1st Edition

Kinematic Geometry of Surface Machining

By Stephen P. Radzevich Copyright 2011
    536 Pages 212 B/W Illustrations
    by CRC Press

    The principle of Occam’s razor loosely translates to “the simplest solution is often the best”. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multi-axis NC machines. He has developed a method to quickly calculate the necessary parameters, greatly reduce trial and error, and achieve efficient machining processes by using less input information, and in turn saving a great deal of time.

    This unique method will allow youto calculate optimal values for all major parameters of sculptured surface machining on multi-axis NC machines.It is much faster than conventional methods because it requires only minimal input information for the development of extremely efficient machining operations. Radzevich simply utilizes the geometric information of a particular part surface to be machined for developing optimal surface machining process rather than wasting time dealing with unnecessary data.

    This one-of-a-kind resource guides you through this cutting-edge technique beginning with an analytical description of part surfaces, the basics of differential geometry for sculptured surfaces, and the principal elements of the multi-parametric motion on a rigid body in E3 space theory. The book reveals the analytical method for investigating cutting tool geometry and explains a set of described conditions required for proper part surface generation. Next, the author illustrates the selection of criterion for optimization and describes the synthesis of optimal machining operations. He includes examples of the DG/K based method of surface generation implementation.

    Written by a leading expert in the field who holds over 150 patents, Kinematic Geometry of Surface Machining invokes Occam’s well-known philosophical principle so that you can apply the simplest solution to achieve optimal, time-saving surface machining processes.

    Part I: Basics
    Part Surfaces: Geometry
    Elements of differential geometry of surfaces
    On difference between classical differential geometry and engineering geometry
    On classification of surfaces
    Kinematics of Surface Generation
    Kinematics of sculptured surface generation
    Generating motions of the cutting tool
    Motions of orientation of the cutting tool
    Relative motions those causing sliding of a surface over itself
    Feasible kinematic schemes of surface generation
    On a possibility of the replacement of axodes with pitch surfaces
    Examples of implementation of the kinematic schemes of surface generation
    Applied Coordinate Systems and Linear Transformations
    Applied coordinate systems
    Coordinate system transformation
    Useful equations
    Chains of consequent linear transformations and a closed loop of consequent coordinate systems transformations
    Impact of the coordinate systems transformations on fundamental forms of the surfaces
    Part II: Fundamentals
    The Geometry of Contact of Two Smooth Regular Surfaces
    Local relative orientation of a part surface and of the cutting tool
    The first order analysis: common tangent plane
    The second order analysis
    Rate of conformity of two smooth regular surfaces in the first order of tangency
    Plücker’s conoid: more characteristic curves
    Feasible kinds of contact of the surfaces p and t
    Profiling Of the Form Cutting Tools of the Optimal Design
    Profiling of the form cutting tools for sculptured surface machining
    Generating of enveloping surfaces
    Profiling of the form cutting tools for machining parts on conventional machine tools
    Characteristic line  of the part surface  and of the generation surface  of the cutting tool
    Selection of the form cutting tools of rational design
    The form cutting tools having continuously changeable the generating surface
    Incorrect problems in profiling of the form cutting tools
    Intermediate conclusion
    Geometry of Active Part of a Cutting Tool
    Transformation of the body bounded by the generating surface T into the cutting tool
    Geometry of the active part of cutting tools in the tool-in-hand system
    Geometry of the active part of cutting tools in the tool-in-use system
    On capabilities of the analysis of geometry of the active part of cutting tools
    Conditions of Proper Part Surface Generation
    Optimal work-piece orientation on the worktable of multi-axis NC machine
    Necessary and sufficient conditions of proper part surface generation
    Global verification of satisfaction of the conditions of proper part surface generation
    Accuracy of Surface Generation
    Two principal kinds of deviations of the machined surface from
        the nominal part surface
    Local approximation of the contacting surfaces P and T
    Computation of the elementary surface deviations
    Total displacement of the cutting tool with respect to the part surface
    Effective reduction of the elementary surface deviations
    Principle of superposition of elementary surface deviations
    Part III: Application
    Selection of the Criterion of Optimization
    Criteria of the efficiency of part surfaces machining
    Productivity of surface machining
    Interpretation of the surface generation output as a function of   conformity
    Synthesis of Optimal Surface Machining Operations
    Synthesis of optimal surface generation: the local analysis
    Synthesis of optimal surface generation: the regional analysis
    Synthesis of optimal surface generation: the global analysis
    Rational re-parameterization of the part surface
    On a possibility of the DG/K-based CAD/CAM system for optimal sculptured surface machining
    Examples of Implementation of the Dg/K-Based Method of Surface Generation
    Machining of sculptured surfaces on multi-axis NC machine
    Machining of surfaces of revolution
    Finishing of involute gears

    Biography

    Stephen P. Radzevich