safety SF：
    SF=Rp0.2/σred,B (2.17)
    2.9) minimum bearing-surface area Apmin：
    <mrow> <msub> <mi>A</mi> <mrow> <mi>p</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mi>&amp;pi;</mi> <mn>4</mn> </mfrac> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>w</mi> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>d</mi> <mi>h</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.18</mn> <mo>)</mo> </mrow> </mrow>
    Bearing stress pMmax：
    <mrow> <msub> <mi>p</mi> <mrow> <mi>M</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>F</mi> <mrow> <mi>M</mi> <mi>z</mi> <mi>u</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow> <mi>p</mi> <mi>min</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.19</mn> <mo>)</mo> </mrow> </mrow>
    Safety factor for compressive stress Sp：
    <mrow> <msub> <mi>S</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>p</mi> <mrow> <mi>M</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <msub> <mi>p</mi> <mrow> <mi>k</mi> <mi>z</mi> <mi>u</mi> <mi>l</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.20</mn> <mo>)</mo> </mrow> </mrow>
    2.10) minimum pretightning force FVmin：
    <mrow> <msub> <mi>F</mi> <mrow> <mi>V</mi> <mi>min</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>F</mi> <mrow> <mi>M</mi> <mi>z</mi> <mi>u</mi> <mi>l</mi> </mrow> </msub> <msub> <mi>&amp;alpha;</mi> <mi>A</mi> </msub> </mfrac> <mo>-</mo> <msub> <mi>F</mi> <mi>Z</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.21</mn> <mo>)</mo> </mrow> </mrow>
    Resistant slide safety coefficient SG：
    <mrow> <msub> <mi>S</mi> <mi>G</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>F</mi> <mrow> <mi>V</mi> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> <msub> <mi>F</mi> <mrow> <mi>ker</mi> <mi>f</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.22</mn> <mo>)</mo> </mrow> </mrow>
    The maximum shear stress τ caused by slidingmax：
    <mrow> <msub> <mi>&amp;tau;</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mi>F</mi> <mrow> <mi>Q</mi> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <msub> <mi>A</mi> <mi>N</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.23</mn> <mo>)</mo> </mrow> </mrow>
    Fracture-damage SA：
    <mrow> <msub> <mi>S</mi> <mi>A</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;tau;</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <msub> <mi>&amp;tau;</mi> <mrow> <mi>B</mi> <mi>s</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.24</mn> <mo>)</mo> </mrow> </mrow>
    2.11) screw-down torque M is determinedA：
    <mrow> <msub> <mi>M</mi> <mi>A</mi> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mi>M</mi> <mi>z</mi> <mi>u</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <mn>0.16</mn> <mi>P</mi> <mo>+</mo> <mn>0.58</mn> <msub> <mi>d</mi> <mn>2</mn> </msub> <msub> <mi>u</mi> <mi>G</mi> </msub> <mo>+</mo> <mfrac> <msub> <mi>D</mi> <mrow> <mi>k</mi> <mi>m</mi> </mrow> </msub> <mn>2</mn> </mfrac> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2.25</mn> <mo>)</mo> </mrow> </mrow>
    In formula, P is pitch, uGFor thread friction coefficient, ukRubbed for pressure-bearing surface is DkmFor in bolt head or nut bearing area The effective diameter of moment of friction, d2Screw thread pitch diameter；
    3) input and output of module parameter are as follows：
    Module interfaces are divided into six parts：Boundary condition, bolt arrangement size, material properties, connected piece structure, result of calculation with And result output；
    Input torque, bolt performance rate are needed in boundary condition, coefficient, yield limit stress ratio, combined material is tightened and rubs Wipe coefficient, bolt number, thread friction coefficient, pressure-bearing surface coefficient of friction, nut pressure-bearing surface coefficient of friction, permissible compression stress, permitted With shear stress, yield limit and strength degree, while need to select bolt result formats；
    Needed in bolt arrangement size input bolt diameter, path, bolt head diameter, central diameter, spiro rod length and Pitch, while need to select bolt head form；
    Need to input bolt modulus of elasticity, nut or elasticity modulus of materials and connected piece springform respectively in material properties Amount；
    Need to input clamping length, bolt distribution pitch diameter, in two connector contact portions in connected piece structure External diameter and embedded quantity；
    Final calculation result is exported in result of calculation, including the anti-yield factor of safety, resistant slide safety coefficient, resistance to compression safety are Number, fracture-damage and screw-down torque value；
    The storage path of detailed result of calculation report is shown in result output module.
  4. A kind of 4. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the circle The situation of post roller bearing strength check module is as follows：
    According to ISO76/ISO281 standards, the static strength and life-span for carrying out cylinder roller bearing calculate；
    1) LDD loading spectrums are processed into equivalent load TeqIt is as follows：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>&amp;Sigma;</mo> <msubsup> <mi>T</mi> <mi>i</mi> <mrow> <mn>10</mn> <mo>/</mo> <mn>3</mn> </mrow> </msubsup> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&amp;Sigma;</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mn>3</mn> <mo>/</mo> <mn>10</mn> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3.1</mn> <mo>)</mo> </mrow> </mrow>
    In formula, riFor the revolution under each operating mode, TiFor moment of torsion under each operating mode；
    2) derivation of equation is as follows：
    2.1) system checks static strength safely
    <mrow> <msub> <mi>S</mi> <mn>0</mn> </msub> <mo>=</mo> <mfrac> <msub> <mi>C</mi> <mrow> <mn>0</mn> <mi>r</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>o</mi> <mi>r</mi> </mrow> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3.2</mn> <mo>)</mo> </mrow> </mrow>
    In formula, C0rFor the basic rated static load of bearing, PorFor bearing Equivalent static load；
    2.2) Life-span checking of bearing
    <mrow> <msub> <mi>L</mi> <mn>10</mn> </msub> <mo>=</mo> <mfrac> <msup> <mn>10</mn> <mn>6</mn> </msup> <mrow> <mn>60</mn> <mo>&amp;times;</mo> <mi>n</mi> </mrow> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>C</mi> <mi>r</mi> </msub> <msub> <mi>P</mi> <mi>r</mi> </msub> </mfrac> <mo>)</mo> </mrow> <mi>a</mi> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3.3</mn> <mo>)</mo> </mrow> </mrow>
    In formula,aFor fatigue exponent, CrFor basic dynamic load rating, PrFor equivalent radial load, n mean speeds；
    3) input and output of module parameter are as follows：
    Module interfaces are divided into eight parts：Service data, planet carrier bearing, gear, primary planet bearing, secondary planet bearing, it is quiet Load, calculation of dynamic load foundation, result of calculation and result output；
    Defeated ultimate torque, nominal torque, rated speed are needed in service data, while imports loading spectrum；
    The basic rated static load, basic rated static load, secondary planet system weight of input shaft bearing are needed in planet carrier bearing Amount, bearing pitch diameter, single roller quantity, columns, roller effective length, roller diameter, the contact angle of roller；
    Need to input one-level, the number of teeth of secondary gear respectively in gear；
    The basic rated static load, basic rated static load, primary planet system of input shaft bearing are needed in primary planet bearing Centre distance, planetary gear number, the number of each planetary gear upper bearing (metal), load balance coefficient, bearing pitch diameter, single roller number Amount, columns, roller effective length, roller diameter, the contact angle of roller；
    The basic rated static load, basic rated static load, secondary planet system of input shaft bearing are needed in secondary planet bearing Centre distance, planetary gear number, the number of each planetary gear upper bearing (metal), load balance coefficient, bearing pitch diameter, single roller number Amount, columns, roller effective length, roller diameter, the contact angle of roller；
    Supplier's offer or iso standard is selected to calculate according in dead load, calculation of dynamic load；
    Export final calculation result in result of calculation, including Jing'an overall coefficient of ultimate load, contact stress, rated load Contact stress, mathematic(al) expectation, the contact stress of equivalent load, mathematic(al) expectation；
    The storage path of detailed result of calculation report is shown in result output module.
  5. A kind of 5. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the flower The situation that bond strength checks module is as follows：
    According to GBT17855-1999 standards, the bearing capacity of spline is calculated as follows；
    1) bearing capacity calculates
    1.1) contact strength of tooth surface calculates
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>H</mi> </msub> <mo>=</mo> <mfrac> <mi>W</mi> <msub> <mi>h</mi> <mi>w</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4.1</mn> <mo>)</mo> </mrow> </mrow>
    [σH]=σ0.2/(SH·K1K2K3K4) (4.2)
    1.2) teeth bending strength calculates
    Involute spline：
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>F</mi> </msub> <mo>=</mo> <mn>6</mn> <mi>h</mi> <mi>W</mi> <mi> </mi> <msub> <mi>cos&amp;alpha;</mi> <mi>D</mi> </msub> <mo>/</mo> <msubsup> <mi>S</mi> <mrow> <mi>F</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4.3</mn> <mo>)</mo> </mrow> </mrow>
    Rectangular spline：
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>F</mi> </msub> <mo>=</mo> <mn>6</mn> <mi>h</mi> <mi>W</mi> <mo>/</mo> <msubsup> <mi>S</mi> <mrow> <mi>F</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4.4</mn> <mo>)</mo> </mrow> </mrow>
    [σF]=σb/(SF·K1K2K3K4) (4.5)
    1.3) tooth root shear strength calculates
    τFmax=τtn·αtn (4.6)
    [τF]=[σF]/2 (4.7)
    1.4) flank of tooth wear resistance calculates
    Permissible compression stress：
    [σH1] for spline pair 108Permissible compression stress when being worked under secondary period, selected according to heat treatment and flank of tooth average hardness Select；
    [σH2]=n × ball hardness number (4.8)
    1.5) torsion of external splines calculates with bending strength
    <mrow> <msub> <mi>&amp;sigma;</mi> <mi>v</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>F</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mn>3</mn> <msubsup> <mi>&amp;tau;</mi> <mrow> <mi>t</mi> <mi>n</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4.9</mn> <mo>)</mo> </mrow> </mrow>
    [σV]=σ0.2/(SF·K1K2K3K4) (4.10)
    In formula 4.1-4.10, σHFor face pressure, W is position specific loading, hwFor the wokring depth of tooth, σ0.2It is strong for the surrender of material Degree, SHFor the calculating safety coefficient of contact strength of tooth surface, K1For coefficient of utilization, K2For backlash coefficient, K3Distribution coefficient, K4For Axial load unbalance loading coefficient, [σH] it is flank of tooth permissible compression stress, αDFor normal pressure angle, SFnFor chordal tooth thickness, h is fully teeth height, σFFor Face pressure angle, [σF] it is Dedenda's bending stress allowable, SFSafety coefficient, σ are calculated for bending strengthbFor the tensile strength of material, τFmaxFor tooth root the maximum shear stress, τtnShear stress, αtnFor the factor of stress concentration, [τF] it is shear stress allowable, [σH2] flower Permissible compression stress of the key pair long-term work without abrasion, n are the coefficient related to heat treatment, σvFor equivalent stress σFnShould for bending Power, τtnFor shear stress, [σV] reversed and allowable stress during bending strength to calculate spline；
    2) input and output of module parameter are as follows：
    Module interfaces divide quinquepartite：Basic parameter, material characteristics, service condition and loading coefficient, result of calculation and result Output；
    Defeated axle and hub modulus, pressure angle, helical angle, height of teeth root coefficient, root fillet coefficient, height of teeth top are needed in basic parameter Coefficient, the grade of tolerance, accuracy class；
    Yield strength, tensile strength, tooth surface abrasion permissible compression stress, the flank of tooth pressure allowable of input material are needed in material characteristics Stress；
    Input torque, coefficient of utilization, backlash coefficient, distribution coefficient, axial direction are needed in service condition and loading coefficient partially Carry coefficient；
    Final calculation result, including flank of tooth compression, root stress, tooth root shear stress, the flank of tooth mill are exported in result of calculation Damage compression；
    The storage path of detailed result of calculation report is shown in result output module.
  6. A kind of 6. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the biography The situation of dynamic pin strength check module is as follows：
    1) derivation of equation is as follows
    Because trundle is subjected only to moment of torsion effect, therefore the cross force suffered by single trundle is：
    <mrow> <mi>F</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mo>*</mo> <mi>T</mi> </mrow> <mrow> <mi>Z</mi> <mo>*</mo> <msub> <mi>D</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.1</mn> <mo>)</mo> </mrow> </mrow>
    In formula, F is single bolt cross force, and T is ultimate torque, DiThe central diameter where pin, Z is pin number；
    Secondary planet frame shears safety coefficient：
    <mrow> <msub> <mi>&amp;tau;</mi> <mi>p</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;sigma;</mi> <mi>s</mi> </msub> <mi>a</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.2</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>&amp;tau;</mi> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>*</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mi>F</mi> </mrow> <mrow> <mfrac> <mrow> <msup> <mi>&amp;pi;D</mi> <mn>2</mn> </msup> </mrow> <mn>4</mn> </mfrac> <mo>-</mo> <mfrac> <mrow> <msup> <mi>&amp;pi;d</mi> <mn>2</mn> </msup> </mrow> <mn>4</mn> </mfrac> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.3</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>S</mi> <mi>&amp;tau;</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;tau;</mi> <mi>p</mi> </msub> <mi>&amp;tau;</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.4</mn> <mo>)</mo> </mrow> </mrow>
    In formula 5.2-5.4, τpFor the shear stress allowable of determination, σsFor the yield limit of bearing pin material, a is according to different surrenders Condition criterion value differs, meter Sai Si yield conditions a=30.5, Leix in the wrong adds yield condition a=2, τ to be under Lateral Force Shear stress, D is pin external diameter, and d is pin internal diameter, K1For dynamic load factor, K2For load balance coefficient；
    The extruding safety coefficient of most weak connected piece：
    <mrow> <msup> <msub> <mi>&amp;tau;</mi> <mi>p</mi> </msub> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mi>s</mi> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <mi>a</mi> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.5</mn> <mo>)</mo> </mrow> </mrow>
    σR0.2=1.15* τp'(5.6)
    <mrow> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> <mo>*</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mo>*</mo> <mi>F</mi> </mrow> <mrow> <msub> <mi>l</mi> <mi>s</mi> </msub> <mi>D</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.7</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>S</mi> <mi>&amp;sigma;</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>R</mi> <mn>0.2</mn> </mrow> </msub> <mo>&amp;prime;</mo> </msup> </mrow> <msub> <mi>P</mi> <mi>s</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5.8</mn> <mo>)</mo> </mrow> </mrow>
    In formula 5.5-5.8, σs' for the yield limit of relatively weak connected piece, i.e., shear stress allowable, σR0.2For relative thin The extrusion stress allowable of weak connected piece, PsTo act on the compression on relatively weak connected piece, lsTo act on phase To the effective length of the connected piece endoporus of weakness, SσFor the extruding safety coefficient of most weak connected piece；
    2) input and output of module parameter are as follows：
    Module interfaces are divided into three parts：Basic parameter, result of calculation and result output；
    In basic parameter, user needs self-defined basic parameter, and main input parameter has input limits moment of torsion, loading coefficient, Carry coefficient, pin number, planet carrier hole depth, flange hole depth, pin external diameter, pin internal diameter, pin pitch circle diameter, planet carrier surrender pole Limit, spline flange yield limit and trundle yield limit, while yield condition needs to carry out relevant parameter by following menu Definition；
    Final calculation result is exported in result of calculation, including the anti-shearing safety coefficient of pin and the extruding of relatively weak part are pacified Overall coefficient；
    The storage path of detailed result of calculation report is shown in result output module.
  7. A kind of 7. planetary drive gear-box Strength co-mputation integrated system according to claim 1, it is characterised in that the work( Rate loss is as follows with the situation of efficiency calculation module：
    1) derivation of equation is as follows：
    Planetary bearing no-load torque is lost：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mrow> <mi>V</mi> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1.6</mn> <mo>&amp;times;</mo> <msup> <mn>10</mn> <mrow> <mo>(</mo> <mo>-</mo> <mn>8</mn> <mo>)</mo> </mrow> </msup> <msub> <mi>f</mi> <mn>0</mn> </msub> <msubsup> <mi>d</mi> <mi>m</mi> <mn>3</mn> </msubsup> <mo>&amp;CenterDot;</mo> <mi>k</mi> <mo>&amp;CenterDot;</mo> <mi>x</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&lt;</mo> <mn>2000</mn> <msup> <mi>mm</mi> <mn>2</mn> </msup> <mo>/</mo> <mrow> <mo>(</mo> <mi>s</mi> <mo>&amp;CenterDot;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6.1</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mrow> <mi>V</mi> <mi>L</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>(</mo> <mo>-</mo> <mn>10</mn> <mo>)</mo> </mrow> </msup> <msub> <mi>f</mi> <mn>0</mn> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>/</mo> <mn>3</mn> <mo>)</mo> </mrow> </msup> <msubsup> <mi>d</mi> <mi>m</mi> <mn>3</mn> </msubsup> <mo>&amp;CenterDot;</mo> <mi>k</mi> <mo>&amp;CenterDot;</mo> <mi>x</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>v</mi> <mrow> <mi>o</mi> <mi>i</mi> <mi>l</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>&amp;GreaterEqual;</mo> <mn>2000</mn> <msup> <mi>mm</mi> <mn>2</mn> </msup> <mo>/</mo> <mrow> <mo>(</mo> <mi>s</mi> <mo>&amp;CenterDot;</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6.2</mn> <mo>)</mo> </mrow> </mrow>
    In formula, TVLFor the system bearing no-load torque loss of planet single-planetary gear train, f0To have with the lubrication of bearing type and bearing The coefficient of pass, voilFor the lubricant movement viscosity under running temperature, n1For planet wheel speed, dmBearing central diameter, k are single-stage planetary Wheel system planetary gear number, x are single planetary gear upper planet bearing number；
    Planetary bearing load torque is lost：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>V</mi> <mi>L</mi> <mi>P</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <msubsup> <mi>P</mi> <mn>1</mn> <mi>a</mi> </msubsup> <msubsup> <mi>d</mi> <mi>m</mi> <mi>b</mi> </msubsup> <mo>&amp;CenterDot;</mo> <msup> <mn>10</mn> <mrow> <mo>(</mo> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </msup> <mo>&amp;CenterDot;</mo> <mi>k</mi> <mo>&amp;CenterDot;</mo> <mi>x</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6.3</mn> <mo>)</mo> </mrow> </mrow>
    For the roller bearing of radial load：
    TVLP2=0 (6.4)
    For the roller bearing of the additional axial thrust of band：
    <mrow> <msub> <mi>T</mi> <mrow> <mi>V</mi> <mi>L</mi> <mi>P</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <msub> <mi>F</mi> <mi>a</mi> </msub> <msubsup> <mi>d</mi> <mi>m</mi> <mi>b</mi> </msubsup> <mo>&amp;CenterDot;</mo> <msup> <mn>10</mn> <mrow> <mo>(</mo> <mo>-</mo> <mn>3</mn> <mo>)</mo> </mrow> </msup> <mo>&amp;CenterDot;</mo> <mi>k</mi> <mo>&amp;CenterDot;</mo> <mi>x</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6.5</mn> <mo>)</mo> </mrow> </mrow>
    In formula 6.3-6.5, f1The coefficient chosen for reference standard, P1For single planet bearing load, a, b are the mechanism with bearing Relevant index, TVLP1The power attenuation of radial load bearing, TVLP2The power attenuation of axial load bearings, FaAxially pushed away to be additional Power；
    Because planet carrier bearing calculates no k, x value, remaining method is consistent with planetary bearing computational methods；
    2) input and output of module parameter are as follows：
    Module interfaces are divided into four parts：Basic parameter, service condition, result of calculation and result output；
    In basic parameter, user needs to input one-level, the engagement monodentate power loss of secondary planet system, internal messing monodentate work( It is rate loss, planetary bearing internal diameter, planetary bearing external diameter, the ring gear number of teeth, the sun gear number of teeth, centre-to-centre spacing, planetary gear number, single Planet wheel bearing number, coefficient f0、f1、f2, index a, b, planet carrier bearing bore diameter, planet carrier bearing outside diameter；
    Input speed, rated power, kinematic viscosity in service condition；
    Final calculation result, including the total-power loss of primary planet bearing, secondary planet bearing total work are exported in result of calculation Rate loss, the total-power loss of planet carrier bearing, gear-box total-power loss, gear-box efficiency；
    The storage path of detailed result of calculation report is shown in result output module.
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CN108871745A (en) * 2018-05-10 2018-11-23 哈尔滨电气股份有限公司 It is a kind of without cone cervical approach orchid strength check methods
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CN112580156A (en) * 2020-11-09 2021-03-30 东风汽车集团有限公司 Gasoline engine cylinder head bolt type selection and checking method
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CN108871745A (en) * 2018-05-10 2018-11-23 哈尔滨电气股份有限公司 It is a kind of without cone cervical approach orchid strength check methods
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