Control of ring rolling with variable thickness and curvature
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Abstract
RadialAxial Ring Rolling (RARR) is an industrial forging process for making strong, seamless metal rings. Conventionally, rings are made circular with constant crosssection. In this work we demonstrate a sensing and control strategy to create rings with variable radial wall thickness and variable curvature using standard RARR hardware. This has a number of potentially useful applications but also provides an understanding of how to control these properties for conventional RARR. The sensing uses a calibrated video camera to take a series of images of the ring top surface. Image processing is employed to measure and track the ring material insitu. The complete state of the ring is represented by the ring thickness and curvature as a function of its volume fraction, which is computed by combining the measurements from the unoccluded areas with estimates of the ring shape elsewhere. Additionally, we present a marking technique for tracking of material as it rotates through the rolling machine, even after significant deformation of the ring has occurred. We show that rings with a wide range of variation in local thickness and curvature can be formed using conventional RARR hardware and a photogrammetric state measurement technique, combined with openloop scheduling and feedback control of thickness and curvature. Rings with both variable thickness and noncircular shapes have been produced virtually using numerical simulations and in reality using modelling clay as a material to simulate metals at forging temperatures. We demonstrate that this technique extends the range of shapes achievable with standard RARR hardware.
Keywords
Process automation Process control Digital image correlation Industrial control Ring rolling Variable geometryIntroduction

the mandrel compresses the ring wall radially against the forming roll in the radial pass, and the forming roll is driven to draw the ring into the roll gap using friction whilst the mandrel rotates idly;

the radial roll gap between the mandrel and forming roll is closed over successive rotations to reduce the radial wall thickness;

the axial rolls are also driven and their roll gap can be closed to reduce the ring’s axial height;

the guide rolls apply a restoring moment to prevent the centre of the ring drifting away from the Xaxis;

the ring diameter grows as the cross section area reduces over successive radial and axial passes, up to reaching the target diameter.
Conventional industrial ring rolling processes have closedloop control systems for the various degrees of freedom of the different rolls [13]. Usually, a singlepoint measurement of the ring diameter is taken using a contacting roll or a laser distance sensor. The displacements to be prescribed for the different rolls are determined based on this measurement and a rolling curve, which prescribes the path from initial to final cross section [14]. Effectively, the closedloop control system only accounts for the ring diameter, whereas the evolution of the crosssection is controlled with and openloop tool path.
The use of a camera measurement system in this work enables the control of ring curvature and radial thickness along its circumference. Recent developments in sensing in ring rolling using photogrammetry have shown that it is a practical observation technique [4, 6, 15, 16]. [6] showed that the function of the guide rolls could be replaced by controlling the relative driving speeds of the axial and forming rolls to keep the ring centred.
The majority of previous research in RARR has focused on improving the reliability of the conventional process or on the development of new process designs that increase the range of allowable ring geometry [2, 3]. This relates mainly to nonrectangular ring cross sections, for which each desired cross section requires its own specific tool geometry [10, 20]. Recently, a ring rolling process has been developed to produce rings with different cross sections, without using partspecific tooling [8, 9]. Such an increase in production flexibility significantly extends the applicability of ring rolling for products, which are produced in small batches. The current work aims at extending the flexibility of ring rolling processes, through simultaneous control of variable radial thickness [6] and variable curvature [5]. It will be shown that creating rings with both variable radial thickness and variable curvature is possible using conventional rolling hardware with additional sensing and control.
Geometry measurement during RARR
In addition to measuring the overall shape of the ring, it is also necessary to track the movement of the ring material relative to the tools. The relative speed of the forming roll and the ring material are difficult to determine accurately due to changing contact conditions that lead to variable amounts of slipping. Therefore, an optical tracking strategy has been adopted. Surface features are invariably apparent in hot ring rolling, but for faster detection and more robust tracking, markers were applied to the rings in this work to locate the ring material. In practice, it is anticipated that periodic water jet spraying or hightemperature paint may be applied in the industrial process to assist with tracking. It may be possible to use digital image correlation to track arbitrary random surface features, but the computational effort in identifying known patterns is less than tracking random surface features, although this may be necessary when marking is not appropriate.
In this paper, the image processing procedure for tracking of the state of the ring is explained in Chapter “Image processing”. Process control for variable thickness and variable curvature is discussed in Chapter “Process control”. Chapter “Test results” presents trials for two different rings which have been simulated and produced with clay material. Finally, conclusions and discussion are found in Chapter “Conclusions and future research opportunities”.
Image processing
Extracting ring boundaries
The boundary points of the ring in the RGB (redgreenblue) colour image are determined to nearestpixel precision by segmenting the image into ring material and nonring material. The scene containing the ring, as shown in Fig. 4, is configured to make the segmentation and edge detection task simpler. The background is kept dark and nonreflective. In hot RARR, the ring glows with heat, which contrasts clearly with the dark background, but in cold rolling the ring has to be illuminated by a light near the camera, so that the top surface of the ring is more strongly lit than the inner ring wall (the effect of which is shown in the simulated rendering of Fig. 4). The inner wall can also be painted black to enhance the contrast.
Additional filtering of the ring edges is applied by interpolating the radii (calculated relative to a centre determined by fitting an ellipse to the boundary) of the boundaries linearly with angle. This reduces the number of erroneous boundary points because the paths of the boundaries are close to tangential.
Ring midline and thickness
The objective of the image processing algorithms is to estimate the current state of the ring geometry necessary for control of the process. The ring is assumed to maintain a rectangular wall crosssection, and therefore the state of geometry can be described by the ring’s axial height and radial thickness along a closed path within the ring wall. It is assumed that the ring height is constant across the ring, and that the derivative of the path is continuous along the closed path  the path stretches and bends only.
As plastic deformation is a local state variable defined at each material point, it is essential to prescribe and track the evolution of plastic deformation relative to each material point. Therefore, the prescribed thickness and curvature of the ring is defined relative to each slice of ring material. Since the total ring volume remains constant in RARR, the ring material is parametrized as the fraction of total ring volume, v_{f}(s) = v(s)/V_{T}, along the path s. This Lagrangian approach to tracking is essential for comparison between the current state of geometry and the targeted curvature and thickness evolution.
Ring rotation
To control the deformation of the ring material, it is necessary to know v_{f}(s) along the midline to align the targeted thickness and curvature relative to the current state. The speed of the ring cannot be accurately estimated by the speed of the rollers because they slip against the surface of the ring, so surface marking was employed which could be measured from the same images used to estimate the ring’s boundary shape.
To estimate the position of the ‘origin’ in the ring, and v_{f} from there, the tracking of only one location on the ring is required, and the position of the remainder of the midline can be estimated by integrating height and thickness along its length. However, this is not accurate when assumptions about the shape have been violated or disturbances in sensor data are present. Also, in practice, large fractions of the ring are periodically occluded, so the origin point would be lost. The practical solution to these issues in this work has been to use 12 initiallyevenlyspaced markers and then estimate v_{f}(s) in between, only over 1/12th of the ring. It is possible to increase the number of markers that are tracked, but more markers could be easily confused from one frame to the next, if they are closely spaced. Fewer markers could also be applied, but the error in estimating v_{f} over a larger midline section would increase, and when fewer markers are visible between the tools there is a greater chance of losing the estimate of the origin position entirely if other disturbances prevent the tracking of some markers.
Occluded regions and ring segmentation
When the ring passes under the axial rolls or through the radial roll gap, its upper surface edges are occluded from view by the camera. In these zones the thickness of the ring material perpendicular to the midline and the length of the midline is assumed not to change until it crosses the XZplane of the mill (Fig. 1). The thickness of the ring at a particular volume fraction along the midline changes as it passes through the rollers, and it is difficult to accurately predict the change in thickness without full knowledge of the parameters governing the rolling conditions, such as friction, aspect ratio, temperature, etc. For this reason, the ring thickness and midline length between the roll gap exit side of the XZplane and the point at which the ring reappears in view of the camera are estimated by assuming that the thickness of the ring is equal to the roll gap as it passed through. The midline length is calculated by knowing the volume of this region and assuming uniform ring height in this region. Practically, the region after the roll gap does not need to be estimated because it will be measured properly when the camera can see it again, and only the estimated geometry of the material that is about to enter the roll gap is needed for the controller.
Temporal filtering
Once the material is tracked, the thickness at any particular volume fraction is measured repeatedly (where visible) and the thickness should remain constant at a given volume fraction v_{f} between the exit side of one roll gap until entering the following roll gap. This permits the normal thickness estimates at all unnoccluded positions to be improved by filtering their thicknesses over several frames using median and movingaverage filters. This filtering helps alleviate any errors in edge detection due to image noise, lighting changes, etc.
Process control
The photogrammetric procedure outlined in the previous section enables continuous tracking of the midline M_{s}(s), thickness T_{s}(s) and volume fraction v_{f}(s) as function of the path length s (with s = 0 being the ‘origin’ of the ring). These continuous measurements are used for variable thickness and curvature control. The radial gap between the mandrel and the forming roll is used to control the ring thickness, whereas the axial roll speed is used to control the local ring curvature. Hence, control of local thickness and local curvature are decoupled. In this chapter, the mechanisms for control of ring thickness and curvature are discussed. Openloop scheduling and modelling for feedback control of ring thickness are discussed in “Openloop radial gap planning for thickness control” and “Modelling for thickness feedback control” respectively. Openloop scheduling and modelling for feedback control of ring curvature are discussed in “Openloop curvature planning” and “Modelling for curvature feedback control” respectively.
Openloop radial gap planning for thickness control
Due to the mechanical constraints of the rolling process, the thickness reduction per revolution must be limited. Conventional rolling closes the radial roll gap at a constant rate until the ring has reached its target diameter (wherupon the radial roll gap is held constant), whilst the forming roll rotates at a constant rate, which leads to a reduction in the ring’s angular velocity as its radius grows.
With a variable wall thickness target, the radial roll gap must change much more rapidly in the final revolution of the ring to maintain contact with the ring. However, there is some choice in specifying the revolution in which the plastic change in thickness is obtained. For instance the ring could be rolled in the conventional manner, keeping constant thickness throughout the ring, until the thickness is at the maximum targeted thickness in the reference ring, and only then start reducing the thickness of the thinner segments in subsequent passes. In this work, the plastic change in thickness is divided into equal fractions per revolution to achieve the targeted thickness in a defined number of revolutions, but without exceeding the maximum thickness reduction permitted by the mechanics of the rolling conditions. The openloop tool path is determined under the assumption of rigid plastic material behaviour, meaning that the resulting ring thickness is equal to the roll gap. In “Modelling for thickness feedback control” , a process model for feedback control is developed. This model accounts for springback, machine compliance and transverse strain in the axial roll pass. It will be shown that this model can be used to determine an improved openloop tool path.
Modelling for thickness feedback control
The open loop tool path is determined under the assumption of rigid plastic material behaviour. However, axial passes increase the radial thickness due to the Poisson effect, and the thinning effect of radial passes is reduced by machine compliance and material springback (part of the deformation in the forming zone is elastic, and these compressive elastic strains reduce after leaving the forming area, leading to less thinning). Therefore, feedback control may be employed to increase forming accuracy. In this section, a feedback control algorithm is proposed based on mechanical modelling of the ring rolling process.
It is assumed that the cross section of each ring segment remains rectangular during rolling, and can be described with an axial thickness t^{a} and a radial thickness t^{r}. In this work, variable radial thickness is targeted, while the axial roll gap is kept constant in order to keep constant axial thickness during rolling. Let the radial thickness of a segment before the k th rotation be \({t^{r}_{k}}\), after the k th radial rolling pass be \(t^{r}_{k + 0.5}\) and after the k th rotation through both rolling stages be \(t^{r}_{k + 1}\). The roll gap between the mandrel and forming roll for that segment in the k th rotation is \({u_{k}^{r}}\).
In the following derivation, it is assumed that the thickness evolution at a specific segment is independent of the thickness evolution in neighbouring segments. The derivation holds for a single ring segment, and is decoupled from other ring segments. It is key to keep in mind that the time index k represents different passes through the roll gaps of a single ring segment only. One could extend the model in order to relate the thickness evolution of neighbouring segments, but that it not considered in this work.
For illustration, it is assumed that the model parameters are correctly chosen (\(\lambda _{a}^{\mathrm {M}} = \lambda _{a}^{\mathrm {R}}\), \(\lambda _{r}^{\mathrm {M}} = \lambda _{r}^{\mathrm {R}}\) and \(c_{r}^{\mathrm {M}} = c_{r}^{\mathrm {R}}\)) and that the value of \(\lambda _{a}^{\mathrm {R}} = \lambda _{r}^{\mathrm {R}} = 0.6\). In this case, it follows that α + β/2 < 3.78 is the condition for system stability. Additional constraints should be taken into account to ensure that the tool and the ring do not lose contact.
Openloop curvature planning
All circular rings have mean normalised curvature of \(\hat {\bar {\kappa }}^{v}= 2\pi \) by definition.
The angle δ can be changed by adjusting the speed of the axial rolls relative to the forming roll so that the tangential ring speeds are not equal for both rolling stages. When the magnitude of the rolling speed at the axial roll gap is greater than at the radial roll gap, the axial rolls displace the ring wall in the Y direction by a different amount to the radial roll gap and this creates an ‘opening’^{1} or a ‘closing’ bending moment within the radial roll gap. If the bending moment exceeds the plastic bending moment for the ring wall within the radial roll gap then a plastic hinge forms there, causing a permanent change in ring wall curvature. Because the ring is a closed loop, there must be an opposite change in curvature in the ring wall remote from the bent region for compatibility to be maintained, but this is distributed over a longer arc length by elastic bending caused by the residual stresses. Assuming that the axial rolls impose a force on the ring which acts perpendicular to the mill axis (i.e. in Y direction), the maximum bending moment in the ring occurs at the radial rolls. In combination with compressive forces applied by the mandrelforming roll pair, the material will yield at the radial roll gap, leading to localisation of the plastic bending, which is useful for decoupling the effect of changing the curvature in one region of the ring wall from neighbouring regions.
Modelling for curvature feedback control
Simplifying assumptions about the mechanisms of curvature evolution in RARR have been used for construction of the openloop curvature path in the previous section. In order to improve geometrical product accuracy, feedback control may be employed. A control diagram including openloop and feedback control is shown in Fig. 13. Such a feedback control system can be tuned based on process data or using a process model, similar to the analytic model used for thickness feedback control in “Modelling for thickness feedback control”. Furthermore, a model may account for the change of process response with evolving product state, which will be difficult to identify based on process data only. In this section, it is discussed how such a model may be developed.
Developing a model for the curvature evolution in ring rolling is not as straight forward as for the thickness reduction. Several analytical models have been developed for ring rolling, with the objective to estimate ring growth rate (e.g [22]), process forces (e.g. [19]) or constraints of process conditions (e.g [7]). With respect to curvature evolution, [17] reviewed analytical and numerical curvature evolution models for the sheet rolling process, which has strong similarities with the ring rolling process. They showed that these works present contradictory results, as curvature evolution depends on many factors and is therefore difficult to predict. Following to this work, [18] developed a modelling framework of the ring rolling process, which accounts for noncircular, noncentred and noncoaxial rings. He uses an extended slab method for the deformation zone and an elastic curved beam model for the rest of the ring. Although no appropriate coupling of these models was found to ensure system convergence, the equations can be used as a starting point for the development of a curvature evolution model for process control. As the extended slab model depends on the roll gap, the thickness reduction and curvature evolution models will become coupled, which must be accounted for in the controller design.
Test results
Past work has demonstrated that variable thickness rings with uniform curvature [4] and variable curvature rings with uniform thickness [5] can be created using conventional RARR hardware and the additional sensing described earlier. This paper has covered the theory behind the implementation of the control strategy in more depth for these two processes. We now present two trials of forming rings with combined varying thickness and varying curvature. The target geometries and openloop tool paths are presented in “Target rings”. The trials have been first simulated. The simulation procedure is explained in “Simulation procedure” and the results are presented in “Simulation results”. Finally, experimental clay trial results are presented in “Clay trials”.
Target rings
Simulation procedure
The trials were conducted using the finite element method to simulate the mechanics of the rolling mill and the material deformation. The procedure was first outlined in [5] but can be summarised as follows: a 3D model of a ring is modelled using Abaqus Explicit with an additional user subroutine which periodically outputs the coordinates of the mesh to a text file. This text file was then read with Matlab and the ring was rendered as an image, as if being photographed by the optical camera in a realworld situation; the image processing and control algorithms were implemented in Matlab and a file containing actuation instructions was written and made available for Abaqus to read and implement over the course of the next period. In this way, the sensing and the control strategy did not have to be changed to control the simulated ring or a realworld rolling mill. The only significant operational difference between a real mill and the Abaqussimulated mill is that the processing time could be, in effect, reduced to zero if so desired. However, a simulated delay in calculating the actuator settings was imposed to emulate the practical situation, although investment in improved computational hardware would reduce processing time for a real controller.
The simulations are performed to show that thickness and curvature of the rings can be controlled simultaneously. It is not intended to use the model for prediction of the manufacturing accuracy of the rolling procedure. Therefore, basic assumptions and settings have been used in the finite element model. A total of 1920 8node linear brick elements with reduced integration have been used for the ring. A material model with a Young’s modulus of 120 GPa, a Poisson’s ratio of 0.3, and a yield strength of 500 MPa with linear work hardening is used.
Simulation results
Clay trials
The trial shapes were also produced using the same control strategy using a desktopscale RARR mill capable of rolling plasticine, which simulates the behaviour of metal at temperatures greater than half of the melting temperature [1]. In these realworld trials there were additional sources of error in the rolling process, primarily from underpowered actuators and a lack of machine stiffness.
Conclusions and future research opportunities
This work has described in detail a sensing and control strategy for adapting the conventional radialaxial ring rolling process to produce rings with variable wall thickness and variable curvature. Previous work has described the processes in isolation, but this is the first time that their combination has been shown to produce rings with a wide range of shapes. This is shown through numerical simulations and clay trials for two different target rings.
Using openloop normalised tool path generation for the targeted shapes as a function of ring volume fraction permits the comparison of the evolving deforming body of the ring with the reference shape. This comparison is fundamental to the forming process and could be built upon further to automatically calculate the tool paths online using constrained feedback control. The control algorithm can be further improved through the development of better process models, or, if computational power permitted, through the use of other control strategies such as Model Predictive Control. Additional flexibility in the process can be achieved by incorporating simultaneous control of a variable axial height too, which will require additional sensing as well.
The development of a sensing and control system for production of rings with variable thickness and curvature using conventional RARR hardware leads to a major increase in the range of allowable ring geometry. This is of great importance to modern industry, as a wider range of products may potentially be produced with the benefits of RARR, such as efficient material usage and high material strength.
Footnotes
 1.
‘Opening’ here means that the ring has reduced curvature and hence increased radius of curvature.
Notes
Compliance with Ethical Standards
Conflict of interests
The authors declare that they have no conflict of interest.
References
 1.Aku S, Slater R, Johnson W (1967) The use of plasticine to simulate the dynamic compression of prismatic blocks of hot metal. Int J Mech Sci 9(8):495–500CrossRefGoogle Scholar
 2.Allwood J, Tekkaya A, Stanistreet T (2005) The development of ring rolling technology. Steel Res Int 76(23):111–120CrossRefGoogle Scholar
 3.Allwood J, Tekkaya A, Stanistreet T (2005) The development of ring rolling technology  part 2: Investigation of process behaviour and production equipment. Steel Res Int 76(7):491–507CrossRefGoogle Scholar
 4.Arthington M, Cleaver C, Allwood J, Duncan S (2015) Measurement and control of variable geometry during ring rolling. In: IEEE Multiconference on systems and control, Sydney, pp 1448–1454Google Scholar
 5.Arthington M, Cleaver C, Huang J, Duncan S (2016) Curvature control in radialaxial ring rolling. IFACPapersOnLine 49(20):244–249CrossRefGoogle Scholar
 6.Arthington MR, Cleaver C, Allwood J, Duncan S (2014) Realtime measurement of ringrolling geometry using lowcost hardware. In: 2014 UKACC International conference on control, CONTROL 2014  proceedings. IEEE, pp 603–608Google Scholar
 7.Berti G, Quagliato L, Monti M (2015) Setup of radial–axial ringrolling process: Process worksheet and ring geometry expansion prediction. Int J Mech Sci 99:58–71CrossRefGoogle Scholar
 8.Cleaver C, Allwood J (2017) Incremental profile ring rolling with axial and circumferential constraints. CIRP Ann 66(1):285–288CrossRefGoogle Scholar
 9.Cleaver C, Allwood J (2017) Incremental ring rolling to create conical profile rings. Procedia Eng 207:1248–1253CrossRefGoogle Scholar
 10.Davey K, Ward M (2002) The practicalities of ring rolling simulation for profiled rings. J Mater Process Technol 125126:619–625CrossRefGoogle Scholar
 11.Davis J, Semiatin S (1988) ASM Metals Handbook Volume 14: Forming and Forging. ASM International, OhioGoogle Scholar
 12.Epp J, Surm H, Kovac J, Hirsch T, Hoffmann F (2011) Interdependence of distortion and residual stress relaxation of coldrolled bearing rings during heating. Metall and Mater Trans A 42(5):1205–1214CrossRefGoogle Scholar
 13.Jenkouk V, Hirt G, Franzke M, Zhang T (2012) Finite element analysis of the ring rolling process with integrated closedloop control. CIRP Ann 61(1):267–270CrossRefGoogle Scholar
 14.Kluge A, Lee YH, Wiegels H, Kopp R (1994) Control of strain and temperature distribution in the ring rolling process. J Mater Process Technol 45(14):137–141CrossRefGoogle Scholar
 15.Meier H, Briselat J, Hammelmann R, Flick H (2010) Image Processing Methods for Online Measurement in RadialAxial Ring Rolling. In: Proceedings of the 36th International MATADOR Conference. Springer, pp 355–358Google Scholar
 16.Meier H, Briselat J, Husmann T, Kreimeier D (2011) Online measurement of RadialAxial rolled rings with an image processing system. In: Proceedings of the 18th International Forgemasters MeetingGoogle Scholar
 17.Minton J, Brambley E (2017) Metaanalysis of curvature trends in asymmetric rolling. Procedia Eng 207:1355–1360CrossRefGoogle Scholar
 18.Minton JJ (2017) Mathematical modelling of asymmetrical metal rolling processes. PhD thesis, University of CambridgeGoogle Scholar
 19.Parvizi A, Abrinia K (2014) A two dimensional upper bound analysis of the ring rolling process with experimental and fem verifications. Int J Mech Sci 79:176–181CrossRefGoogle Scholar
 20.Qian D, Zhang Z, Hua L (2013) An advanced manufacturing method for thickwall and deepgroove ring—combined ring rolling. J Mater Process Technol 213(8):1258–1267CrossRefGoogle Scholar
 21.Wang C, Geijselaers H, Omerspahic E, Recina V, Van Den Boogaard A (2016) Influence of ring growth rate on damage development in hot ring rolling. J Mater Process Technol 227:268–280CrossRefGoogle Scholar
 22.Xu W, Yang X, Gong X, Zhou J (2012) A new mathematical model for predicting the diameter expansion of flat ring in radial–axial ring rolling. I J Adv Manuf Technol 60(9):913–921CrossRefGoogle Scholar
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