CN110378053B - Method for determining optimal straightening curvature of circular arc roller shape in pipe two-skew-roller straightening process - Google Patents
Method for determining optimal straightening curvature of circular arc roller shape in pipe two-skew-roller straightening process Download PDFInfo
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Abstract
The invention belongs to the technical field of metal pressure processing, and provides a method for determining the optimal straightening curvature of a pipe two-oblique-roller straightening circular arc roller shape. The method mainly comprises the following steps: 1. determining the initial values of the optimal straightening curvature search range and the related variables; 2. determining the residual curvature of the pipe after a certain bending curvature action by using a classical bending elastic equation; 3. judging the straightening curvature of the arc roller shape based on the loop iteration calculation of the residual curvature; 4. and searching for the optimal straightening curvature within the allowable range of the bending curvature by taking the minimum residual curvature (namely the highest straightening precision) of the pipe after the cyclic iterative computation as a target. The method can search and determine the optimal straightening curvature of the circular arc roller-shaped straightening roller straightened by the two inclined rollers of the pipe, can be used for structural design and roller-shaped curve design of the straightening roller, and further effectively improves the quality and the precision of the straightened pipe.
Description
Technical Field
The invention belongs to the technical field of metal pressure processing, and relates to a method for determining the optimal straightening curvature of a pipe two-oblique-roller straightening circular-arc roller shape.
Background
In recent years, the demand for high-precision metal pipes has sharply increased in the fields of industry, aerospace, military, petrochemical industry, and the like, such as: the high-temperature alloy fine thin-wall pipe for spaceflight, the precision honing pipe for high-precision cylinders and hydraulic cylinder bodies and the titanium alloy pipe widely applied to national defense industry such as nuclear energy and the like require that the product has higher straightness and roundness, and the residual stress in the pipe causes bending and distortion of different degrees due to external force action or uneven cold and heat in the production, processing, transportation and stacking processes, and the pipe needs to be finished and straightened before leaving a factory or being used. (Z.Q.Zhang, Y.H.Yan, H.L.Yang, A simple model of Maximum cross-Section deflecting in connecting correct routing Process of in-called loop round tube, Journal of Material routing Technology, Vol.238(2016), p.305-314.) (Z.qqn.ZHANK, predictionof Maximum cross-Section deflecting of in-called loop round tube routing Process, Journal of Iron and SteelResearch, International, Vol.23(2016), p.745)
However, before straightening, the pipe has different axial bending directions and curvatures, and has uncertainty, and at present, the following three straightening methods are mainly used: (1) three-point bending pressure straightening (Zhai hua. research On straightening technology Cam System [ J ], Chinese Journal Of Mechanical Engineering,2003,16(2): 175-. The method needs to accurately measure the original bending of the workpiece and accurately control the position and the rolling reduction of the pressure head, and the production efficiency is low. (2) The method comprises the following steps of (1-7) straightening by using multiple inclined rollers in a staggered manner (CHEN Min, JIANNG Xiaomin, ZHAO Zuxin. Innovation in the computing system of straightening force [ J ]. Chinese journal of Mechanical Engineering,2010,23 (1)), wherein a pipe spirally advances along an axis and is repeatedly bent by sequentially passing through the staggered straightening roller system, thereby achieving the aim of straightening. However, for the thin-walled tube, due to the limitation of the degree of bending at each time, the number of straightening rollers is large, and often more than 14 rollers are needed, so that the equipment cost and the control difficulty are increased. (3) The method comprises the steps of multi-curvature two-skew roller straightening (a Pai straightening principle and a straightening machine [ M ]. Beijing: a publishing company in the metallurgical industry, 2002.), wherein a pipe spirally advances along an axis and passes through a pair of straightening rollers with multi-section curvature roller gaps, the straightening rollers are composed of convex rollers and concave rollers, the convex rollers and the concave rollers are arranged in a staggered manner in a tilted manner in space, a certain included angle is formed between the straightening rollers and a pipe and a rod to be straightened, the pipe is repeatedly bent for 2 times every time the pipe advances by one lead in the roller gaps, the pipe is uniformly bent with large curvature at an inlet stage, the straightening is further realized by adopting small curvature at an outlet, and the roller length is 5-8 leads to meet the requirement of bending times. However, the deformation rate of the pipe at the curvature abrupt change position in the roll gap is high, and the phenomena of instability and buckling are easy to occur, so that the curvature abrupt change in the deformation process can be effectively avoided if the straightening roll is designed into an arc roll with single curvature.
Specifically, in the straightening process using the arc roll type, a pipe material having an initial curvature advances while rotating in a straightening roll gap, and is bent with a bending curvature k assuming that a certain orientation of the pipe section is bent in the vertical direction by straightening rollswThe orientation then follows the unloading as a result of the rotation of the tube. When the pipe advances by half a lead and rotates by an angle of pi at the same time, the direction is contacted with the straightening roller to be bent, the bending direction of the pipe is just opposite relative to the previous bending, and the bending curvature is still kwAnd the residual curvature of the previous bending is the initial curvature of the current bending and the directions are opposite, so that the section of the pipe can be bent positively and negatively for 2 times in one lead. When the pipe continues to advance helically, unloading occurs again in that orientation and produces a residual curvature that is the initial curvature in the next bending run and in the opposite direction, and so on. Due to the continuity of the roll gaps, the same repeated bending and unloading processes are carried out in other directions of the section of the pipe at different moments, if the residual curvature of the pipe is gradually reduced in the process, after the pipe leaves the straightening roll, the residual curvature meets the straightening precision requirement, the pipe can be straightened by the straightening roll system, and the bending curvature of the roll shape of the straightening roll is the straightening curvature. Usually the straightening curvatures are distributed within a certain range, and if a value can be found within this range, which can achieve the straightening of the pipe while minimizing the residual curvature of the pipe, the straightening curvature is the optimum straightening curvature.
However, since straightening deformation is a complex elastoplasticity problem, the elasticity of the steel plate needs to be recovered after each bending, and the elastic recovery amounts of different initial bending degrees are different, so how to find the optimal straightening curvature is a key problem to be solved urgently in the process of the two-oblique-roller straightening process. However, in the past, when a straightening device using a circular arc roller shape is designed, an experience chart is still used for estimating the straightening curvature by combining manual experience and repeated trial and correction, so that the straightening curvature is set inaccurately, and further, the product precision is not high, the quality stability is poor, and the production efficiency is low.
Disclosure of Invention
Aiming at the practical problems, the invention provides a method for determining the optimal straightening curvature of the arc roller shape in the pipe two-oblique-roller straightening process. The method uses a classical bending elastic-restoring equation to calculate the residual curvature of the pipe after bending, provides a determination method of the straightening curvature of the circular arc roller type based on the cyclic iterative calculation of the residual curvature, and provides a search and determination method of the optimal straightening curvature within the allowable range of the bending curvature by taking the minimum residual curvature (namely, the highest straightening precision) of the pipe after the cyclic iterative calculation as a target.
The invention adopts the following specific technical scheme:
the method comprises the following steps: and determining the initial values of the optimal straightening curvature search range and the related variable.
The search range for the straightening curvature is set to [0, k ]wcr]Wherein k iswcrThe critical curvature for pipe bend instability can be determined from the associated data chart. Followed by a bending curvature kwSearch step length Δ kwOptimal straightening curvature kwopAnd minimum residual curvature kcopAnd assigning an initial value.
Step two: determining the residual curvature of the pipe after a certain bending curvature.
The initial curvature distribution of the pipe is usually within a certain range, i.e., -b, a]Where a, b are positive real constants, so for a certain bending curvature kwThe pipe can be reversely bent (the original curvature and the bending curvature have the same sign) or be bent in the same direction (the original curvature and the bending curvature have different signs) in the roll gap. Will k0fAs the reverse maximum initial bending curvature, its initial value is a; k is a radical of0tThe maximum isotropic initial bending curvature has an initial value of-b. Then based on the initial curvature pair sourceJudging the initial bending, if the initial bending is the same-direction bending and the bending degree is larger than the straightening deformation degree in the roll gap, namely k0f<0&|k0f|≥kwAlthough the bending in the roll gap can reduce the initial deformation degree of the pipe, the reduction amount is small, and it is considered that the initial curvature is directly given to the residual curvature if the deformation degree of the pipe after bending is approximately constant in this case. Otherwise, calculating the residual curvature k after bending by adopting the formula (1) aiming at the reverse bendingcf：
Calculating residual curvature k after bending by adopting formula (2) for equidirectional bendingct：
In the formula: e is the elastic modulus, I is the inertia product of the cross section to the neutral layer, and M is the axial bending moment of the cross section of the thin-walled tube in the elastic-plastic deformation region, and can be calculated by adopting the formula (3). Thus, the residual curvature k of the pipes with different initial curvatures after a certain bending curvature action can be determinedc。
Step three: and judging the straightening curvature.
The residual curvature of the pipe after the current bending becomes the initial curvature of the next bending, and k is calculated by adopting the formulas (1) and (2)cfkctAssigned to k0fk0tWhen the pipe section is bent next time in a certain direction, the pipe section needs to rotate by an angle of pi along the axis, and the direction of the initial curvature is reversed, so that the residual curvature sign needs to be changed during assignment. And then, calculating the residual curvature of the pipe after the second bending by adopting the step two, wherein for the two-roller straightener, the length of the roller body is less than 8 leads, so that the bending time is 16 times at most, and the residual curvature after 16 times of repeated bending can be obtained by repeatedly adopting the step twoAnd (4) rate. Finally, two residual curvature radiuses k are obtainedcfkctComparing with the straightening accuracy, if | kcf|≤&|kctIf | is less than or equal to this, k iswI.e. the straightening curvature to be determined, otherwise the requirement of straightening precision cannot be met, kwNot the straightening curvature to be determined. Usually, the straightening precision is the maximum bending deflection of each meter of pipe:
and the minimum residual curvature meeting the accuracy requirement is defined as straightening accuracy in the calculation process, and if the maximum bending deflection is known, the straightening accuracy can be as follows:
step four: and searching and determining the optimal straightening curvature.
Using the method of step three, if kwTo straighten the curvature, two residual curvatures k are comparedcfkctIs greater than the minimum residual curvature kcopSmaller, if max { | kcf|,|kct|}≤kcopDescription of the tubes in kwThe straightening accuracy under action is higher than before, and the maximum of the residual curvature is assigned to the minimum residual curvature kcopHas k ofcop＝max{|kcf|,|kctL, and assigning the straightening curvature at the moment to the optimal straightening curvature kwop＝kwThen to kwOne step is added. If k iswAfter being judged, the curvature is not straightening curvature or max { | kcf|,|kct|}≥kcopThen k iswOne step is directly increased. Next, it is judged kwIf it is in the search range, if kwIs still at [0, kwcr]And if so, repeating the third step and the fourth step to perform the next calculation. When k iswAfter traversing the entire domain, i.e. kwExceeds [0, kwcr]Range, judgment kcopIf it is not rewritten, it indicates that a k cannot be found in the search rangewCan cause the pipe to realize two-roller straightening, so that the pipe cannot be straightened at the timeAnd realizing two-roller straightening. If k iscopIf the straightening curvature is rewritten in the calculation process, the optimal straightening curvature which enables the straightening precision of the pipe to be the highest is found, and the pipe can be straightened by the two rollers. The optimal straightening curvature at this time is kwopThe straightening precision is kcop。
The optimal straightening curvature of the arc roller-shaped straightening roller straightened by the two inclined rollers of the pipe obtained by the invention can be used for structural design and roller-shaped curve design of the straightening roller, thereby effectively improving the quality and precision of the straightened pipe.
Drawings
FIG. 1 is a flow chart of a technical scheme of a method for determining an optimal straightening curvature.
Detailed Description
The present invention will be described in further detail below with reference to specific embodiments for determining the optimum straightening curvature of the circular-arc roll type straightening roll in straightening stainless steel pipes.
The method comprises the following steps: determining initial values of optimal straightening curvature search range and related variables
The stainless steel 1Cr18Ni9Ti pipe (yield strength. sigma. 205MPa, elastic modulus E. 206GPa) with an outer diameter of 21mm and a thickness of 1mm was used as the straightening object, and the straightening accuracy was 0.3 mm/m. Firstly, the search range of the optimal straightening curvature is determined to be 0, 0.5]Then initializing the corresponding variable, here the bending curvature kwOptimal straightening curvature kwopHas an initial value of 0 and a minimum residual curvature kcopThe initial value of (A) is the original curvature k of the pipe0Search step size Δ kwThe initial value of (A) is 0.001.
Step two: calculation for determining the residual curvature of a tube after the action of a certain bending curvature
Here the range of the original curvature distribution of the tube is [ -0.213, 0.213 [ -0.213 [ ]]At a certain bending curvature kwThe residual curvature calculation process is illustrated under the action of 0.125. Here the maximum initial bending curvature k will be reversed on first bending0fThe value assigned is 0.213; maximum initial bending curvature k in the same direction0tThe value is assigned-0.213. Then, the original bending is judged based on the initial curvature, and if the original bending is the same-direction bending and the bending degree is larger than the roll gapDegree of straightening deformation, i.e. k0f<0&|k0f|≥kwThe initial curvature is directly assigned to the residual curvature, hence for k0tResidual curvature of-0.213 is-0.213, and for k0fWhen 0.213, the residual curvature k after bending is calculated by the equation (1)cf0.047, so that the residual curvature of the tube after the first bend is given in table 1:
TABLE 1 initial and residual curvatures of pipes at different bending times
Step three: determination of straightening curvature
The residual curvature of the pipe after the first bending becomes the initial curvature of the second bending, but because the section of the pipe needs to rotate for pi angle along the axis during the second bending and the direction of the initial curvature is reversed, the sign of the residual curvature needs to be changed during the assignment, so that the reverse initial curvature k of the second bending0fIs 0.213, initial curvature k in the same direction0tThe value of (A) is-0.047. And then, the residual curvature after the second bending is obtained by adopting the method for calculating the residual curvature in the second step as shown in table 1, and the residual curvatures in each of 16 bending processes are obtained in sequence in the same way as shown in table 1. Will finally remain the curvature kcf、kctComparing with the straightening accuracy, at the moment | kcf|≤&|kct| is less than or equal to
Then the curvature k of the bendwThe straightening curvature is 0.125.
Step four: search for optimal straightening curvature
K obtained by calculation in step threewTo straighten the curvature, two residual curvatures k are comparedcfkctMaximum and minimum residual curvature kcopFinding max{|kcf|,|kct|}≤kcopDescription of the bending curvature kwThe straightening accuracy of the pipe under the action of 0.125 is higher than that under the action of other bending curvatures before, and then the maximum of the residual curvature is assigned to the minimum residual curvature kcopHas k ofcop＝max{|kcf|,|kctL, and assigning the straightening curvature at the moment to the optimal straightening curvature kwop＝kw0.125, then pair kwIncrease a step length and judge kwWhether it is in the search range [0, 0.5 ]]In this case kwIf the current time is still within the range, the calculation is repeated by using the third step and the fourth step. When k iswAfter traversing the whole definition domain, k is foundcopIs not rewritten, so kwThe best straightening curvature which can lead the straightening precision to be the highest is 0.125, and the highest straightening precision is kcop＝0.00184。
Claims (1)
1. A method for determining the optimal straightening curvature of a circular arc roller shape in a pipe two-oblique roller straightening process is characterized by comprising the following steps of,
the method comprises the following steps: determining the initial values of the optimal straightening curvature search range and the related variables;
the search range for the straightening curvature is set to [0, k ]wcr]Wherein k iswcrThe critical curvature for the bending instability of the pipe can be determined by a related data chart; followed by a bending curvature kwSearch step length Δ kwOptimal straightening curvature kwopAnd minimum residual curvature kcopAssigning an initial value;
step two: determining the residual curvature of the pipe after a certain bending curvature;
the original curvature distribution of the pipe is in a certain range, namely [ -b, a [ -b]A and b are positive real constants; will k0fAs the reverse maximum initial bending curvature, its initial value is a; k is a radical of0tThe maximum initial bending curvature in the same direction is-b; then, the original bending is judged based on the initial curvature, and if the original bending is the same-direction bending and the bending degree is larger than the straightening deformation degree in the roll gap, namely k0f< 0 and | k0f|≥kwThen is straightThen, the initial curvature is given to the residual curvature; otherwise, calculating the residual curvature k after bending by adopting the formula (1) aiming at the reverse bendingcf：
Calculating residual curvature k after bending by adopting formula (2) for equidirectional bendingct：
In the formula: e is elastic modulus, I is the product of inertia of the cross section to the neutral layer, M is the axial bending moment of the cross section of the thin-walled tube in the elastic-plastic deformation region, and k0Calculating the original curvature of the pipe by adopting the formula (3) to determine the residual curvature k of the pipe with different initial curvatures after a certain bending curvaturec；
In the formula, σsYield limit, t wall thickness;
step three: judging the straightening curvature;
the residual curvature of the pipe after the current bending becomes the initial curvature of the next bending, and k is calculated by adopting the formulas (1) and (2)cfkctAssigned to k0fk0tWhen the pipe section is bent for the next time in a certain direction, the pipe section needs to rotate by an angle pi along the axis, and the direction of the initial curvature is reversed, so that the residual curvature sign needs to be changed during assignment; then, calculating the residual curvature of the pipe after the second bending by adopting the second step, and repeatedly adopting the second step to obtain the residual curvature after repeated bending; finally, two residual curvature radiuses k are obtainedcfkctComparing with the straightening accuracy, if | kcfLess than or equal to and kctIf | is less than or equal to this, k iswI.e. the straightening curvature to be determined, otherwise the requirement of straightening precision cannot be met, kwIs not the straightening curvature to be determined; will satisfyThe minimum residual curvature required for accuracy is defined as the straightening accuracy, which if the maximum bending deflection is known is:
step four: searching and determining the optimal straightening curvature;
using the method of step three, if kwTo straighten the curvature, two residual curvatures k are comparedcfkctIs greater than the minimum residual curvature kcopSmaller, if max { | kcf|,|kct|}≤kcopDescription of the tubes in kwThe straightening accuracy under action is higher than before, and the maximum of the residual curvature is assigned to the minimum residual curvature kcopHas k ofcop＝max{|kcf|,|kctL, and assigning the straightening curvature at the moment to the optimal straightening curvature kwop＝kwThen to kwIncreasing one step size; if k iswAfter being judged, the curvature is not straightening curvature or max { | kcf|,|kct|}≥kcopThen k iswDirectly increasing one step length; next, it is judged kwIf it is in the search range, if kwIs still at [0, kwcr]If the range is within the range, repeating the third step and the fourth step to carry out the next calculation; when k iswAfter traversing the entire domain, i.e. kwExceeds [0, kwcr]Range, judgment kcopIf it is not rewritten, it indicates that a k cannot be found in the search rangewThe pipe can be straightened by two rollers, so that the straightening by two rollers cannot be realized; if k iscopIf the correction is rewritten in the calculation process, the optimal straightening curvature which enables the pipe straightening precision to be the highest is found, so that the pipe can be straightened by two rollers; the optimal straightening curvature at this time is kwopThe straightening precision is kcop。
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