# Surface Quality Evolution Model and Consistency Control Method of Large Shaft Multi-Pass Grinding
## 1 Introduction  
Large shaft is widely used in industry to bear heavy load and transfer motion [1], and multi-pass grinding is the final process to obtain high surface quality [2]. Surface roughness and glossiness are common surface quality indexes, and the requirements of these two indexes are high in large shaft grinding. Moreover, surface quality consistency needs to be ensured, which means the value difference of each surface quality index along the whole shaft should be small. Both surface roughness and glossiness are affected by grinding parameters, so the reasonable selection of grinding parameters is the basis to obtain the desired surface quality [3, 4]. Some studies reveal the mechanism of grinding surface formation through physical modeling of the grinding process, and then obtain the correlation between grinding parameters and surface roughness [5, 6]. [PERSON] et al. proposed a conventional method determining the surface roughness using the mean value of the grain protrusion heights [7]. [PERSON] et al. developed a predictive model for grinding surface roughness based on micro-interacting mechanism modeling [8]. [PERSON] et al. simplified the abrasive particles into a cone and calculated the surface roughness by obtaining the topography of the grinding surface through a simulation method [9]. The above research established surface roughness prediction models based on physical modeling and simulation, but these models are difficult to describe the random factors in the actual grinding process, so the prediction performancesare not high enough. Another kind of surface roughness modeling method is the empirical method, by which the correlation between grinding parameters and surface roughness is established by numerical method [10; 11]. [PERSON] et al. proposed a surface roughness prediction model based on a respond surface model for external cylindrical grinding of SCM440 steel [12]. [PERSON] et al. used the Taguchi method to establish the correlation between grinding depth, grinding wheel speed, and surface roughness [13]. [PERSON] et al. developed the least squares vector machine and spider support vector machine to predict the surface roughness of stainless steel turning [14]. [PERSON] et al. used an artificial neural network to accurately describe the influence of grinding parameters on surface roughness [15]. In general, the empirical method is the most commonly used method for predicting surface roughness with grinding parameters due to its convenient calculation and high precision [16; 17]. Recently, some studies predict surface roughness by monitoring grinding signals, such as image [18] and acoustic emission signals [19]. However, this method is not helpful to the selection of grinding parameters. Glossiness is an optical parameter to represent the reflective capacity of the surface, which also reflects the surface roughness [20]. Generally, the higher the surface roughness, the lower the glossiness [21]. The existing research seldom discusses the correlation between process parameters and glossiness based on the modeling of the machining process, but mostly focuses on the correlation between roughness and glossiness. [PERSON] et al. performed polishing experiments on building stone tiles with SiC abrasive particles and found an exponential relationship between the surface roughness and glossiness of the workpiece [22]. Nevertheless, by testing polymer surfaces, [PERSON] et al. pointed out that surfaces with similar roughness can also have very different glossiness [23]. [PERSON] et al. simulated the surface roughness and glossiness with non-Gaussian topography features, and it is found that there can be other indexes deciding the final glossiness besides surface roughness [24]. Overall, current research on glossiness modeling is insufficient. The above researchers have made achievements in the building correlation between grinding surface quality and process parameters, but there are still two limitations.