The Research Of Multi-objective Tool Axis Optimization Based On Collision Avoidance In Blade Machining

Tool-axis optimization for multi-axis machining is a challenging topic and greatly affects machining quality and efficiency.There are previous works dedicated to various aspects of tool-axis optimization,including smoothing of orientation change,maintaining optimal direction,and collision avoidance,but most of these works addressed one or two of these requirements and/or are limited to certain types of cutters and workpiece geometry.As a result,the computed tool axes are not completely satisfactory.To solve above problems,a unified mathematical framework is presented to address a comprehensive set of machining requirements.The unified model treats various machining requirements as either objective functions or constraints in an optimization framework.The smoothing of axis variation and the optimal(preferred)orientation are presented as objective functions,while the free-of-collision and forced alignment are incorporated as constraints.A FEM numerical recipe is provided to solve the unified optimization problem.The case of four-axis blade roughing is presented as an application.The tool-axis is formulated using the lead angle.The gouge-free condition is expressed as an in-equality constraint(bounded range of allowed values),alongside the smooth variation objective function.Ahead of the tool-axis optimization,the initial values of the lead angle are determined using the preferred optimal direction,and the allowed boundary ranges are computed via a gouge detection method based on the cutter profile.To solve this four-axis tool-axis optimization problem,the objective functions and constraints are numerically approximated by an FEM recipe.The numerical FEM optimization is then solved by an SQP solver to obtain the smoothed and optimized tool-axis in the fouraxis tool path.The second application is the more complex five-axis blade finishing problem.Instead of the free choice of lead and tilt angles,our model fixes the B-axis of the machine tool to achieve better rigidity.Again,the gouge-free condition is expressed as an in-equality constraint and the smoothness as an objective function.The initial values of the lead/tilt angles are determined using the preferred optimal direction(with the fixed B-axis constraint),and the allowed ranges of lead/tilt angle combinations are computed via a project-and-lift-or-tilt gouge detection method.A numerical FEM recipe is used to approximate the objective functions and constraints,and again an SQP solver is used to solve this five-axis optimization problem.However,due to the very large size of the degrees of freedom(the number of unknowns in the problem space),the SQP solver is slow to converge and often trapped in local minima.Based on the Multi-Grid(MG)method,we apply a Pseudo-Multi-Grid(PMG)method to solve the optimization problem of the very-large-size numerical FEM model.The proposed PMG is a simplified version of full MG.It divides the tool path into different regions and solve the optimization in steps,achieving faster convergence rate and free of being trapped in false minima.Experiments with real industrial blade parts are performed to validate the effectiveness of the proposed tool-axis optimization method with the above-mentioned two applications of four-axis blade roughing and five-axis blade finishing.For each application,the experiments cover material-removal NC simulations and actual CNC machining.The results indicate that the method produces satisfactory parts with good finished quality.