Contents lists available at ScienceDirect Precision Engineering journal homepage: www.elsevier.com/locate/precision A self-calibration rotational stitching method for precision measurement of revolving surfaces M.Y. Liu a,* , C.F. Cheung a , X. Feng b , C.J. Wang a , R.K. Leach b a Partner State Key Laboratory of Ultra-precision Machining Technology, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong b Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham, Nottingham, NG8 1BB, United Kingdom ARTICLE INFO Keywords: Rotational stitching Revolving surfaces Precision measurement Self-calibration Ultra-precision machining ABSTRACT When measuring revolving objects, it is often desired to obtain not only the geometrical form of the workpiece, but also the topography of the surface, as they both affect the performance of the part. However, holistic measurement of the entire three-dimensional surface of a revolving part is challenging since most surface measurement instruments only have limited measurement ability, where the bottom and the side surfaces cannot be measured. One solution to obtain geometrical form and surface topography information simultaneously is to add a precision axis to rotate the object while performing surface topography measurement. However, this solution requires a high-cost precision rotation stage and adjustable mounting and alignment aids. Moreover, errors in the rotation will be added to the measurement result, which can be difficult to compensate. Stitching is a method often used for measuring revolving surfaces without the need for precision motion axes, as the method is applied at the software level, and errors in the rotation can be compensated by the stitching algorithm. Nevertheless, the overall accuracy of stitching is limited when the number of sub-surfaces is large, since the measurement and stitching error accumulate along the stitching chain. In this paper, a self-calibration rotational stitching method is presented which can compensate for the accumulated error. The self-calibration method utilises the inherent nature of a revolving surface and compensates for the registration error by aligning the last dataset with the first dataset. The proposed method is demonstrated by measuring grinding wheels with a co- herence scanning interferometer and simultaneously rotating the grinding wheels with a low-cost stepper-motor. It is demonstrated that the proposed stitching measurement method is effective in compensating for accumulated registration error. The proposed self-calibration rotational stitching method can be easily extended to a wide range of applications for measuring revolving surfaces using various measuring instruments. 1. Introduction Revolving surfaces, such as precision rollers [1], shafts [2] and grinding wheels [3], are widely used in precision engineering. They are usually produced by a machining process that involves the rotational motion of spindles or motors, such as turning and grinding. There is an increasing demand for precision not only in the geometrical form of the machined part, but also in the surface texture, in applications such as producing microlens arrays on a roller stamper in order to replicate them onto a continuous flexible substrate [4] and optimising the micro- topography on a diamond grinding wheel for improved grinding per- formance [5]. To holistically obtain both geometrical form and surface texture requires measuring the revolving surface with a surface mea- suring instrument and extracting both large-scale and small-scale in- formation from the measurement. Measuring a revolving surface with a surface measuring instrument is a challenging task as most surface measuring instruments, such as coherence scanning interferometers (CSIs) and focus variation microscopes (FVMs), only have 2.5-dimen- sional (2.5D) measurement capability, where the bottom surface or the surface with high slope angle cannot be measured. In order to achieve three-dimensional (3D) measurement of the revolving surface, an ad- ditional precision rotational axis can be used to rotate the object, so that the entire surface can be measured. However, this method requires a high-cost precision rotational axis, and sometimes additional devices for tilting and alignment adjustment, which are not available to most surface measuring instruments, especially when large workpieces, such as precision roller drums in the roll-to-roll industry, are involved [6]. Measurement accuracy is often affected by the motion error of the rotational axis such as runout, angle error, misalignment between the workpiece and the rotational axis, and misalignment between the https://doi.org/10.1016/j.precisioneng.2018.05.002 Received 15 February 2018; Received in revised form 9 April 2018; Accepted 8 May 2018 * Corresponding author. E-mail address: samuel.liu@connect.polyu.hk (M.Y. Liu). Precision Engineering 54 (2018) 60–69 Available online 16 May 2018 0141-6359/ © 2018 Elsevier Inc. All rights reserved. T