Sanjay G. Dhande

Slicing procedures in layered manufacturing: a review

Layered manufacturing (LM) or rapid prototyping is a process in which a part is produced using layer‐by‐layer addition of the material. In LM, slicing of the CAD model of a part to be produced is one of the important steps. Slicing of CAD model with a very small slice thickness leads to large build time. At the same time if large slice thickness is chosen, the surface finish is very bad due to staircasing. These two contradicting issues namely reduction in build time and better surface quality have been a major concern in laminated manufacturing. This contradiction has led to the development of number of slicing procedures. The present paper reviews various slicing approaches developed for tessellated as well as actual CAD models.

Real time adaptive slicing for fused deposition modelling

Improvement of part surface quality and geometric accuracy in Rapid Prototyping has been a major concern. Reduction in build time and increase of part surface quality are two factors which contradict with each other as decreasing build time detracts part quality because of staircase effect. There has been a number of attempts to tackle this problem and adaptive slicing procedures are proposed. In these procedures the layer edge profiles are implicitly assumed as rectangular. But in real practice the edge profiles of a layer manufactured part are not rectangular and is found to be parabolic in case of Fused Deposition Modelling. A geometrical parameter known as cusp height is limited to a pre-specified value in existing adaptive slicing procedures, which is defined for rectangular edge profiles only. In this paper, a slicing procedure is proposed for Fused Deposition Modelling based on real time edge profile of deposited layers. The procedure is implemented and examples are included to explain the adaptive slicing method.

Analysis and synthesis of mechanical error in path-generating linkages using a stochastic approach

A stochastic model of the four-bar, path-generating linkage has been made. Tolerances and clearances have been assumed to be random variables. The mechanical error in the path of a coupler point is analyzed for the three-sigma band of confidence level. For a specified path, the mechanical error depends on the selection of either the original or its cognate mechanism. A synthesis procedure to allocate tolerances and clearances on different members and joints of a linkage so as to restrict the output error in the path of the coupler point within specified limits is developed. The synthesis procedure helps the designer in finding out how much the tolerance or clerance on particular variable is critical in terms of affecting the output error in the path of a coupler point. Results of an illustrative example are given in the paper.

Curve and surface reconstruction from points: an approach based on self-organizing maps

Abstract Modeling of shapes for free form objects from point cloud is an emerging trend. Recognition of shape from the measured point data is a key step in the process of converting discrete data set into a piecewise smooth, continuous model. Shape recognition is to find the topological relation among the points, and in case of thick unorganized point cloud, the step requires both thinning and ordering. The present paper outlines a new approach based on growing self-organizing maps (GSOM) for piecewise linear reconstruction of curves and surfaces from unorganized thick point data. Inferences on selection of self-organizing map (SOM) algorithm parameters for this problem domain have been derived after extensive experimentation. A better quality measure to evaluate and compare various runs of SOM for the domain of curve and surface reconstruction has also been presented.

A Unified Approach to the Analytical Design of Three-Dimensional Cam Mechanisms

The paper presents a unified approach for the analytical design of three-dimensional cam follower systems. Generalized expressions for various cam parameters, such as the equation of the conjugate cam profile, the pressure angle at the point of contact and locations of the cutter and the grinding wheel axes are derived. The effectiveness of the proposed method is illustrated by applying it to camoids, three-dimensional cylindrical cams with translating and oscillating followers, globoidal cams with oscillating followers and two-dimensional disk cams with translating and oscillating roller followers.

Algorithms for development of certain classes of ruled surfaces

Abstract Surfaces that are one-parameter family of planes are called developable surfaces. Such surfaces form a special case of ruled surfaces and can be mapped isometrically onto a plane. The isometric mapping gives the development view of the surface. In the present paper, the condition of developability for two classes of ruled surfaces has been investigated. Based on this condition and the invariance of the geodesic curvature during isometric mapping, algorithms for development of these two classes of ruled surfaces have been developed. These algorithms have been found to be suitable for developing computer programs so as to get the development of conical, cylindrical and convolute surfaces.

Virtual hybrid-FDM system to enhance surface finish

Many rapid prototyping systems which produce prototypes by layer-by-layer material deposition are now commercially available. The layer-by-layer deposition process leads to a stepped surface known as staircase. Staircase formation is a geometric constraint of the layered manufacturing, which can not be eliminated. The presence of staircase on the surface of a prototype detracts from the surface finish and hence restricts functionality of prototypes. It is realized that there is a need to make modifications in RP (rapid prototyping) systems so that prototypes with better surface finish can be produced without incurring high production costs. A virtual hybrid fused deposition modelling system (hybrid-FDM) is proposed in the present work that uses both layer-by-layer deposition and machining. In this system, CAD model is sliced adaptively using limited centre line average (Ra) value as a criterion (Pandey et al. 2003a). Hot cutter machining/ploughing (HCM) (Pandey et al. 2003b) is recommended to machine the build edges (staircase) of ABS material. Numerically controlled x−y traversing mechanism is proposed as an attachment to move hot cutters along the periphery of slices to machine build edges. In this paper, geometrical designs of cutters are proposed. A process planning system to decide the number of layers to be deposited and then machined in order to access intricate features of a part is implemented. The developed system simulates surface roughness, before and after hot cutter machining. An experimental study is carried out by machining the build edges of an axisymmetric FDM part on lathe machine to form a basis for a hybrid-FDM system.

A flexible surface tooling for sheet-forming processes: conceptual studies and numerical simulation

All sheet-forming processes suffer from a limitation that tooling in the form of molds/dies is a precursor for realizing any simple or complex shape. In order to overcome this limitation, discrete surface tooling has been proposed in the past. This consists of a large number of closely spaced surface tool elements arranged in a matrix form whose heights can be adjusted to approximate the contour of desired surface shapes. Such a tooling has been successfully demonstrated experimentally. In this paper, a variation of discrete surface tooling, called as flexible surface tooling, has been proposed. The proposed tooling consists of discrete surface tool elements draped with flexible sheet of rubber-like material to provide a continuous surface required for tooling applications. Computational simulation of the proposed tooling is carried out for feasibility studies. Computational simulation involves the deformation analysis of rubber-like membranes in multiple contact by FEM. The results of the analysis indicate that the flexible surface tooling is an option for sheet-forming processes in general and for processes like composite layup in particular.

Geometric Modeling of Manufacturing Processes Using Symbolic and Computational Conjugate Geometry

The present paper describes a unified symbolic model of conjugate geometry. This model can be used to study the geometry of a cutting tool and the surface generated by it on a blank along with the kinematic relationships between the tool and the blank. A symbolic algorithm for modeling a variety of shape generating processes has been developed. It has been shown that using this algorithm one can develop geometric models for conventional machining processes such as milling, turning, etc. as well as unconventional or advanced machining techniques such as Electric Discharge Machining (EDM), Laser Beam Machining (LBM) etc. The proposed symbolic algorithm has been implemented using the symbolic manipulation software, MACSYMA. The algorithm is based on the concepts of envelope theory and conjugate geometry of a pair of mutually enveloping surfaces. A case study on the manufacture of a helicoidal surface and an illustrative example are given at the end of the paper.

Geometric Modeling of Fluted Cutters

Geometries of cutting tools are usually represented by two-dimensional models. This paper outlines the construction of detailed computer aided design models for a variety of fluted cutters that includes slab mills, end mills, and drills; and establishes a new three-dimensional definition for the geometry of fluted cutters in terms of biparametric surface patches. This work presents unified models of both plain and helical slab mills, end mills (with different end geometries), and drills (with a variety of point styles). The surfaces meant for cutting operations, known as flutes, are modeled as helicoidal surfaces. To model the flutes, sectional geometry of tip-to-tip profile is developed and then it is swept according to a sweeping rule, determined by the type of the cutter under consideration. The slab mill consists of flutes and two planar end surfaces, while the end mills and drills have shanks and end geometries also (in addition to the flutes). The geometric models of shank and end geometries are separately developed. The transitional surfaces of these cutters are modeled as bicubic Bezier surfaces or biparametric sweep surfaces. The proposed models employ a novel nomenclature that defines the form of cutting tools in terms of three-dimensional rotational angles. The relations required to map the proposed three-dimensional angles to conventional angles (forward mapping) and their reverse relations (inverse mapping) are also developed for all three types of fluted cutters. The new paradigm offers immense technological advantages in terms of numerous downstream applications.