## 1 Introduction  
Optical glasses are widely used in optical and aerospace applications. However, they are very brittle and have low fracture toughness, thus being prone to micro-cracks developing in the subsurface layers during conventional grinding processes. The maximum depth of subsurface cracks has a significant effect on the machining quality and even efficiency of the following processing [1]; thus, correct prediction of the maximum subsurface cracks depth is important for controlling the subsurface damage and overall grinding process efficiency. UVAG has clear technical advantages in substantially reducing the average cutting force and quantity of micro-cracks [2]. However, inducing high-frequency vibrations and modifying abrasive grain motion significantly change the stresses at the contact area between the abrasive grains and the glass material compared to conventional grinding [3]. This directly affects the grinding force and dynamic impulse and the formation and propagation of subsurface cracks. The subsurface cracks may not propagate in a single form. Furthermore, abrasive grains used on the grinding wheel are of different varieties and their shapes are random. Thus, the subsurface cracks in UVAG of the optical glasses often exhibit diverse forms and are numerous. Due to the different influencing factors of the grinding loads, the quantities and distributions of multiple cracks forms are also significantly different. This may lead to uncertainty in estimating the crack maximum propagation depth. Hence, predictingthe maximum subsurface crack depth while considering the different effects of the process parameters is of great significance. During the past decade, research has focused on the formation and prediction of subsurface cracks, and a number of useful results have been obtained. [PERSON] [4] analyzed the effects of process parameters on subsurface crack depth; the changing law of subsurface damage was also researched by changing each parameter. However, it proved hard to evaluate these effects using the adopted approach. [PERSON] [5] developed a regression model for subsurface crack depth (SSCD) estimation by combining theoretical mechanical analysis and experimental approach, but the scratching tests conducted in this work differed from the practical machining, as the abrasive grains used in the latter are often random in shape and quantity. There are also many useful studies on the prediction of SSCD by using simulations [6] and regression analysis [7]. To develop an analytical approach, [PERSON] [8] used the damage-zone analysis method and verified the accuracy of the proposed model experimentally. To investigate the maximum subsurface crack depth (MSSCD), [PERSON] [9] researched the critical formation conditions of MSSCD by conducting a double indentation test. Based on the mechanical analysis of indentation test results, [PERSON] [10] and [PERSON] [11] analyzed the relationship between the MSSCD and surface roughness and drew a similar conclusion that the two parameters had the same trends. However, some important actual machining factors were not considered, such as the different influences of various crack forms and process parameters. [PERSON] [12] developed an analytical SSCD model based on the analysis of crack sizes and microscopic asperity (Rz). However, the crack forms considered in that work were strictly limited to the median and lateral cracks, whereas subsurface cracks often vary in both shape and size [13]. [PERSON] innovatively researched the fracture behavior and the threshold load in radial crack propagation by conducting a nanoindentation test [14]. [PERSON] pointed an easily visible technique for authentication of epoxy composites by using UV visible and IR light, which may provide new methods for investigating the subsurface cracks in grinding of optical glasses [15]. It can be concluded from the above literature survey that few reports provide a deeper understanding of multiple subsurface crack forms in the actual UVAG process.