Investigation of complex surfaces of propellers of vehicles by a mechatronic profilograph

Introduction. The technology of investigation of screw propellers complex surfaces, which include the marine and aircraft propellers of vehicles, mechatronic profilers for the implementation of reverse engineering, is considered. A review of the scientific literature shows that at present the problem of monitoring complex surfaces of products at various stages of its life cycle requires further research, since the use of available devices and methods does not always provide the necessary accuracy, technological effectiveness and sufficient information on measurements. The purpose of the work is to develop a new technology for studying complex surfaces of propellers, which include marine and aircraft propellers of vehicles by means of a mechatronic profilograph to implement reverse engineering. Methods. The paper considers the implementation of the innovative technology for studying complex surfaces of propellers using the developed mechatronic profilograph. This ingenious mechatronic profilograph is designed to measure the profile and study the shape of complex surfaces of various products, as well as to determine the geometric and morphological parameters of these surfaces. On the basis of theoretical studies the main design and technological parameters are found and the hyperbolic dependence of the angular rate of the laser sensor movement on the scanning radius is determined for the developed mechatronic profilograph. For example, if a constant pitch of the trajectory along the Archimedes spiral is 2 mm, the value of the sensor angular rate should gradually decrease from the maximum value of 2 rad/s to the minimum value of 0.574 rad/s, i.e. by 3.484 times. Results and discussion. It is revealed that the use of cylindrical coordinates for processing the obtained data by a profilograph is logical and has a number of advantages. An express analysis of the propeller surfaces with rotary symmetry is carried out and differences in the shapes of the surfaces of the propeller blades by deviation values in the longitudinal and transverse directions for different radii are established. On the basis of the experimental data, a two-factor power model describing deviations with a determination coefficient of 0.967 is obtained, according to its analysis, it is clear that on average the angle of deviation in the perpendicular direction to the radius  - increases from 0 to 0.3, and the angle of deviation along the radius  increases from 0 to 5.4.

A weighted fusion method with multi-system for improving measurement accuracy of structured light 3D profilometry

It is a challenge to improve the accuracy of 3D profile measurement based on binary coded structured light for complex surfaces. A new method of weighted fusion with multi-system is presented to reduce the measurement errors due to the stripe grayscale asymmetry, which is based on the analysis of stripe center deviation related to surface normal and the directions of incident and reflected rays. First, the stripe center deviation model is established according to the geometric relationship between the stripe center deviation, the incident and reflected angles at any measured point. The influence of each variable on stripe center deviation is analyzed, and three subsystems are formed by a binocular structured light framework to achieve multiple measurements based on the influence regularity. Then in order to improve the measurement accuracy, different weights are assigned to the measured point in different subsystems according to the stripe center deviation model and its relationship with measurement error, and the weighted data from different subsystems are fused. Experiments are carried out to validate the presented method, and the experimental results demonstrate that it effectively improves the measurement accuracy of complex surfaces and measurement accuracy is improved by about 27% compared with the conventional method.

Processing of quasi-equidistant surfaces with the detection of the dependence of the roughness parameters on the tool pitch in the cam system

This article discusses the basic principles of generating a tool path when processing quasi-equidistant surfaces. The review and analysis of the origin of the automation of technological preparation of production in the world is carried out. The concept of integrated automated production is revealed. Considered are the leading enterprises that were among the first to introduce computer-aided design systems. The article discusses technologies for processing complex surfaces with the maximum removal of the metal layer from the work piece, with the maximum approximation to the given shape. The types of complex spherical surfaces have been identified, the processing of which is a complex technological process that requires a high level of qualifications of a specialist and expensive equipment. Before the introduction of automated machine control, such types of complex surfaces were almost impossible to process, the geometry was only close to the real one. Here we consider a modern CAM-system, which is a complex software package. Over the past decade, several generations of CAM systems have changed. When forming the tool path, it is possible to use the functions of their viewing and editing. In most cases, the system automatically generates the tool path based on the cutting geometry and machining parameters. The authors proposed a method for creating a machining path in the NX CAM environment. In this work, the optimal trajectory of the tool movement is determined, the cutting pattern is selected for processing quasi-equidistant surfaces, the cutting modes, the cutting tool, and the overlap step between passes are determined.

On the classification of non-big Ulrich vector bundles on surfaces and threefolds

In this paper, we classify Ulrich vector bundles that are not big on smooth complex surfaces and threefolds.

Biharmonic submanifolds in metallic Riemannian manifolds

In this paper, we study the biharmonic submanifolds of Riemannian manifolds endowed with metallic and complex metallic structures. In case of both the structures, we obtain the necessary and sufficient conditions for a submanifold to be biharmonic. Particularly, we find the estimates for mean curvature of Lagrangian and complex surfaces.

Conversion Between Cubic Bezier Curves and Catmull–Rom Splines

Splines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.