Journal of Materials Processing Technology 211 (2011) 24–34 Contents lists available at ScienceDirect Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec Error compensation in flexible end milling of tubular geometries T.C. Bera, K.A. Desai, P.V.M. Rao ∗ Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India article info Article history: Received 19 June 2010 Received in revised form 16 August 2010 Accepted 19 August 2010 Keywords: Peripheral milling Tubular geometries Tool deflection Workpiece deflection Surface error Error compensation abstract There are many machining situations where slender tools are used to machine thin walled tubular work- pieces. Such instances are more common in machining of aircraft structural parts. In these cases, cutting force induced tool as well as workpiece deflections are quite common which result into surface error on machined components. This paper presents a methodology to compensate such tool and workpiece induced surface errors in machining of thin walled geometries by modifying tool paths. The accuracy with which deflections can be predicted strongly depends on correctness of the cutting force model used. Tra- ditionally employed mechanistic cutting force models overestimate tool and workpiece deflections in this case as the change of process geometry due to deflections is not accounted in modeling. Therefore, a cutting force model accounting for change in process geometry due to static deflections of tool and workpiece is adopted in this work. Such a force model is used in predicting tool and workpiece deflec- tion induced surface errors on machined components and then compensating the same by modifying tool path. The paper also studies effectiveness of error compensation scheme for both synclastic and anti-clastic configurations of tubular geometries. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Milling of complex thin walled geometries is becoming increas- ingly important in aerospace industries due to its ability to produce complex parts as monolithic structures. The need for expensive multi-part manufacturing, large set up times on different machines and assembling of pieces together into finished product is elimi- nated here because the complete part is manufactured from a single piece by material removal processes. Many of the thin walled com- ponents produced in these industries are tubular in nature. Closed nature of tubular structures provides much needed stiffness to the components in resisting machining induced forces. In spite of this, a major problem associated with milling of thin walled tubular components is cutting force induced static deflections of cutter and workpiece which manifest in form of surface error on finished parts. Highly non-linear and complex nature of surface error pro- files during milling of such components not only deteriorates its dimensional accuracy but also geometric tolerances. It is challenging task for the process planner to obtain tight dimensional and geometric tolerances dictated by functional requirements of the product. One of the approaches is to use con- servative cutting conditions and multi-pass machining to limit cutting forces. Such an approach reduces surface error but ham- pers productivity of machining operation significantly. Yet another ∗ Corresponding author. Tel.: +91 11 26591427; fax: +91 11 26582053. E-mail address: pvmrao@mech.iitd.ac.in (P.V.M. Rao). approach is to use final “float” cut to bring machined surface within required tolerance. It is not advisable to take “float” cut in thin walled machining as it may not be effective due to compliant nature of the workpiece. In such machining situations, single pass off-line tool path modification strategy can be considered as one of the efficient ways to produce thin walled quality parts with- out sacrificing productivity. This paper presents a methodology to predict and compensate surface errors in milling of thin walled tubular geometries. Prior work related with the use of error com- pensation methodology is mainly focused at machining situations where either tool or workpiece is flexible. But in machining of thin walled components, tool and workpiece both deflect easily under the action of cutting forces. This paper addresses compensation of combined errors due to tool and workpiece deflections by using a cutting force model which accounts for change in process geome- try due to deflections. Tubular geometries have an option of being machined from either concave side (anti-clastic machining) or con- vex side (synclastic machining). It is also of great interest to know the effectiveness of error compensation methodology in both these cases. 2. An overview of previous work Number of research attempts can be found in literature that deals with reduction of cutting force induced tool or work- piece deflection errors. But very few of these attempts are focused on reduction of combined tool and workpiece deflec- tion errors. Research attempts focusing on reduction of deflection 0924-0136/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2010.08.013