A CNC interpolation algorithm for boundary machining

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.     

A method for producing a uniform contact stress distribution in composite bodies with interference

One of the most important problems in the design of press- and shrink-fitted assemblies is to avoid stress concentrations at the contact of two bodies. A method is presented whereby the contact-stresses can be made uniform by using variable interferences. In the proposed method the finite element technique is applied to determine the stresses of composite bodies, ignoring the effects of friction at the contact surfaces. A method of optimum structural design is used to obtain a uniform contact stress within the limit of the contraction force. In this method, interferences at contact nodal points are used as design variables. Some simple examples are presented and the effectiveness of the proposed approach is also demonstrated.     

Mesh-based morphing method for rapid hull form generation

Morphing is an interpolation technique that changes one form into another through a seamless transition, producing, in the process, an infinite number of ‘intermediate’ forms between the original and the target. This paper examines the possibility of using the morphing technique for generating a large number of hull forms rapidly based on a number of target forms, existing or newly generated.The paper discusses the technique developed for applying morphing technique to hull form definition. The algorithm first projects the vertices of the original and target 3D surfaces onto 2D planes. After ‘regularising’ the vertices on 2D, they are projected back on the 3D surfaces. The corresponding vertices of the two surfaces are then used for interpolation. It has been found that the interpolated hull forms can be generated almost instantaneously, allowing the whole algorithm to be embedded in an optimisation program.     

An iterative procedure for finite-element stress analysis of frictional contact problems

A simple, efficient, versatile and easily adaptable, iterative finite-element technique is described for solving frictional contact problems. The method is based on logical steps to establish the contact geometry and regions of slip and nonslip. Unlike previous techniques, the approach can be extended readily to multiple contact surfaces. The scheme is demonstrated by analyzing a mechanical joint in orthotropic wood. In this case, mixed coordinate systems are used to enhance accuracy of the stresses near the pin contact region. The numerically computed values agree with those reported elsewhere.     

A solution method for static and dynamic analysis of three-dimensional contact problems with friction

A solution method is presented for the analysis of contact between two (or more) three-dimensional bodies. The surfaces of the contacting bodies are discretized using quadrilateral surface segments. A Lagrange multiplier technique is employed to impose that, in the contact area, the surface displacements of the contacting bodies are compatible with each other. Distributed contact tractions over the surface segments are calculated from the externally applied forces, inertia forces and internal element stresses. Using the segment tractions, Coulomb's law of friction is enforced in a global sense over each surface segment. The time integration of dynamic response is performed using the Newmark method with parameters and . Using these parameters the energy and momentum balance criteria for the contacting bodies are satisfied accurately when a reasonably small time step is used.

The applicability of the algorithm is illustrated by selected sample numerical solutions to static and dynamic contact problems.     

Mixed finite element method for contact problems

In the paper the model of finite elements for elastic contact problems was used. Real structures are modeled by finite elements and rigid finite elements. We calculate stresses in the surface of two substructures using Coulomb model of friction.The method given here is an iterative procedure which is planed to incorporate this technique in the system allowing for incremental elastic solution. The computer program is adapted to solving spatial problems.     

Finite element analysis of elastodynamic sliding contact problems with friction

This paper presents a general but effective finite element technique to analyze elastodynamic sliding contact problems with friction. The deformed contact area is obtained using the constraint conditions developed by a quadratic mathematic programming technique. Lagrangian multipliers are introduced to evaluate the contact pressures due to friction and determine the adhesion or release of contact surface. Based on these, the sliding process between two contact surfaces is accurately modelled. This work also provides the correction formulae for modelling the transient response of velocities and accelerations on the contact surface when the initial impact or release of the contact surface occurred. Several numerical examples are carried out to demonstrate the validity and accuracy of this work. The complete scheme of the transient sliding response of two contact components subjected to oblique impact loadings is drawn.     

The influence of surface profiles on leakage in room temperature seal-bonding

We have developed a characterization method based on measured surface profiles for room temperature seal-bonding using surface activated bonding (SAB) technique and investigated the quantitative influence of surface profiles on leakage. We used the model for the bonding between the perfect flat surface which is not deformed and the metal surface with sub-nanometer rms surface roughness based on AFM surface profiles. The leak rates of the model were calculated by the Monte–Carlo method. Specific critical contact ratio P_sc gives the necessary contact ratio to disappear leak paths at a bonding interface. The P_sc was also calculated by the simulation with a basic plastic deformation law. Surface profiles of as-sputtered Au and chemical mechanical polished Cu surfaces were used as the metal surfaces. Investigating the relationship between the contact ratio and the leak rate, it was found that leak rates decrease drastically at a contact ratio close to the P_sc and leak rates decrease as the surface roughness decreases. Because of the drastic decrease of the leak rate, the vacuum sealing using SAB technique needs the contact ratio which is higher than P_sc. We also found that in the case of the as-sputtered Au deposited by the same conditions (only the deposition time change), P_sc has the tendency to decrease as the surface roughness decreases: if the rms roughness of the as-sputtered Au surface decreased from 1.5 to 0.5, the P_sc decreased from 0.6 to 0.52.     

Reasoning about nature of contact for planning manipulators tasks

Extracting information about contact between two convex bodies from the measured force vector is a prerequisite for any fine compliant motion control strategy. Contact information contains the direction and orientation of the contact surface normal and its relative location and orientation with respect to the compliant reference frame system.A method for interpreting the contact force feedback during compliant robot motion control, using kinematic screws, is presented. Domain specific rules combined with partial a priori knowledge of mating parts geometry and interpreted force signals are used to reason and make inferences about the initial contact configuration. The likely contact surfaces are predicted and point(s) or line(s) of contact are fully defined. These surfaces are idealized and represented by quadratic equations or polyhedral surfaces. The geometric properties of surfaces at the contact location are used to select the contact configuration when multiple solutions exist.An algorithm for predicting the Expected Contact Configuration (ECC) has been developed and is illustrated here with examples. Experimental validation of the developed expert system prototype, using a 6R manipulator, a six-axis force sensor, and a host computer is described.     

Generalized concept of meshing and contact of involute crossed helical gears and its application

A general approach for generation and design of standard and non-standard involute crossed helical gears is proposed. The conjugation of gear tooth surfaces is based on application of two generating rack-cutters with a common normal section. The investigation of the geometry is based on a new approach for presentation of the line of action A (the line of points of contact of tooth surfaces). Line A is represented in a plane Π that is tangent to the pinion base cylinder and position of A is determined analytically. Edge contact of tooth surfaces is avoided by limitation of shift of line of action caused by errors Δγ and ΔE of the crossing angle and the shortest distance, respectively. Simulation of meshing and contact is computerized by developed computer program. Enhanced stress analysis approach is proposed. The developed theory is illustrated with numerical examples.     

Determination of dynamic contact angles within microfluidic devices

Here, we report a single-point detection method for the determination of dynamic surface conditions inside microfluidic channels. The proposed method is based on monitoring fluorescence amplitude as a function of the convolution of a laser beam with segmented flow consisting of two immiscible liquids, one containing fluorescent dye. The fluorescence amplitude is determined by the flow rate and the droplet shape, which is affected by the channel surface properties. We modeled the interaction of a droplet and a laser beam via computer-aided design software, using the laser beam location in relation to the droplet shape as a parameter. The method was applied to fused silica capillaries with both unmodified and modified surfaces, with segmented flow exhibiting water contact angles of ≈?30° and ≈?100°, respectively. The method allows discrimination between hydrophillic and hydrophobic surfaces, as well as the quality of the treatment. The results were verified using fluorescence imaging of the droplets via a stroboscopic technique. We also applied this method to the analysis of microfabricated channels with non-circular cross sections. We demonstrated that the technique enables the determination of the hydrophobicity of channel surfaces, a crucial property required for the generation of segmented flow or emulsions for applications such as digital PCR.     

Computational service life estimation of contacting mechanical elements in regard to pitting

A computational model for determining the service life of contacting surfaces in regard to surface pitting is presented. The model considers the material fatigue process leading to pitting, i.e. the conditions required for the short fatigue crack propagation originating from the initial crack in a single material grain. In view of small crack lengths observed in surface pitting, the simulation takes into account the short crack growth theory. The stress field in the contact area and the required functional relationship between the stress intensity factor and the crack length are determined by the finite element method. An equivalent model of two contacting cylinders is used for numerical simulations of crack propagation in the contact area. On the basis of numerical results, and with consideration of some particular material parameters, the probable service life period of contacting surfaces is estimated for surface curvatures and loadings that are most commonly encountered in engineering practice.     

A mathematical framework for rigid contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C² continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton–Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C² continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super) ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.     

Tetrahedra Based Adaptive Polygonization of Implicit Surface Patches

This paper presents a tetrahedra based adaptive polygonization technique for tessellating implicit surface patches. An implicit surface patch is defined as an implicit surface bounded by its intersections with a set of clipping surfaces and which lies within an enclosing tetrahedron. To obtain the polygonization of an implicit surface patch, the tetrahedron containing the patch is adaptively subdivided into smaller tetrahedra according to the criteria introduced in the paper. The result is a set of tetrahedra each containing a facet approximating the surface. The intersections between the facets and the clipping surfaces are used to locate the surface patch boundary. Ambiguous results in generating the facets for highly curved surfaces or surfaces with singular points are also addressed. The result of the polygonization is a set of triangular facets that can be used for visualization and numerical analysis. The proposed method is also suitable for locating the intersection of two implicit surfaces.     

Determination of wheel–rail contact points with semianalytic methods

The multibody simulation of railway vehicle dynamics needs a reliable and efficient method to determine the location of the contact points between wheel and rail that represent the application points of the contact forces and influence their directions and intensities. In this work, two semi-analytic procedures for the detection of the wheel–rail contact points (named the DIST and the DIFF methods) are presented. Both the methods consider the wheel and the rail as two surfaces whose analytic expressions are known. The first method is based on the idea that the contact points are located in the point in which the distance between the contact surfaces has local maxima, and is equivalent to solve an algebraic 4D-system. The second method is based on the idea that in the contact points the difference between the surfaces has local minima and is equivalent to solve an algebraic 2D-system. In both cases, the original problem can be reduced analytically to a simple 1D-problem that can be easily solved numerically.     

A boundary integral equation method for axisymmetric elastic contact problems

A numerical method for the solution of axisymmetric contact problems has been developed using the Boundary Integral Equation (BIE) technique. An automatic load incrementation technique is implemented in a BIE axisymmetric computer program using isoparametric quadratic elements. The method is successfully applied to some frictionless contact problems and the results are compared to other numerical and analytical solutions to demonstrate the accuracy of the BIE method.     

A fast and stable penalty method for rigid body simulation

Two methods have been used extensively to model resting contact for rigid body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits expected-case polynomial complexity in the number of contact points, and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures, while exhibiting much faster performance both asymptotically and empirically.     

Modified approach for tooth contact analysis of gear drives and automatic determination of guess values

An approach for the development of a computer program for simulation of meshing and contact of gear tooth surfaces is proposed for the following specific conditions: (i) the basic machine-tool settings applied for generation of meshing gears are given, and (ii) the location of the mean contact point of the contacting surfaces is not known. The contribution of the authors cover: (i) automatic determination of the guess values for derivation of the first contact point of tooth surfaces Σ₁ and Σ₂; (ii) development of a modified computer program for tooth contact analysis (TCA) for the most general case when the tooth surfaces are represented by three related parameters. The determination of guess values is based on the following considerations: (i) the generating surfaces are represented discretely by cells; (ii) the cells for both gears are located on planes of surface parameters that contains n and q cells, respectively; (iii) pairing of cells and their combination is considered in the domains of n × q cells; (iv) determination of a single pair of cells that provides: (a) minimization of deviation of tooth surface normals, (b) minimization of distance between the two cells or (c) an integrated factor m based on conditions (a) and (b). A numerical example for determination of guess values and deciphering of TCA is represented.     

Computing minimum distance between two implicit algebraic surfaces

The minimum distance computation problem between two surfaces is very important in many applications such as robotics, CAD/CAM and computer graphics. Given two implicit algebraic surfaces, a new method based on the offset technique is presented to compute the minimum distance and a pair of points where the minimum distance occurs. The new method also works where there are an implicit algebraic surface and a parametric surface. Quadric surfaces, tori and canal surfaces are used to demonstrate our new method. When the two surfaces are a general quadric surface and a surface which is a cylinder, a cone or an elliptic paraboloid, the new method can produce two bivariate equations where the degrees are lower than those of any existing method.