CN107545123A - Consider the lifting decelerator dynamic reliability method under a variety of uncertainties - Google Patents
Consider the lifting decelerator dynamic reliability method under a variety of uncertainties Download PDFInfo
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Abstract
The present invention discloses a kind of lifting decelerator dynamic reliability method considered under a variety of uncertainties,For traditional static Reliability Modeling by design parameter in mechanical structure system,Limitation of the load bearing process as certainty variable,The method of the present invention is designing to lifting decelerator,Manufacture,Each uncertainty of service stage is analyzed,Quantify,Its invalidation functions function is established according to the different failure modes of lifting decelerator,The relation of external load effect number and the function of time is established with reference to its specific works environment,Finally will analysis,The data of quantization,Power function under different failure modes,Effect number brings the dynamic reliability model of foundation into time function relation,Solve and calculate its life distribution function under different failure modes,The present invention method overcome traditional static Reliability Modeling calculate lifted the decelerator life-span when accuracy bottom the problem of,More conform to engineering practice.
Description
Technical field
The invention belongs to reliability engineering field, is related to dynamic reliability modeling and analysis technical field, and in particular to examine
Consider the lifting decelerator dynamic reliability analysis and modeling method under a variety of uncertainties.
Background introduction
The current research for large-sized mining dredger both at home and abroad, it is most not consider to be related to its design, production with application entirely
A variety of uncertainties in life cycle, design parameter in excavator structure is handled as certainty variable mostly；But
Most information in engineering structure, external applied load etc. is all non-precision as suffered by design parameter, model parameter and structure
, this carrys out very big influence to the Reliability modeling of mechanical structure (system) with analytic band, can cause product failure very when serious
To causing heavy economic losses.Therefore, the uncertainty comprehensively in analysis and cognitive structure (system) is advantageous to properties of product
Lifting and the improvement of quality.
Large-sized mining dredger lifting decelerator (hereinafter referred to as lifting decelerator) is used as between lifting motor and scraper bowl and moved
The intermediate link of power transmission, it is the important component of digging operation, is withstood shocks all the time in work, oscillating load.Lifting
Decelerator reliability is directly connected to the Reliability Assurance of whole excavator, during lifting decelerator progress fail-safe analysis
Consider that a variety of uncertain factors can make analysis result more be bonded engineering reality.It is not true it is therefore desirable to be carried out to lifting decelerator
Qualitative analysis and quantization, to study its dynamic reliability.
The content of the invention
It is a primary object of the present invention to overcome above mentioned problem of the prior art, there is provided one kind considers a variety of uncertainties
Under lifting decelerator dynamic reliability method, comprise the following steps：
Step 1：It is uncertain according to present in three design, use and processing links, it is by sources different to lifting
Decelerator carries out corresponding analysis of uncertainty, finds out main uncertain source existing for lifting decelerator；
Step 2：Uncertainty corresponding to the main uncertain source determined to step 1 quantifies, and is not known
Property quantized data；
Step 3：According to multi-invalidation mode, choosing corresponding to the main uncertain source of the step S1 lifting decelerators determined
Take and calculate parameter value corresponding to multi-invalidation mode, lifting decelerator is then established in each failure according to the parameter value being calculated
Power function expression formula under pattern；
Step 4：The dynamic characteristic of analysis lifting decelerator, it is determined that lifting decelerator institute effect number loaded and time letter
Several relations；
Step 5：Consider influence of the load effect number to lifting decelerator, establishing lifting using progressive distribution theory slows down
The dynamic reliability model of device；
Step 6：Function letter under each failure mode that uncertain quantized data that step 2 is obtained, step 3 obtain
The effect number obtained in number, step 4 is brought into the dynamic reliability model established in step 5 with time function relation, is counted
Calculate life distribution function of the lifting decelerator under different failure modes.
Further, the uncertainty includes：The ginseng of gears at different levels in principal and subordinate's motor output synchronism, lifting decelerator
Number is uncertain, the parameter uncertainty of lifting decelerator axis, parameter uncertainty, the Zhu Cong electricity for lifting decelerator middle case
Machine input torque parameter uncertainty and extraneous load are uncertain.
Further, main uncertain source existing for the lifting decelerator is axle.
Further, the uncertainty quantification method in the step 2 is taken based on the mode of probability and measured.
Further, step 4 specifically includes：
Step 41：Force analysis is carried out to lifting decelerator, its maximum weighted position is found out, dangerous spot is used as using the position
Assumed (specified) load acts on the influence of number；
Step 42：Statistics, drawing cycle histogram, and work period average value is obtained, each portion is obtained respectively
Institute's effect number loaded in part a cycle, determine the relation of load effect number and the function of time.
The beneficial effects of the invention are as follows：It will design and join in mechanical structure system for traditional static Reliability Modeling
Number, load bearing process as certainty variable limitation, method of the invention to lifting decelerator design, manufacture, use rank
Each uncertainty of section is analyzed, quantifies to start with, and its invalidation functions letter is established according to the different failure modes of lifting decelerator
Number, the relation of external load effect number and the function of time, the number that will finally analyze, quantify are established with reference to its specific works environment
According to the dynamic reliability model for bringing foundation into, solve and calculate its life distribution function under different failure modes, it is of the invention
Method overcomes traditional static Reliability Modeling and the problem of accuracy bottom, more conformed to when calculating the lifting decelerator life-span
Engineering practice, while the design optimization for follow-up lifting decelerator provides theoretical foundation, is advantageous to carrying for properties of product
The improvement of liter and quality.
Brief description of the drawings
Fig. 1 is the protocol procedures figure of the application；
Fig. 2 is power shovel stress diagram；
Fig. 3 is lifting torque time-domain curve figure；
Fig. 4 is work period histogram；
Fig. 5 is lifting motor speed diagram；
Fig. 6 is the DYNAMIC RELIABILITY curve map for considering static strength failure axle；
Wherein, Fig. 6 (a) represents that axle I considers the DYNAMIC RELIABILITY curve of static strength failure, and it is quiet that Fig. 6 (b) represents that axle II considers
The DYNAMIC RELIABILITY curve of Strength Failure；
Fig. 7 is the life distribution function curve map for considering static strength failure axle；
Wherein, Fig. 7 (a) represents that axle I considers the life distribution function curve of static strength failure, and Fig. 7 (b) represents that axle II considers
The life distribution function curve of static strength failure；
Fig. 8 is the DYNAMIC RELIABILITY curve map for considering fatigue strength failure axle；
Wherein, Fig. 8 (a) represents the DYNAMIC RELIABILITY curve of axle I, and Fig. 8 (b) represents the DYNAMIC RELIABILITY curve of axle II；
Fig. 9 is the life distribution function curve map for considering fatigue strength failure axle；
Wherein, Fig. 9 (a) represents the dynamic life time curve of axle I, and Fig. 9 (b) represents the dynamic life time curve of axle II.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to drawings and Examples, to this hair
It is bright to be further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and do not have to
It is of the invention in limiting.
The present embodiment decelerator is that certain type machinery face shovel type mine excavator lifts decelerator, decelerator input Rated motor
Power is 1153KW, and rated speed 475rpm, the one-level little gear number of teeth is 18, and canine tooth tooth number is 148, two level pinion gear teeth
Number is 19, and two level canine tooth tooth number is 117, and little gear meshing frequency is 142.5Hz, and secondary gear meshing frequency is
18.3Hz, extreme overload torque Tlim=35000Nm, transmission efficiency 0.98, axle material therefor are 17CrNiMo6, and surrender is strong
Spend σsIt is recommended as 750MPa, considers the uncertain factor during manufacture, heat treatment etc., it is material yield to take 750MPa
The maximum of intensity, coefficient of variation CσsIt is taken as 0.06.
It is the protocol procedures figure of the application as shown in Figure 1, the technical scheme of the application is：Consider under a variety of uncertainties
Decelerator dynamic reliability method is lifted, is comprised the following steps：
Step 1：Analysis of uncertainty, according to the mantenance data being collected into, the present invention analyzes the decelerator event that is improved
It is mostly gear, axle and casing to hinder position, is mainly shown as that gear tooth fracture, tooth surface abrasion are serious, off-axis and box deformation are tight
Again etc..So the present embodiment mainly considers gear, axle and casees at different levels in master and slave motor output synchronism and lifting decelerator
Parameter uncertainty, motor input torque parameter uncertainty and the extraneous load of body are uncertain, except gear, axle and casing
Other outer parts do not consider its parameter uncertainty.Material elements is as follows：Modulus m, coefficient of facewidth φd, helixangleβ,
Coefficient of utilization KA, dynamic load factor KV, Longitudinal Load Distribution Factors KHβ, KFβ, load share between teeth KHα, KFα, the compound system of tooth form
Number YFS, elastic properties of materials coefficient ZE, the strength of gear teeth distribution σHS, σFS(unit MPa, similarly hereinafter), single lifting motor torque T, axle
Material properties yield strength σs, tensile strength sigmab, nowel body thickness k, top box body thickness k2 and Rib Thickness h, tank material
Yield limit σ '；
Step 2：Uncertainty quantifies, and the present embodiment is carried out by the way of based on probability to the uncertainty in step 1
Measurement, its parameter and distribution situation are as shown in table 1；
The uncertain parameters of table 1 and distributed intelligence
Step 3：The failure mode of research lifting decelerator axis, chooses, calculates corresponding parametric values, and establishes it and respectively fail
Power function expression formula under pattern, power function of the axle under different failure modes are as shown in table 2；
Power function of the axle of table 2 under different failure modes
In table 2, τδFor the torque yield limit；MTFor total torque；wτFor anti-shearing section modulus；σδBent for the tension of material
Take the limit；M is moment of flexure；W is module of anti-bending section；σ is maximum stress in bend；τ is maximum twist stress；[θ] is deflection allowable
Angle；[y] Allowable deflection；KFFor bearing spider load condition coefficient；F is maximum external applied load；L is the length of axle；G is shearing elasticity
Modulus；I is polar moment of inertia；τ0kFor pulsating cyclic fatigue limit；σ-1kFor symmetrical fatigue strength limit；α stress correction coefficient (according to
Depending on moment of torsion suffered by axle)；ωcFor the subcritical vibration frequency of axle；N is rotating speed；K is the stiffness coefficient of axle；W1For axle gear
Gravity.
For the machinery of this low-speed heave-load of large-sized mining dredger, its axle lifted in decelerator belongs to transmission more
(lifting reducer output shaft in the course of work of reality, does not bear torque, only to axle because of its special connecting mode
It is subjected only to moment of flexure caused by the deadweight of parts on shaft), and the main failure forms of these axles are static strength failure and fatigue strength
Failure.Therefore, the present embodiment mainly considers both failure modes in the failure of analysis lifting decelerator axis.
Step 4：Research, analysis lifting decelerator dynamic characteristic, it is determined that lifting decelerator institute it is loaded effect number with
The relation of the function of time；Specifically include following steps：
Step 41：Force analysis is carried out to lifting decelerator, its maximum weighted position is found out, dangerous spot is used as using the position
Assumed (specified) load acts on the influence of number；
Load effect number obtains inconvenience and is not easy to characterize in Practical Project, and therefore, the present embodiment will establish load work
With the relation between number and operation time of excavator.It is determined that the cycle is excavated with being needed before load effect number relation to scraper bowl
Force analysis is carried out, determines scraper bowl maximum weighted position, the influence of number is acted on using the position as dangerous spot assumed (specified) load.Figure
2 be force diagram of the scraper bowl in mining process, Fa、FbFor two components of pushing force；G1For material gravity；G2For scraper bowl and bucket
Bar is conducted oneself with dignity；F1、F2The excavating resistance for being scraper bowl in mining process；FtFor boom hoist cable pulling force.Excavating resistance is only present in digging
In the pick stage, excavating resistance disappears immediately after scraper bowl leaves ground.Therefore, stress maximum point is that scraper bowl is loaded with thing in mining process
Material will be left at ground, and now lifting motor torque is maximum, and the stress such as reducer shaft, gear is maximum.
Remember that the excavator excavation cycle is t1(s), rotation speed of excavator n1(rpm), k is that parts rotate a circle load effect
Number, then now load effect number w ' be：
Because series excavator early stage is not marked in test process to excavating whole story position, built according to expert
View, to lift torque, drastically as the foundation for judging excavation whole story position, it is as shown in Figure 3 that cycle demarcation is carried out to it for variation tendency
Draw a circle to approve position.
Step 42：Statistics, drawing cycle histogram, and work period average value is obtained, each portion is obtained respectively
Institute's effect number loaded in part a cycle, determine the relation of load effect number and the function of time；
From figure 3, it can be seen that in continuously lifting torque, the lifting torque at some moment can from large to small and then again
Become suddenly big.Therefore using this point that increases sharply as the whole story position of work period, continuous data is intercepted to obtain independent
190 groups of work period.And statistical analysis is done to the work period, it is as shown in Figure 4 to obtain work period histogram.
As seen from Figure 4, the excacation cycle between 21s~57s, is concentrated mainly between 31s~45s.According to
Average asks for formula and obtains excavation cycle T (s) mean μ according to statisticsTFor：
Other statistical natures of work period are shown in Table 3.
It is little in view of the gap between statistical sample average and measurement period frequency maximum, for the follow-up side of calculating
Just, choose the most sample of cycle occurrence number (sample that i.e. cycle is 36s) and be used as periodic quantity, i.e., one excavation cycle takes
36s。
The duty cycle time statistical form of table 3
Measurement of rotating speed data statistics are as shown in Figure 5.As can be known from Fig. 5, the average value of rotation speed of excavator, absolute value and
Go the negative average value later stage essentially identical, and the respectively less than specified speed of walking around of motor；Carried when simultaneously in view of excavating in actual condition
Lotus impact is more serious to cause the lifting motor fluctuation of speed larger.To make design more safe and reliable, the present embodiment chooses motor
The input speed of motor when rated speed acts on number as assumed (specified) load.
It is as shown in table 4 in an excavation cycle internal load effect number that each gear and axle are calculated according to formula 1.
4 one, table excavates (36s) number of load in the cycle
Step 5：Consider influence of the load effect number to lifting decelerator, establishing lifting using progressive distribution theory slows down
The dynamic reliability model of device；
When normal state random load S (average μ, variance σ) is acted on w times, I type can be equivalent to by progressive distribution theory
The extreme value distribution load S ', and S ' distribution function is as shown in Equation 2.
Fe(S')=exp {-exp- [aw(S-uw)]} (2)
Average and variance are respectively
In formula
Accordingly, it is considered to when load acts on number, the power function of gear can be represented by formula 7
G (X, w)=fδ(w)-fs(w) (7)
In formula, fδ(w) it is the probability density function of intensity, fs(w) equivalent load probability density letter when being acted on w times for load
Number.
Understand that the DYNAMIC RELIABILITY index of power function can be calculated by formula 8 according to perturbation method and FOSM：
In formula, μg(w)For the average of power function, δg(w)For power function standard deviation.
R=Φ [β (w)]=P (g (X, w) ＞ 0) (9)
Formula 9 is reliability of the part when load effect number is w, represents that limited load effect number w (be on active service by design
Phase) internal load when acting on every time intensity be more than the probability of stress.
Step 6：The uncertainty quantification data obtained in step 2, step 3, step 4, effect number and the function of time are closed
Power function under system and different failure modes is brought into the dynamic reliability model established in step 5, is calculated lifting and is subtracted
Life distribution function of the fast device under different failure modes, draw its DYNAMIC RELIABILITY curve and dynamic life time component curve；
Life distribution function of the axle under static strength failure；
When calculating the static stress of axle according to table 2, input torque T chooses T=according to the breakdown torque average in step 2
22509.80Nm, it is M=28578Nm that total moment of flexure size, which is calculated, below by taking the first from left level pinion shaft as an example, with reference to
Three strength theories and table 2, solve the power function during failure of its static strength.
The yield stress limit average τ of axleδIt is taken as 0.5 σδ, the result τ according to table 1 in step 2δ308MPa is taken as, is made a variation
Coefficient is taken as 0.06.This embodiment assumes that axle institute is loaded separate between its intensity, consider that axle is quiet during load effect number
Shown in power function such as formula (11) under Strength Failure, Low confidence limit can be asked for by formula (12).
g1=τδ-τ′ (11)
In formula, τ ' expressions load repeatedly acts on lower suffered stress value, can be according to the dynamic reliability model established in step 5
Formula tries to achieve its statistical property value.
Due to the difference of connecting mode between lifting reducer output shaft and casing, output shaft is primarily subjected to Moment but simultaneously
Unique bearing object of non-moment of flexure, and such as there is not being broken at the failure in output shaft in practical work process.Therefore, the present embodiment master
Primary axis and two level axle are analyzed.According to above-mentioned analysis process and combine the dynamic reliability model established in step 5
Stress statistical property suffered by axle can be tried to achieve and yield limit statistical property is as shown in table 5.
The stress of table 5, yield limit statistical property
According to above-mentioned formula, obtain reliability of the axle under static strength failure and change with time rule, as shown in fig. 6,
Consider that the life-span distribution curve of static strength failure axle is as shown in Figure 7.
Life distribution function of the axle under fatigue strength failure；
The Fatigue Strength Statistical Characteristics of axle can be by the approximate calculation of formula 13 and 14.
In formula,
Power function under the failure of axle fatigue strength is as shown in Equation 15.
Axle fatigue strength failure under reliability, life distribution function changing rule, as shown in Figure 8,9.
As can be seen that more obvious using what initial stage, reliability declined from Fig. 6 and Fig. 8, the later stage gradually tends towards stability, this
Kind characteristic meets tub curve initial failure rule；I axles and II axle reliability change curves are contrasted, II axles reliability is substantially compared with I
Axle is low, and in the case of identical material and heat treatment mode, the low stress of II rotating speeds is big, and the maintenance record provided according to manufacturer is shown,
Apparently higher than I axles, this is consistent II axles fault rate substantially with theory analysis situation, has proved the feasible of method therefor of the present invention indirectly
Property.
One of ordinary skill in the art will be appreciated that embodiment described here is to aid in reader and understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such especially statement and embodiment.This area
Those of ordinary skill can make according to these technical inspirations disclosed by the invention various does not depart from the other each of essence of the invention
The specific deformation of kind and combination, these deform and combined still within the scope of the present invention.
Claims (5)
1. consider the lifting decelerator dynamic reliability method under a variety of uncertainties, it is characterised in that comprise the following steps：
Step 1：It is uncertain according to present in three design, use and processing links, it is by sources different that lifting is slowed down
Device carries out corresponding analysis of uncertainty, finds out main uncertain source existing for lifting decelerator；
Step 2：Uncertainty corresponding to the main uncertain source determined to step 1 quantifies, and obtains uncertain amount
Change data；
Step 3：According to multi-invalidation mode corresponding to the main uncertain source of the step S1 lifting decelerators determined, choose simultaneously
Parameter value corresponding to multi-invalidation mode is calculated, lifting decelerator is then established in each failure mode according to the parameter value being calculated
Under power function expression formula；
Step 4：The dynamic characteristic of analysis lifting decelerator, it is determined that lifting decelerator institute number and the function of time loaded of acting on
Relation；
Step 5：Consider influence of the load effect number to lifting decelerator, utilize progressive distribution theory to establish lifting decelerator
Dynamic reliability model；
Step 6：Power function under each failure mode that uncertain quantized data that step 2 is obtained, step 3 obtain,
The effect number obtained in step 4 is brought into the dynamic reliability model established in step 5 with time function relation, is counted
Calculate life distribution function of the lifting decelerator under different failure modes.
2. the lifting decelerator dynamic reliability method according to claim 1 considered under a variety of uncertainties, its feature
It is, the uncertainty includes：Principal and subordinate's motor output synchronism, lifting decelerator in gears at different levels parameter uncertainty,
Lift the parameter uncertainty of decelerator axis, lift parameter uncertainty, the principal and subordinate's motor input torque of decelerator middle case
Parameter uncertainty and extraneous load are uncertain.
3. the lifting decelerator dynamic reliability method according to claim 1 considered under a variety of uncertainties, its feature
It is, main uncertain source existing for the lifting decelerator is axle.
4. the lifting decelerator dynamic reliability method according to claim 1 considered under a variety of uncertainties, its feature
It is, the mode that the uncertainty quantification method in the step 2 is taken based on probability is measured.
5. the lifting decelerator dynamic reliability method according to claim 1 considered under a variety of uncertainties, its feature
It is, step 4 specifically includes：
Step 41：Force analysis is carried out to lifting decelerator, finds out its maximum weighted position, is calculated using the position as dangerous spot
Load acts on the influence of number；
Step 42：Statistics, drawing cycle histogram, and work period average value is obtained, each part one is obtained respectively
Institute's effect number loaded in the individual cycle, determine the relation of load effect number and the function of time.
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