This book introduces students and machining professionals to the Computer Numerical Control (CNC) programming and technology. Using an applied, hands-on, step by step methodology which is easy to understand and follow, provides the mode of operation and programming of a modern CNC machining centre in two of the most widely used control systems, Fanuc and Heidenhain. Using as examples a series of useful mechanical parts, coverage includes manufacturing drawings, tooling and G-code programming with all program commands fully explained.
This paper presents a convenient and an easy to use manufacturing method for parts with axisymmetric geometry on CNC milling machines. The desired form of the cavities is achieved by selecting as generatrix curve any plane curve, implicitly or parametrically defined, which fulfills specific imposed by the user criteria (functional, aesthetic or other). Each machining pass is modelled as a path composed of generatrix curve segments and semicircular arcs. The surface quality is controlled by keeping the distance between successive scallops within a programmed value. Tool motion along the desired paths is generated by G-code algorithms that exploit the parametric programming technique, a powerful CNC programming tool. The effectiveness of the proposed method is verified by simulation tests for three representative curves..
While drilling a usual hole consists one of the most common and easy to perform machining operations, drilling a deep hole becomes one of the most complicated and challenging metal cutting processes due to the extreme required tolerances of straightness, roundness, concentricity, surface finish, etc. The instruction set of modern CNC milling machines provides special G-codes to accommodate drilling operations in the form of canned cycles. However, these canned cycles lack of the capability in a dynamic variation of important drilling parameters as pecking distance, feedrate and spindle speed are. The use of the optimal values in different hole-depths for these parameters is critical for a successful completion of a deep hole drilling operation. The paper presents the development of a G-code algorithm based on the powerful parametric programming technique which provides to the user the flexibility to dynamically adapt the required parameters values to the needs of each individual deep hole drilling case.
Hole-drilling is the most common machining operation performed on CNC machine-tools or machining workshops. Drilling appears to be a relatively simple process however, when it involves drilling deep holes, it becomes one of the most complicated metal cutting processes. Although modern machine tool controllers are equipped with special drilling canned cycles, these cycles have significant constraints mainly due to their limited framework of application. The present work proposes a general G-code algorithm intended to accommodate effective deep hole drilling. The algorithm is characterized by flexibility in the pecking strategy and adaptability to the needs of each individual drilling case. The development of the proposed algorithm is based on parametric programming which is a powerful CNC programming technique.
This paper presents a manufacturing method for parts with trochoidal profile on CNC milling machines. The method is based on a new real-time interpolation algorithm capable to drive the cutter along the offset of trochoid curves with precision equal to the resolution of the machine. The structure of the presented algorithm may be adapted accordingly so as to be used either for parts with an epitrochoidal or a hypotrochoidal profile. Both types of curves, known as trochoid curves, have important industrial applications such as gears with trochoidal tooth-profile, cams, trochoidal-shaped housings for rotary internal combustion engines and rotary piston pumps etc. The effectiveness and accuracy of the proposed method is verified by simulation tests of the generated tool path for the machining of two representative mechanical parts, an inner rotor of a hypogerotor pump and an epitrochoidal-shaped housing..
This paper proposes a set of four elliptical features that can enhance the programming capabilities of a modern CNC system. Namely, a real-time interpolation algorithm for motion generation along an ellipse and its offset, machining of an elliptical pocket, and drilling a series of equidistant holes along an elliptical path. The paper analytically describes the implementation of the new functions while the G-codes, along with their complementary requisite data needed to be introduced in the CNC part program, are exemplified with simulation and actual machining tests for each feature.
Focusing on the just-in-time (JIT) operations management, earliness as well as, tardiness of jobs’ production and delivery should be discouraged. In accordance to this philosophy, scheduling problems involving earliness and tardiness penalties are very critical for the operations manager. In this paper, a new population heuristic based on the particle swarm optimization (PSO) technique is presented to solve the single machine early/tardy scheduling problem against a restrictive common due date. This type of scheduling sets costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs, thus pushing the completion time of each job as close as possible to the due date. The problem is known to be NP-hard, and therefore large size instances cannot be addressed by traditional mathematical programming techniques. The performance of the proposed PSO heuristic is measured over benchmarks problems with up to 1000 jobs taken from the open literature, and found quite high and promising in respect to the quality of the solutions obtained. Particularly, PSO was found able to improve the 82% of the existing best known solutions of the examined benchmarks test problems.
A high precision method is described for CNC milling of axisymmetric die cavities used to manufacture parts of revolution by processes such as casting, forging, injection, molding etc. The desired form of the cavities is achieved by selecting as generatrix curve (profile) any plane curve, implicitly or parametrically defined, which fulfills specific imposed by the user criteria. Tool center motion is generated by modeling each machining pass as a path composed of generatrix curve segments and semicircular arcs. The surface quality is controlled by keeping the distance between successive scallops within a programmed value. Each segment of the generatrix is processed by highly accurate real-time interpolation algorithm which generates cutting steps equal to the machine's resolution, while semicircular arcs are processed by the existing in all CNC systems standard circular motion. As it is shown, the whole machining task can be programmed in a single block of the part program. The effectiveness of the proposed system is verified by simulation tests for three representative applications..
This paper presents an algorithm for improving the interpolation accuracy in turning operations. The parts considered are formed by revolving a free-form profile which is implemented in terms of Bézier formulation around a center linear axis. The demand for the manufacturing of such geometric shapes is frequently met in parts produced by casting and forging methods. The method employs a computer numerical control (CNC) turning machine and is based on the locus tracing concept. The algorithm described utilizes a real-time CNC interpolator providing the highest possible accuracy of which the turning machine is capable. The whole machining task can be programmed as a canned cycle, essentially extending the feature generating capabilities of the existing G70/G73 CNC turning fixed cycles.
A method for machining a particular set of revolved parts is proposed. The partsconsidered are formed by revolving a free-form profile which is implemented in terms of Bezier formulation around a center linear axis. The demand for manufacturing of such geometric shapes is frequently met in parts produced by casting and forging methods. The algorithm described, utilizes a real-time CNC interpolator providing the highest possible accuracy of which the turning machine is capable. The whole machining task can be programmed as a canned cycle, essentially extending the feature generating capabilities of the existing G70/G73 CNC turning fixed cycles..
A machining strategy for milling a particular set of pockets with epitrochoidal boundary is proposed. The method is suitable to be integrated into the controller of a CNC milling machine and is particularly useful for machining chambers of rotary internal combustion engines (Wankel), rotary piston pumps and generally epitrochoidal-shaped housings. Motion generation is achieved by an algorithm which utilizes real-time CNC interpolation providing the highest possible accuracy, of which the milling machine is capable. The surface quality is controlled by applying roughing and finishing passes. The whole machining task can be programmed in a single block of the part program. Finally, the effectiveness of the proposed method is verified by simulation tests of the generated tool path..
A machining strategy for milling a particular set of surfaces, obtained by the technique of cross-sectional design is proposed. The surfaces considered are formed by sliding a Bezier curve (profile curve) along another Bezier curve (trajectory curve). The curves are located in perpendicular planes. The method employs a three-axis CNC milling machine equipped with suitable ball-end cutter and is based on the locus-tracing concept. The algorithm described, utilizes a real-time CNC interpolator providing the highest possible accuracy, of which the milling machine is capable. The surface quality is controlled by keeping the distance between scallops within a programmed value. Finally, the whole machining task can be programmed in a single block of the part program.
This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.
The aim of this paper is to propose an interpolation algorithm for tracing the equidistant (bisector) of two planar curves. The structure of the algorithm may be adapted accordingly so as to be used either for purely computing purposes or for presentation purposes. As a computing tool, the algorithm is suitable for computation of offset intersections and construction of Voronoi diagrams. In this case the step size is adjusted appropriately in order to reach the desired position in a small number of steps but with high accuracy. As a presentation tool, it may be embedded in a CAD system, entrusted with the task of drawing equidistants or even it may be used for plotting equidistants by driving the plotting tip. In this case, a fixed step size is selected to satisfy the specific precision requirements of the presentation. The development of the algorithm is achieved by treating equidistant generation as a locus-tracing problem. Using analytic concepts and the locus-defining geometric property, we formulate two sophisticated constructive operations. The repeated application of these operations generates a succession of points on the desired path (the locus) accurately and efficiently.
This paper proposes a series of machine codes selected for integrating advanced programming capabilities into the control of a modern CNC system. The new programming capabilities were developed and tested in the framework of a PC-based milling machine controller. Namely, tool-motion along space curves, cutter offsetting for free-form curves and two machining cycles for revolved (external or internal) surfaces with free-form profiles, constitute the new characteristics proposed to be integrated into the system of a CNC milling machine. Based on recently developed algorithms whose mathematical description, formulation and verification are available in respective referred published articles, this paper describes how the new functions are properly integrated into a CNC milling system. In this direction, a new class of machine codes for the specification of each of the functions is proposed, while certain topics arised in practice are extensively further discussed. The selected machine codes, together with their complementary requisite data, needed to be introduced in the NC program, are exemplified via certain examples and actual machining tests are presented for each of the cases
This paper presents an efficient and accurate algorithm for machining boundaries formed at the intersection of two surfaces, an important manufacturing problem in CNC machining. The algorithm is developed using a locus tracing technique implemented on the basis of Danielson's step selection rules. A vertical ball-end milling cutter moves along the considered boundary, in contact with the two surfaces. The algorithm guides the center of the spherical end of the cutter, to maintain exact contact (within 1 step) along the entire path. A seamless formulation is used, allowing the contact points to move freely from the ball-end to the cutter periphery and vice-versa. The surfaces forming the boundary may be implicitly or parametrically defined. The reliability of the algorithm is demonstrated for both cases, by treating a complex boundary machining example. The boundary considered is formed by the intersecting quadratic surfaces of a sphere and an elliptic hyperboloid.
This paper presents a new interpolation algorithm for tool motion generation along planar offset curves, an important manufacturing problem in CNC machining. The development of the algorithm is based on a locus tracing concept. The main advantage of the concept is the fact that is applicable not only when an analytic expression of the desired path is available but also in situations where, although the path is geometrically defined, its analytic description is either impossible to compute, or too cumbersome to work with. The presented locus tracing algorithm, uses the locus defining geometric property to generate a succession of points on the desired path (the offset), through repeated application of two analytically implemented construction operations. These operations are formulated on the basis of the direction and proximity criteria introduced by Danielson, which guarantee a locus position error of at most one step. The effectiveness and simplicity of the algorithm is demonstrated by two representative examples. The first example uses an ellipse as the generator curve while the second example treats with a more complex case such is the case of a free-form curve implemented in terms of a Bezier curve.
Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. This paper proposes an efficient and accurate method for developing a class of precise interpolation algorithms which can drive the cutter of a CNC machine along three-dimensional (3D) trajectories. Engaging a pair of primitive shapes, the method uses their implicit or parametric definition to interpolate their intersection curve on the basis of Danielson’s step selection rules. The presence of Danielson’s criteria guarantees a position error of at most one step. A general-purpose computer for path generation and real-time control of the machine is employed. The user first chooses a suitable combination of shapes whose intersection gives the desired form of the 3D trajectory and then initiates the algorithm with the desired information of the two shapes..
An accurate, flexible and simple method is proposed for machining the surfaces obtained, either by revolving around an axis (surface of revolution), or by moving along a straight line (swept surface), a free-form profile which is implemented in terms of Bezier formulation. In the first case, the profile curve is coplanar with the symmetry axis, while in the second case it lies in a plane perpendicular to the direction of translation. The demand for manufacturing of such geometric shapes is frequently met in sculptured surfaces of molds, stamping dies, forging tools, rolling shapes, etc.
An efficient and accurate algorithm for generating circular arcs on arbitrary planes is presented and its implementation in the context of CNC is discussed. Besides having significant application potential as a CNC feature, it exemplifies a class of precise interpolation algorithms which can be developed on the basis of an integer programming formulation of Danielson’s step selection criteria.
An interactive system is described for machining the die or mould cavities used in the manufacture of axisymmetric parts by processes such as forging, injection moulding, casting, etc. The system is easy to use, flexible, accurate and fully automatic.