Dynamic modeling of gripper type hard rock tunnel boring machine

A multi-system coupled closed-form dynamic model for controller design of hard rock Tunnel Boring Machine (TBM) is presented with consideration of the closed chain structure and interactions with rocks. Based on the analysis of closed chain structure, the motion equations of each rigid body in the TBM system are derived in terms of generalized coordinates. To obtain the mathematical model for controller design, the nonholonomic constraints are novelly proposed to describe the complex interactions between the TBM shield body and rocks instead of the traditional finite element method. With the nonholonomic constraints assumption, a closed-form mathematical model with Lagrangian multiplier is obtained by applying the Lagrangian approach. The interactions between the cutter-head and rocks as the main load acting on the TBM during excavation are described by the widely used Colorado School of Mines (CSM) model. The simulations of excavation performance of TBM in different distribution conditions of rocks with various UCS and TS are compared and discussed.