CN105890884B - A kind of analysis of main shaft of hoister reliability calculates appraisal procedure - Google Patents
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Abstract
A kind of analysis the invention discloses main shaft of hoister reliability calculates appraisal procedure, includes the following steps：Strain parameter in S1, detection lifting process of elevator；S2, the cycling principal stress suffered by reel disc is obtained as strain parameter and cycles shear stress；S3, the making a concerted effort of force analysis node, analysis reel disc acts on the torque of two load points of main shaft of hoister together and motor acts on the torque of main shaft of hoister；The main shaft bending moment diagram and torque diagram of S4, the owner's axis that gets a promotion, with the strength formula of dangerouse cross-sectionFoundation of the distortion energy concentration criterion as main shaft reliability design, and carry out Calculation of Reliability assessment.The present invention main shaft of hoister reliability analysis calculate appraisal procedure, using perturbation method carry out reliability design, not only in view of load uncertainty but also easily acquire reliability index, the fail-safe analysis for making main shaft of hoister is more with practical value.
Description
Technical field
The present invention relates to main shaft of hoister reliability prediction technical fields, and it is reliable to relate in particular to a kind of main shaft of hoister
Property analysis calculate appraisal procedure.
Background technology
With manufacturing accelerated development, the demand of various raw material and the energy is increasing, frictional mine hoist
Being undertaken for task also increasingly aggravates, therefore the reliability of elevator receives much attention.In practical work process, km deep-well carries
The lifting device of the machine of liter often works long hours, the main devices such as the dead weight by itself and main shaft coiling of main shaft of hoister
Gravity is applied to the steel wire rope tension of main shaft by reel and motor is applied to the torque of main shaft, so main shaft is rotating through
Fatigue failure is also easy to produce in journey, it is therefore necessary to analysis is carried out to the reliability of main shaft of hoister and calculates assessment.
To determine the force-bearing situation of parts on main shaft and carrying out reliability design, there has been proposed many methods.At present,
In terms of the fail-safe analysis of main shaft of hoister calculates assessment, mainly there are method of safety coefficients, fuzzy Reliability Model method etc..With
Traditional method of safety coefficients carries out reliability design, it is impossible to preferably consider that the strength of materials has discreteness；What Jin Minjie was established
The Fuzzy reliability design model of main shaft of hoister fatigue strength calculates more complicated.
The content of the invention
The purpose of the present invention is in view of the above-mentioned defects in the prior art, provide a kind of analysis meter of main shaft of hoister reliability
Calculate appraisal procedure, using perturbation method carry out reliability design, not only in view of load uncertainty but also easily acquire reliability index,
The fail-safe analysis for making main shaft of hoister is more with practical value.It uses and is interference fitted in view of reel disc and the main shaft shaft shoulder,
In a lifting process main shaft and reel be synchronized with the movement and the two suffered by the maximum stress moment it is identical, by disc loading process
And the loading process of corresponding mathematical model characterization main shaft, it determines therefrom that the danger position in main shaft rotary course and carries out reliable
Property design, the method not only avoided error of the load through wire rope transfers to main shaft but also more actually characterized the stress feelings of main shaft
Condition.
To achieve these goals, the technical scheme is that：
A kind of analysis of main shaft of hoister reliability calculates appraisal procedure, includes the following steps：
In static, acceleration and the strain parameter of decelerating phase reel disc in S1, detection lifting process of elevator；
A1, the reel disc based on elevator and the main shaft shaft shoulder use interference fit, in lifting process of elevator
Main shaft of hoister and reel be synchronized with the movement and the two suffered by the maximum stress moment it is identical, by reel disc loading process and corresponding
Mathematical model characterization main shaft of hoister loading process；
A2, using perturbation method, by strain detecting get a promotion in lifting process of machine it is static, accelerate and deceleration rank
The strain parameter ε of section reel disc0°、ε90°、ε45；
S2, the strain parameter as reel disc obtain the cycling principal stress σ suffered by reel discy、σzWith Xun Huan shear stress
τyz；Main shaft of hoister is transferred force to by the steel wire rope being wrapped on reel in view of loading, it may be determined that main shaft of hoister
Stress be：
S3, supporting function point, the reel disc that bearing acts on to main shaft of hoister act on the load of main shaft of hoister
The G that makes a concerted effort of each part in main shaft of hoister and main shaft gravity itself is decomposed and carried as stress node by action point
The reel disc of analyzing with joint efforts, together for rising on each stress node of owner's axis and analyzing these stress nodes acts on promotion owner
The torque of two load points of axis and motor act on the torque of main shaft of hoister；
The main shaft bending moment diagram and torque diagram of S4, the owner's axis that gets a promotion, elevator is determined by main shaft bending moment diagram and torque diagram
The dangerouse cross-section of main shaft, with the strength formula of dangerouse cross-sectionDistortion energy concentration criterion is as main shaft reliability
The foundation of design, obtains：
In formula：E --- the elasticity modulus of reel disc material；G --- the modulus of shearing of reel disc material；μ --- volume
The Poisson's ratio of cylinder disc material；
S5, Calculation of Reliability assessment：
B1, the target reliability degree R that main shaft of hoister is calculated according to following formula：
R=∫G (X) ＞ 0fX(X)dX
In formula：fX(X) --- essentially random parameter vector X=(X1, X2..., Xn)TJoint probability density, g (X) ---
Function of state represents the two states of parts,
B2, the target reliabilities index β that main shaft of hoister is calculated according to following formula：
In formula：μg, E [g (X)] --- the average of function of state g (X)；σg, Var [g (X)] --- the institute of function of state g (X)
There is variance and covariance；
B3, the result of calculation from target reliability degree R and reliability index β draw the reliability of main shaft of hoister；
B4, according to stress-strength interference theory, the main shaft of hoister state equation represented with limiting range of stress state：
In formula r be main shaft of hoister the strength of materials, basic random variables vector X=(r ε0°ε90°ε45°E G μ)T, these
Average E (X)=(μ of basic random variables vector Xrμε0°με90°με45°μEμGμμ)T；Variance and covariance
And it is the mutual independent stochastic variable of Normal Distribution to think these stochastic variables；
As the improvement to above-mentioned technical proposal, during perturbation method strain detecting, strain gauge adhesion step and strain
Signal acquisition method is tested referring to reel disc strain detecting in frictional mine hoist key rotary body Research on Dynamic Characteristic
In strain gauge adhesion step and strain signal acquisition method.The China delivered in June, 2014 in this method visible Wang Chong autumns
Mining industry University Ph.D. Dissertation.
As the improvement to above-mentioned technical proposal, the dangerouse cross-section is that the reel disc of close motor side acts on promotion
Section residing for the load point of owner's axis.
As the improvement to above-mentioned technical proposal, according to impact theory of control, the acceleration of promotion and decelerating phase are using ladder
Shape acceleration method controls.
Compared with prior art, the advantageous effect acquired by the present invention is：
The analysis of the main shaft of hoister reliability of the present invention calculates appraisal procedure, and reliability design is carried out using perturbation method,
Not only the uncertainty of load had been considered but also had easily acquired reliability index, the fail-safe analysis of main shaft of hoister is made to have more practical valency
Value.In view of reel disc and the main shaft shaft shoulder using being interference fitted, in a lifting process main shaft be synchronized with the movement with reel and
The maximum stress moment is identical suffered by the two, and the loading process of main shaft is characterized by disc loading process and corresponding mathematical model,
It determines therefrom that the danger position in main shaft rotary course and carries out reliability design, the method had both avoided load and passed through steel wire rope
It is delivered to the error of main shaft and more actually characterizes the stressing conditions of main shaft.
Description of the drawings
It in order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention, for those of ordinary skill in the art, without having to pay creative labor, may be used also
To obtain other attached drawings according to these attached drawings.
Fig. 1 is the graph of relation that No. 1 foil gauge (0 ° of direction) strain changes over time in a lifting process；
Fig. 2 is the graph of relation that No. 2 foil gauge (90 ° of directions) strains change over time in a lifting process；
Fig. 3 is the graph of relation that No. 3 foil gauge (45 ° of directions) strains change over time in a lifting process；
Fig. 4 is the three-dimensional strain of detection, stress state analysis result figure；
Fig. 5 is main shaft of hoister structure and force analysis figure；
Fig. 6 analyzes schematic diagram for main shaft of hoister Force Calculation；
Fig. 7 is main shaft of hoister Bending Moment Analysis schematic diagram；
Fig. 8 is main shaft of hoister torsional analysis schematic diagram；
Fig. 9 is the graph of relation that main shaft of hoister stress changes over time in a lifting process；
Figure 10 is the graph of relation that main shaft of hoister rotational angle changes over time in a lifting process.
Specific embodiment
Below in conjunction with the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other without making creative work
Embodiment, any modifications, equivalent replacements and improvements are made should all be included in the protection scope of the present invention.
The analysis of the main shaft of hoister reliability of the present invention calculates appraisal procedure, includes the following steps：
The simulation of 1 disc strain detecting result
The stressing conditions of reel disc in a lifting process, specific strain gauge adhesion step are obtained by strain detecting first
Rapid and strain signal acquisition method is tested referring to reel disc strain detecting.According to theory of control is impacted, added using trapezoidal
The acceleration and deceleration process of speed control elevator can reduce tension amplitude and the elastic vibration of steel wire rope so as to reach steady promotion
Effect, therefore use trapezoidal acceleration control promoted acceleration and the decelerating phase.The strain stress of No. 1, No. 2, No. 3 foil gauge0°、
ε90°、ε45°Corresponding testing result as shown in Figure 1, Figure 2, Figure 3 shows, be illustrated respectively in a lifting process three directions strains with
The relation curve of time change.0-1s is the elevator stationary state before experiment starts in Fig. 1, Fig. 2, Fig. 3, and each foil gauge is not examined
Measure data；1-67s represents boost phase, constant velocity stage and each strain measurement knot in decelerating phase once to promote the cycle
Fruit.
2 main shaft reliability designs
2.1 principal stress are analyzed
As shown in figure 4, the three-dimensional strain stress to detection0°、ε45°、ε90°After being analyzed, frictional mine hoist volume is obtained
Suffered by cylinder disc be two differ in size, the mutually perpendicular asymmetric cycle principal stress σ in directiony、σzAnd two size phases
Deng the mutually perpendicular asymmetric cycle shear stress τ in, directionyz.Power is passed by the steel wire rope being wrapped on reel in view of loading
Main shaft of hoister is delivered to, so reel disc stress can characterize the size for promoting load, therefore can be by disc
Stress analyzes the stress of main shaft.
The stress on reel disc is synthesized according to above formula and is perpendicularly oriented in the direct stress σ and same plane of main-shaft axis
The shearing stress τ vertical with direct stress σ, to carry out force analysis to main shaft.
In formula：Every meter of quality of q --- main shaft (kg/m), g --- acceleration of gravity (m/s2)
P1-4--- it is assigned to the partical gravity (kN) of each stress node
L1-5--- by the length (m) of every section of main shaft after stress node allocation
Fig. 5 show main shaft of hoister structure and force diagram, the gravity G of each part and main shaft on main shaft in itself
Belong to the load being applied on main shaft, therefore force analysis and definite dangerouse cross-section are carried out to main shaft for convenience, gravity G is pressed
Formula (2) is assigned on each stress node of main shaft.
Fig. 6 show the F of main shaft calculation diagram, wherein A, D section1、F4For the holding power that bearing provides and P in formula (2)1、
P4Make a concerted effort, direction is along positive direction of the y-axis；B, the F in C sections2、F3For the pressure that reel disc provides and P in formula (2)2、P3Conjunction
Power, direction is along negative direction of the y-axis, and there be the torque T in the same direction greatly such as two that reel disc provides in B, C section1、T2(along X-axis
Negative direction is viewed as clockwise)；E sections are the torque T that motor provides3(being viewed as counterclockwise along X-axis negative direction).With reference to figure
Main shaft stressing conditions shown in 6 obtain main shaft bending moment diagram as shown in Figure 7 and main-shaft torque figure as shown in Figure 8, and determine
The dangerouse cross-section of main shaft of hoister is C sections, i.e., the section that the reel disc close to motor one side is interference fitted with main shaft.
Spindle material uses 45Mn, since main shaft is primarily subjected to bend and reverses, therefore can concentration criterion work with above formula distortion
For the foundation of main shaft reliability design.
In formula：E --- the elasticity modulus of reel disc material
G --- the modulus of shearing of reel disc material
μ --- the Poisson's ratio of reel disc material
With the disc strain stress of detection0°、ε45°、ε90°ExpressionIn stress σ, τ can obtain formula (4) with
And the relation curve that main shaft of hoister stress changes over time in a lifting process as shown in Figure 9, and with reference to shown in Figure 10
The relation curve that changes over time of main axis angle, obtain the maximum stress moment suffered by reel disc as 57.9s, this moment
Spindle rotation angle degree is 86 ° (horizontal level shown in Fig. 4 is 0 °, is clockwise positive direction), carries out reliability design accordingly below.
2.2 reliability design
Reliability design is carried out using perturbation method herein, the target of one side reliability design is can according to formula (5) calculating
By spending R, on the other hand formula (6) can be used to calculate reliability index β, so as to directly weigh the reliability of parts.
R=∫G (X) ＞ 0fX(X)dX (5)
In formula：fX(X) --- essentially random parameter vector X=(X1, X2..., Xn)TJoint probability density；g(X)——
Function of state represents the two states of parts,
In formula：μg, E [g (X)] --- the average of function of state g (X)；σg, Var [g (X)] --- the institute of function of state g (X)
There is variance and covariance
According to stress-strength interference theory, main shaft of hoister state equation such as formula (7) institute represented with limiting range of stress state
Show
In formula r be main shaft the strength of materials, basic random variables vector X=(r ε0°ε90°ε45°E Gμ)T, these substantially with
Average E (X)=(μ of machine variable vector Xrμε0°με90°με45°μEμGμμ)T；Variance and covariance
And it is the mutual independent stochastic variable of Normal Distribution to think these stochastic variables.
In formula：[·][2]--- Kronecker powers
According to the needs of engineering reality and mathematical derivation it is numerous easily, generally as shown in formula (8) and formula (9), take function of state g
(X) Two-order approximation average and first approximation variance, therefore function of state g (X) is sought local derviation to basic random variables vector X
Number.And function of state is obtained in the known conditions substitution formula (8) shown in obtained partial derivative result and formula (10) and formula (9)
Then average and variance substitute into the expression formula (5) of reliability index β and the expression formula (6) of reliability R, determine that out main shaft again
Reliability index β=2.5189, reliability R=0.9941.
2.3 sensitivity analysis
When carrying out Design of Reliability Analysis to engineering goods, in order to understand the influence journey that each factor fails to engineering goods
Degree, will study Mechanical Product Reliability sensitivity on the basis of reliability design, to evaluate each design parameter pair
The influence degree of engineering goods failure.
With reliability to the average of basic random variables, the partial derivative of variance represents sensitivity.If value is just, the ginseng is represented
The increase of numerical value can improve the reliability of engineering goods；Conversely, then reduce.
Reliability is to random parameter vector X averages, the sensitivity expression formula of variance
In formula：
Wherein：--- the density function of Standard Normal Distribution；--- Kronecker is accumulated.
According to the reliability index and reliability of the main shaft of hoister drawn above, calculate in relation to main shaft reliability 7
The sensitivity of parameter is as follows：
From above sensitivity data, spindle material intensity r and disc strain stress45°Increase can improve main shaft
Reliability；Disc strain stress0°、ε90°, the elastic modulus E of reel disc material, the shear modulus G of reel disc material, reel spoke
The increase of the Poisson's ratio μ of plate material reduces the reliability of main shaft.The strain stress in wherein three directions0°、ε45°、ε90°To reliability
It influences maximum；Poisson's ratio μ, the spindle material intensity r of reel disc material take second place；Shear modulus G, the elasticity of reel disc material
Modulus E is minimum to reliability effect.
In addition, the increase of stochastic variable parameter variance all can reduce main shaft reliability, stochastic variable parametric covariance
Change the influence to main shaft reliability to be not quite similar.
Force analysis is carried out herein by main shaft of hoister, has obtained main shaft dangerouse cross-section as reel disc and main shaft mistake
It is full of the section of cooperation, should focuses on to strengthen this dangerouse cross-section when designing main shaft.To main shaft dangerouse cross-section in a lifting process point
Analysis, the stress that the acceleration obtained in promotion of slowing down increases suffered by the conversion stage main shaft between acceleration reduction is maximum, answers
To this, the stage carries out appropriate regulation, to reduce failure probability.In addition, the strain stress in three directions of sensitivity analysis the results show0°、
ε45°、ε90°Sensitivity is big；Spindle material intensity r and reel disc material Poisson's ratio μ take second place；The modulus of shearing of reel disc material
G and elastic modulus E are minimum to main shaft reliability effect, should be weighed in product maintenance, design.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and replacement can also be made, these improve and replace
Also it should be regarded as protection scope of the present invention.
Claims (3)
1. a kind of analysis of main shaft of hoister reliability calculates appraisal procedure, which is characterized in that includes the following steps：
In static, acceleration and the strain parameter of decelerating phase reel disc in S1, detection lifting process of elevator；
A1, the reel disc based on elevator and the main shaft shaft shoulder use interference fit, are promoted in lifting process of elevator
Owner's axis and reel be synchronized with the movement and the two suffered by the maximum stress moment it is identical, by reel disc loading process and corresponding number
Learn the loading process of model characterization main shaft of hoister；
A2, using perturbation method, by strain detecting get a promotion in lifting process of machine it is static, accelerate and the decelerating phase rolls up
The strain parameter ε of cylinder disc0°、ε90°、ε45°；
S2, the strain parameter as reel disc obtain the cycling principal stress σ suffered by reel discy、σzWith Xun Huan shear stress τyz；It examines
Consider load and main shaft of hoister is transferred force to by the steel wire rope being wrapped on reel, it may be determined that the stress of main shaft of hoister
For：
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S3, supporting function point, the reel disc that bearing acts on to main shaft of hoister act on the load effect of main shaft of hoister
The G that makes a concerted effort of each part in main shaft of hoister and main shaft gravity itself is decomposed elevator by point as stress node
On each stress node of main shaft and analyze these stress nodes make a concerted effort, together analysis reel disc act on main shaft of hoister
The torque of two load points and motor act on the torque of main shaft of hoister；
The main shaft bending moment diagram and torque diagram of S4, the owner's axis that gets a promotion, main shaft of hoister is determined by main shaft bending moment diagram and torque diagram
Dangerouse cross-section, with the strength formula of dangerouse cross-sectionDistortion energy concentration criterion is as main shaft reliability design
Foundation, obtain：
In formula：E --- the elasticity modulus of reel disc material；G --- the modulus of shearing of reel disc material；μ --- reel spoke
The Poisson's ratio of plate material；
S5, Calculation of Reliability assessment：
B1, the target reliability degree R that main shaft of hoister is calculated according to following formula：
R=∫G (X) ＞ 0fX(X)dX
In formula：fX(X) --- essentially random parameter vector X=(X1, X2..., Xn)TJoint probability density, g (X) --- state
Function represents the two states of parts,
B2, the target reliabilities index β that main shaft of hoister is calculated according to following formula：
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In formula：μg, E [g (X)] --- the average of function of state g (X)；σg, Var [g (X)] --- all sides of function of state g (X)
Difference and covariance；
B3, the result of calculation from target reliability degree R and reliability index β draw the reliability of main shaft of hoister；
B4, according to stress-strength interference theory, the main shaft of hoister state equation represented with limiting range of stress state：
In formula r be main shaft of hoister the strength of materials, basic random variables vector X=(r, ε0°, ε90°, ε45°, E, G, μ)T, these
Average E (X)=(μ of basic random variables vector Xrμε0°με90°με45°μEμGμμ)T；Variance and covariance And it is the mutual independent stochastic variable of Normal Distribution to think these stochastic variables；
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2. the analysis of main shaft of hoister reliability calculates appraisal procedure according to claim 1, which is characterized in that the danger
Section is that the reel disc of close motor side acts on the section residing for the load point of main shaft of hoister.
3. the analysis of main shaft of hoister reliability calculates appraisal procedure according to claim 1, which is characterized in that according to impact
Theory of control, the acceleration of promotion and decelerating phase are controlled using trapezoidal acceleration method.
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| CN107291989B (en) * | 2017-05-25 | 2018-09-14 | 中国矿业大学 | Km deep-well main shaft of hoister multi-invalidation mode reliability estimation method |
| CN108052730B (en) * | 2017-12-11 | 2021-05-04 | 电子科技大学 | Reliability evaluation method for reduction gearbox of lifting mechanism of large mining excavator |
| CN108083047B (en) * | 2017-12-15 | 2019-05-07 | 中国矿业大学 | A kind of lifting system load identification method based on guide wheel shaft strain |
| CN109977550B (en) * | 2019-03-27 | 2023-07-18 | 湖北汽车工业学院 | Importance sampling method for shaft reliability design |
| CN110378000B (en) * | 2019-07-11 | 2020-11-24 | 上海理工大学 | Structural static strength design method based on strength field |
| CN112966225B (en) * | 2021-03-22 | 2023-03-31 | 南昌航空大学 | Steel wire rope safety life assessment method based on normal distribution |
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