Precision Engineering 38 (2014) 849–860 Contents lists available at ScienceDirect Precision Engineering jo ur nal ho me p age: www.elsevier.com/locate/precision A novel surface analytical model for cutting linearization error in fast tool/slow slide servo diamond turning Dennis Wee Keong Neo ∗ , A. Senthil Kumar, Mustaﬁzur Rahman Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, 9 Engineering Drive 1, Block EA, Singapore 117576, Singapore a r t i c l e i n f o Article history: Received 14 January 2014 Received in revised form 30 April 2014 Accepted 5 May 2014 Available online 27 May 2014 Keywords: Cutting linearization error Critical machining parameters Fast tool/slow slide servo diamond turning Freeform surfaces a b s t r a c t Fast tool/slow slide servo (FTS/SSS) technology plays an important role in machining freeform surfaces for the modern optics industry. The surface accuracy is a sticking factor that demands the need for a long-standing solution to fabricate ultraprecise freeform surfaces accurately and efﬁciently. However, the analysis of cutting linearization errors in the cutting direction of surface generation has received little attention. Hence, a novel surface analytical model is developed to evaluate the cutting linearization error of all cutting strategies for surface generation. It also optimizes the number of cutting points to meet accuracy requirements. To validate the theoretical cutting linearization errors, a series of machining experiments on sinusoidal wave grid and micro-lens array surfaces has been conducted. The experimental results demonstrate that these surfaces have successfully achieved the surface accuracy requirement of 1 m with the implementation of the proposed model. These further credit the capability of the surface analytical model as an effective and accurate tool in improving proﬁle accuracies and meeting accuracy requirements. © 2014 Elsevier Inc. All rights reserved. 1. Introduction The new era of ultraprecision machining technologies for freeform optics requires the advancement of design and testing for innovative optical function and improved optical performance [1]. Fast tool/slow slide servo (FTS/SSS) diamond turning [2,3] is one of these technologies which is widely employed for the machining of freeform surfaces. The surface accuracy is a dominant factor for the optical performance of freeform optical surfaces. Much research work has been conducted in the area of surface generation with ultraprecise surface accuracy for freeform optics. Over the past decades, much research has been conducted on the surface generation methods, machine dynamics, error analysis and methodologies of error compensation. In the FTS/SSS processes, there are two different types of surface errors, namely cutting resid- ual and cutting linearization errors. The cutting residual error is the formation of tool marks on the surface along the feed direction [4–8]. Kwok et al. [5] and Yu et al. [8] have studied and success- fully developed their models for predicting this residual error in the FTS/SSS processes. They also conclude that the residual error ∗ Corresponding author. Tel.: +65 90478176. E-mail addresses: weekeong.neo@nus.edu.sg, dennis.sm07@gmail.com (D.W.K. Neo), mpeask@nus.edu.sg (A.S. Kumar), mpemusta@nus.edu.sg (M. Rahman). dominates the errors by the tool nose radius and feedrate, and is analogous to surface roughness. Thus, a proper selection of fee- drate and tool nose radius should be optimized for machining accurate freeform surfaces. In contrast, cutting linearization error is the peak-to-valley error (PV err ) between the ideal surface pro- ﬁle and the linear tool trajectory in the spiral cutting direction. This PV err depends mainly on the cutting distance between the two corresponding points in the cutting direction. It has been reported that the best proﬁle accuracy results can be achieved by the spline interpolation method in the DiffSys software [9,10]. However, the details for selecting cutting parameters in the spline interpola- tion method were not reported. Zhou et al. [11] have conducted a comparison studies on surface quality of machined surface based on constant-angle and constant arc-length methods. When the constant-angle method is employed, the surface quality of outer regions is worse than that of central regions due to arc-lengths between the corresponding points on outer regions are sparser than those on central regions. Whereas the constant-arc method shares the same number of cutting points as constant-angle ones, the surface quality of machined surface is uniform. Liu et al. [12] explain that the selection of critical incremental arc-lengths plays an important role for achieving ultraprecision surface accuracy of freeform surfaces. Notwithstanding the fact that the constant arc- length method demonstrated its capability for better overall proﬁle accuracy, only sinusoidal wave grid (SWG) proﬁles were served as http://dx.doi.org/10.1016/j.precisioneng.2014.05.002 0141-6359/© 2014 Elsevier Inc. All rights reserved.