CN108345762B - Fatigue life prediction method for large-modulus gear rack - Google Patents

Fatigue life prediction method for large-modulus gear rack Download PDF

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CN108345762B
CN108345762B CN201810227408.0A CN201810227408A CN108345762B CN 108345762 B CN108345762 B CN 108345762B CN 201810227408 A CN201810227408 A CN 201810227408A CN 108345762 B CN108345762 B CN 108345762B
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gear
rack
fatigue life
fatigue
life
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冯定
何良
施雷
亢博文
陈新龙
彭太峰
李光金
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Yangtze University
Sinopec Oilfield Equipment Corp
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Sinopec Oilfield Equipment Corp
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    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract

The invention relates to a fatigue life prediction method for a large-modulus gear rack of a gear rack drilling machine; belongs to the technical field of detecting the fatigue life of a gear and a rack. The method comprises the steps of establishing a gear rack finite element model by utilizing drilling machine data for a large-modulus gear rack, establishing a fatigue life prediction model according to a selected material definition S-N curve, setting load appearing on a gear according to a designed drilling machine service area, obtaining the life change condition of the gear through finite element fatigue life analysis, and predicting the fatigue life of the large-modulus gear based on a linear fatigue accumulation damage theory in combination with the cycle times appearing in different hooking loads. The method can quickly and effectively predict the fatigue life of the gear, does not need a test mechanism, and is simpler and more effective in a design stage; a new way is provided for early design and service life verification of the large-modulus gear rack, and meanwhile, a guidance basis is provided for safe operation of the gear in the later period.

Description

Fatigue life prediction method for large-modulus gear rack
Technical Field
The invention relates to a fatigue life prediction method for a large-modulus gear rack of a gear rack drilling machine; belongs to the technical field of detecting the fatigue life of a gear and a rack.
Background
With the wide application of large-module gear racks in gear rack drilling machines and large-scale heavy-duty mechanical equipment, in the face of requirements on normal operation of the equipment, reasonable arrangement of maintenance plans, safety guarantee of personnel and the like, more and more attention is paid to how to predict the reliability and the service life of the racks. In the process of gear and rack transmission, fatigue damage can be generated on a gear and a rack, and the fatigue damage accumulation of the gear has influence on the fatigue life of the gear, so that the fatigue life calculation and prediction of the gear are required, and a basis is provided for preventive maintenance of the gear.
At present, much research is made on the structure of a gear rack at home and abroad, the bending strength of the gear rack is mostly analyzed and checked, the fatigue life research of the large-modulus gear rack in meshing transmission is less, so that the fatigue life of a transmission gear is researched by a method based on virtual simulation and theoretical calculation aiming at the current situation that the fatigue life research of the large-modulus gear rack is relatively weak, a new way is provided for early design and life verification of the large-modulus gear rack according to relevant conclusions, a guide basis is provided for later-stage safe operation of the gear, and reference can be provided for fatigue life research of other mechanical large-modulus gears.
Disclosure of Invention
The invention aims to: the large-modulus gear and rack fatigue life prediction method for the gear and rack drilling machine is used for carrying out combined research through finite element fatigue life analysis and a linear fatigue accumulated damage theory, can be used for rapidly and effectively predicting the fatigue life of a gear, and provides a guidance basis for safe operation in the later period of the gear.
The technical scheme of the invention is as follows:
a large-modulus gear and rack fatigue life prediction method for a gear and rack drilling machine is characterized by comprising the following steps: it comprises the following steps:
1) establishing a model according to the structure of the gear and the rack;
2) establishing a fatigue life analysis model in a finite element according to fatigue life curves S-N of different materials of the gear and the rack;
3) finite element analysis of a gear rack;
in the process of gear and rack transmission, the load on the gear and rack is constantly changed, and the minimum cycle times of the gear under different loads are analyzed through finite elements;
4) determining the load frequency of the gear rack in one drilling period:
carrying out preliminary calculation, and determining the possible load frequency of the rack and pinion in one drilling period by referring to the possible service area of the rack and pinion drilling machine;
5) determining the load frequency of the gear rack after working for a period of time:
the method comprises the steps that a rack and pinion drilling machine is assumed to conduct multiple times of drilling in different areas in a certain working period, and the frequency of loads of racks and pinions occurring in the certain working period (multiple drilling periods) is counted according to possible working environments;
6) and calculating the linear accumulated fatigue damage of the gear by adopting Miner theory according to the following formula:
Figure 338104DEST_PATH_IMAGE001
in the formula (I), the compound is shown in the specification,
Figure 934170DEST_PATH_IMAGE002
linear cumulative fatigue damage;
Figure 283987DEST_PATH_IMAGE003
the frequency of the gears after a period of operation under different loads;
Figure 651514DEST_PATH_IMAGE004
minimum cycle times for gears under different loads;
Figure 752194DEST_PATH_IMAGE005
stress level loaded on the gear;
7) and judging fatigue damage:
if the loading history of the component is changed
Figure 761739DEST_PATH_IMAGE006
，
Figure 733106DEST_PATH_IMAGE007
，……，
Figure 802693DEST_PATH_IMAGE008
Etc. of
Figure 859511DEST_PATH_IMAGE009
Are formed by different stress levels, each stress level having a life of
Figure 672746DEST_PATH_IMAGE010
，
Figure 84DEST_PATH_IMAGE011
，……，
Figure 240573DEST_PATH_IMAGE012
The number of cycles at each stress level is
Figure 784687DEST_PATH_IMAGE013
，
Figure 136034DEST_PATH_IMAGE014
，……，
Figure 222938DEST_PATH_IMAGE015
Then, it can be found that:
Figure 758962DEST_PATH_IMAGE016
when the damage is equal to 1, the component is destroyed, i.e.
Figure 931317DEST_PATH_IMAGE017
When the cumulative damage is less than 1, the component is deemed to meet the safety requirements of the limited life design, i.e.
Figure 210989DEST_PATH_IMAGE018
The invention has the beneficial effects that:
the fatigue life prediction method for the large-modulus gear and rack of the gear and rack drilling machine is used for establishing a fatigue life prediction model aiming at the meshing process of the large-modulus gear and rack, establishing a gear and rack finite element model by utilizing data of the drilling machine, defining an S-N curve according to selected materials, setting load appearing on a gear according to a designed drilling machine service area, analyzing the life change condition of the gear through finite element fatigue life, combining cycle times appearing in different hooking loads, and predicting the fatigue life of the large-modulus gear based on a linear fatigue accumulation damage theory. The method utilizes a finite element fatigue analysis method and a linear fatigue accumulated damage theory to quickly and effectively predict the fatigue life of the gear without a test mechanism, and is simpler and more effective in a design stage; a new way is provided for early design and service life verification of the large-modulus gear rack, and meanwhile, a guidance basis is provided for safe operation of the gear in the later period.
Drawings
FIG. 1 is a flow chart of a method for predicting fatigue life of a large-modulus gear according to an embodiment of the invention;
FIG. 2 is a graph of the maximum stress variation of gears under different hook loads in an embodiment of the present invention.
Detailed Description
The method for predicting the fatigue life of the large-modulus gear rack for the gear rack drilling machine comprises the following steps of:
structural modeling:
the large-modulus gear rack is applied to a gear rack drilling machine, the derrick of the drilling machine is fixed on a base part, the deformation of the upper part of the derrick is larger relative to other positions, a group of gear racks on the upper part of a gear box is selected from a plurality of groups of gears at a time for analysis, the gear modulus is 25mm, the tooth number is 12, the reference circle diameter is 300mm, a finite element contact model is established through SolidWorks and ANSYS, and the contact part is subjected to refining treatment to divide grids.
Establishing a finite element fatigue life analysis model;
according to different materials adopted by the gear rack, the S-N curves of the different materials are inquired in the national standard, and the S-N curves under the condition of 99% survival rate are adopted, the fatigue life S-N curve of the gear rack is defined in the finite element analysis model, and the finite element fatigue life analysis model is established;
analyzing the minimum cycle times of the gear rack under different loads by using a finite element;
the gear rack is used as a transmission mechanism of the drilling machine, the load borne by the gear rack is always in a state of changing constantly, therefore, the load borne by the gear teeth is divided into different amplitude ranges, the average value of each group of amplitude is taken, the condition of the minimum cycle times of the gear teeth under different loads is analyzed through finite elements (see table 1),
TABLE 1 situation of minimum number of gear cycles for different hook loads
Figure 152400DEST_PATH_IMAGE019
As can be seen from Table 1, the change rule of the minimum cycle number of the gear teeth is basically consistent with the S-N curve of the gear.
According to the maximum stress change rule of the gear under different hooking conditions, when the load is 2500kN at most, the maximum stress of the gear is 465.6MPa at most and is smaller than the yield strength of the gear 835MPa, and the material of the gear cannot be damaged, so that the contact fatigue life of the gear can be analyzed according to the contact stress of the gear and the fatigue damage theory, and the minimum cycle number of the gear teeth occurs at the position where the maximum stress occurs in the gear teeth (see figure 2).
According to the minimum fatigue life change condition of the gear under different loads shown in table 1, when the load is less than 875kN, the fatigue life of the gear is 3.81e +6 times, and the gear is considered to be in the infinite fatigue life condition at the moment; when the load is larger than 875kN, the gear is in a limited fatigue life stage, the fatigue life of the gear is reduced along with the increase of the load, the fatigue life of the gear is only 802 times when the load is 2500kN, under the load, the gear can be subjected to premature fatigue failure, and the situation is avoided as much as possible during the drilling process of a drilling machine.
Setting a loading frequency;
predicting the fatigue life of the gear provides a reference basis for the design of the gear and the rack, and performing pre-calculation, so that specific numerical values of the frequency of loads borne by the gear in one drilling period of the drilling machine are shown in a table 2 by referring to the working condition of a JJ 160/41-K type well frame in a Daqing oil field aiming at the service area of the designed gear and rack drilling machine;
TABLE 2 frequency of gear loads during drilling cycle
Figure 734691DEST_PATH_IMAGE020
Determining the number of cycles of the drilling rig under different loads over a period of time;
determining the loading frequency of the drilling machine on the gear within the working time of one year (multiple drilling cycles) according to the possible loading frequency of the gear within one drilling cycle (shown in a table 3);
TABLE 3 minimum cycle times and load frequency of the internal gear teeth in one year of working time
Figure 751932DEST_PATH_IMAGE021
Predicting fatigue life of large-modulus gear rack
The fatigue life of the gear and the rack is calculated by adopting a nominal stress method, and in the working process of the gear and the rack, the deformation of the gear and the rack is small and is in a linear elasticity range, and the fatigue life of the gear teeth is feasible to be researched by adopting the nominal stress method. In the drilling process of a rack and pinion drilling machine, the external load acting on a rack and pinion of a hoisting mechanism is constantly changed, so that the fatigue life of a component cannot be obtained through a material S-N curve, at the moment, the fatigue life must be researched by combining a linear fatigue accumulation damage theory, namely a Miner theory, and a P-M theory adopts the following basic hypothesis:
(1) the damage is linear with the number of cycles.
(2) During stress cycling, the energy absorbed per unit volume of component material reaches a certain limit resulting in fatigue failure.
(3) The fatigue damage may be linearly superimposed.
(4) The loading sequence is independent of material damage and life
According to the Miner theory adopted, the linear accumulated fatigue damage of the gear is calculated by the following formula
Figure 710661DEST_PATH_IMAGE022
In the formula (I), the compound is shown in the specification,
Figure 631212DEST_PATH_IMAGE002
linear cumulative fatigue damage;
Figure 384405DEST_PATH_IMAGE003
the frequency of the gears after a period of operation under different loads;
Figure 265773DEST_PATH_IMAGE004
minimum cycle times for gears under different loads;
Figure 887247DEST_PATH_IMAGE005
stress level loaded on the gear;
the linear fatigue cumulative damage theory employed uses the following basic assumptions:
(1) the damage is linear with the number of cycles.
(2) During stress cycling, the energy absorbed per unit volume of component material reaches a certain limit resulting in fatigue failure.
(3) The fatigue damage may be linearly superimposed.
If the loading history of the component is changed
Figure 803251DEST_PATH_IMAGE006
，
Figure 851978DEST_PATH_IMAGE007
，……，
Figure 955063DEST_PATH_IMAGE008
Etc. of
Figure 616114DEST_PATH_IMAGE009
Are formed by different stress levels, each stress level having a life of
Figure 652203DEST_PATH_IMAGE010
，
Figure 747198DEST_PATH_IMAGE011
，……，
Figure 462213DEST_PATH_IMAGE012
The number of cycles at each stress level is
Figure 300856DEST_PATH_IMAGE013
，
Figure 316086DEST_PATH_IMAGE014
，……，
Figure 581982DEST_PATH_IMAGE015
Then, it can be found that:
Figure 784293DEST_PATH_IMAGE023
when the damage is equal to 1, the component is destroyed, i.e.
Figure 426627DEST_PATH_IMAGE024
(4) The loading sequence is independent of material damage and life
On the basis of the above assumptions, the cumulative damage of the component is calculated, and when the cumulative damage is less than 1, the component is considered to meet the safety requirements of the limited life design, i.e. it is considered to meet the safety requirements of the limited life design
Figure 906150DEST_PATH_IMAGE025
Therefore, the fatigue life prediction of the large-module gear rack is completed.
The fatigue life prediction model is established according to the structural parameters and the working environment of the large-modulus gear rack. Meanwhile, in the process of gear rack transmission, the external load acting on the gear rack is constantly changed, and the fatigue life of a component cannot be obtained through a material S-N curve, so that research must be carried out by combining a linear fatigue accumulation damage theory. The fatigue life of the gear is predicted according to the calculation result, a new way can be provided for early design and life verification of the large-modulus gear rack, and meanwhile, a guidance basis is provided for safe operation of the gear in the later period.
The method comprises the steps of establishing a fatigue life prediction model aiming at a large-modulus gear and rack meshing process, establishing a gear and rack finite element model by utilizing drilling machine data, defining an S-N curve according to selected materials, setting load appearing on a gear according to a designed drilling machine service area, obtaining the service life change condition of the gear through finite element fatigue life analysis, combining cycle times appearing in different hook loads, and predicting the fatigue life of the large-modulus gear based on a linear fatigue accumulation damage theory; the method can provide a new way for early design and service life verification of the large-modulus gear rack, and simultaneously provides a guidance basis for later safe operation of the gear.

Claims (1)

1. A fatigue life prediction method for a large-modulus gear rack is characterized by comprising the following steps: it comprises the following steps:
1) establishing a model according to the structure of the gear and the rack;
2) establishing a fatigue life analysis model in a finite element according to fatigue life curves S-N of different materials of the gear and the rack;
3) finite element analysis of a gear rack;
in the process of gear and rack transmission, the load on the gear and rack is constantly changed, and the minimum cycle times of the gear under different loads are analyzed through finite elements;
4) determining the load frequency of the gear rack in one drilling period:
carrying out preliminary calculation, and determining the possible load frequency of the rack and pinion in one drilling period by referring to the possible service area of the rack and pinion drilling machine;
5) determining the load frequency of the gear rack after working for a period of time:
counting the load frequency of the gear rack in a period of working time according to the possible working environment within the period of working time of the gear rack drilling machine;
6) calculating the linear accumulated fatigue damage of the gear by adopting Miner theory according to the following formula
Figure DEST_PATH_IMAGE001
In the formula (I), the compound is shown in the specification,Dlinear cumulative fatigue damage;
Figure DEST_PATH_IMAGE003
representing the frequency of occurrence of the gear after a period of operation under different loads;
Figure DEST_PATH_IMAGE005
representing the minimum cycle times of the gear under different loads;
r represents the number of stress levels loaded on the gear;
7) and judging fatigue damage:
if the loading history of the component is changed
Figure DEST_PATH_IMAGE006
，
Figure DEST_PATH_IMAGE007
，……，
Figure DEST_PATH_IMAGE008
Etc. of
Figure DEST_PATH_IMAGE009
Are formed by different stress levels, each stress level having a life of
Figure DEST_PATH_IMAGE010
，
Figure DEST_PATH_IMAGE011
，……，
Figure DEST_PATH_IMAGE012
The number of cycles at each stress level is
Figure DEST_PATH_IMAGE013
，
Figure DEST_PATH_IMAGE014
，……，
Figure DEST_PATH_IMAGE015
Then, it can be found that:
Figure DEST_PATH_IMAGE016
when the damage is equal to 1, the component is destroyed, i.e.
Figure DEST_PATH_IMAGE017
When the cumulative damage is less than 1, the component is deemed to meet the safety requirements of the limited life design, i.e.
Figure DEST_PATH_IMAGE018
。
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CN109540487A (en) * 2018-11-27 2019-03-29 中国科学院国家天文台 A kind of telescope reflecting surface structure fatigue life monitoring method based on digital twins' technology
CN110443001B (en) * 2019-08-15 2023-04-28 中国矿业大学 Dynamic reliability prediction method for permanent magnet semi-direct drive cutting transmission system of coal mining machine
CN111950178B (en) * 2020-07-22 2022-08-16 中国第一汽车股份有限公司 Gear automatic loading method based on Hyperworks software
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