Modeling and Validation of Indentation Depth of Abrasive Grain into Lithium Niobate Wafer by Fixed-Abrasive Lapping

The prediction of indentation depth of abrasive grain in hydrophilic fixed-abrasive (FA) lapping is crucial for controlling material removal rate and surface quality of the work-piece being machined. By applying the theory of contact mechanics, a theoretical model of the indentation depth of abrasive grain was developed and the relationships between indentation depth and properties of contact pairs and abrasive back-off were studied. Also, the average surface roughness (Ra) of lapped wafer was approximately calculated according to the obtained indentation depth. To verify the rationality of the proposed model, a series of lapping experiments on lithium niobate (LN) wafers were carried out, whose average surface roughness Ra was measured by atomic force microscope (AFM). The experimental results were coincided with the theoretical predictions, verifying the rationality of the proposed model. It is concluded that the indentation depth of the fixed abrasive was primarily affected by the applied load, wafer micro hardness and pad Young's modulus and so on. Moreover,the larger the applied load, the more significant the back-off of the abrasive grain. The model established in this paper is helpful to the design of FA pad and its machining parameters, and the prediction of Ra as well.