A systematic study on three-roll continuous straightening process for LSAW pipes

Aiming at the low efficiency and unstable accuracy of the current mold-pressing straightening for LSAW pipes, a three-roll continuous straightening process is proposed in this study, which uses the roller straightening instead of mold bending. According to the novel technology, the calculation model of the theoretical straightening moment is derived based on the springback equation of plane bending with small curvature, and the calculation model of initial curvature is established for the new deflection detection method. Furthermore, the numerical simulation analysis is carried out for the LSAW pipe case, and a straightening experimental platform is built for experiments. The research shows that the accuracy of the theoretical moment equation required for straightening is directly related to the initial curvature, rather than the fitting accuracy of the deflection curve, and the low-order simple-fitting curvature calculation model has the highest reliability. In order to control the section distortion and the straightening blind area, the straightening roller should follow the equal diameter design principle, and the empirical formula of span estimation is given. Under the optimal conditions, the straightness of the corrected tubes can be controlled within 1.5‰ and the ovality of the section can be within 0.5%, which proves the feasibility and reliability of the new process. What’s more, the straightening system built in this work, including process analysis software, is conducive to the automation and popularization of the new process.


Introduction
Straightening is a necessary process in the production of large longitudinally submerged arc welding (LSAW) pipes. The industry general standard API specification 5L (API Spec 5L) [1], established by the American Petroleum Institute (API), has made strict provisions on the straightness and ovality of finished welded pipes, especially in terms of straightness. It is required that the straightness of the whole pipe should be less than 2‰, and the local deviation within the 1000 mm length of the pipe end should be less than 4.0 mm. According to the cross-section characteristics, bending shape, and correction target, the common straightening technologies of shaft and tube parts include pressure straightening, multi-staggered roll straightening, and tworoll straightening. Pressure straightening can be used on almost any part [2,3], especially for those large workpieces with severe deflection, variable cross-section, or asymmetric cross-section. Moreover, this technology has been widely used in Mittelstand businesses because of its simple and flexible operation [4,5]. However, pressure straightening has great limitations in accuracy and efficiency [6]. Multistaggered roll straightening turns single-point bending into continuous-overall bending, which is based on the three-step reverse-bending straightening theory, that is, "first unify, then straighten, and then supplement" [7,8]. The development of straightening machine is relatively mature [9,10], with the advantages of high efficiency, high precision, and high degree of automation. Now the research mainly focuses on the calculation of a roll profile curve, the control of crosssection distortion, and the design of large-scale and highprecision straighteners [11][12][13]. The two-roll straightening process uses the curvature change in the roll gap of a pair of concave convex rolls to realize the omni-directional straightening of the workpiece. It is a special cross-roll straightening process, which is commonly used in the fine process after multi-staggered roll straightening. The advantages are that the straightening blind area is avoided, the surface finish can be improved, and the structure of the equipment is simple and easy to adjust [14]. The disadvantage is that the straightening speed is low, which is generally 1/2-1/30 lower than that of the multi-staggered roll straightener, and the curvature of the workpiece to be straightened is required to be less than 0.5% [15]. The applicability of both multistaggered roll and two-roll straightening is limited, and it is only applicable to shafts or thin-walled pipes with diameters less than 200 mm [16]. In addition, Huang et al. [17][18][19] also proposed a comprehensive correction process integrating straightening and rounding, which can realize the synchronous correction of straightness and ovality.
The LSAW pipe is a typical large thin-walled pipe. Affected by the forming equipment and welding thermal stress, the deflection curve of the formed welded pipe presents the following characteristics [20]: the pipe presents in-plane bending, which is different from space bending, and the bending plane almost passes through the weld; the pipe body bends in one direction and toward the inner side of the weld; the deflection curve is a continuous, smooth, and unimodal plane curve; the initial curvature is a continuous unimodal curve. Limited by the geometry of LSAW pipes, the traditional threepoint pressure straightening process is still used in the production site. This technology depends on the experience of operators to determine the straightening position, straightening load, or reduction. What's more, the repeated pressure test and repeated loading lead to low efficiency and poor accuracy.
Considering the geometric and deflection characteristics of the LSAW pipes, and fully drawing on the advantages of multi-roll straightening process, the three-roll continuous straightening process has been innovatively proposed [21]. This method combines the advantages of pressure straightening and roller straightening, and can be used for large and thin-walled pipes while maintaining efficiency. At the same time, a deflection detection device is integrated to help automate the straightening process [22]. This paper continues the systematic research on the new process, including numerical simulation analysis and experimental research. On this basis, process analysis software was developed, which laid the foundation for the popularization of the new technology.

Three-roll continuous straightening process
The three-roll continuous straightening process, as shown in Fig. 1, mainly includes a roll system composed of an upper roll and two lower rolls. The active rotating upper roll drives the tube to move axially, and the predicted straightening moment is fully loaded by a continuous load. In theory, this method can realize one-time continuous straightening, which greatly improves the efficiency and accuracy, compared with the traditional mold straightening. Using its structural characteristics, a laser displacement sensor is installed between the two lower rollers, which can realize the online detection of deflection at the same time. This integrated design can greatly save equipment cost and space, and the simplified process flow provides the basis for the intellectualization of the straightening process.
The key problems involved in the new process include the prediction of the straightening moment, the calculation of overall deflection and straightness, process planning, and experimental system design. Among them, the research work of deflection detection and curve fitting based on laser displacement sensor has been completed [21], accompanied by the preliminary design of three-roll continuous straightening experimental system. Therefore, this study focuses on the determination of the straightening moment and initial curvature, as well as the complete process planning and verification.

Springback analysis of over-bend straightening
The straightening process of LSAW pipes is essentially a pure-bend and over-bend straightening process of plane curved beams with symmetrical sections. From the perspective of curvature change, this process can be considered the curvature of the curved beam, whose initial curvature of the geometric center layer is K 0 , becomes K under the action of loading moment M , and the curvature after springback is 0 so as to achieve the purpose of straightening.
According to the springback equation of plane bending with small curvature [23] and straightening conditions, the springback equation in the over-bend straightening process of a plane curved beam is where M is the loading moment, E is the elastic modulus, and I is the sectional moment of inertia.
On the other hand, according to the assumption of conventional elastic-plastic material model, the assumption of initial equivalent strain, and the moment calculation method of a curved beam with an arbitrary section, the loading moment is determined as where K 0 and K are the curvature of the neutral layer of the curved beam before and after loading, respectively.
Therefore, for the pure-bend and over-bend straightening of curved beams with arbitrary symmetrical sections, once the material parameters, section shape parameters, and initial curvature are known, the theoretical straightening curvature and moment can be obtained by combining Eqs. (1) and (2). This also shows that the straightening process is to apply the straightening moment M(x) to the corresponding section through technical means, so that the curvature distribution of the workpiece after bending is (x).

Theoretical straightening moment
For LSAW pipes, the bilinear hardening model is used to describe the stress and strain of the material as where σ s is the yield stress, ε s is the elastic limit strain, and D is the plastic modulus.
For pipes with outer radius and inner radius R 1 and R s , respectively, z s is defined as the boundary position of elastoplastic distinction in the over-bend straightening process. According to its value, that is, the deformation state of the pipe section, this process can be divided into three stages. Stage I: z s > R 1 , that is, the fully elastic deformation stage. The relationship between the section moment and geometric neutral curvature is After unloading, the microbeam becomes the initial state, that is, the curvature is still K 0 after springback.
Stage II: R 2 < w s < R 1 , and the moment M is With the increase of the loading moment M , the plastic deformation zone gradually extends to the center of the section. It is defined that the bending moment when plastic deformation just occurs at z = R 2 is the boundary moment M d , and its expression is At this point, the bending curvature is defined as the boundary curvature K d , and its expression is It can be seen that the boundary moment M d and boundary curvature K d have nothing to do with K 0 , but with the geometric dimensions and material parameters of the pipe fittings.
Stage III: z s < R 2 , at this time, M > M d , the relationship between bending moment M and curvature K is Obviously, the initial curvature K 0 plays an important role in this relationship, which is also the reason why the research on the initial curvature is paid special attention.
Furthermore, according to the relationship between the initial curvature | | K 0 | | and the boundary curvature | | K d | | , the theoretical straightening curvature K is determined as The theoretical straightening moment M can be finally determined by substituting the solution result of the above equation into Eq. (1).

Initial curvature
The theoretical straightening moment is directly related to the initial curvature. According to the previously established piecewise-fitting algorithm for the deflection curve [21], the curvature is very sensitive to the fitting order of the curve and varies greatly. Therefore, four curvature calculation models are established to find the better one to describe the initial curvature that cannot be directly detected or measured.

High-order piecewise-fitting curvature calculation model
According to the deflection detection method based on the laser displacement sensor, a piecewise deflection curve fitting algorithm is proposed, and it is confirmed that the higher the fitting order, the higher the fitting accuracy. However, for practical physical problems, high-order polynomial curves are prone to oscillation, and the higher the order, the more severe the oscillation, which leads to the instability of the curvature calculation. When the optimal fitting order of the middle curve segment is determined to be 10, the curvature calculation model is The relevant parameters in the equation can be obtained by the piecewise deflection curve fitting algorithm. It should be noted that this is a calculation model of the overall curvature, and the length of the linear segment at the end is half span, so the calculation result is related to the span.

Low-order simple-fitting curvature calculation model
Since the initial curvature distribution of the LSAW pipes is a continuous curve with a single peak, and the curvature is directly related to the second derivative, a low-order simplefitting curvature calculation model is proposed, that is For the deflection distribution data x i , y i (i = 1, 2, ⋯ , n) , the least square method combined with the determination condition of multivariate extreme value is adopted for curve fitting, and then, it is deduced that This is a linear system of equations with respect to the parameters a k (k = 0, 1, 2, 3, 4) , and there is a unique solution. Substituting this result into Eq. (12), the expression of the low-order fitting of the deflection curve can be determined, and its initial curvature distribution can be obtained as

Local average-curvature calculation model
In the deflection detection method based on the laser displacement sensor, the local deflection value of the curved pipe is directly measured, and the overall deflection curve and the overall curvature curve are further calculated. Therefore, a direct calculation based on the local value was attempted, that is, a local average-curvature calculation model, as shown in Fig. 2.
In Fig. 2, the local deflection at the point P i detected by the sensor is h i , and the actual deflection line between the two lower rollers o 1 o 2 is simplified into an arc, and then, the curvature at the measured point P i is where L is the span. Different from the overall curvature calculation model, the K ave (i) skips the deflection curve fitting process, which has certain advantages for the deflection detection method based on the laser displacement sensor.

Empirical-curvature calculation model
An empirical equation was used to simulate the bending deformation of the piston rod [25], which is where v(x) is the longitudinal deflection, f is the maximum deflection, and L is half the length of the curved part or half the distance between the two lower fulcrums.
Some researchers used the empirical equation in the deflection curve fitting in the pressure straightening process [25,26] and further obtained the curvature equation as , which is related to the maximum deflection and length of the curved part.

Pipe case
As shown in Fig. 3, a LSAW pipe with excessive straightness produced by an enterprise is taken as the research object. The geometric dimensions and mechanical properties are shown in Table 1, and the measurement results of the overall deflection distribution [27] are shown in Fig. 4.

Fig. 2
Local average-curvature calculation model

Roller shape
Section distortion cannot be avoided during pipe straightening, although established mechanical models can predict it. For safety's sake, the pass of the straightening roll should be the same diameter as the pipe, that is, the equal diameter design principle, so as to limit the deformation of the pipe section and reduce its impact on the straightening process and effect. At the same time, the section ovality under the numerical simulation conditions of the same span and the same load is analyzed to test the rationality of the pass design principle. Specifically, for the pipe case with an outer radius of 228.6 mm, the pass radius of the straightening roll in the FEM is set to R , 1.025R , 1.05R , 1.075R , and 1.1R , respectively, that is, 228.6 mm, 234.31 mm, 240 mm, 245.75 mm, and 251.46 mm.

Arrangement of roller system
According to the arrangement position of the upper one relative to the two lower rollers, the roller system structure can be divided into symmetrical and asymmetrical arrangements. Based on the pure-bend equivalence theorem of the in-plane curved beams [28], the over-bend straightening process of in-plane curved beams with initial curvature K 0 is equivalent to the pure-bend process of straight beams with curvature K 0 after springback. At the same time, one of the deflection characteristics of LSAW pipes is the in-plane bending with single radian. Therefore, the pipes in the straightening process are described as a simply supported beam under the action of concentrated force in material mechanics, to analyze the relationship between the position of the upper roller and the deflection distribution.
As shown in Fig. 5, the two lower rollers correspond to two fulcrum positions A and B , and the distance is L , that is, the span. The upper roller corresponds to the pressure point position C under the action of concentrated force F , and the distance from the two fulcrums is a and a , respectively, and a + b = L . When a = b , this is a symmetrically arranged roller system; otherwise, it is arranged asymmetrically.
According to the mechanics of materials, the deflection distribution on the simply supported beam under the action of concentrated force is where E is the elastic modulus, and E is the sectional moment of inertia.
When a = b , the maximum deflection position is in the middle of the span, which is also the pressure point position. When a ≠ b , the maximum deflection position is determined by the extreme value, and there is For the asymmetric roller system, when b << L , that is, the pressing point is infinitely close to the right fulcrum, it can be considered that b ≈ 0 , then, Therefore, when the pressure point is extremely close to the lower fulcrum, the maximum deflection position is still near the midspan, that is, no matter where the concentrated load acts, the maximum deflection section is located near the midspan. It can also be inferred from the pure-bend equivalence theorem that the compression point should be placed at the maximum deflection, and the fulcrum should be symmetrically distributed on both sides of the compression point so as to avoid the deformation of the section with small initial curvature. The three-roll continuous straightening is a continuous three-point bending process, and each section will be loaded by the upper roller. Finally, the optimal position is determined as the midpoint of the two lower rolls, and the roll system is symmetrically arranged.

Span
Span L refers to the distance between two lower rollers, which will directly affect the loading load as In the three-point bending pressure straightening process, the reasonable fulcrum distance should keep the change rate of the initial curvature and the straightening moment as consistent as possible [7]. In fact, for a given part to be straightened, these two rates of change are constant, and that of moment is equal to the fulcrum reaction. Therefore, increasing the fulcrum distance is equivalent to reducing the change rate of the moment.
Then, there must be a fulcrum distance, making the two curvature change rates approximately equal, which is also the reason why the fulcrum distance of the straightener is adjustable. However, the discussion on the consistency of the change rate is still qualitative analysis, and its quantitative analysis is difficult.
On the other hand, the three-roll continuous straightening process, as well as the traditional three-point bending pressure straightening, has a straightening blind zone, that is, the curved parts cannot be loaded within the half span of both ends. Therefore, increasing the span will increase the blind area. Especially for parts with serious end deformation, special attention should be paid to this problem. The above analysis shows that there is no quantitative method to determine the span, which is usually estimated according to the specific part and straightening experience. This value in the traditional three-point pressure straightening is usually 1/3-2/3 of the pipe length [5]. In order to further clarify this problem, the span parameters in the FEM are 4000 mm, 4500 mm, 5000 mm, 5500 mm and, 6000 mm, respectively, and the determination principle of span is tried to be established by the analysis of section distortion.

Theoretical straightening moment
The straightening moment can be obtained directly according to the theoretical model given above, on the premise that the initial curvature is known. After applying the above four curvature models to the LSAW pipe case, the obtained K exp is abnormal.
As shown in Fig. 6, the fitting accuracy of the deflection curve at the pipe end is low, especially the error of the initial section is very large, which further leads to the unreasonable initial curvature distribution curve. Obviously, this empirical equation is not suitable for the calculation of the deflection curve and initial curvature of the three-roll continuous straightening process for LSAW pipes, so the theoretical straightening moment based on this equation will not be discussed.

FEM
The FEM of three-roll continuous straightening process is established by using the software ABAQUS. The geometric and material parameters of the curved pipe are set according to Table 1 and Fig. 2.
Considering the symmetry of in-plane bending, the half of the pipe is modeled. More specifically, the pipe is set as 3D deformable, the element type is an 8-node linear incompatible hexahedral element (C3D8I), and the elements along the wall thickness direction are divided into 4 layers. All three straightening rollers are set as 3D analytical rigid. The contact mode between the pipe and the roller is surfaceto-surface contact. Finally, the ABAQUS/standard analysis module is used to solve.
For the three-roll continuous straightening process, the press-bending model and the roller-bending model are established, respectively, as shown in Fig. 7.
In the press-bending model shown in Fig. 7a, the threepoint bending and the springback process are numerically simulated at the position of maximum deflection. Based on the low-order simple-fitting curvature calculation model, it is determined that the maximum deflection position is x = 6600mm , the initial curvature is K 0 = 5.82 × 10 −6 mm −1 , and the required theoretical straightening moment is M = 8.32 × 10 −8 N • mm . In addition, the pass radius and the span of the straightening roller are set according to the previous analysis, and different bending loads are applied to the upper roll correspondingly. Then, the design principles of span and roller shape parameters are explored through the section ovality analysis after springback.
In the roller-bending model shown in Fig. 7 b and c, the span is 5000 mm and the pass radius is 228.6 mm. The straightening load is calculated according to the three curvature models K hig (x) , K low (x) , and K ave (i) , respectively. Finally, the straightness and section ovality after straightening are analyzed to determine the optimal initial curvature calculation model.

Roller shape
Based on the press-bending model, for the LSAW pipes with radius R , the pass radii of the straightening rollers are R , 1.025R, 1.05R, 1.075R, and 1.1R, respectively. The section ovality after springback under the same span and the same load is counted, and the results are shown in Fig. 8. Obviously, with the increase of the roller radius, the deformation of the pipe section gradually increases. Therefore, the small roller should be used, which also proves the rationality of the equal diameter design principle.
When the roller diameter is 1.1R, the deformation of the section in direct contact with the roller after springback is analyzed, as shown in Fig. 9. It can be seen that the section is deformed from a standard circle to a transverse ellipse, that is, the section is flattened. It can be inferred that the local contact between the pipe and the roller leads to stress concentration, which intensifies the section deformation. At the same time, a smaller roller can change the contact state from a point to a line, thereby reducing stress concentration and section distortion, which also explains the rationality of the equal diameter design principle.

Span
Based on the press-bending model, under the conditions of roller radius R = 228.6mm , loading moment M = 8.32 × 10 −8 N • mm , and different spans, the ovality of the section after springback is counted, and the results are shown in Fig. 10. It can be seen that with the increase of span, the section deformation gradually decreases, and when this value increases to 5000 mm, the section distortion tends to be stable. At the same time, according to the process characteristics, the larger the span, the larger the straightening blind area; the smaller the span, the greater the load under the same loading moment, and the higher the energy consumption of the equipment. Therefore, considering comprehensively, the span of the LSAW pipe case should be selected as 5000 mm.
Further analysis, under the condition of ensuring the quality of the section, the span should be as small as possible to reduce the scope of the straightening blind area. For curved pipes with the same diameter, the larger the relative thickness (the ratio of wall thickness to diameter), the stronger the deformation resistance and the larger the allowable span. On the other hand, for pipes with the same relative thickness, the larger the diameter is, the larger the allowable span value is. It can be deduced that the span is negatively correlated with the relative thickness and positively correlated with the pipe diameter.
Define a span correlation coefficient γ with where D is the outer diameter of the pipe to be straightened and t is the wall thickness. For the pipe case, this coefficient is

Fig. 6 Empirical equation initial curvature
Using this value, the empirical formula for estimating the span L in the three-roll continuous straightening process is This method uses the geometric parameters of pipes to describe the deformation resistance of the section, which can provide a reference for the determination of span in new technology.

Calculation model of initial curvature
Through the analysis of the press-bending model, it is determined that the span is 5000 mm, and the roller diameter is equal to the pipe diameter, which is 228.6 mm. Based on this result, using the roller-bending model, the initial curvature calculation model continues to be discussed.  Fig. 4, three models are used to calculate the initial curvature of the pipe case, and the corresponding theoretical straightening moment is further calculated, as shown in Fig. 11. It can be seen that the initial curvature curve based on K hig is double peaked and fluctuates greatly, which is related to high-order fitting. At the same time, the corresponding straightening moment M hig is also much larger than the other two models. In contrast, the relative error of the moments M low and M ave obtained based on K low and K ave is small. Therefore, the calculation accuracy of the two needs to be further evaluated by the straightening effect.
For straightness, the overall straightness and end deflection of the straightened pipes are shown in Table 2. It can be seen that the pipe based on K hig has over bending, indicating that the straightening has failed, which is consistent with the larger moment shown in Fig. 11b. It is concluded that the higher-order piecewise-fitting curvature calculation model is not suitable for the initial curvature in the over-bend straightening theory, but it can still be used for the fitting of deflection data to calculate the initial straightness.
On the other hand, the straightening moments based on K low and K ave have corrected the overall straightness to less than 1.5‰, reaching the standard requirement of 2‰, and the straightened straightness based on K low is smaller. At the same time, the local deflection within 1000 mm of the pipe end does not exceed the 4 mm required by the standard.
For the section ovality, the pipe body and the end section of the straightened pipe are measured, and the section position of the maximum value is counted, as shown in Table 3. It can be seen that the section ovality of the pipes with qualified straightness does not exceed 0.5%, meeting the standard requirements, and the sections with most serious distortion are located near x = 7000mm .  According to the two initial curvature models, the maximum curvature is located at x = 6600mm , indicating that the section distortion with large axial curvature is serious. Fortunately, this does not exceed the standard requirements through the limitation of the straightening rollers.
In conclusion, the reliable initial curvature distribution can be obtained based on K low and K ave , and the straightness and section ovality of the corrected pipes can meet the requirements. Moreover, the comprehensive straightening effect based on the low-order simple-fitting curvature calculation model is better.

Experimental system
The three-roll continuous straightening process makes the traditional step-by-step process continuous, and it is easy to realize the accurate and automatic control through closedloop loading. A semi-automatic experimental system integrating deflection detection and continuous straightening    is built, as shown in Fig. 12. This system mainly includes mechanical system, electro-hydraulic control system, and detection device [21].

Straightening experiment
The test tube is made of 20 steel, and its geometric parameters are shown in Table 4. These purchased tubes with standard straightness are first prepared into bending parts to study the straightening process. Considering the influence of the Bauschinger effect, the tension/compression loading test with cycle 1 was carried out to obtain the accurate material properties after the second reverse-bending. This test was completed on Instron 8801, as shown in Fig. 13. The tensile strain is 0.003, 0.005, and 0.007, and the compressive strain is − 0.003. Then, the bilinear hardening material model is used to fit the real stress-strain data during the reverse loading of the sample, and the average value is taken as the material parameter, as shown in Table 5.
According to the design principle of the equal diameter pass roll profile and the empirical Eq. (24) of span estimation, the radius of the straightening roller is determined to be 30.2 mm, the span is 400 mm, and the step length of axial movement of tubes is 50 mm. Fig. 12 The experimental system for the three-roll continuous straightening process. a Whole system. b Electro-hydraulic control system. c Mechanical system and monitoring device The experimental steps mainly include curved tube preparation, deflection detection and deflection curve fitting, initial curvature and straightening moment calculation, straightening load calculation, overall deflection control experiment, and straightness inspection.

Results and discussion
The three-roll continuous straightening experimental system can not only carry out the deflection test but also complete the research on the three-roll continuous straightening process. In the previous experiments, the deflection detection of five tubes has been completed in Ref. [21], and this work continues to study the straightening process on these pipes.
The initial curvature and the theoretical straightening moment of five tubes are calculated, respectively, as shown in Fig. 14. The data obtained based on K low are smooth and continuous curves, and the discrete data corresponding to the monitoring points are obtained based on K ave , but there trends are consistent. Moreover, the calculation results based on K ave have large fluctuations, and the overall distribution is slightly smaller than that of K low . It can be inferred that due to the influence of factors such as sensor accuracy and pipe surface roughness, the detected local deflection data will have a certain error, resulting in fluctuations. Furthermore, the curvature calculated directly will have some abnormal values without any mathematical means.
Furthermore, the three-roll continuous straightening process of five tubes is analyzed by numerical simulation and physical experiments, respectively, and their straightness is shown in Table 6. According to the simulation analysis, using the process parameters calculated based on the two curvature models, the straightness after straightening meets the standard requirements, that is, less than 2‰, but the one based on K low is smaller. In addition, the detection of local deflection in K ave will be affected by the span, and the calculated value will produce some fluctuations.
Compared with the numerical simulation, the residual straightness of the experiment based on K low is larger but controlled within 1.50‰. Therefore, considering the model accuracy and the straightening effect, the loworder simple-fitting curvature calculation model K low is finally determined as the optimal model of the initial curvature in the three-roll continuous straightening process.

Process analysis software
The new three-roll continuous straightening process can complete the deflection detection, straightening, and residual straightness inspection of LSAW pipes with unknown deflection. Combined with the electromechanical hydraulic integration technology, this method can also realize the automation and intelligence. For the application and promotion of the new process, the objectoriented visual operation interface is developed by using  the Matlab GUI platform, that is, the three-roll continuous straightening process analysis software of LSAW pipes, as shown in Fig. 15, and its calculation process is shown in Fig. 16. This process software consists of four modules: basic parameter setting, initial straightness calculation, straightening load calculation, and residual straightening straightness calculation, and the experimental system together constitutes a complete three-roll continuous straightening experimental platform. For example, this software analyzes tube no. 3 used in the previous experiment. After setting the basic parameters and reading the online deflection test data, the initial straightness is calculated to be 0.88%. It is judged that the tube is unqualified, and the position-load data required for straightening is calculated. After straightening, the residual straightness calculation module calculates the residual value of 0.10% according to the input local residual deflection data. It is judged to be qualified, and the straightening is completed. The final software interface is shown in Fig. 17.

Conclusions
Aiming at the problems of low efficiency and unstable accuracy of the current mold-pressing straightening process for LSAW pipes, a three-roll continuous straightening process is proposed in this study. In the systematic research, a new deflection detection method is established, the calculation accuracy of multiple initial curvature distribution models is compared and analyzed, and the relevant process parameters are determined. Finally, a three-roll continuous straightening experimental platform is built, and the feasibility of the new process is verified by experiments. The following conclusions are obtained: (1) Through the continuous loading of the upper roller, the three-roll continuous straightening process can completely load the theoretical straightening moment to the corresponding section and theoretically realize the one-time straightening of the curved pipe. And this process uses roller straightening instead of mold bending, which can greatly improve the straightening efficiency.
(2) Based on the pure-bend over-bend straightening theory of the in-plane curved beam with a symmetrical section, the theoretical moment equation required for straightening is determined, and its accuracy is directly related to the initial curvature, rather than the fitting accuracy of the deflection curve. Compared with the high-order piecewise-fitting curvature calculation model K hig , the local average-curvature calculation model, and the empirical-curvature calcu- Fig. 15 Three-roll continuous straightening process software for LSAW pipes lation model K ave , the low-order simple-fitting curvature calculation model K low has the highest reliability.
(3) In order to control the section distortion and the straightening blind area, the straightening roller should follow the equal diameter design principle, and the empirical formula of span estimation is given. The simulation analysis and experimental research show that the straightness of the straightened tubes can be controlled within 1.5‰ and the ovality of the section can be within 0.5%, which proves the feasibility and reliability of the new process. (4) The three-roll continuous straightening experimental system is built, and the process analysis software is developed, which lays the foundation for the promotion and intellectualization of the new process.