ratchev_2004_milling error prediction and compensation in machining of low_rigidity parts

8/6/2019 Ratchev_2004_milling Error Prediction and Compensation in Machining of Low_rigidity Parts

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International Journal of Machine Tools & Manufacture 44 (2004) 16291641

www.elsevier.com/locate/ijmactool

Milling error prediction and compensation in machiningof low-rigidity parts

S. Ratchev, S. Liu , W. Huang, A.A. Becker

School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, University Park,Nottingham NG7 2RD, UK

Received 15 March 2004; accepted 2 June 2004

Abstract

The paper reports on a new integrated methodology for modelling and prediction of surface errors caused by deflection duringmachining of low-rigidity components. The proposed approach is based on identifying and modelling key processing character-istics that influence part deflection, predicting the workpiece deflection through an adaptive flexible theoretical force-FEA deflec-tion model and providing an input for downstream decision making on error compensation. A new analytical flexible force modelsuitable for static machining error prediction of low-rigidity components is proposed. The model is based on an extended perfectplastic layer model integrated with a FE model for prediction of part deflection. At each computational step, the flexible force iscalculated by taking into account the changes of the immersion angles of the engaged teeth. The material removal process at anyinfinitesimal segment of the milling cutter teeth is considered as oblique cutting, for which the cutting force is calculated using anorthogonaloblique transformation. This study aims to increase the understanding of the causes of poor geometric accuracy byconsidering the impact of the machining forces on the deflection of thin-wall structures. The reported work is a part of an ongo-ing research for developing an adaptive machining planning environment for surface error modelling and prediction and selectionof process and tool path parameters for rapid machining of complex low-rigidity high-accuracy parts.# 2004 Elsevier Ltd. All rights reserved.

Keywords: Milling force; Deflection prediction; Error compensation

1. Introduction

High-quality, high-value manufacturers constantlyseek to improve their product quality and reduce costand lead times by producing right first time machinedcomponents. The accuracy of the surface profile is oneof the key factors for achieving the required dimen-

sional and geometric tolerances and plays a significantrole in ensuring the overall product quality because it isoften directly related to the products functional per-formance. Using advanced computational methods inprecision machining for predicting and compensatingthe surface profile is very important to satisfy therequired tight tolerances, eliminate hand-finishing pro-cesses and assure part-to-part accuracy.

Achieving the right profile in machining low-rigidity(flexible) parts increasingly depends on the use ofCAE/CAD/CAM packages for defining optimal cut-ting strategies and tool paths. The NC part program-ming for complex surfaces has been well supported bysignificant developments in tool path modelling andverification techniques. However, most of the existing

techniques and models are based on idealised geome-tries and do not take into account factors such as vari-able cutting forces, part/tool deflection and static anddynamic compliance during machining leading toadditional machining errors that are difficult to predictand control [1]. The current industrial practicesemployed to compensate for such errors are based onextensive experimentation using trial-and-error approa-ches leading to increased cost and lead times.

A number of specialist FEA software packageshave been used to simulate manufacturing processessuch as precision metal cutting. These packages use

Corresponding author. Tel.: +44-115-8466083; fax: +44-115-9514000.

E-mail address: [email protected] (S. Liu).

0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijmachtools.2004.06.001


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2. Adaptive machining planning methodologyanoverview

In machining low-rigidity thin-walled parts, such asturbine blades in the aerospace and power industries,the deflection of the workpiece induced by cutting(milling) forces cannot be ignored since it plays a sig-nificant role in the formation of the total surface error.Machining low-rigidity (flexible) parts is a widelypractised process in industry today.

The proposed methodology (see Fig. 1) includesmodelling and prediction of cutting forces, analysis andprediction of deflection of the part as a result of theapplication of the cutting forces, and analysis ofthe resultant surface errors and their compensation.The research is specifically focused on low-rigidityparts and the deflection of the cutting tool is initiallyignored. The cutting forces are identified using a flex-ible theoretical force prediction model that is specific to

machining low-rigidity parts [21,22]. Previously repor-ted results on cutter deflection [2325] are planned tobe incorporated later in the model in cases where therigidity of the tool and the part are of the similar mag-nitude. The cutting forces are input into a FE modelfor prediction of the dynamic behaviour of the partduring cutting. The predicted deflected part profile isused to identify the real material volume that is

removed during machining instead of the ideal onedefined by currently used static NC simulationpackages. An iterative algorithm is used for erroranalysis and compensation by comparing the nominal(control) surface and the actual predicted surface. Aknowledge-based approach is applied for corrective

actions by recalculation of the tool path. The approachaims to utilise the available company specific knowl-edge and priorities in selecting processing alternativesand deflection compensation strategies.

3. Modelling of flexible cutting forces

The process of machining of thin-wall parts presentsa special case of non-linear correlation between proces-sing parameters and the dynamic behaviour of thepart. As a result, most of the traditional approaches tocutting force prediction need to be further modified totake into account the deflection of the part. In parti-cular, the cutting models need to include the variationsin the immersion boundaries (or transient surface) ofthe cutter along the toolworkpiece contact zone. As aresult of the deflection, the chip thickness becomes avariable function of the part deflection, which is afunction of the cutting forces which in turn are determ-ined using the chip thickness value. Most existing

Fig. 1. An adaptive machining planning environment methodology overview.

S. Ratchev et al. / International Journal of Machine Tools & Manufacture 44 (2004) 16291641 1631


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flexible force models do not take into account thematerial properties and tool geometry and as a resultwhen the material properties and/or tool geometry arechanged, the model needs to be re-calibrated.

To adequately represent the nature of the process ofmachining low-rigidity parts, the theoretical force

model needs to take into account among the factorsthe deflection of the workpiece (see Fig. 2). The differ-ential cutting force on the engaged infinitesimal toolcutting edge varies with the cutting depth that is thefunction of the immersion angle determined by work-piece deflection. Elements of cutting mechanics areused to model the shear zone, friction zone and rub-bing zone. The model assumes that material in the cut-ting zone is sheared away on the shear plane and slidealong the tool face.

For any infinitesimal segment of the tooth on a mill-ing cutter, its cutting mechanics is assumed to have thesame behaviour of the oblique cutting. Once the local

tangential, radial and axial cutting forces, Ft(/), Fr(/)and Fa(/), on the toothworkpiece contact point aredetermined theoretically [10], three force componentsFx(/), Fy(/) and Fz(/) acting on the cutter in the refer-ence Cartesian coordinate system can be expressedthrough the following transformation (Fig. 3):

Fx/Fy/Fz/

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ratchev_2004_milling error prediction and compensation in machining of low_rigidity parts

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