Circular Interpolation Research Articles

A new approach to contour error control in high speed machining

High speed machining technology attempts to maximize productivity through the use of high spindle speeds and axis traverse rates. The technology is dependent upon the development of suitable mechanical hardware, electrical drives and associated control software to ensure that all components are used to maximum advantage. The role of the control software is particularly demanding since one needs to maximize traverse rates while providing the necessary accuracy, and indeed providing a margin of safety to deal with unexpected changes in process, or system parameters. There have been relatively few improvements in commercial CAD or CAM systems that would help machine tool users to take maximum advantage of high speed machining; rather the majority of the approaches have been undertaken at the machine tool controller level. This paper uses circular interpolation and corner tracking to compare several such control techniques, (Cross Coupled Control (CCC), Zero Phase Error Tracking Control (ZPETC), and Realtime Frequency Modulated Interpolation (FMI)), each of which have been proposed in the literature order to improve machining accuracy. None of these approaches are found to be universally successful when used alone and the authors, in this paper, examine the use of these systems in combination. Particular attention is focused upon an extension of a simplified version of cross coupled control together with Frequency Modulated Interpolation. It is shown that the combined system performs extremely well, and is easily actuated at high frequencies with conventional hardware. A custom built high speed x-y table is used to confirm system performance with multiple constraints present.

A study on motion of machine tools’ hexapod table on freeform surfaces with circular interpolation

Accuracy is greatly affected by nonlinear motion of hexapods. This need is more obvious when these mechanisms are used in machining environments where precision and surface qualities are of critical importance. In this paper, comprehensive algorithm for hexapod tool path programming is developed. Using C#.Net, this algorithm is developed based on circular motion and rotation of the table which has the capability of checking nonlinear error and keeping it in a controlled limit as well. Improved Tustin algorithm is used for interpolating circular path. To evaluate the accuracy of the developed algorithm on a freeform surface, a turbine blade is scanned, and its CAD model is developed. Taking zigzag strategies, movement on turbine blade surface is approximated with smaller circles using the algorithm presented in this paper. The output accuracy resulted from interpolation algorithm for passing on turbine blade surface is studied in SimMechanics of MATLAB software. Using Total Station camera, motion path of two turbine blades with different radius curves on the hexapod table is experimentally obtained. Finally, it can be stated that the developed algorithm based on circular interpolation has the capabilities of motion on freeform curves.

Control System Design and Trajectory Planning for SCARA Robots

Based on STM32F407ZET6 microprocessor with ARM Cortex-M4 core, we designed a controller for servo motors and servo drivers of a 4-axis Selective Compliance Assembly Robot Arm (SCARA) robot. The forward and inverse kinematic equations are established, circular interpolation equations in three-dimensional space are derived by using the digital differential analyzer method. The adopted circular interpolation algorithm avoids to judge quadrant and feeding direction, which simplifies the program.

A biarc-based shape optimization approach to reduce stress concentration effects

In order to avoid stress concentration, the shape boundary must be properly designed via shape optimization. Traditional shape optimization approach eliminates the stress concentration effect by using free-form curve to present the design boundaries without taking the machinability into consideration. In most numerical control (NC) machines, linear as well as circular interpolations are used to generate the tool path. Non-circular curves, such as nonuniform rotational B-spline (NURBS), need other more advanced interpolation functions to formulate the tool path. Forming the circular tool path by approximating the optimal free curve boundary with arcs or biarcs is another option. However, these two approaches are both at a cost of sharp expansion of program code and long machining time consequently. Motivated by the success of recent researches on biarcs, a reliable shape optimization approach is proposed in this work to directly optimize the shape boundaries with biarcs while the efficiency and precision of traditional method are preserved. Finally, the approach is validated by several illustrative examples.

The Method of Fillet Contour Error Compensation Applied in End Cylindrical Crankshaft Grinder

The Contour accuracy of a crankshaft transition fillet is important for the crankshaft working reliability. The front end surface, cylindrical surface and the transition fillet of a crankshaft are grinded by an end cylindrical grinder. During this machining, due to the roller’s shape error and other factors, the contour error of the fillet cannot be guaranteed while 90 degree circular arc interpolation was taken. In this paper, a fillet contour error compensation model was established, the appropriate compensation macro program was designed, and the radical contour error compensation was implemented through 9 circular arcs approaching. The practical application is shown that the satisfactory result is achieved and this method can also be applied in the fillet compensation for wheel dressing when applying diamond disk or stylus.

Wireless CNC Motion Controller Designed with PSoC

Numerical control (NC) technology is a kind of technology combined with electronics, machinery manufacturing, and other interdisciplinary combination of technologies. It is an important part of modern manufacturing. Currently, NC technology is developing towards the open CNC system with extensibility and interchangeability, while the modern electronic technology is developing towards the programmable technology and SoC (System-on-Chip) technology. However, current CNC controller designed with SoC is still in the research stage and not practical yet. In this paper, a practical CNC motion controller is built with modern PSoC (Programmable System-on-Chip) with wireless Ethernet interface. This controller has a high-performance microprocessor, numbers of free configurable analog and digital devices and IO (input/output) interfaces, and many kinds of communication interfaces. Therefore, it has good real-time control functions and communication functions. Experiments for controlling a three joint-axis engraving machine show that the controller can achieve high performance of parallel control of the three joint-axis linear interpolation and two joint-axis circular interpolation, and high performance of the trapezoidal and S-shape speed control. In addition, in order to reduce the impact to the motor and increase the system efficiency, a kind of look-ahead algorithm for velocity control with low time cost is used.

A Comparison of Standard One-Step DDA Circular Interpolators with a New Cheap Two-Step Algorithm

We present and study existing digital differential analyzer (DDA) algorithms for circle generation, including an improved two-step DDA algorithm which can be implemented solely in terms of elementary shifts, addition, and subtraction.

Evaluation of Linear Axis Motion Error of Machine Tools Using an R-test Device

The existing accuracy test standard for machining centers (ISO10791) is being revised in order to add a test method for five-axis machining centers. In the revised part of the standard (ISO10791-6), simultaneous three-axis interpolation motion accuracy tests for two linear axes and one rotary axis are proposed as an interpolation accuracy test for five-axis machining centers. These tests enable the measurement of the motion error in three directions, e.g., X, Y, and Z. Two devices can be used as the measurement instrument in these tests. One is a ball bar device, and the other is a combination of a ball and a displacement sensor. An R-test device that incorporates three displacement sensors has been designed for the latter. Using the ball bar device, measurement in three directions can be performed independently, and the radii of circular interpolations for each measurement are different. Using the R-test device, time is shortened by measuring three measurement directions at once, and the acquired data can be analyzed in various ways. The original goal of the measurement method using the R-test device was to measure the dynamic accuracy of the rotary axes. In the present study, the R-test device was actually prototyped and several machines were measured. In addition to the dynamic error of the rotary axes, incorrect pitch error compensation settings for the numerical controller, straightness, or squareness of the linear axes can be well detected.

Circular Interpolation Method of Formulating High-speed Train Diagram with Computer: Optimization Model and Algorithm

Circular Interpolation Method of Formulating High-speed Train Diagram with Computer: Optimization Model and Algorithm

The Circular Interpolation Method of Formulating High-speed Train Diagram with Computer

Train diagram is the basis on which passengers make their choice on trains before going on a trip. It is directly related to the level of service to passengers. Based on passengers’ travel demand and with the limitation of the starting time interval, station dwell time and other operation time intervals, this study constructs a high-speed train diagram optimization model, aiming to minimize the total expenses of passengers’ travel. Meanwhile, with the goal to maximize reduction of passengers’ travel expense incurred by the addition of every train to the working diagram, the study adds every train to the diagram circularly in different orders and then deletes it from the diagram so as to calculate the largest reduction of passengers’ travel expense, based on which is proposed the circular interpolation method of formulating high-speed train diagram with computer. It’s demonstrated through the analysis of the example that, formulating the high-speed train diagram with a computer based on circular interpolation method brings good convergence and optimization.

Simulation and Implementation of an Improved Inscribed Chord Interpolation Algorithm

In order to improve the shortcomings of the realization of the traditional quadratic curve interpolation inscribed chord method, this paper proposes an improved internal chord interpolation algorithm. The program flow chart of the algorithm achievement and the interpolation method of circular arc interpolation and linear interpolation of a detailed operation process is given in this paper. Finally through a calculation example the simulation is conducted, and the point by point comparison method were compared. The simulation results show the improvement on the quadratic curve interpolation in the inner string interpolation speed, good flexibility, and it worth popularizing in the interpolation algorithm for real time interpolation.

Full Software CNC System Based on RTLinux

In order to meet the real-time performance of the full software CNC system, the full software CNC based on RTLinux is designed. Linux+RTLinux system is used as development platform, the timer parameter is changed by the method of hardware interrupt, and the real-time requirement of the CNC system is solved. The idea of modular design is used on CNC system to divide the function module, and the software design of the full software CNC system based on RTLinux is completed. C language is used as the main development language, the development of functional modules of the system management layer and the control layer is realized. Linear, circular interpolation function of CNC system can be realized.

Study on Error in Interpolation Algorithm of the-5-DOF-Hybrid Robot

In order to improve the accuracy of the-5-DOF-hybrid robot motion control, it is necessary to establish a mathematical model of the error in the interpolation process. On the basis of the structure characteristics of five degrees of freedom hybrid robot and the algorithm of linear interpolation and circular interpolation, the error calculation patterns about the concave surface machining and convex surface machining are set up respectively in the paper. Then, examples are analyzed. The results show that the nonlinear error caused by using the straight-line interpolation method is much smaller than the normal vector rotation error and linear approximation error; when conducting surface machining, the error caused by the application of circular interpolation algorithm is less than linear interpolation error. By the comparison of the error analysis of different interpolation method, the control methods for reducing errors are proposed.

Improved Algorithm for the Circular Interpolation Time Division Method in CNC System

In order to process parts of different shapes, CNC systems require interpolation operations. Clockwise circular interpolation, for example, the time of the CNC system segmentation algorithm was improved compared with the original algorithm, which is more convenient, accurate, and prove that fully meet the requirements of CNC system. For the CNC programming and improve processing speed is very favorable.

An Algorithm of Adaptive Variable Spacing for Arc Fitting Non-Circular Curve

The Numerical Control (NC) systems are only linear and circular interpolation function, and the non-circular curve must be fitted with them before processed. There are many algorithms of fitting curve with arc, but most of them have some shortcomings, such as the numbers of fitting data points and arcs segments are too many, the error controlling are difficult in arc fitting , the programming are difficult to meet the real-time NC processing requirement and so on. This paper proposed a new algorithm, which could quickly and automatically determine the best node for fitting curve with arc according to the change of curvature and the machining error. It could ensure the machining precision and efficiency. The algorithm could be directly completed programming and processing by the NCs macro program function without any other auxiliary software. The detailed algorithm process and the application programming were given.

Design of the NC Software of a Micro Mill Based on LabVIEW

LabVIEW provides a new development platform for the design of NC software for its multi-task parallel and real-time processing. This paper discussed the design of the NC software of a micro mill based on LabVIEW. Six modules of the NC software, composed of such as algorithms of decoder, cutter compensation, interpolation, were analyzed in detail with structured analysis methods. NC codes simulation was carried out using the software. The results showed that it can complete NC functions such as line interpolation, circular interpolation, and cutter compensation.

ANALYTICAL AND EXPERIMENTAL STUDY OF FEED RATE IN HIGH-SPEED MILLING

In the context of high-speed milling (HSM), during the machining process dynamic machine response has to be identified. To achieve this, we have to calculate the feed rate evolution in linear and circular interpolation according to dynamic performance of machine. In addition to that, actual trajectory for transition passages between two interpolations must be estimated with take into account of specific machining tolerances. This article proposes a model of machine tool behavior for a tool path with linear and circular interpolations and machining cycle time prediction. The method involves subdividing the trajectories into elementary geometries according to the type of interpolation (circular or linear). At points where different trajectories meet, there is often a discontinuity in curvature or in tangency, which decreases the feed rate. At the points of discontinuity in tangency, a fillet radius is inserted. In this article, the influence of the geometry for elementary trajectories was determined. Then, the value of the fillet radius between linear and circular contours in different combinations was modeled. An industrial application was carried out in order to validate models and to determine the influence of feed rate evolution on the machining cycle time.

An Improvement and Simulation of NURBS Curve Algorithm

Although the chord height error might be ensured, the adaptive algorithm of the NURBS curve circular interpolation feed rate is still likely to result in the speed fluctuation which is not in accordance with given acceleration or deceleration rules. On the foundation of the analytic principle of the NURBS curve circular interpolation, a kind of interpolating algorithm based on the NURBS curve continuous small segments of S-shaped acceleration and deceleration is presented. And considering the chord height error, the variable step and feed rate can be effectively combined to make a better estimation. The simulation results on real examples show that the method not only simplifies the complicated calculation of curve interpolation process, simultaneously improves the speed of Motion Smoothing Implementation for NURBS curve interpolation, but also ensures the interpolation precision. The algorithm can be commonly applied in real manufacturing for high-speed and high-precision curve process.

CNC System Based on FPGA for Line Contact Machining

A novel CNC system for line contact machining is put forward to mill ruled surface efficiently. The motion control card based on FPGA is designed in the system for line contact machining. To meet the complex interpolation requirements of CNC system, NC embedded PC structure is used to improve the performance of the CNC system. Computer input and output program by C + + Builder are operated in DLL with WinIO component, to realize the communication between PC and movement control card. Three interpolation modules are simulated in Quartus II. Simulation result shows that linear interpolation, circular interpolation and complex interpolation function are realized on the motion control card based on FPGA, and the line contact machining can be realized in the CNC system efficiently.

A Practical Evaluation Approach to Form Deviation for Surface of Revolution Based on Discrete Point Coordinate Data

This paper proposes a practical evaluation approach to form deviation for surface of revolution based on discrete point coordinate data. An approximate curve composed of circular arc segments decided from an optimal interpolation process is accepted for computing the form deviation at measured points instead of the generating line of the surface to be inspected. This operation significantly simplifies the algorithm and improves the efficiency in the evaluation calculation. At the same time, it is also guaranteed that the difference of both form deviation values relative to the approximate surface or to the original surface is restricted within the specified accuracy in the circular arc interpolation operation. The effectiveness and efficiency of the approach are verified through a practical example of the surface of revolution with a generating line in the form of cubic Bézier curve.