MPCC-Based Set Point Optimisation for Machine Tools

Numerical control code is typically used for manufacturing a workpiece using machine tools. Most state-of-the-art approaches decouple the set point optimisation into two steps: the geometry and the feed rate optimisation that does not necessarily result in time-optimal set points for the desired geometry. Given the originally programmed geometry through the numerical control code, dynamic constraints of the machine tool, and maximum permissible contour error for the optimisation, a model predictive contouring control based set point optimisation approach is developed to generate time-optimal set points for machine tools globally. A suitable error definition and its linearisation are used whereby the optimisation problem can be represented by a quadratic programming problem with linear constraints. Compared to most state-of-the-art methods, a direct approach is presented and no previous geometry optimisation step is required. Depending on the demands of accuracy, different maximum contour error constraints and penalisation as well as various maximum permissible axis velocities and accelerations are presented and tested on a test bench. The method is shown to be adaptable to different demands on the set points, and the contour errors can be affected by either the constraints or penalising factors.

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Special Issue on Multiaxis Control and Multitasking Machine Tools

International Journal of Automation Technology ◽

10.20965/ijat.2007.p0077 ◽

2007 ◽

Vol 1 (2) ◽

pp. 77-77 ◽

Cited By ~ 3

Author(s):

Yoshimi Takeuchi ◽

Keyword(s):

Machine Tools ◽

State Of The Art ◽

Numerical Control ◽

Plant Production ◽

Precision Machining ◽

Accuracy Evaluation ◽

Special Issue ◽

Complex Products ◽

Current State ◽

Control Machine

Machine tools using numerical control (NC) devices are typical mechatronics products and a powerful way to automate plant production. The introduction of multiaxis control and multitasking machine tools to workshops is growing to meet the requirements of highly efficient, precision machining of a variety of complex products and mold dies. The increase in the number of control axes and multitasking capability in one chucking process enable machine tools to manufacture complex products efficiently and accurately. Given the strong attention and interest multiaxis control and multitasking machine tools are attracting, it is about time to introduce the current state of the art of these tools and their practical and applicable technologies, especially in Japan. This special issue covers the development of 5-axis control machining centers, machine tools having multispindle heads with 5-axis control, 5-axis control CAMs, accuracy evaluation for 5-axis control machine tools, and more. We thank the authors for their interesting papers to this special issue, and are certain that both general readers and specialists will find the information they provide both interesting and informative.

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Smooth Cornering Strategy for High Speed CNC Machine Tools With Confined Contour Error

Volume 2: Materials; Biomanufacturing; Properties, Applications and Systems; Sustainable Manufacturing ◽

10.1115/msec2016-8529 ◽

2016 ◽

Cited By ~ 1

Author(s):

Shingo Tajima ◽

Burak Sencer

Keyword(s):

Machine Tools ◽

High Speed ◽

Cnc Machine Tools ◽

Contour Error ◽

Smoothing Algorithm ◽

Cnc Machine ◽

Computationally Efficient ◽

Positioning Systems ◽

Tool Paths ◽

Time Optimal

Conventional tool-paths for CNC (computer numerical controlled) machine tools or NC positioning systems are mainly composed of linear motion segments, or so called the G1 commands. Interpolating along linear tool-paths exhibits serious limitations in terms of achieving the desired part geometry and productivity in high-speed machining. Velocity and acceleration discontinuities occur at the junction points of consecutive segments. In order to generate smooth and continuous feed motion, a kinematic corner smoothing algorithm is proposed in this paper, which plans smooth acceleration and jerk profiles around the segment junction to realize continuous velocity transition between consecutive linear segments. The proposed corner-smoothing algorithm eliminates the need for geometry based corner-blending techniques and presents a computationally efficient interpolation scheme. The cornering error is controlled analytically allowing the end-user to control the cornering tolerance. Drive’s acceleration and the jerk limits are fully utilized to minimize overall cornering duration. This delivers a time optimal cornering motion within user specified cornering error tolerances. Simulation studies are used to demonstrate the effectiveness of proposed high-speed cornering scheme.

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Modeling and adaptive compensation of tooth surface contour error for internal gearing power honing

Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture ◽

10.1177/0954405418780169 ◽

2018 ◽

Vol 233 (5) ◽

pp. 1500-1514 ◽

Cited By ~ 1

Author(s):

Jiang Han ◽

Yonggang Zhu ◽

Lian Xia ◽

Xiaoqing Tian ◽

Bin Yuan

Keyword(s):

Machine Tools ◽

Tracking Error ◽

Cross Coupling ◽

Error Modeling ◽

Numerical Control ◽

Tooth Surface ◽

Contour Error ◽

Adaptive Compensation ◽

Surface Contour ◽

Gear Machine

The machining of high precision gears requires a strict and accurate co-movement relationship controlled by the electronic gearbox between the moving axes of the gear machine tools. This article proposes a tooth surface contour error modeling method and an adaptive electronic gearbox cross-coupling controller for internal gearing power honing. First, the electronic gearbox model is structured according to the generative machining principle of internal gearing power honing and the tooth surface contour error is established by means of homogeneous coordinate transformation and meshing principle. Then, the adaptive electronic gearbox cross-coupling controller is designed, which comprises the electronic gearbox cross-coupling controller and the fuzzy proportional–integral–derivative controllers whose universes of membership functions in fuzzy rules are optimized by particle swarm optimization to improve the adaptability and robustness to disturbance fluctuation and model uncertainty of the system. Finally, experiments are carried out on a self-developed gear numerical control system. The results have demonstrated that the estimated tooth surface contour error using the proposed method is very close to the actual one, and the proposed adaptive electronic gearbox cross-coupling controller can effectively reduce the tracking error and the tooth surface contour error when compared to the electronic gearbox cross-coupling controller and non–electronic gearbox cross-coupling controller (electronic gearbox controller without cross-coupling and adaptive compensation).

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Performances and Shapes of Acceleration-deceleration Curve of Kinematical Linkages

International Journal of Mechanics ◽

10.46300/9104.2020.14.16 ◽

2020 ◽

Vol 14 ◽

Keyword(s):

Machine Tool ◽

Machine Tools ◽

Mobile Element ◽

Industrial Robots ◽

Numerical Control ◽

Design Stage ◽

Contour Error ◽

Maximum Acceleration ◽

Positioning Accuracy ◽

Acceleration And Deceleration

The transient duty has a very important role within the kinematical linkages of the numerical control machine tools and industrial robots. The acceleration and deceleration of the movable element of the kinematical linkage participates directly to achieving the positioning accuracy and to the path error. This work presents the main shapes of the acceleration- deceleration curve of the kinematical linkage, as well as their performances. Shapes of the acceleration-deceleration curve are presented for positioning linkages as well as for contouring linkages. The extent of influence upon the contour error in case of the linear and exponential acceleration-deceleration of kinematical linkage is also presented. The works is also giving recommendations on the way of choosing the type of curve being used in case of various transient processes, by the machine tool builders, with a view to obtaining high dynamical performances. In general, the recommendations are considering the inertia of the mobile element and the imposed path error. By knowing the acceleration shape, the machine tool designer and builder can know, even from the design stage, the area of the transient duty where the acceleration is maximal. The maximum acceleration imposes the rate of the impulsion torque of the drive servomotor based on which the kinematical linkage is sized, in terms of its components.

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CONTROL PARAMETER OPTIMIZATION-BASED MACHINING CONTROL TECHNOLOGY OF STATE-OF-THE ART COMPUTER NUMERICAL CONTROL MACHINE TOOLS

International Journal of Mechatronics and Applied Mechanics ◽

10.17683/ijomam/issue10/v2.21 ◽

2021 ◽

Vol 1 (10) ◽

Keyword(s):

Parameter Optimization ◽

Machine Tools ◽

Control Parameter ◽

State Of The Art ◽

Computer Numerical Control ◽

Numerical Control ◽

Control Technology ◽

Machining Control ◽

Control Machine

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A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

International Conference on Control '94 ◽

10.1049/cp:19940244 ◽

1994 ◽

Cited By ~ 2

Author(s):

V.M. Becerra

Keyword(s):

Nonlinear Systems ◽

Tracking Problem ◽

New Approach ◽

Set Point ◽

Point Tracking ◽

Optimal Set

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The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations

Mathematics ◽

10.3390/math8081303 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1303 ◽

Cited By ~ 1

Author(s):

Carl Leake ◽

Hunter Johnston ◽

Daniele Mortari

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

State Of The Art ◽

Linear Constraints ◽

Prior Work ◽

Partial Differential ◽

Seminal Paper ◽

Functional Connections ◽

Mathematical Proofs ◽

Multivariate Theory

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits the underlying functional structure presented in the seminal paper on the Theory of Functional Connections to ease the derivation of these interpolating functionals—called constrained expressions—and provides rigorous terminology that lends itself to straightforward derivations of mathematical proofs regarding the properties of these constrained expressions. Furthermore, the extension of the technique to and proofs in n-dimensions is immediate through a recursive application of the univariate formulation. In all, the results of this reformulation are compared to prior work to highlight the novelty and mathematical convenience of using this approach. Finally, the methodology presented in this paper is applied to two partial differential equations with different boundary conditions, and, when data is available, the results are compared to state-of-the-art methods.

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Study of Machining of Gears with Regular and Modified Outline Using CNC Machine Tools

Materials ◽

10.3390/ma14112913 ◽

2021 ◽

Vol 14 (11) ◽

pp. 2913

Author(s):

Rafał Gołębski ◽

Piotr Boral

Keyword(s):

Machine Tools ◽

Coordinate Measuring Machine ◽

Optical Microscope ◽

Numerical Control ◽

Cnc Machine Tools ◽

Cnc Milling ◽

Cnc Machine ◽

Cylindrical Gears ◽

Measuring Machine ◽

Five Axis

Classic methods of machining cylindrical gears, such as hobbing or circumferential chiseling, require the use of expensive special machine tools and dedicated tools, which makes production unprofitable, especially in small and medium series. Today, special attention is paid to the technology of making gears using universal CNC (computer numerical control) machine tools with standard cheap tools. On the basis of the presented mathematical model, a software was developed to generate a code that controls a machine tool for machining cylindrical gears with straight and modified tooth line using the multipass method. Made of steel 16MnCr5, gear wheels with a straight tooth line and with a longitudinally modified convex-convex tooth line were machined on a five-axis CNC milling machine DMG MORI CMX50U, using solid carbide milling cutters (cylindrical and ball end) for processing. The manufactured gears were inspected on a ZEISS coordinate measuring machine, using the software Gear Pro Involute. The conformity of the outline, the tooth line, and the gear pitch were assessed. The side surfaces of the teeth after machining according to the planned strategy were also assessed; the tests were carried out using the optical microscope Alicona Infinite Focus G5 and the contact profilographometer Taylor Hobson, Talysurf 120. The presented method is able to provide a very good quality of machined gears in relation to competing methods. The great advantage of this method is the use of a tool that is not geometrically related to the shape of the machined gear profile, which allows the production of cylindrical gears with a tooth and profile line other than the standard.

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