CN115358093B - Method for monitoring cracks of main beam of bridge crane in real time - Google Patents
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Abstract
A bridge crane girder crack real-time monitoring method relates to the field of hoisting machinery, and comprises the following steps: s1, determining an initial state of a girder crack, and obtaining a shape coefficient Y of the initial crack; s2, acquiring a load spectrum to obtain an equivalent stress amplitude load; s3, estimating the crack length in real time; s4, estimating the critical dimension of the crack and the residual fatigue life; the real-time monitoring method does not need to frequently carry out nondestructive inspection on the girder, and estimates the expansion state of the girder cracks by using a fracture mechanics method according to the daily operation data of the crane, thereby realizing the real-time monitoring of the girder cracks.
Description
Technical Field
The invention relates to the field of hoisting machinery, in particular to a method for monitoring cracks of a main beam of a bridge crane in real time.
Background
It is known that the failure modes of crane metal structures are mostly fatigue fractures, mainly due to fatigue cracks; the existing detection means of cracks of a crane girder mainly comprise ultrasonic flaw detection, ray flaw detection and magnetic particle flaw detection, the flaw detection means need special equipment and professionals, if the flaw detection is frequently carried out on the crane, a large amount of manpower and material resources are consumed, and if the regular evaluation is not carried out on the crane with cracks, the potential safety hazard exists;
in order to detect the running state of a crane and ensure the safe running of the crane, china proposed a crane safety monitoring management system standard in 2012, which can monitor and record the running state of the crane in real time through various sensors, such as parameters of lifting capacity, lifting height, descending depth, cart and trolley running travel, working time and the like, and stipulate that the sampling time interval is not more than 100ms, and the data can well reflect the use condition of the crane, but the data parameters are basic parameters.
Disclosure of Invention
In order to overcome the defects in the background art, the invention discloses a method for monitoring cracks of a main beam of a bridge crane in real time, which does not need to perform nondestructive inspection on the main beam frequently, estimates the expansion state of the cracks of the main beam by using a fracture mechanics method according to daily operation data of the crane and realizes the real-time monitoring of the cracks of the main beam.
In order to achieve the purpose, the invention adopts the following technical scheme:
a bridge crane girder crack real-time monitoring method comprises the following steps:
s1, determining the initial state of the girder crack, including the initial position, shape and initial length of the cracka 0 And obtaining the shape coefficient Y of the initial crack; s2, acquiring a load spectrum to obtain an equivalent stress amplitude load; s2.1, calculating the comprehensive stress of the position where the crack is located corresponding to each recorded data according to the data of one working cycle collected by the crane safety monitoring system, and obtaining stress time history data in the working cycle; s2.2, counting stress time history data according to a three-peak valley rain flow counting method to obtain a load spectrum generated by the working cycle and obtain a plurality of stress amplitudes∆σ i And corresponding cycle numbern i (ii) a S2.3, counting the stress in one working cycle into an equivalent stress amplitude according to an RMP equivalent load method obtained by a Paris formula:
(ii) a In the formula (I), the compound is shown in the specification, mthe material coefficient in the Paris formula is determined by experiments; n is the total number of stress cycles in the working cycle; s3, estimating the crack length in real time; s3.1, setting the shape coefficient Y, the equivalent stress amplitude load and the crack length before the start of the working cyclea i The stress intensity factor at this duty cycle is obtained by substituting the following equation:
(ii) a S3.2, on the basis of the Paris formula, considering the overload hysteresis effect of crack plastic region expansion, and calculating the size of the crack after one working cycle by adopting a Wheeler formula:
(ii) a Wherein C is a material constant, and is measured by an experiment;C p,i is a hysteresis factor; s4, estimating the critical dimension of the crack and the residual fatigue life; the critical crack size is calculated according to the following formula:
(ii) a In the formula (I), the compound is shown in the specification,∆σ max is the maximum stress amplitude of the cyclic stress, K c for the fracture toughness of the material, test by materialObtaining by inspection; crack from initial lengtha 0 Extend toa c The total number of stress cycles experienced by a critical crack is:
(ii) a In the formula (I), the compound is shown in the specification,C p =1, stress intensity factor∆KIs the length of the crackaFunction of (c):
(ii) a In the formula (I), the compound is shown in the specification,∆σ n the stress amplitude of a typical working condition is screened out according to the existing load data.
Further, in step S1, the initial state of the main beam cracks is determined by using a nondestructive testing means, and the shape coefficient Y of the cracks is determined by referring to a stress intensity factor manual and combining a finite element method.
Further, in step S2.1, the operation condition of one working cycle of the crane, including the large and small car lifting brakes, the large and small car positions and the lifting capacity, establishes a bridge crane structural mechanics model, and calculates the nominal stress of the crack position under each working condition of the main beam according to the simple beam model according to the data of one working cycle acquired by the crane safety monitoring system; because the stress of the main beam is mainly bending moment, shearing force and torque, the nominal stress comprises positive stress sigma generated by the bending moment 0 And shear stress tau generated by shearing force and torque, and calculating the comprehensive stress of the crack position according to a VonMises criterion:
。
further, if the crack is located at the position of the welding seam where the web plate and the cover plate intersect, constraint torsion and constraint bending should be considered, actual stress is larger than stress of free bending and free torsion, and actual stress at the position of the welding seam needs to be calculated:
。
further, the bending moment and the shearing force of the section where the crack is located are calculated according to the following formula:
bending distance:
shearing force:
in the formulaP 1 、P 2 The pressure is applied to a small wheel of the trolley,xis composed ofP 1 The position of the device is determined,L x is the base distance of the trolley,Sis the span of the crane,L 0 in order to locate the position of the crack,Q m the self weight of the main beam; the wheel pressure of the trolley is calculated according to the lifting load and the self weight of the trolley and the specific layout of the trolley; and substituting the bending moment and the shearing force obtained by calculation into the following formula to calculate the normal stress and the shearing stress of the section where the crack is located: normal stress:
(ii) a Shear stress:
(ii) a In the formula (I), the compound is shown in the specification, I Y is the moment of inertia of the main beam,ythe distance from the crack to the centroid of the main girder, Ais the cross-sectional area of the main beam.
Further, in S2.2, a series of stress data points are counted according to a three peak valley rain flow methodP 1 ，P 2 ，P 3 ，…，P n Statistical, rho |P i -P i-1 ｜≤｜P i -P i+1 Will | beP i -P i-1 | is recorded as a stress cycle amplitude, stress pointP i The mark is counted, and the residual stress point data continues to be counted next time.
Further, in S2.2, before the three-peak-valley rain flow counting method is performed, the stress time history data is first subjected to the compression of the equivalent point and the detection of the peak-valley value, adjacent repeated stress values and non-peak-valley points are screened out to form a complete stress time history curve, then the data of the head and the tail of the obtained load history data are adjusted to be the same, the curve is detached from the highest peak, and the head and the tail are butted to form a new stress time history curve for counting and counting.
Further, in S3.2, the hysteresis factorC p,i Calculated from the following formula:
in the formula (I), the compound is shown in the specification,a ol,i the crack length at the last overload cycle,a y,i for the crack length at the start of this loading cycle,h y,i for the size of the plastic zone resulting from this loading cycle,h ol,i the size of the plastic area caused by the last overload cycle can be calculated by an Irwin formula:
；
(ii) a In the formula (I), the compound is shown in the specification,∆K i for the stress intensity factor of this cycle,∆K ol,i is the stress intensity factor, σ, at the last overload cycle s Is the yield strength of the material.
Further, in step S4, one working cycle in the typical working condition includes the number of stress cyclesN m Then the remaining fatigue cycle number of the girder is:
。
due to the adoption of the technical scheme, the invention has the following beneficial effects:
the invention discloses a method for monitoring cracks of a main beam of a bridge crane in real time, which considers the influence of different loading sequences of the crane on the crack propagation rate and considers the influence of the overload delay effect of a metal material on the crack propagation rate, is closer to the actual using working condition of the crane, provides a method for conveniently monitoring the crack propagation state in real time, provides a basis for judging fatigue damage and provides a reference for a user to monitor the health state of the crane, so that the main beam does not need to be subjected to nondestructive inspection frequently, and the maintenance cost of the crane is greatly reduced.
Drawings
FIG. 1 is a schematic view of a mechanical model of a main beam;
fig. 2 is a schematic view of a load counting process in a three-peak valley rain flow counting method.
σ in FIG. 2 i The peak to valley points of the stress time history data,S a （i）in order to be the magnitude of the stress cycle,S m （i）mean values of stress cycles.
Detailed Description
The technical scheme of the invention is explained below by combining the attached drawings in the embodiment of the invention:
a bridge crane girder crack real-time monitoring method comprises the following steps:
s1, determining the initial state of the main beam crack by using nondestructive inspection means such as ultrasonic waves, rays and the like, including the initial position, shape and initial length of the cracka 0 And (5) determining the shape coefficient Y of the crack by referring to a stress intensity factor manual and combining a finite element method.
S2, acquiring a load spectrum to obtain an equivalent stress amplitude load;
s2.1, calculating the comprehensive stress of the position where the crack is located corresponding to each recorded data according to the data of one working cycle collected by the crane safety monitoring system, and obtaining stress time history data in the working cycle;
firstly, the running condition of one working cycle of the crane comprises large and small car lifting and braking, and largeThe method comprises the steps of establishing a bridge crane structural mechanical model according to the position and the lifting load of a trolley, establishing a model shown in figure 1 according to data of a working cycle acquired by a crane safety monitoring system, and calculating the nominal stress of a crack position under each working condition of a main beam according to a simply supported beam model; because the stress of the main beam is mainly bending moment, shearing force and torque, the nominal stress comprises positive stress sigma generated by the bending moment 0 And shear stress tau generated by shearing force and torque, and calculating the comprehensive stress of the crack position according to a VonMises criterion:
(ii) a According to the requirement, the bending moment and the shearing force of the section where the crack is located are calculated according to the following formula:
bending distance:
shearing force:
in the formulaP 1 、P 2 The pressure is applied to a small wheel of the trolley,xis composed ofP 1 The position of the device is determined,L x the distance between the base of the trolley and the base of the trolley,Sis the span of the crane,L 0 in order to locate the position of the crack,Q m the self weight of the main beam; the wheel pressure of the trolley is calculated according to the lifting capacity and the self weight of the trolley and the concrete layout of the trolley; and substituting the calculated bending moment and shearing force into the following formula to calculate the normal stress and the shear stress of the section where the crack is located: normal stress:
(ii) a Shear stress:
(ii) a In the formula (I), the compound is shown in the specification, I Y is the moment of inertia of the main beam,yis the distance of crackThe distance between the centroids of the main beams,Ais the cross-sectional area of the main beam;
in addition, if the crack is located at the position of the weld joint where the web plate and the cover plate intersect, the constrained torsion and the constrained bending should be considered, the actual stress is greater than the stress of the free bending and the free torsion, and the actual stress at the position of the weld joint needs to be calculated:
。
s2.2, according to the three-peak valley rain flow counting method, as shown in figure 2, a series of stress data pointsP 1 ，P 2 ，P 3 ，…，P n Statistical, if | valuesP i -P i-1 ｜≤｜P i -P i+1 Will | beP i -P i-1 | is recorded as a stress cycle amplitude, stress pointP i Marking the statistical data, continuously counting the residual stress point data for the next time to obtain a load spectrum generated by the working cycle, and obtaining a plurality of stress amplitudes∆ σ i And corresponding cycle numbern i ；
Before the three-peak valley rain flow counting method is carried out, first, the stress time history data are compressed at equivalent points and detected at peak valley values, adjacent repeated stress values and non-peak valley value points are screened out, a complete stress time history curve is formed, then the head and tail data of the obtained load history data are adjusted to be the same, the curve is disassembled from the highest peak, the head and the tail are butted, and a new stress time history curve is formed for counting statistics.
S2.3, according to an RMP equivalent load method obtained by a Paris formula, counting the stress in a working cycle into an equivalent stress amplitude:
in the formula (I), the compound is shown in the specification, mthe material coefficient in the Paris formula is determined by experiments; n isTotal number of stress cycles in the duty cycle.
S3, estimating the crack length in real time;
s3.1, setting the shape coefficient Y, the equivalent stress amplitude load and the crack length before the start of the working cyclea i The stress intensity factor at this duty cycle is obtained by substituting the following equation:
；
s3.2, on the basis of the Paris formula, considering the overload hysteresis effect of crack plastic region expansion, and calculating the size of the crack after one working cycle by adopting a Wheeler formula:
(ii) a Wherein C is a material constant, and is measured by an experiment;C p,i is a hysteresis factor; hysteresis factorC p,i Calculated from the following formula:
in the formula (I), the compound is shown in the specification,a ol,i the crack length at the last overload cycle,a y,i for the crack length at the beginning of this loading cycle,h y,i for the size of the plastic zone resulting from this loading cycle,h ol,i the size of the plastic area caused by the previous overload cycle can be calculated by an Irwin formula:
in the formula (I), the compound is shown in the specification,∆K i for the stress intensity factor of this cycle,∆K ol,i is the stress intensity factor, σ, at the last overload cycle s Is the yield strength of the material; and substituting the load spectrum data acquired by the safety monitoring system into the formula to calculate the current crack size.
S4, estimating the critical dimension of the crack and the residual fatigue life;
according to fracture mechanics, crack propagation is mainly divided into three stages, initial defects are converted into initial cracks after a period of rapid growth, then the propagation rate of the cracks becomes very slow, after the cracks are propagated for a long time, the crack size is developed to exceed a critical size, then a rapid growth stage is entered, at the moment, the structure is failed, and the duration of the slow development stage of the cracks is generally defined as the fatigue life of the structure; the critical crack size is calculated according to the following formula:
in the formula (I), the compound is shown in the specification,∆σ max is the maximum stress amplitude of the cyclic stress, K c the fracture toughness of the material is obtained by a material test;
crack from initial lengtha 0 Extend toa c The total number of stress cycles experienced by a critical crack is:
(ii) a In the formula (I), the compound is shown in the specification,C p =1, stress intensity factor∆KIs the length of the crackaFunction of (c):
(ii) a In the formula (I), the compound is shown in the specification,∆σ n screening out the stress amplitude of a typical working condition according to the existing load data;
according to requirements, one working cycle in a typical working condition comprises the number of stress cycles ofN m And then the number of the remaining fatigue cycles of the girder is as follows:
。
the first embodiment is as follows:
1) The analysis is carried out by taking a crane with rated lifting capacity of 20t and span of 22.5m in a certain workshop as an example, and the base distance of the trolley isL x =2000mm, the self weight of the main beam isQ m =5.5t, material Q235B;
2) Flaw detection is carried out on the main beam of the bridgeL 0 A fine crack with a length of 11250mma 0 =0.5mm, coefficient of materialC=2.606×10 -13 M =2.965, shape factor Y =1;
3) Intercepting data recorded by three working cycles according to crane operation data collected by a safety monitoring system, calculating stress data of a main beam in the working cycles by using a calculation formula established in the text, and removing non-peak-valley points which do not participate in rain flow counting method statistics to obtain 24 stress points in total, wherein part of the stress data are shown in the following table:
4) The stress data are counted according to a three-peak valley rain flow counting method to obtain 16 stress cycles in total, and the stress amplitude corresponding to part of the cycles is shown in the following table:
5) Calculating the equivalent stress amplitude according to a formula:
6) At the initial crack length, the corresponding strength factor for this stress pair is:
7) The plastic zone size corresponding to the stress intensity factor is:
8) Due to initial crackinga 0 The duty cycle data before formation is unknown, i.e. the size of the plastic zone produced by the last duty cycleh ol,i And crack length before cycle initiationa ol,i Are unknown, and the hysteresis factor can be assumed to beC p,0 And =1, calculating the crack propagation amount corresponding to the three working cycles according to a Wheeler formula:
9) According to the material experiments, the fracture toughness is assumed to be
Then, the fatigue life under the action of the equivalent stress amplitude is as follows:
。
example two:
1) The analysis is carried out by taking a crane with 50t of rated lifting capacity and 28m of span in a certain workshop as an example, and the base distance of the trolley isL x =2800mm, the weight of the main beam isQ m =12.3t, material Q235B;
2) Flaw detection is carried out on the girder of the bridge to obtain the spanL 0 A tiny crack exists at the position of 8500mm, and the length of the crack is longa 0 =0.3mm, coefficient of materialC=2.606×10 -13 M =2.965, shape factor Y =1;
3) According to crane operation data collected by a safety monitoring system, data recorded by two working cycles are intercepted, stress data of a main beam in the working cycles are calculated by utilizing a calculation formula established in the text, non-peak and non-valley points which do not participate in rain flow counting method statistics are removed, 20 stress points are obtained in total, and part of the stress data are shown in the following table:
4) The stress data are counted according to a three-peak valley rain flow counting method to obtain 8 stress cycles, and the stress amplitude corresponding to part of the cycles is shown in the following table:
5) Calculating the equivalent stress amplitude according to a formula:
6) At the initial crack length, the corresponding strength factor of this stress pair is:
7) The plastic zone size corresponding to the stress intensity factor is:
8) Due to initial crackinga 0 The duty cycle data before formation is unknown, i.e. the plastic zone size produced by the last duty cycleh ol,i And crack length before cycle initiationa ol,i Are unknown, and the hysteresis factor can be assumed to beC p,0 And =1, calculating the crack propagation amount corresponding to the three working cycles according to a Wheeler formula:
(ii) a At this time the crack length is
；
9) Acquiring new two working cycle data, counting according to a three-peak valley rain flow counting method, and obtaining 9 stress cycles in total, wherein the cycle amplitude is as follows:
10 The equivalent stress amplitude is calculated according to the formula:
11 At the initial crack length, the corresponding strength factor for this stress pair is:
12 The plastic region dimensions for this stress intensity factor are:
13 Due to)
According to Wheeler's formula, the overload hysteresis factor isC p,0 =1, the crack propagation amount caused by this working cycle is:
。
the invention is not described in detail in the prior art, and it is apparent to a person skilled in the art that the invention is not limited to details of the above-described exemplary embodiments, but that the invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof; the present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein, and any reference signs in the claims are not intended to be construed as limiting the scope of the claims.
Claims (6)
1. A bridge crane girder crack real-time monitoring method is characterized by comprising the following steps: comprises the following steps:
s1, determining the initial state of the girder crack, including the initial position, shape and initial length of the cracka 0 And obtaining the shape coefficient Y of the initial crack;
s2, acquiring a load spectrum to obtain an equivalent stress amplitude load;
s2.1, calculating the comprehensive stress of the position of the crack corresponding to each recorded data according to the data of one working cycle acquired by the crane safety monitoring system, and obtaining stress time history data in the working cycle;
s2.2, counting and counting the stress time history data according to a three-peak valley rain flow counting method to obtain a load spectrum generated by the working cycle and obtain a plurality of stress amplitudes∆σ i And corresponding cycle numbern i ；
S2.3, according to an RMP equivalent load method obtained by a Paris formula, counting the stress in a working cycle into an equivalent stress amplitude:
in the formula (I), the compound is shown in the specification,mthe material coefficient in the Paris formula; n is the total stress cycle number in the working cycle;
s3, estimating the crack length in real time;
s3.1, setting the shape coefficient Y, the equivalent stress amplitude load and the crack length before the start of the working cyclea i The stress intensity factor at this duty cycle is obtained by substituting the following equation:
；
s3.2, on the basis of the Paris formula, considering the overload hysteresis effect of crack plastic region expansion, and calculating the size of the crack after one working cycle by adopting a Wheeler formula:
；
wherein C is a material constant;C p,i for hysteresis factor, calculated by:
in the formula (I), the compound is shown in the specification,a ol,i the crack length at the last overload cycle,a y,i for the crack length at the start of this loading cycle,h y,i for the size of the plastic zone resulting from this loading cycle,h ol,i the size of the plastic area caused by the previous overload cycle can be calculated by an Irwin formula:
in the formula (I), the compound is shown in the specification,∆K i for the stress intensity factor of this cycle,∆K ol,i is the stress intensity factor, σ, at the last overload cycle s Is the yield strength of the material;
s4, estimating the critical dimension of the crack and the residual fatigue life;
the critical crack size is calculated according to the following formula:
in the formula (I), the compound is shown in the specification,∆σ max is the maximum stress amplitude of the cyclic stress, K c is the fracture toughness of the material;
crack from initial lengtha 0 Extend toa c The total number of stress cycles experienced by a critical crack is:
(ii) a In the formula (I), the compound is shown in the specification,C p =1, stress intensity factor∆KIs the length of the crackaFunction of (c):
(ii) a In the formula (I), the compound is shown in the specification,∆σ n the stress amplitude of a typical working condition is screened out according to the existing load data.
2. The bridge crane girder crack real-time monitoring method according to claim 1, characterized in that: in step S1, the initial state of the main beam cracks is determined by using a nondestructive inspection means, and the shape coefficient Y of the cracks is determined by referring to a stress intensity factor manual and combining a finite element method.
3. The bridge crane girder crack real-time monitoring method according to claim 1, characterized in that: in step S2.1, the operation condition of one working cycle of the crane comprises large and small car lifting brake, large and small car position and lifting load, a bridge crane structural mechanical model is established, and the main beam is used for calculating the crack under each working condition according to a simple beam model according to the data of one working cycle acquired by the crane safety monitoring systemNominal stress at the location of the seam; since the stress of the main beam is bending moment, shearing force and torque, the nominal stress comprises positive stress sigma generated by the bending moment 0 And shear stress tau generated by shearing force and torque, and calculating the comprehensive stress of the crack position according to a VonMises criterion:
4. the bridge crane girder crack real-time monitoring method according to claim 3, wherein the method comprises the following steps: if the crack is located at the position of the welding seam where the web plate and the cover plate are intersected, the constraint torsion and the constraint bending should be considered, the actual stress is larger than the stress of the free bending and the free torsion, and the actual stress at the position of the welding seam needs to be calculated:
。
5. the bridge crane girder crack real-time monitoring method according to claim 1, characterized in that: in S2.2, a series of stress data points are counted according to a three peak valley rain flow counting methodP 1 ，P 2 ，P 3 ，…，P n Statistical, if | valuesP i -P i-1 ｜≤｜P i -P i+1 | and then |P i -P i-1 | is recorded as a stress cycle amplitude, stress pointP i The mark is counted, and the residual stress point data continues to be counted next time.
6. The bridge crane girder crack real-time monitoring method according to claim 1, characterized in that: in S2.2, before a three-peak valley rain flow counting method is carried out, first, the stress time history data is subjected to equivalent point compression and peak-valley value detection, adjacent repeated stress values and non-peak-valley value points are screened out, a complete stress time history curve is formed, then, the data of the head and the tail of the obtained load history data are adjusted to be the same, the curve is detached from the highest peak, the head and the tail are in butt joint, and a new stress time history curve is formed for counting statistics.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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