Jerk Limited Acceleration Research Articles

Time and energy optimal trajectory generation for coverage motion in industrial machines

The increase in computer numerical control machine efficiency highly contributes to environmental emission reduction and energy-savings. Path and trajectory optimizations are used to improve machine efficiency in a coverage motion such as pocket milling, polishing, inspection, gluing, and additive manufacturing. Several studies have proposed coverage motion optimization in improving machine efficiency for time and energy consumption. Ensuring the smoothness and satisfaction of the machine constraints in coverage motion is necessary. This paper proposes a multi-objective path and trajectory optimization to obtain a trade-off between time and energy consumption for coverage motion. Jerk limited acceleration profiles describe the trajectory where velocity profiles generated for each linear segment attain desirable velocities. The energy model of an industrial two-axis feed drive system is used in finding solutions to the optimization problem. The non-dominated sorting genetic algorithm II generates a Pareto front for trade-off time and energy consumption solutions. Simulation results of the proposed method are validated through experiments using the industrial two-axis feed drive system. Experimental results show the effectiveness of the proposed approach where time reduction and energy savings are 10.05% and 2.10%, respectively. In addition, the optimized path has a lower maximum error of 76.6% compared to the constantly commanded velocity optimized path.

Analytical time constant design for jerk-limited acceleration profiles to minimize residual vibration after positioning operation in NC machine tools

The positioning operation of the axes of numerically controlled (NC) machine tools is essential before initiating their machining operation. Residual vibration following the positioning operations of the axes deteriorates the cycle time and quality of the machined parts. This study aims to develop a novel acceleration and deceleration design method to suppress the residual vibration during the high-speed positioning of NC machine tools. The proposed method suppresses the vibration by appropriately designing the jerk-limited acceleration profile during acceleration and deceleration. To design the jerk profile, the amplitude map that can represent the relationships between the acceleration parameters and the estimated vibration amplitude is developed. The proposed method suppresses the vibration amplitude without changing the total positioning time. To evaluate the effectiveness of this method, the residual vibration following the high-speed positioning motions was measured and simulated. The results confirm that the proposed method can effectively suppress the residual vibration.

A Trade-off Between Energy Saving and Cycle Time Reduction by Pareto Optimal Corner Smoothing in Industrial Feed Drive Systems

Apart from improving motion accuracy, increasing productivity while reducing computer numerical control machine tools' carbon footprint is vital in the manufacturing industry. Several studies have proposed corner smoothing methods that improve cycle time for piecewise linear paths by exploiting axial limits to achieve time-optimal trajectories. Energy-saving is not considered an objective in these methods. This paper presents a method of generating Pareto optimal corner smoothing trajectories that trade-off the contradicting objectives of minimizing cycle time and energy consumption. The trajectories along linear paths and smoothed corners are respectively described using jerk limited acceleration profiles and kinematic corner smoothing methods. An energy consumption model of an industrial two-axis feed drive system is identified and used in solving the bi-objective optimization problem. From the resulting Pareto frontier, the best trade-off trajectory is selected as the one that minimizes both objectives. The proposed method's effectiveness is vindicated experimentally, where the best trade-off trajectory achieves respectively 65.87 % and 60.44 % of the time and energy-saving potentials.

Pareto Optimization of Cycle Time and Motion Accuracy in Trajectory Planning for Industrial Feed Drive Systems

Manufacturing industries aim to improve product quantity and quality. These trade-off objectives are typically manifested as cycle time reduction and motion accuracy improvement. Corner smoothing approaches that reduce the cycle time of piecewise linear trajectories are proposed in the literature. This study tackles the two objectives by Pareto-optimal corner smoothing with constraints imposed as kinematic limits, continuity conditions and user-specified cornering tolerance. Linear and cornering motions along a contour are respectively described by jerk-limited acceleration profiles and a modified kinematic corner smoothing with interrupted acceleration (KCSIA) approach. A Pareto frontier is generated by the divide and conquer algorithm, where the solution nearest to the utopia point is selected as the best trade-off solution. The effectiveness of the proposed method is validated through experiments, where the best trade-off solution reduces the maximum and average contouring errors by 47.53% and 25.40% while it increases cycle time by 2.53% compared to KCSIA.

Acceleration smoothing algorithm based on jounce limited for corner motion in high-speed machining

In high-speed and high precision machining, cornering acceleration profiles of the feed motion are always not smooth enough and cause severe inertial vibrations in feed drive system, which severely affect machining quality and elongate machining time. In view of this problem, many experts and scholars have proposed kinematic corner smoothing algorithms based on the jerk limited acceleration profile from the perspective of kinematics that generate continuous acceleration transition profiles. But continuous acceleration profiles still have non-differentiable points. In order to further generate smooth and continuous acceleration transition profiles, an acceleration smoothing algorithm based on the jounce limited acceleration profile is proposed in this paper. Firstly, by adding different velocity, acceleration, and displacement boundary conditions to the jounce limited acceleration profile and combined with user-specified contour error, the fastest cornering velocity is deduced. Next, by the fastest cornering velocity and motion performance of the motor driver, the cornering duration is deduced. Finally, smooth acceleration and velocity transition profiles can be controlled analytically by accurately calculating cornering duration. The proposed algorithms are divided into interrupted acceleration smoothing algorithm and uninterrupted acceleration smoothing algorithm based on additional different acceleration boundary conditions. Through the experimental analysis and comparison, the proposed algorithms can reduce overall machining time around 6–7% and deliver curvature smoothing motion profiles, curvature continuous velocity profiles, and tangent continuous acceleration profiles. The proposed algorithms achieve smooth acceleration transitions and improve machining quality.

Global tool-path smoothing for CNC machine tools with uninterrupted acceleration

Majority of tool-paths for high-speed machining is composed of series of short linear segments, so-called G01 moves. This discrete tool-path format limits the achievable speed and accuracy of CNC machines. To generate continuous feed motion along sharp cornered tool-paths, most NC systems smooth corners locally using a pre-specified curve or a spline and slow down to be able to change the feed direction within machine kinematic limits. Path speed is dramatically reduced for accuracy if sharp corners are within close vicinity. This paper proposes a new real-time interpolation algorithm for NC systems to generate continuous rapid feed motion along short segmented linear tool-paths by smoothing local and adjacent corners that are within close vicinity. Instead of locally modifying the corner geometry with a spline, the proposed algorithm directly blends axis velocities between consecutive linear segments based on the jerk limited acceleration profile (JLAP) and generates cornering trajectories within user-specified contour errors and kinematic limits of the drives. A novel Look-Ahead Windowing (LAW) technique is developed to plan tangential feed profile with uninterrupted acceleration to continuously smooth the path. The feed profile is optimized to generate rapid motion along overlapping adjacent corners. Simulation and experimental results demonstrate effectiveness of the proposed method to interpolate accurate Cartesian high-speed motion along short-segmented tool-paths for machining free-form surfaces found in dies, molds and aerospace parts.

Motion Control Techniques for Synchronous Motions of Translational and Rotary Axes

This study proposes motion control techniques which can improve dynamic synchronous accuracy between translational and rotary axes in five-axis machining centres. The proposed techniques consist of servo gain tuning, feed forward controller design, signal delay and backlash compensator, rotational fluctuation compensator and jerk limited acceleration process design. In order to evaluate the effect of proposed techniques, experimental tests are carried out. An experimental apparatus consists of X, Y, and C axes is provided for the experiments. Any control algorithm can be implemented into the experimental apparatus because the system is controlled by a personal computer with a DSP board. Translational X and Y axes are powered by AC servo motors and ball screws. A rotary C axis is powered by an AC servo motor, spur and worm gears. Three kinds of synchronous motions are applied to evaluate the dynamic synchronous accuracies. They are; non-uniformed simultaneous 3-axis motion, simultaneous 2-axis motion of X and C axes, and ellipse shape machining motion using simultaneous 3-axis motion. It is clarified from the experiments various factors including signal delay of rotary encoders influence the dynamic synchronous accuracy between translational and rotary axes, and the proposed motion control techniques can significantly improve the dynamic synchronous accuracy without velocity limitations.

The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments

A numerical control (NC) program generated by a complex CAD/CAM system mainly composes a number of short line segments. For continuous short line segment machining, the traditional machining approach and the direct transitional approach cause the oscillations of the federate and affect machining efficiency. Moreover, the arc transitional approach enhances machining efficiency, but it brings about the greater machining error. To increase the smoothness of velocity profile and machining efficiency of continuous short line segment machining, this paper presents a parametrical cubic spline curve transitional approach with the S-shaped jerk-limited acceleration and deceleration with look-ahead. The trajectory error of the transitional curve is deduced according to the correlative factors, the preconditions of the transitional curve are put forward and analyzed, the mathematical model of the parametrical cubic spline curve is constructed, and the constraint conditions of the transforming velocity are built. In addition, the velocity control method is adopted for the smoother velocity profile. Thus, the machining productivity is dramatically increased and the velocity profile is more smoothness. The simulative and experimental results verify the feasibility and validity of the proposed approach.

A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.

Real-time NURBS interpolator: application to short linear segments

This study proposes the use of a real-time non-uniform rational B-spline (NURBS) interpolator with a look-ahead function to handle numerous short linear segments. The short linear segments conforming to the continuous short block (CSB) criterion can be fitted into NURBS curves in real time. A modified maximum feedrate equation based on the geometric characteristics of the fitting curves and the dynamics of the servo control system has been derived in this paper. Taking advantage of the multi-thread design and the look-ahead function, the real-time NURBS interpolator can process enough G01 block information and complete feedrate planning before interpolation. In addition, the S-shaped jerk-limited acceleration method is adopted for smoother feedrate profiles. Two part shapes, which possess more than 1,000 short linear segments, are tested on our PC-based real-time control system. Both simulation and experimental results verify the feasibility and precision of the proposed interpolation algorithm.

An Optimal Feed Interpolation with Jerk-Limited Acceleration for Five-Axis Grinding

To overcome the acceleration discontinuity and feed fluctuation of the conventional five-axis grinding interpolator, a jerk-limited acceleration is utilized and two aspects of constraints is taken into account: (1) the machining dynamics, including the constraints of power, velocity, acceleration and jerk represented by upper bounds for each axis (2) the contour constraints of linear segments, including the linear distance of the segment and sharp corner at the segment junctions. With the analysis of these constrains, the optimal feed for each segment and the joint feed at the segment junctions is derived. The corresponding adjusted interpolation algorithm with jerk-limited acceleration is presented such that a smooth motion during the machining can be maintained. The presented algorithm is demonstrated by the simulation result.

A study on a generalized parametric interpolator with real-time jerk-limited acceleration

The impossibility of exact arc length computation for ‘standard’ parametric curves such as Bézier/B-spline curves makes it difficult to generate a feedrate profile with desired accelerations in real-time. This paper presents a new recursive trajectory generation method that estimates an admissible path increment and determines the initiation of the final deceleration stage according to the distance left to travel estimated at every sampling time, resulting in exact feedrate trajectory generation through jerk-limited acceleration profiles for the parametric curves. The proposed approach allows the feedrate profile to be dynamically adjusted according to geometrical path constraints for the curved path. The simulation result has been also provided to illustrate the generation of smooth feedrate profile encompassing a sequence of mixed NC blocks including traditional linear and circular blocks.

Weitek solids modeling engine

Majority of tool-paths for high-speed machining is composed of series of short linear segments, so-called G01 moves. This discrete tool-path format limits the achievable speed and accuracy of CNC machines. To generate continuous feed motion along sharp cornered tool-paths, most NC systems smooth corners locally using a pre-specified curve or a spline and slow down to be able to change the feed direction within machine kinematic limits. Path speed is dramatically reduced for accuracy if sharp corners are within close vicinity. This paper proposes a new real-time interpolation algorithm for NC systems to generate continuous rapid feed motion along short segmented linear tool-paths by smoothing local and adjacent corners that are within close vicinity. Instead of locally modifying the corner geometry with a spline, the proposed algorithm directly blends axis velocities between consecutive linear segments based on the jerk limited acceleration profile (JLAP) and generates cornering trajectories within user-specified contour errors and kinematic limits of the drives. A novel Look-Ahead Windowing (LAW) technique is developed to plan tangential feed profile with uninterrupted acceleration to continuously smooth the path. The feed profile is optimized to generate rapid motion along overlapping adjacent corners. Simulation and experimental results demonstrate effectiveness of the proposed method to interpolate accurate Cartesian high-speed motion along short-segmented tool-paths for machining free-form surfaces found in dies, molds and aerospace parts.