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Simulation methods for skew rolling
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ICAFT/SFU/AutoMetForm 2018 ICAFT/SFU/AutoMetForm 2018
Simulation Simulation methods methods for for skew skew rolling rolling
Manufacturing Engineering Society International a* Conferencea2017, MESIC 2017, 28-30 June C. Guilleaume 2017, Vigo (Pontevedra), Spaina C. Guilleaumea*,, A. A. Brosius Brosius a a
Institute of Manufacturing Technology, Chair of Forming and Machining Processes, Technische Universität Dresden, 01062 Dresden, Germany Institute of Manufacturing Technology, Chair of Forming and Machining Processes, Technische Universität Dresden, 01062 Dresden, Germany
Costing models for capacity optimization in Industry 4.0: Trade-off Abstract between used capacity and operational efficiency Abstract
A number of different rolling processes are summarized under the term skew rolling. The process variant investigated in this A number of different rolling processes are asummarized under a,* the term skewb rolling. The process b variant investigated in this paper is an incremental flexible process with kinematic forming of the geometry. Two sets of actively driven work rolls A. rolling Santana , P. Afonso , A. Zanin , R. Wernke paper is an incremental flexible rolling process with kinematic forming of the geometry. Two sets of actively driven work rolls are used in a transverse rolling process to selectively reduce the diameter of a cylindrical workpiece to form circumferential are used in a transverse rolling processa University to selectively reduce the diameter of Portugal a cylindrical workpiece to form circumferential of Minho, 4800-058 Guimarães, grooves. Simultaneously, the excess material is pushed in axial direction, thereby forming a bulge that can be used to join e.g. a b is pushed in axial direction, thereby forming a bulge that can be used to join e.g. a grooves. Simultaneously, the excess material Unochapecó, 89809-000 Chapecó, SC, Brazil gear wheel onto an axle. Since this is done in a cold rolling process the positive influence of the induced residual compressive gear wheel onto an axle. Since this is done in a cold rolling process the positive influence of the induced residual compressive stress as well as strain hardening can be used to improve fatigue strength of the workpiece under cyclical loads. The authors stress as well as strain hardening can be used to improve fatigue strength of the workpiece under cyclical loads. The authors discuss the advantages of this hybrid skew and cross rolling process and propose a simplified numerical model to quickly analyze discuss the advantages of this hybrid skew and cross rolling process and propose a simplified numerical model to quickly analyze process parameters like axial and radial work roll feed and the influence of initial stress profiles in the workpiece. The model Abstract process parameters like axial and radial work roll feed and the influence of initial stress profiles in the workpiece. The model uses a 2 ½ D axis-symmetric approach in LS-Dyna R10.1.0 with implicit solver. Additionally, preliminary results of first tests on uses a 2 ½ D axis-symmetric approach in LS-Dyna R10.1.0 with implicit solver. Additionally, preliminary results of first tests on rolled specimen from 42CrMo4 are briefly discussed. Under the concept of "Industry 4.0",discussed. production processes will be pushed to be increasingly interconnected, rolled specimen from 42CrMo4 are briefly
information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published Published by by Elsevier Elsevier B.V. B.V. © 2018 2019 The The Authors. © Authors. Published byof Elsevier B.V. goes beyond the traditional aim capacity maximization, contributing also for organization’s profitability and value. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is anlean open management access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Indeed, and continuous improvement approaches suggest capacity optimization instead of of ICAFT/SFU/AutoMetForm 2018. Selection and peer-review under responsibility of the scientific committee Selection and peer-review responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. maximization. The studyunder of capacity optimization and costing models is an important research topic that deserves contributions from both theModelling; practicalResidual and theoretical perspectives. This paper presents and discusses a mathematical Keywords: Rolling; Simulation; Stress; Fatigue Keywords: Rolling; Simulation; Modelling; Residual Stress; Fatigue model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity 1. Introduction optimization might hide operational inefficiency. ThisThe paper focusses on a by hybrid cold rolling process, its simulation in virtual experiments and the influence of © 2017 Authors. Published Elsevier B.V. This paper focusses on a hybrid cold rolling process, its simulation in virtual experiments and the influence of selected process parameters on thescientific formation of residual in theEngineering workpiece.Society Essentially any manufacturing Peer-review under responsibility of the committee of thestresses Manufacturing International Conference selected process parameters on the formation of residual stresses in the workpiece. Essentially any manufacturing 2017. process that changes the surface or shape of a workpiece also influences the residual stresses either by inducing them or process that changes the surface or shape of a workpiece also influences the residual stresses either by inducing them or by releasing them partially. These changes and the profile of the residual stresses have a strong influence on the part by releasing Models; them partially. TheseCapacity changes and the profile of theOperational residual Efficiency stresses have a strong influence on the part Keywords: ABC;toTDABC; Management; Idle Capacity; propertiesCost with regards yield strength and most importantly also fatigue resistance. In general terms, compressive properties with regards to yield strength and most importantly also fatigue resistance. In general terms, compressive 1. Introduction * Corresponding author. Tel.: +49 351 463 31972; fax: +49 351 463 37014 *The Corresponding author. Tel.: +49 463 31972; fax: +49 351 463 37014 cost of idle capacity is 351 a fundamental information for companies and their management of extreme importance E-mail address: [email protected] E-mail address: [email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier B.V.hours of manufacturing, etc. The management of the idle capacity in several©ways: tons of production, available 2351-9789 © 2018 The Authors. Published by Elsevier B.V. This is anAfonso. open access under the761; CC BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) * Paulo Tel.: article +351 253 510 +351 253license 604 741 This is an and openpeer-review access article under the CCfax: BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. E-mail address: [email protected] Selection and peer-review under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018.
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. 10.1016/j.promfg.2018.12.035
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C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–000
residual stresses are considered to have a positive influence on the strength and fatigue behavior while tensile residual stresses have a negative impact by reducing the load capacity and life time cycles. Therefore, it is very important to take the formation of residual stresses into consideration when choosing process parameters for a forming process. Until recently the main focus was to keep residual stresses as low as possible as to limit their overall influence on the part properties. This, however, severely reduces the process window and makes processes less efficient overall. Thus, it is of high interest to predict the resulting residual stresses of a forming process accurately and moreover, to selectively induce compressive residual stresses to make use of their positive effects. Here, a hybrid cold rolling process is investigated that is aimed at combining the known and documented positive effects of deep rolling with additional strain hardening and the possibility to form joints between different materials. 2. State of the art 2.1. Residual stress in metal forming Residual stresses are static multi-axial internal loads within a workpiece that is not otherwise subjected to an external load. Without additional external forces, these stresses are per definition in a state of equilibrium [1]. During subsequent manufacturing steps or during the use of a manufactured part, additional external loads are superimposed to these internal stresses [2]. Both the external and internal loads affect the workpiece as a collective either reinforcing or countering each other. This is relevant, because residual stresses are already present in the semi-finished products like cold drawn rods that are the basis for all cold bulk metal forming processes. Their influence on the subsequent processes, therefore, cannot be disregarded. Rudkins et al. found that extruded and drawn rods have ten-times higher residual stresses in axial than in radial direction [3]. Starting from the rotational axis with very distinct compressive stresses, the stress state continuously changes into dominating tensile stresses with increasing distance to the axis. This gradient, however, is highly dependent on the production process [2]. Reiß et al. compare cold forged and machined parts with different annealing conditions [4]. They determined that the induced near-surface compressive residual stresses have a positive influence on the fatigue strength of the investigated flange hub. This is in agreement with a study by Blasón et al. on the improvement of the fatigue strength of notched specimen using a deep rolling process [5]. The level of residual stresses generated here was close to the tensile strength of the material. Generally, deep rolling processes are the most common application where the positive influence of residual stresses is used. This secondary cold rolling surface treatment improves the fatigue life of products through a combination of strain hardening, improvement of the surface roughness and induced compressive residual stress. One way to limit the influence of the residual stress profiles in semi-finished goods is by a subsequent heat treatment of the product. Such a thermal treatment does not necessarily lead to a homogenization of the residual stresses however and furthermore measuring them without additional information regarding the strain and stress states can lead to ambiguous analytical results [2]. In a study regarding the heat treatment of bearing rings, Epp et al. found that cold rolled rings retained their induced residual stresses up to relatively high temperatures and that the relaxation at higher temperature is mainly due to recrystallization effects in the material [6]. 2.2. Hybrid rolling process The hybrid cold rolling process analyzed in this paper is a combination of skew and cross rolling which also includes some aspects of deep rolling surface treatments, as presented by Tscheuschner et al. [7]. The geometry is formed by two sets of work rolls that move both in axial and radial direction. The rotation of the workpiece is the result of the transmitted momentum via friction forces by the actively driven work rolls. Each set of work rolls simultaneously also functions as the counter bearing for the other regarding the axial movement. This cold rolling process is used to create a circumferential notch in the workpiece while pushing the excess material in axial direction towards a possible join partner like e.g. a gear wheel, see Fig. 1 a). An example of such a combined workpiece is displayed in Fig. 1 c). This process is highly flexible due to the kinematic forming of the geometry relatively independent from a specific work roll geometry. It allows to join parts out of different materials allowing the combination of their respective advantages like wear resistance and tensile strength.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–00
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Fig. 1. (a) Schematic of hybrid rolling process stage; (b) rolled specimen without and (c) with joined gear wheel.
The biggest benefit is the improved fatigue life of the resulting notched specimen. The reason for this is quite similar to the effects used in deep rolling surface treatments - the rolling process improves the surface roughness, see zone I in Fig. 1 b), causes a high level of strain hardening in the most critical part of the specimen (zone II) and induces compressive residual stresses that further improve fatigue resistance under cyclic loads. Preliminary tests on 42CrMo4 that was rolled on Profiroll 2-PR-15e skew rolling machine have shown that the improvement of tensile strength and fatigue resistance is so high, that the specimens do not fail in the notched section when being tested. 2.3. Numerical simulation of residual stresses induced by rolling processes Measuring residual stresses is a challenging procedure. Generally, the non-destructive testing methods using Xray, neutron or synchrotron diffractometry can only detect near-surface stress states and are highly dependent on measuring parameters and material properties [8]. Destructive testing like borehole or saw-cut method, however, change the initial stress state during the necessary material removal and need a calibration function for analyzing the measuring signal [9]. The high experimental effort needed to measure residual stresses is the main reason that this is rarely done when designing forming processes. Here, numerical simulations combined with a suitable material characterization can provide an alternative method to investigate residual stress formation and limit the amount of necessary measurements. Wronski et al. investigated the effects of cross-rolling on residual stress, texture and plastic anisotropy on low carbon ferrite steel and polycrystalline copper using a combination of experimental tests and numerical simulations [10]. Mehner et al. studied the residual stress evolution of cold rolled DC04 steel sheets with different initial stress states again using experimental tests as well as FEA methods [11]. The numerical approach allowed an easy variation of the process route and initial stress states and the results were in agreement with selective experimental tests. The cold rolling process for a bearing ring was simulated by Lan et al. in order to determine the residual stress state responsible for their asymmetric post process springback behavior [12]. The authors point out that for rolling processes that subject the material to incremental cyclic loads, a corresponding material characterization that considers these cyclic loads and a suitable material model need to be employed. Perenda et al. simulated the residual stresses after deep rolling of a high strength steel torsion bar using an explicit solver [13]. A fine mesh was used since the deep rolling effects are mainly relevant in the surface layers. In order to speed up the simulation, some simplifying model adjustments were made. 3. Virtual experiment Virtual experiments of the hybrid cross rolling process of 42CrMo4 steel are carried out in order to identify the relevant process parameters and investigate the sensitivity of the residual stress formation to the work roll path and initial stress state of the workpiece. The objective is to determine work roll paths that lead to compressive residual stresses in the most critical area of the part, which is the notch forming when the material is pushed in radial and axial direction. Additionally, the influence of assumed initial stress states that are typical for cold drawn semifinished products is to be investigated. This specific steel was chosen due to its high strain hardening characteristic and its relevance in industrial applications.
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3.1. Model and parameters The cross-rolling process is simulated with a simplified 2½ D model using LS-Dyna R10.1.0 with an implicit solver. The y-axis of the workpiece is used for the rotational symmetry. This reduced approach has the advantage of a much faster simulation time than a full 3D model. This allows for a faster and broader variation of the key process parameters like the work roll path and the initial stress state. The disadvantage is a minimally different local stress state, but since the main objective is a qualitative comparison of the resulting stress states regarding the influence of rolling parameters and initial stresses, this method is viable. Using the symmetry axis, the rolling process is modelled as a circumferential indentation without cyclical loading of the material. For the material formulation a linear piecewise approximation of the flow curve in combination with an isotropic hardening behavior was used for plasticity. The flow curve is the result of tensile tests done on the specific material batch used and some additional extrapolation points acquired from datasheets. A very fine mesh with an element size of 0.05 mm was chosen for the workpiece in order to have a fine resolution of the local stress states. The rolling process causes high strains and high mesh distortions in front of the work roll, so an automatic remeshing is done at fixed intervals to ensure a sufficient element quality. The influence on the resulting equivalent stress and triaxiality factor of two main parameters is investigated. First of all, the path of the work rolls in relation to workpiece is varied, as shown in Fig. 2 a). A linear, progressive and degressive tool path with the same final position are chosen with the goal to determine which forming history leads to an advantageous stress distribution with regards to the critical notched section of the workpiece. Secondly, the initial stress profiles of the workpiece were varied to identify their influence on the resulting stress states after forming. The assumed stress profiles for this investigation are in accordance with published profiles of cold drawn rods [14], see Fig. 2b). The triaxiality factor is used as an indicator of the dominant stress state in the workpiece, since it is highly relevant if the residual stresses are tensile or compressive and this information cannot be extracted from the residual equivalent stress.
Fig. 2. (a) Work roll paths; (b) initial stress profiles.
3.2. Results and discussion For all work roll paths, high effective plastic strains of up to 4 were reached in the area of the notch ground, resulting in a high amount of strain hardening in that area which is desirable regarding the fatigue strength of this smaller crosssection. The equivalent stress in the same area for all tool paths is also high with up to 1855 MPa, which is to be expected at these levels of plastic strain, see Fig. 3 a). It is noticeable that the work roll feed direction during the final stages of forming determines the area with the highest stress levels - both for the final load step and after relaxation. For a progressive work roll path, the final movement happens mainly in radial direction towards the workpiece axis while for the degressive work roll path, the final movement is mostly in axial direction towards the y-symmetry plane. Thus, for a progressive tool path, the entire area under the notch surface has a high stress level, while for the degressive tool path, mostly the area in axial feed direction has a high stress level. This is especially relevant after the relief step, when examining the residual stress distribution. Here, the overall level of residual stress around the notch is around 500-900 MPa, with a very small zone for each tool path where the high stress level from the forming process is retained just below the workpiece surface, see Fig 3. Since only compressive residual stresses are desirable in the critical notch ground, the triaxiality factor for each tool path is analyzed, see Fig. 4. The scale of the diagram is set so that areas with pure compressive stress states appear in blue, and areas with multi-axial tensile stress states appear in red.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–00
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Fig. 3. Equivalent stress (v. Mises) for (a) final load step and (b) after relief.
For all work roll paths, the triaxiality factor indicates that the area of compressive stress is significantly reduced during the relief phase due to the springback behavior of the material. For all tool paths the area just below the notch ground retains compressive residual stresses, which is considered to be positive for this critical cross-section. For all tool paths, however, there is also a significant area with tensile residual stresses forming close to the workpiece axis, see Fig. 4 b). This critical zone extends almost to the notch ground for the progressive tool path and could adversely affect the tensile and fatigue strength. Overall the area with tensile residual stress is the smallest for the degressive tool path. Simultaneously it results in the largest area with compressive residual stress close to the notch ground. This indicates that a degressive tool path is most likely to significantly improve tensile strength and fatigue resistance.
Fig. 4. Triaxiality for different work roll paths (a) for final load step and (b) after relief.
Finally, the effect of different initial stress profiles shown in Fig. 2 b) on the resulting residual stresses is examined using the numerical model. It is used to determine if for future research regarding rolling parameters and resulting residual stresses, the initial stress state of the semi-finished product has to be characterized and considered extensively. Fig 5 shows the comparison of all residual stress profiles for the combination of all three work roll paths and three initial stress states.
Fig. 5. Equivalent stress (v. Mises) after relief for different initial stress profiles, (a) no stress, (b) stress profile 1, (c) stress profile 2.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–000
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For each tool path, the characteristic size of the area with significant residual stresses and the level of equivalent stress remain almost unchanged by the induced initial stress profile 1 and 2. Near the symmetry axis some low residual stress remains from the initial profiles, but does not affect the relevant forming zone. The explanation is that the high equivalent plastic strain that the material is undergoing in the forming zone and the resulting high equivalent stresses during the process almost completely overwrite any low level initial stress profile imposed on the workpiece before. Regarding further investigations of rolling parameters and resulting stress states, this result can be considered positive, because it limits the experimental effort needed to characterize the initial stress state of the semi-finished cold drawn rods and prior steps of the process chain can be equalized. 4. Conclusion and outlook The presented approach for analyzing a hybrid cold rolling process using a simplified 2½ D numerical model was used to qualitatively compare different work roll paths and initial stress profiles regarding the resulting residual equivalent stresses and trixiality factors. Both of these results combined can give an indication as to the suitability of certain tool paths for selectively inducing compressive residual stresses in the critical area of a workpiece. The analysis showed clear qualitative differences regarding the residual stress distribution and level of residual stresses in different zones of the specimen depending on the chosen work roll path. The analysis of different initial stress profiles showed that their influence is insignificant compared to the large equivalent strain and resulting high equivalent stresses induced by the cold rolling process. As a next step further process parameters will the virtually tested and the real initial stress state of the semi-finished specimen used for experimental investigations will be measured selectively. Finally, cold rolled specimen manufactured with parameters identified by this numerical analysis will be tested in tensile and cyclic fatigue tests. Acknowledgements Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Priority Program 2013 "Targeted Use of Forming Induced Residual Stresses in Metal Components" under the grant numbers KA 3309/7-1 and BR 3500/21-1. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
K. H. Kloos, Eigenspannungen, Definition und Entstehungsursachen, Materialwissenschaft und Werkstofftechnik, 10(9) (1979) 293-302. E. Brinksmeier, J. T. Cammett, W. König, P. Leskovar, J. Peters, K. H. Tönshoff, Residual Stresses – Measurement and Causes in Machining Processes, CIRP Annals - Manufacturing Technology 31 (1982) 491-510. N. T. Rudkins, G. F. Modlen, P. J. Webster, Residual stresses in cold extrusion and cold drawing: a finite element and neutron diffraction study, Mater. Process. Technol. 45 (1994) 287-292. A. Reiß, U. Engel M. Merklein, Investigation on the influence of manufacturing parameters on the fatigue strength of components, Key Eng. Mater. Vol. 554-557 (2013) 280-286. S. Blasón, C. Rodríguez, J. Belzunce, C. Suárez: Fatigue behaviour improvement on notched specimens of two different steels through deep rolling, a surface cold treatment, Theoretical and Applied Fracture Mechanics 92 (2017) 223-228. J. Epp, H. Surm, T. Hirsch, F. Hoffmann, Residual stress relaxation during heating of bearing rinds produced in two different manufacturing chains, Journal of Materials Processing Technology 211 (2011) 637-643. T. Tscheuschner, M. Schomäcker, A. Brosius, Fügen hybrider rotationssymmetrischer Bauteile durch Profil-Axial-Walzen, Proceedings, 23. Sächsische Fachtagung Umformtechnik, Dresden 7./8. December (2016) 139-147. C. O. Ruud, Residual Stress Measurements, ASM Handbook Volume 8, Mech. Testing and Evaluation, ASM International (2000) 886-904. G. S. Schajer (Ed.), Practical residual stress measurement methods, John Wiley & Sons Ltd (2013). S. Wronski, M. Wrobel, A. Baczmanski, K. Wierzbanowksi, Effects of cross-rolling on residual stress, texture and plastic anisotropy in f.c.c. and b.c.c. metals, Materialscharacterization 77 (2013) 116-126. T. Mehner, A. Bauer, S. Härtel, B. Awiszus, T. Lampke, Residual-stress evolution of cold-rolled DC04 steel sheets for different initial stress states, Finite Elements in Analysis and Design 144 (2018) 76-83. J. Lan, S. Feng, L. Hua, The residual stress of the cold rolled bearing race, Procedia Engineering 207 (2017) 1254-1259. J. Perenda, J. Trajkovsi, A. Žerovnik, I. Prebil, Residual stresses after deep rolling of a torsion bar made from high strength steel, Journal of Materials Processing Technology 218 (2015) 89-98. J. Gerhardt, A. E. Tekkaya, Advanced Technology of Plasticity, Vol. 2, Springer (1987) 841.
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ICAFT/SFU/AutoMetForm 2018 ICAFT/SFU/AutoMetForm 2018
Simulation Simulation methods methods for for skew skew rolling rolling
Manufacturing Engineering Society International a* Conferencea2017, MESIC 2017, 28-30 June C. Guilleaume 2017, Vigo (Pontevedra), Spaina C. Guilleaumea*,, A. A. Brosius Brosius a a
Institute of Manufacturing Technology, Chair of Forming and Machining Processes, Technische Universität Dresden, 01062 Dresden, Germany Institute of Manufacturing Technology, Chair of Forming and Machining Processes, Technische Universität Dresden, 01062 Dresden, Germany
Costing models for capacity optimization in Industry 4.0: Trade-off Abstract between used capacity and operational efficiency Abstract
A number of different rolling processes are summarized under the term skew rolling. The process variant investigated in this A number of different rolling processes are asummarized under a,* the term skewb rolling. The process b variant investigated in this paper is an incremental flexible process with kinematic forming of the geometry. Two sets of actively driven work rolls A. rolling Santana , P. Afonso , A. Zanin , R. Wernke paper is an incremental flexible rolling process with kinematic forming of the geometry. Two sets of actively driven work rolls are used in a transverse rolling process to selectively reduce the diameter of a cylindrical workpiece to form circumferential are used in a transverse rolling processa University to selectively reduce the diameter of Portugal a cylindrical workpiece to form circumferential of Minho, 4800-058 Guimarães, grooves. Simultaneously, the excess material is pushed in axial direction, thereby forming a bulge that can be used to join e.g. a b is pushed in axial direction, thereby forming a bulge that can be used to join e.g. a grooves. Simultaneously, the excess material Unochapecó, 89809-000 Chapecó, SC, Brazil gear wheel onto an axle. Since this is done in a cold rolling process the positive influence of the induced residual compressive gear wheel onto an axle. Since this is done in a cold rolling process the positive influence of the induced residual compressive stress as well as strain hardening can be used to improve fatigue strength of the workpiece under cyclical loads. The authors stress as well as strain hardening can be used to improve fatigue strength of the workpiece under cyclical loads. The authors discuss the advantages of this hybrid skew and cross rolling process and propose a simplified numerical model to quickly analyze discuss the advantages of this hybrid skew and cross rolling process and propose a simplified numerical model to quickly analyze process parameters like axial and radial work roll feed and the influence of initial stress profiles in the workpiece. The model Abstract process parameters like axial and radial work roll feed and the influence of initial stress profiles in the workpiece. The model uses a 2 ½ D axis-symmetric approach in LS-Dyna R10.1.0 with implicit solver. Additionally, preliminary results of first tests on uses a 2 ½ D axis-symmetric approach in LS-Dyna R10.1.0 with implicit solver. Additionally, preliminary results of first tests on rolled specimen from 42CrMo4 are briefly discussed. Under the concept of "Industry 4.0",discussed. production processes will be pushed to be increasingly interconnected, rolled specimen from 42CrMo4 are briefly
information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization © 2018 The Authors. Published Published by by Elsevier Elsevier B.V. B.V. © 2018 2019 The The Authors. © Authors. Published byof Elsevier B.V. goes beyond the traditional aim capacity maximization, contributing also for organization’s profitability and value. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is anlean open management access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Indeed, and continuous improvement approaches suggest capacity optimization instead of of ICAFT/SFU/AutoMetForm 2018. Selection and peer-review under responsibility of the scientific committee Selection and peer-review responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. maximization. The studyunder of capacity optimization and costing models is an important research topic that deserves contributions from both theModelling; practicalResidual and theoretical perspectives. This paper presents and discusses a mathematical Keywords: Rolling; Simulation; Stress; Fatigue Keywords: Rolling; Simulation; Modelling; Residual Stress; Fatigue model for capacity management based on different costing models (ABC and TDABC). A generic model has been developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s 1. Introduction value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity 1. Introduction optimization might hide operational inefficiency. ThisThe paper focusses on a by hybrid cold rolling process, its simulation in virtual experiments and the influence of © 2017 Authors. Published Elsevier B.V. This paper focusses on a hybrid cold rolling process, its simulation in virtual experiments and the influence of selected process parameters on thescientific formation of residual in theEngineering workpiece.Society Essentially any manufacturing Peer-review under responsibility of the committee of thestresses Manufacturing International Conference selected process parameters on the formation of residual stresses in the workpiece. Essentially any manufacturing 2017. process that changes the surface or shape of a workpiece also influences the residual stresses either by inducing them or process that changes the surface or shape of a workpiece also influences the residual stresses either by inducing them or by releasing them partially. These changes and the profile of the residual stresses have a strong influence on the part by releasing Models; them partially. TheseCapacity changes and the profile of theOperational residual Efficiency stresses have a strong influence on the part Keywords: ABC;toTDABC; Management; Idle Capacity; propertiesCost with regards yield strength and most importantly also fatigue resistance. In general terms, compressive properties with regards to yield strength and most importantly also fatigue resistance. In general terms, compressive 1. Introduction * Corresponding author. Tel.: +49 351 463 31972; fax: +49 351 463 37014 *The Corresponding author. Tel.: +49 463 31972; fax: +49 351 463 37014 cost of idle capacity is 351 a fundamental information for companies and their management of extreme importance E-mail address: [email protected] E-mail address: [email protected]
in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier B.V.hours of manufacturing, etc. The management of the idle capacity in several©ways: tons of production, available 2351-9789 © 2018 The Authors. Published by Elsevier B.V. This is anAfonso. open access under the761; CC BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) * Paulo Tel.: article +351 253 510 +351 253license 604 741 This is an and openpeer-review access article under the CCfax: BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. E-mail address: [email protected] Selection and peer-review under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018.
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of ICAFT/SFU/AutoMetForm 2018. 10.1016/j.promfg.2018.12.035
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C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–000
residual stresses are considered to have a positive influence on the strength and fatigue behavior while tensile residual stresses have a negative impact by reducing the load capacity and life time cycles. Therefore, it is very important to take the formation of residual stresses into consideration when choosing process parameters for a forming process. Until recently the main focus was to keep residual stresses as low as possible as to limit their overall influence on the part properties. This, however, severely reduces the process window and makes processes less efficient overall. Thus, it is of high interest to predict the resulting residual stresses of a forming process accurately and moreover, to selectively induce compressive residual stresses to make use of their positive effects. Here, a hybrid cold rolling process is investigated that is aimed at combining the known and documented positive effects of deep rolling with additional strain hardening and the possibility to form joints between different materials. 2. State of the art 2.1. Residual stress in metal forming Residual stresses are static multi-axial internal loads within a workpiece that is not otherwise subjected to an external load. Without additional external forces, these stresses are per definition in a state of equilibrium [1]. During subsequent manufacturing steps or during the use of a manufactured part, additional external loads are superimposed to these internal stresses [2]. Both the external and internal loads affect the workpiece as a collective either reinforcing or countering each other. This is relevant, because residual stresses are already present in the semi-finished products like cold drawn rods that are the basis for all cold bulk metal forming processes. Their influence on the subsequent processes, therefore, cannot be disregarded. Rudkins et al. found that extruded and drawn rods have ten-times higher residual stresses in axial than in radial direction [3]. Starting from the rotational axis with very distinct compressive stresses, the stress state continuously changes into dominating tensile stresses with increasing distance to the axis. This gradient, however, is highly dependent on the production process [2]. Reiß et al. compare cold forged and machined parts with different annealing conditions [4]. They determined that the induced near-surface compressive residual stresses have a positive influence on the fatigue strength of the investigated flange hub. This is in agreement with a study by Blasón et al. on the improvement of the fatigue strength of notched specimen using a deep rolling process [5]. The level of residual stresses generated here was close to the tensile strength of the material. Generally, deep rolling processes are the most common application where the positive influence of residual stresses is used. This secondary cold rolling surface treatment improves the fatigue life of products through a combination of strain hardening, improvement of the surface roughness and induced compressive residual stress. One way to limit the influence of the residual stress profiles in semi-finished goods is by a subsequent heat treatment of the product. Such a thermal treatment does not necessarily lead to a homogenization of the residual stresses however and furthermore measuring them without additional information regarding the strain and stress states can lead to ambiguous analytical results [2]. In a study regarding the heat treatment of bearing rings, Epp et al. found that cold rolled rings retained their induced residual stresses up to relatively high temperatures and that the relaxation at higher temperature is mainly due to recrystallization effects in the material [6]. 2.2. Hybrid rolling process The hybrid cold rolling process analyzed in this paper is a combination of skew and cross rolling which also includes some aspects of deep rolling surface treatments, as presented by Tscheuschner et al. [7]. The geometry is formed by two sets of work rolls that move both in axial and radial direction. The rotation of the workpiece is the result of the transmitted momentum via friction forces by the actively driven work rolls. Each set of work rolls simultaneously also functions as the counter bearing for the other regarding the axial movement. This cold rolling process is used to create a circumferential notch in the workpiece while pushing the excess material in axial direction towards a possible join partner like e.g. a gear wheel, see Fig. 1 a). An example of such a combined workpiece is displayed in Fig. 1 c). This process is highly flexible due to the kinematic forming of the geometry relatively independent from a specific work roll geometry. It allows to join parts out of different materials allowing the combination of their respective advantages like wear resistance and tensile strength.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–00
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Fig. 1. (a) Schematic of hybrid rolling process stage; (b) rolled specimen without and (c) with joined gear wheel.
The biggest benefit is the improved fatigue life of the resulting notched specimen. The reason for this is quite similar to the effects used in deep rolling surface treatments - the rolling process improves the surface roughness, see zone I in Fig. 1 b), causes a high level of strain hardening in the most critical part of the specimen (zone II) and induces compressive residual stresses that further improve fatigue resistance under cyclic loads. Preliminary tests on 42CrMo4 that was rolled on Profiroll 2-PR-15e skew rolling machine have shown that the improvement of tensile strength and fatigue resistance is so high, that the specimens do not fail in the notched section when being tested. 2.3. Numerical simulation of residual stresses induced by rolling processes Measuring residual stresses is a challenging procedure. Generally, the non-destructive testing methods using Xray, neutron or synchrotron diffractometry can only detect near-surface stress states and are highly dependent on measuring parameters and material properties [8]. Destructive testing like borehole or saw-cut method, however, change the initial stress state during the necessary material removal and need a calibration function for analyzing the measuring signal [9]. The high experimental effort needed to measure residual stresses is the main reason that this is rarely done when designing forming processes. Here, numerical simulations combined with a suitable material characterization can provide an alternative method to investigate residual stress formation and limit the amount of necessary measurements. Wronski et al. investigated the effects of cross-rolling on residual stress, texture and plastic anisotropy on low carbon ferrite steel and polycrystalline copper using a combination of experimental tests and numerical simulations [10]. Mehner et al. studied the residual stress evolution of cold rolled DC04 steel sheets with different initial stress states again using experimental tests as well as FEA methods [11]. The numerical approach allowed an easy variation of the process route and initial stress states and the results were in agreement with selective experimental tests. The cold rolling process for a bearing ring was simulated by Lan et al. in order to determine the residual stress state responsible for their asymmetric post process springback behavior [12]. The authors point out that for rolling processes that subject the material to incremental cyclic loads, a corresponding material characterization that considers these cyclic loads and a suitable material model need to be employed. Perenda et al. simulated the residual stresses after deep rolling of a high strength steel torsion bar using an explicit solver [13]. A fine mesh was used since the deep rolling effects are mainly relevant in the surface layers. In order to speed up the simulation, some simplifying model adjustments were made. 3. Virtual experiment Virtual experiments of the hybrid cross rolling process of 42CrMo4 steel are carried out in order to identify the relevant process parameters and investigate the sensitivity of the residual stress formation to the work roll path and initial stress state of the workpiece. The objective is to determine work roll paths that lead to compressive residual stresses in the most critical area of the part, which is the notch forming when the material is pushed in radial and axial direction. Additionally, the influence of assumed initial stress states that are typical for cold drawn semifinished products is to be investigated. This specific steel was chosen due to its high strain hardening characteristic and its relevance in industrial applications.
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C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–000
3.1. Model and parameters The cross-rolling process is simulated with a simplified 2½ D model using LS-Dyna R10.1.0 with an implicit solver. The y-axis of the workpiece is used for the rotational symmetry. This reduced approach has the advantage of a much faster simulation time than a full 3D model. This allows for a faster and broader variation of the key process parameters like the work roll path and the initial stress state. The disadvantage is a minimally different local stress state, but since the main objective is a qualitative comparison of the resulting stress states regarding the influence of rolling parameters and initial stresses, this method is viable. Using the symmetry axis, the rolling process is modelled as a circumferential indentation without cyclical loading of the material. For the material formulation a linear piecewise approximation of the flow curve in combination with an isotropic hardening behavior was used for plasticity. The flow curve is the result of tensile tests done on the specific material batch used and some additional extrapolation points acquired from datasheets. A very fine mesh with an element size of 0.05 mm was chosen for the workpiece in order to have a fine resolution of the local stress states. The rolling process causes high strains and high mesh distortions in front of the work roll, so an automatic remeshing is done at fixed intervals to ensure a sufficient element quality. The influence on the resulting equivalent stress and triaxiality factor of two main parameters is investigated. First of all, the path of the work rolls in relation to workpiece is varied, as shown in Fig. 2 a). A linear, progressive and degressive tool path with the same final position are chosen with the goal to determine which forming history leads to an advantageous stress distribution with regards to the critical notched section of the workpiece. Secondly, the initial stress profiles of the workpiece were varied to identify their influence on the resulting stress states after forming. The assumed stress profiles for this investigation are in accordance with published profiles of cold drawn rods [14], see Fig. 2b). The triaxiality factor is used as an indicator of the dominant stress state in the workpiece, since it is highly relevant if the residual stresses are tensile or compressive and this information cannot be extracted from the residual equivalent stress.
Fig. 2. (a) Work roll paths; (b) initial stress profiles.
3.2. Results and discussion For all work roll paths, high effective plastic strains of up to 4 were reached in the area of the notch ground, resulting in a high amount of strain hardening in that area which is desirable regarding the fatigue strength of this smaller crosssection. The equivalent stress in the same area for all tool paths is also high with up to 1855 MPa, which is to be expected at these levels of plastic strain, see Fig. 3 a). It is noticeable that the work roll feed direction during the final stages of forming determines the area with the highest stress levels - both for the final load step and after relaxation. For a progressive work roll path, the final movement happens mainly in radial direction towards the workpiece axis while for the degressive work roll path, the final movement is mostly in axial direction towards the y-symmetry plane. Thus, for a progressive tool path, the entire area under the notch surface has a high stress level, while for the degressive tool path, mostly the area in axial feed direction has a high stress level. This is especially relevant after the relief step, when examining the residual stress distribution. Here, the overall level of residual stress around the notch is around 500-900 MPa, with a very small zone for each tool path where the high stress level from the forming process is retained just below the workpiece surface, see Fig 3. Since only compressive residual stresses are desirable in the critical notch ground, the triaxiality factor for each tool path is analyzed, see Fig. 4. The scale of the diagram is set so that areas with pure compressive stress states appear in blue, and areas with multi-axial tensile stress states appear in red.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–00
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Fig. 3. Equivalent stress (v. Mises) for (a) final load step and (b) after relief.
For all work roll paths, the triaxiality factor indicates that the area of compressive stress is significantly reduced during the relief phase due to the springback behavior of the material. For all tool paths the area just below the notch ground retains compressive residual stresses, which is considered to be positive for this critical cross-section. For all tool paths, however, there is also a significant area with tensile residual stresses forming close to the workpiece axis, see Fig. 4 b). This critical zone extends almost to the notch ground for the progressive tool path and could adversely affect the tensile and fatigue strength. Overall the area with tensile residual stress is the smallest for the degressive tool path. Simultaneously it results in the largest area with compressive residual stress close to the notch ground. This indicates that a degressive tool path is most likely to significantly improve tensile strength and fatigue resistance.
Fig. 4. Triaxiality for different work roll paths (a) for final load step and (b) after relief.
Finally, the effect of different initial stress profiles shown in Fig. 2 b) on the resulting residual stresses is examined using the numerical model. It is used to determine if for future research regarding rolling parameters and resulting residual stresses, the initial stress state of the semi-finished product has to be characterized and considered extensively. Fig 5 shows the comparison of all residual stress profiles for the combination of all three work roll paths and three initial stress states.
Fig. 5. Equivalent stress (v. Mises) after relief for different initial stress profiles, (a) no stress, (b) stress profile 1, (c) stress profile 2.
C. Guilleaume et al. / Procedia Manufacturing 27 (2019) 1–6 Author name / Procedia Manufacturing 00 (2018) 000–000
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For each tool path, the characteristic size of the area with significant residual stresses and the level of equivalent stress remain almost unchanged by the induced initial stress profile 1 and 2. Near the symmetry axis some low residual stress remains from the initial profiles, but does not affect the relevant forming zone. The explanation is that the high equivalent plastic strain that the material is undergoing in the forming zone and the resulting high equivalent stresses during the process almost completely overwrite any low level initial stress profile imposed on the workpiece before. Regarding further investigations of rolling parameters and resulting stress states, this result can be considered positive, because it limits the experimental effort needed to characterize the initial stress state of the semi-finished cold drawn rods and prior steps of the process chain can be equalized. 4. Conclusion and outlook The presented approach for analyzing a hybrid cold rolling process using a simplified 2½ D numerical model was used to qualitatively compare different work roll paths and initial stress profiles regarding the resulting residual equivalent stresses and trixiality factors. Both of these results combined can give an indication as to the suitability of certain tool paths for selectively inducing compressive residual stresses in the critical area of a workpiece. The analysis showed clear qualitative differences regarding the residual stress distribution and level of residual stresses in different zones of the specimen depending on the chosen work roll path. The analysis of different initial stress profiles showed that their influence is insignificant compared to the large equivalent strain and resulting high equivalent stresses induced by the cold rolling process. As a next step further process parameters will the virtually tested and the real initial stress state of the semi-finished specimen used for experimental investigations will be measured selectively. Finally, cold rolled specimen manufactured with parameters identified by this numerical analysis will be tested in tensile and cyclic fatigue tests. Acknowledgements Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within the Priority Program 2013 "Targeted Use of Forming Induced Residual Stresses in Metal Components" under the grant numbers KA 3309/7-1 and BR 3500/21-1. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
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