ORIGINAL ARTICLE Numerical generation of grinding wheel surfaces based on time series method Dongri Liao 1 & Wen Shao 1 & Jinyuan Tang 1 & Jianping Li 1 & Xuan Tao 1 Received: 15 April 2017 /Accepted: 24 July 2017 # Springer-Verlag London Ltd. 2017 Abstract Surface integrity has a significant influence on the functional behavior of engineering components. An effective grinding wheel topography model is the foundation to realize the controllable design and manufacturing of grinding work- piece surface integrity. In this study, a moving average model (MA) based on time series method was proposed to generate the grinding wheel surface topography. 3D grinding wheel topographies were measured by an LSM 700 laser scanning confocal microscope (CLSM). The Johnson transformation system was applied to generate the non-Gaussian sequence with predetermined statistical parameters. To address the con- vergence and memory requirement problems, the non-linear conjugate gradient method (NCGM) with an exact line search by the secant method was employed to solve the system of nonlinear equations. The results showed a good agreement between the measured and the generated sur- faces in terms of the autocorrelation function (ACF) and statistical parameters was achieved. It is worth noting that the computing time of the model developed in this study is only determined by the autocorrelation lengths which are almost independent of the size of the grinding wheel. This technique could be more efficient when applied to grinding wheels with large size. Therefore, this method may serve as an effective way to solve the grinding wheel topography reconstruction problem. Keywords Grinding wheel . Topography . Roughness . Modeling 1 Introduction Surface topography has a significant influence on the functional behavior such as tribological, wear, and lubrication behaviors of machined components. Different machining processes have variant surface texture parameters [1]. Grinding is the final step in most machining processes. The texture and properties of the machined part surface are determined by grinding wheel mor- phology [2] and machining parameters [3]. The topography of the workpiece is generated by the interaction of the workpiece with abrasive cutting points on the grinding wheel surface. Thus, the grinding wheel surface had a remarkable effect on the quality of machined surfaces [4]. For the grinding process, previous studies have been concentrated on grinding forces, power consumption, and workpiece surface integrity. The grinding wheel model is the basis research of the grinding prob- lem from a micro-scale view. However, the grinding wheel cannot be characterized and modeled effectively due to the random distribution of grains and the diversity of the shape of grains on the grinding wheel [5]. The roughness parameters can be generally categorized into four types, i.e., amplitude param- eters, hybrid parameters, functional parameters, and spatial pa- rameters [6]. These parameters are usually used to characterize the workpiece performance in particular aspects, which would be limited when applied to the grinding wheel. The information of any surface is contained in the autocorrelation function (ACF) and amplitude distribution function. Therefore, these functions should be utilized to analyze and reconstruct the grinding wheel topography. Great efforts were made towards the development of grind- ing wheel topography simulation methods [7]. Hou and * Wen Shao shaowen_2013@163.com Jinyuan Tang jytangcsu_312@163.com 1 State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, Hunan 410083, China Int J Adv Manuf Technol DOI 10.1007/s00170-017-0868-y