## 1 Introduction  
Because of their the superior mechanical and thermal properties, advanced ceramics have found increasing applications in aerospace industry, military industry, vehicle engineering and so on. However, there is no effective grinding modeling to predict evaluating parameters, which adds difficulties for machining.  
Previous studies have created many predictive models. [PERSON] [1] built a mathematical model of grinding force per unit grinding width, based on geometric distribution of wheel grit and kinematics of grinding process. [PERSON] [2] held the view that grinding force can be divided into cutting force and friction force. He set up a relation between grinding forces and wear flat of abrasive grain. Several scratching experiments were conducted by [PERSON] _et al._[3; 4; 5]. The results showed that Removal rate was proportional to grain size 1\({}^{1/2}\) and load p\({}^{2}\). Grinding force and surface roughness models were created. [PERSON] _et al._[6] optimized the mathematical model of grinding force per unit width. [PERSON] _et al._[7] established a calculated formula for grinding force per grit and pointed out that grinding force showed an exponential relationship with wear debris area. [PERSON] _et al._ derived a predictive grinding force per grit equation based on the relation between the abrasive indentation model and hardness [8]. [PERSON] _et al._[9] built the grinding force modeling per grit based on undeformed chip thickness. [PERSON] _et al._[10; 11] improved the grinding force and power model by a new analytical undeformed chip thickness, considering the wheel-workpiece contact zone, microscopic contact at the grain level and geometry of depth of cut. [PERSON] _et al._[12] proposed that the grinding force was greatly influenced by mechanism removal. As for it, different grinding force models were established under ductile removal and brittle removal conditions. Seen from the previous models, geometric models and material properties such as hardness, fracture toughness, strength and so on are considered in order to derive predictive force models. However, the result of predictive modeling is far from the experimental result. No allowance is made for direct effects of materials microstructure such as grain, porosity, binding energy, _etc._ Almost all the mechanical models were obtained based on crystalline ceramics. The applicability of mechanical models to non-crystalline ceramics has not been identified.  
Grain size as an important factor of microstructure in affecting the materials has been studied in many aspects. Many indentations and scratch experiments of alumina were conducted on removal mechanism, material removal volume, damage, and so on as a function of grain size [5; 13; 14]. Large studies indicate that the fracture strength of crystalline grains is bigger than grain boundary. They found that the mechanism of material removal in alumina is identified as intergranular fracture and grain dislodgement resulting from grain boundary microcracking irrespective of the grain size. Material removal volume and extent of lateral cracking were proved to be increasing with the grain size [5; 14]. But the conclusions were obtained under large cutting depth conditions and the influences of grain size and depth of cut on grinding force were not investigated.  
This work dedicates to talk about influences of the relation between grain size and maximum undeformed chip-thickness on grinding force modeling and removal mechanisms of crystalline ceramics and non-crystalline ceramics. In this study, a grinding experiment on alumina ceramics and fused silica as representatives of the two kind ceramics was conducted. Therefore, the grinding force modeling can be improved by considering both the grinding parameters and materials microstructure.