Optimum Curve Matching Between Two Free-Form Curves for Modeling and Manufacturing

2007 ◽  
Author(s):  
Kuntal Samanta ◽  
Bahattin Koc
Keyword(s):  
Piecewise Linear ◽  
Optimization Method ◽  
Nc Machining ◽  
Ruled Surfaces ◽  
Free Form ◽  
Curve Matching ◽  
Location Data ◽  
Spline Curves ◽  
Point To Point ◽  
Heterogeneous Object Modeling

A new curve matching method is proposed to generate non-self-intersecting and non-twisted ruled surfaces for application in diverse fields such as heterogeneous object modeling, layered manufacturing, offsetting and multi-axis NC machining. The method establishes point-to-point correspondence represented by a set of ruling lines between two directrices of the ruled surface. The directrices are given as non-self-intersecting, closed, at least C1 continuous, planar, B-spline curves. To match the points on the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the ruling lines and minimize the sum of the lengths of connecting ruling lines. The generated ruling lines can be used as cutter location data for multi-axis NC machining of ruled surfaces. Moreover, by subdividing the ruling lines into equal number of segments, one can construct a series of intermediate piecewise linear curves that represent the metamorphosis between the directrices. Implementation and examples are also presented.

Ruled Layer Generation Between Two Freeform Curves by Normal and Distance Matching

2006 ◽  
Author(s):  
Kuntal Samanta ◽  
Bahattin Koc
Keyword(s):  
Piecewise Linear ◽  
Optimization Method ◽  
Layered Manufacturing ◽  
Cnc Machining ◽  
Curve Matching ◽  
Location Data ◽  
Spline Curves ◽  
Point To Point ◽  
Number Of Segments ◽  
Cutter Location Data

A new curve matching method is proposed to generate non-self-intersecting and non-twisted ruled layers for application in diverse fields such as layered manufacturing, offsetting and multi-axis CNC machining. The method establishes point-to-point correspondence represented by a set of ruling lines between two directrices of the ruled surface. The directrices are given as non-self-intersecting, closed, at least C1 continuous, planar, B-spline curves. To match the points on the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the ruling lines and minimize the sum of the lengths of connecting ruling lines. The generated ruling lines can be used as cutter location data for multi-axis NC machining of ruled surfaces. Moreover, by subdividing the ruling lines into equal number of segments, one can construct a series of intermediate piecewise linear curves that represent the metamorphosis between the directrices. Implementation and examples are also presented.

Application of Convex Hull for Tool Interference Avoidance in 5-Axis CNC Machining

1996 ◽  
Author(s):  
Yuan-Shin Lee ◽  
Tien-Chien Chang
Keyword(s):  
Convex Hull ◽  
Tool Path ◽  
Correction Method ◽  
Nc Machining ◽  
Cnc Machining ◽  
Free Form ◽  
Interference Avoidance ◽  
Tool Interference ◽  
Free Form Surface ◽  
Free Form Surfaces

Abstract In this paper, a methodology of applying convex hull property in solving the tool interference problem is presented for 5-axis NC machining of free-form surfaces. Instead of exhausted point-by-point checking for possible tool interference, a quick checking can be done by using the convex hull constructed from the control polygon of free-form surface modeling. Global tool interference in 5-axis NC machining is detected using the convex hull of the free-form surface. A correction method for removing tool interference has also been developed to generate correct tool path for 5-axis NC machining. The inter-surface tool interference can be avoided by using the developed technique.

Energy efficiency path planning for a quadrotor aerial vehicle

2021 ◽  
pp. 014233122110585
Author(s):  
Fouad Yacef ◽  
Nassim Rizoug ◽  
Laid Degaa ◽  
Omar Bouhali ◽  
Mustapha Hamerlain
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Weather Conditions ◽  
Optimization Method ◽  
Control Approach ◽  
Mission Success ◽  
Aerial Vehicle ◽  
Vehicle Trajectory ◽  
Point To Point

Unmanned aerial vehicles are used today in many real-world applications. In all these applications, the vehicle endurance (flight time) is an important constraint that affects mission success. This study investigates the limitations of embedded energy for a quadrotor aerial vehicle. We consider a quadrotor simple tasked to travel from an initial hover configuration to a final hover configuration. In order to have a precise approximation of the consumed energy, we propose a power consumption model with battery dynamic, motor dynamic, and rotor efficiency function. We then introduce an optimization algorithm to minimize the energy consumption during quadrotor aerial vehicle mission. The proposed algorithm is based on an optimal control problem formulated for the quadrotor model and solved using nonlinear programming. In the optimal control problem, we seek to find control inputs (rotor velocity) and vehicle trajectory between initial and final configurations that minimize the consumed energy during a point-to-point mission. We extensively test in simulation experiments the proposed algorithm under normal and windy weather conditions. We compare the proposed optimization method with a nonlinear adaptive control approach to highlight the saved amount of energy.

scholarly journals Measurement point sampling method for inspection of parts with free-form surfaces

2018 ◽  
Vol 10 (11) ◽  
pp. 168781401880957 ◽  
Author(s):  
Dezhong Zhao ◽  
Wenhu Wang ◽  
Jinhua Zhou ◽  
Ruisong Jiang ◽  
Kang Cui ◽  
...  
Keyword(s):  
Measurement Accuracy ◽  
Sampling Method ◽  
Free Form ◽  
Surface Inspection ◽  
B Spline ◽  
Spline Curves ◽  
Data Points ◽  
Manufacturing Accuracy ◽  
Method Of Measurement ◽  
Free Form Surfaces

Parts must be measured to evaluate the manufacturing accuracy in order to check whether their dimension is in expected tolerance. In engineering, parts with free-form surfaces are generally measured by high-precision coordinate-measuring machines. The measurement accuracy is usually improved by increasing the density of measurement points, which is time-consuming and costly. In this article, a novel sampling method of measurement points for free-form surface inspection is proposed. First, surface inspection is simplified into the inspection of a number of section curves of the surface. Second, B-spline curves constructed with an iterative method are employed to approximate these section curves. Subsequently, data points necessary to construct the B-spline curves are taken as the measurement points. Finally, the proposed method is compared with other two sampling methods. The results indicate that the proposed method greatly reduced the number of measurement points without decreasing the precision of surface modeling.

NURBS Curve Fitting Based on Arc Centripetal Parameterization for Tool Path Generation

2013 ◽  
Vol 274 ◽  
pp. 121-123 ◽  
Author(s):  
Cun Guang Yu
Keyword(s):  
Curve Fitting ◽  
Tool Path ◽  
Nc Machining ◽  
Tool Path Generation ◽  
Sculptured Surface ◽  
Arc Length ◽  
Tool Path Planning ◽  
Nurbs Curve ◽  
Location Data ◽  
Cutter Location Data

NURBS curve fitting is used for tool path planning for sculptured surface NC machining. The cutter location data is parameterized by equal chord arc length parameterization, and Centripetal Parameterization is improved. It is not only more approach to curves nature equation in theory, but also closer to the interpolated curves in actual fitting. It is directly to reflect the curvature of curves of cutter location in NC machining.

scholarly journals Free-Form Optimization Method for Shape Design of Framed Structure

2013 ◽  
Vol 79 (804) ◽  
pp. 2884-2898 ◽  
Author(s):  
Masatoshi SHIMODA ◽  
Fuminori HAYASHI ◽  
Naoki UMEDA ◽  
Yang LIU
Keyword(s):  
Optimization Method ◽  
Free Form ◽  
Shape Design

Automated Tool-Orientation Determinations for 4-Axis Non-Gouge, Non-Interference Milling of Axial-Flow Compressors Airfoils

2007 ◽  
Author(s):  
Zezhong C. Chen ◽  
Gang Liu
Keyword(s):  
Manufacturing Industry ◽  
Axial Flow ◽  
Optimization Method ◽  
Free Form ◽  
Software Systems ◽  
Cnc Milling ◽  
Novel Approach ◽  
Cad Cam ◽  
Free Form Surfaces ◽  
Axial Flow Compressors

As important components of gas turbine engines, axial-flow compressors have been improved with a more complex and accurate airfoil design to meet high aerodynamic requirements; specifically, the pressure and suction surfaces of the airfoils (or blades) are now represented with free-form surfaces in CAD software systems. Since quality of the blades affects efficiency of the engines and safety of the aircrafts, some types of compressors are produced with the blades and the hub as a single piece on 4-axis CNC milling machines. However, it is still quite challenging to automatically determine cutter sizes and orientations without gouging and interference during the 4-axis milling, because the geometric shape of the blades is complex and the blades overlap with each other. As a result, the established method of determining tool size and orientation in industry is by trial and error in a repetitive process of selecting cutters and planning tool-paths with CAM systems. To address this problem, a novel approach is proposed to automatically determine cutter sizes and orientations for 4-axis milling of the axial-flow compressors blades without gouging and interference. The main contribution of this work is that (1) a mathematical model for optimizing cutter sizes in 4-axis milling is established; and (2) by applying a global optimization method — the particle swarm optimization method — to this model, the maximum allowable size of a cutter and its corresponding orientation can be found at each cutter-contact (CC) point on the surface being machined. Therefore, all the maximum allowable sizes of cutters for all the CC points and the corresponding cutter orientations can be computed. A group of standard cutters are then selected; each of which can sweep particular CC points without damaging the compressor. Since it is efficient and reliable, this newly proposed approach can be directly implemented in commercial CAD/CAM software systems to benefit the manufacturing industry.

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