Feedrate Scheduling Research Articles

A novel feedrate scheduling method using modifying S-shaped feedrate profile with a round-off error elimination approach for CNC machining

A novel feedrate scheduling method using modifying S-shaped feedrate profile with a round-off error elimination approach for CNC machining

Reducing the contour error of leading and trailing edge through feedrate scheduling in 5-axis machining of blisk

Reducing the contour error of leading and trailing edge through feedrate scheduling in 5-axis machining of blisk

On the Optimization of Robot Machining: A Simulation-Based Process Planning Approach

The use of industrial robots for machining operations is pursued by industry lately, since they can increase the flexibility of the production system and reduce production costs. However, their industrial adoption is still limited, mainly due to their insufficient structural stiffness and posture-dependent dynamic behavior, leading to limited machining process accuracy. For this purpose, the Digital-Model of a machining robot has been developed, providing a tool for virtual commissioning of the process that can be used during the process planning stage. The Multi-Body Simulation method combined with a Component Mode Synthesis have been adopted, considering flexibility of both the joints and links. On top of that, and motivated from robotic-based machining systems’ flexibility and versatility, two optimization algorithms have been developed, attempting to increase the process accuracy. A workpiece placement optimization algorithm, attempting to maximize the robot stiffness during the process acquiring knowledge from the robot stiffness maps, and a feed-rate scheduling algorithm, attempting to constrain the contour error by regulating the generated cutting forces. The capabilities and functionality of the developed model and optimization algorithms are showcased in two different case studies, with the results proving the improvements on the process accuracy after the application of the optimization algorithms. Finally, an experimental validation of the Digital-Model has been performed, to confirm the consistency between model outputs and real experimental data.

Dynamic look-ahead feedrate scheduling method based on sliding mode velocity control

In the feedrate scheduling of complex curve direct interpolation, dynamic constraints such as axis acceleration and jerk are related to the actual state of the tool. Most existing methods convert dynamic constraints to velocity constraints at sampling points. However, it cannot guarantee the dynamic constraints are satisfied between sampling points. Addressing the issue, this paper proposes a dynamic look-ahead feedrate scheduling method based on sliding mode velocity control, which generates the motion command considering dynamic constraints in every interpolation cycle. To dynamically generate commands based on the current tool state, the acceleration and deceleration method based on sliding mode velocity control has been proposed, which can control tool state to transition to the command state with any initial state. To ensure sufficient distance for acceleration and deceleration, this paper uses braking distance to dynamically estimate the look-ahead distance. Then the minimum value within the look-ahead interval is selected as the command velocity for this scheduling cycle and the actual motion command is determined based on the dynamic constraints of each axis. Simulation and experiment results prove that compared with the existing method, this method effectively reduces the overshoot of dynamic constraints without significantly increasing the machining time. The analysis of real-time computation time has demonstrated the potential of the method proposed in this paper for real-time applications.

Feedrate-preserved motion planning for five-axis directed energy deposition of freeform metal parts

Laser-powder DED (LP-DED) has been investigated extensively for the rapid prototype of complex and customized metallic parts and in-situ repairing tasks. However, unlike the material extrusion type which allows a relatively large overhang angle, the conventional 2.5-axis LP-DED faces a severe overhang issue that deteriorates the printing stability and quality. While five-axis LP-DED is able to effectively resolve the overhang problem, it however introduces new kinematic issues and limited nozzle orientation range due to physical restrictions of DED. The existing computer numerical control systems are mainly designed for machining, where the above issues can be mostly solved by feedrate scheduling, which, however, is not applicable for LP-DED processes, as the feedrate must be preserved as programmed lest deposition height would be altered since in most cases it is not practical to vary the powder flow rate in real-time. In this paper, a feedrate-preserved motion planning method is proposed to optimize the rotational angles of the machine tool in the machine coordinate system (MCS) under the constraints of MCS and workpiece coordinate system (WCS). Given a five-axis DED path as well as its accompanying initial nozzle orientation in WCS, we first map them via inverse kinematics to MCS, which is represented by a cylindrical coordinate system. Then, the motion path in the cylindrical coordinate system is optimized to avoid the singularity. Finally, the physical constraint of nozzle orientation in WCS is introduced into the time-weighted constrained Laplacian smoothing in MCS with the axial speed limits upheld. The experimental results confirm that the actual feedrate is successfully preserved as the theoretical one under the constraints of the axial kinematic limits, while the singularity is avoided.

An Adapted NURBS Interpolator with a Switched Optimized Method of Feed-Rate Scheduling

With the increasing demand for processing precision in the manufacturing industry, feed-rate scheduling is a crucial component in achieving the processing quality of complex surfaces. A smooth feed-rate profile not only guarantees machining quality but also improves machining efficiency. Although the typical offline feed-rate scheduling method possesses good processing efficiency, it may not provide an optimal solution due to the NP-hard problem caused by the feed-rate scheduling of continuous curve segments, which easily results in excess kinetic limitations and feed-rate fluctuations in a real-time interpolation. Instead, the FIR (Finite Impulse Response) method is widely used to realize interpolation in real-time processing. However, the FIR method will filter out a large number of high-frequency signals, leading to a low-processing efficiency. Further, greater acceleration or deceleration is required to ensure the interpolation passes through the segment end at a predefined feed rate and the deceleration in the feed rate profile appears earlier, which allows the interpolation to easily exceed the kinetic limitation. At present, a simple offline or online method cannot realize the global optimization of the feed-rate profile and guarantee the machining efficiency. Moreover, the current feed-rate scheduling that considers both offline and online methods does not consider the situation that the call of offline data and online prediction data will lead to a decrease in the real-time performance of the CNC system. Further, real-time feed-rate scheduling data tend to dominate the whole interpolation process, thus reducing the effect of the offline feed-rate scheduling data. Hence, based on the tool path with C3 continuity (Cubic Continuously Differentiable), this paper first presents a basic interpolation unit relevant to the S-type interpolation feed-rate profile. Then, an offline local smooth strategy is proposed to smooth the feed-rate profile and reduce the exceeding of kinetic limitations and feed-rate fluctuations caused by frequent acceleration and deceleration. Further, a global online smoothing strategy based on the data generated by offline pre-interpolation is presented. What is more, FIR login and logout conditions are proposed to further smooth the feed-rate profile and improve the real-time performance and machining efficiency. The case study validates that the proposed method performs better in kinetic results compared with the typical offline and FIR methods in both the simulation experiment and actual machining experiments. Especially, in actual processing experiments, the proposed method obtains a 28% reduction in contour errors. Further, the proposed method compared with the FIR method obtains a 15% increase in machining efficiency but only a 4% decrease compared with the typical offline method.

Trajectory Generation Method for Serial Robots in Hybrid Space Operations

The hybrid space of robots is divided into task space and joint space, with task space focused on trajectory-tracking accuracy, while joint space considers dynamic responsiveness and synchronization. Therefore, the robot-motion control systems need to effectively integrate both aspects, ensuring precision in task trajectory while promptly responding to unforeseen environmental events. Hence, this paper proposes an online trajectory-generation method for robots in both joint and task spaces. In task space, a planning approach is presented for high-precision NURBS curves. The global NURBS curve is segmented into several rational Bezier curves, establishing local coordinate systems for control points. This ensures that all local control points meet the chord error constraint, guaranteeing trajectory accuracy. To address the feed rate dynamic planning issue for segmented curves, an improved online S-shape feed-rate scheduling framework is introduced. This framework dynamically adjusts the current execution speed to meet task requirements. In joint space, an offline velocity planning based on a time synchronization scheme and a multi-dimensional synchronization technique based on the principle of spatial-coordinate system projection are proposed. Building upon the offline scheme, it allows for the modification of the target state for any sub-dimension during the motion process, with the remaining dimensions adapting accordingly. Simulation and experimentation demonstrate that the two proposed online trajectory generations for robot motion spaces, while ensuring task trajectory accuracy, effectively handle external unexpected events. They ensure joint synchronization and smoothness, carrying significant practical implications and application value for the stability of robot systems.

Concurrent process and feedrate scheduling with convoluted basis functions and its application to fluid jet polishing

Non-traditional laser and fluid jet processes exhibit time-dependent material removal characteristics. The feedrate profile must be planned carefully along the toolpath for accurate surface profile generation while ensuring that the kinematic limits of machine tools are not violated. Conventional methods iteratively solve a deconvolution/convolution problem on the dwell-time density (reciprocal of the feedrate profile) that is computationally heavy, may leave significant residual processing errors, and even generate infeasible feed profiles with the manufacturing equipment. This paper proposes a novel approach that fully addresses the shortcomings above. Dwell-time density is first expressed as a continuous B-spline profile. The associated dwell basis functions (DBF) are convolved with the process influence function (PIF) to generate new process basis functions (PBF). This approach conveniently allows the posing of the problem as a concurrent linear least-squares problem on the control points shared by the DBFs and PBFs while ensuring the numerical stability of the solution and smoothness of the feed profile. To mitigate excessive acceleration peaks and any ringing effect around the edges of the toolpath, this paper also presents methodologies for stabilizing the scheduled feedrate profile by introducing knot vector adjustments (adaptive knot dropping) and linear edge constraints. The effectiveness of the proposed method is demonstrated and validated through simulation case studies and experimentally in fluid jet processing of precision optics. Results indicate that the proposed technique overcomes the limitations of conventional strategies and allows high-frequency surface components beyond the first zero-power frequency of the process footprint to be tracked while still generating a smooth feed profile within the acceleration limits of a machine tool. This ability stems from the localization characteristics associated with the basis functions. By improving the accuracy of high-frequency components, the proposed method exhibits the potential to fabricate topographies with sharper edges, which has been a challenge for conventional techniques.

Toolpath smoothing with reduced curvature and synchronized motion for hybrid robots

G01 commands are the most commonly used toolpath format in Computer Numerical Control (CNC) machining. Due to the discontinuity between adjacent linear segments, toolpath smoothing is necessary to improve machining efficiency and machined surface quality. This paper proposes an analytical C3 continuous local toolpath smoothing and synchronization method for a five-axis hybrid robot. Position and orientation smoothing are decoupled, with quintic B-spline segments replacing the original linear segments. The curvatures of the toolpath are reduced under constrained smoothing errors by weaving transition splines along the linear segments instead of confining them within the corners. A synchronization method based on arc length parameterization tailored to the smoothing method is also proposed. Tool tip position and tool axis orientation are synchronized using another monotonic, C3 continuous spline, which achieves smoother joint motion along the toolpath. For the hybrid robot with highly nonlinear kinematics, improved results in feedrate scheduling considering joint constraints can be realized. Simulations and experiments validate the effectiveness of the proposed method.

A S-shape feedrate scheduling method with rounding error elimination

A S-shape feedrate scheduling method with rounding error elimination

Cubic time-spline fitting and interpolation for five-axis CNC machining

Abstract In CNC machining, G01 codes are widely used to represent the tool path. Directly interpolating these G01 codes is time-consuming and may cause discontinuities. In this paper, we propose a time-spline curve fitting method that combines tool path fitting and feedrate scheduling into a single step for five-axis CNC machining. The input for this method consists of a three-dimensional linear path of the tool tip in the workpiece coordinate system and two-dimensional tool orientations in the machine coordinate system (MCS). The output is a fitted tool path in the MCS represented by a five-dimensional smooth time-parametric B-spline curve, simply referred to as the time-spline curve. The time-spline curve provides not only position information but also kinematic information, including velocity, acceleration, and jerk for each axis, directly derived from the first, second, and third derivatives of the curve. To meet fitting error constraints and axial kinematic constraints, our objective is to find the time-spline curve that is time-optimal. We formulate the optimization problem as a nonlinear optimization model and design a recursive algorithm to solve it. The resulting time-spline curve demonstrates high accuracy and fully utilizes the machine’s kinematic capabilities. Along the tool path defined by the time-spline curve, exact interpolation points can be straightforwardly obtained according to the interpolation period. Simulations and experimental results indicate that the proposed method yields a time-optimal time-spline curve with the desired precision and kinematic constraints.

Offline Feed-Rate Scheduling Method for Ti–Al Alloy Blade Finishing Based on a Local Stiffness Estimation Model

In the aerospace field, Ti–Al alloy thin-walled parts, such as blades, generally undergo a large amount of material removal and have a low processing efficiency. Scheduling the feed rate during machining can significantly improve machining efficiency. However, existing feed-rate scheduling methods rarely consider the influence of machining deformation factors and cannot be applied in the finishing stages of thin-walled parts. This study proposes an offline feed-rate scheduling method based on a local stiffness estimation model that can be used to reduce machining errors and improve efficiency in the finishing stage of thin-walled parts. In the proposed method, a predictive model that can rapidly calculate the local stiffness at each cutter location point and a cutting-force prediction model that considers the effect of cutting angle are established. Based on the above model, an offline feed-rate scheduling method that considers machining deformation error constraints is introduced. Finally, an experiment is performed by taking the finishing of actual blade parts as an example. The experimental results demonstrate that the proposed feed-rate scheduling method can improve the machining efficiency of parts while ensuring machining accuracy. The proposed method can also be conveniently applied to feed-rate scheduling in the finishing stage of other thin-walled parts without being limited by machine tools.

Investigation of conventional and ANN-based feed rate scheduling methods in trochoidal milling with cutting force and acceleration constraints

In CNC milling, the feed rate scheduling is a frequently used method to increase machining quality and efficiency. Among the benefits of feed rate scheduling, this paper focuses on controlling the tool load and optimizing the machining time. Although the advantages of feed rate scheduling are undeniable, some areas remain still to be addressed. In order to control the tool load, geometric methods are often used, which are based on keeping a specific parameter, such as chip thickness or material removal rate (MRR) constant. However, a high level of tool load control can only be provided if cutting force models or experimental-based techniques are used. Besides traditional methods, this paper presents an artificial neural network (ANN)-based feed rate scheduling method to keep the tool load constant, using data gained by preliminary cutting experiments. A case study demonstrates that a significantly higher level of tool load control can be achieved with this method as compared to the geometric models. Besides controlling the tool load, the present feed rate scheduling method also addresses the consideration of acceleration limits which is of great importance for practical uses. The application of feed rate scheduling in trochoidal milling is also discussed in detail in this paper. This area has not received enough attention, as due to the limited fluctuation of cutter engagement, the tool load was considered as well-controlled. However, experiments have shown that in the case of trochoidal milling, the introduction of feed rate scheduling can still further increase the machining efficiency. Using the developed ANN-based feed rate scheduling method, significant progress could be made as compared to conventional technologies in controlling the cutting force and optimizing the machining time. In the present case study, a reduction of 50% in machining time was achievable by adjusting the feed rate without increasing the peak value of cutting force.

A novel tool path planning and feedrate scheduling algorithm for point to point linear and circular motions of CNC-milling machines

The manufacturing process on CNC machines is directed by the Numerical Control (NC) files which include the main tool paths as a combination of numerous instructions such as lines and arcs specified by the G01 and G02/G03 commands. In the literature, the lines and arcs generally are converted to a parametric curve based on the global tool path smoothing or local corner smoothing algorithms. However, the smoothing methods cause the deflection from the tool path in NC-File. In cases where the deflection from the main tool path is not acceptable, point-to-point motion is necessary instead of the smooth trajectory. This study presents a novel trajectory planning and feedrate scheduling algorithm for point-to-point control of linear and circular paths in the NC-File. The proposed method prevents the feedrate fluctuations at the junction points and generates the tool path without deflection from the NC-File. Also, the feedrate scheduling algorithm decrease the operating time of the machine significantly compared to traditional method of point-to-point motion. This study is verified on an industrial 3-Axis CNC-Milling machine by the operating of the roughing milling, drilling, slotting, and face milling process. The measurements of final product and real-time trajectory tracking results show that the proposed method is effective in industrial applications of CNC-Milling machines in which point-to-point motion is necessary.

An effective approach for non-singular trajectory generation of a 5-DOF hybrid machining robot

By taking a newly developed 5-DOF (degree of freedom) hybrid robot as an exemplar, this paper presents a novel and effective approach for non-singular tool trajectory generation. Based upon singularity analysis via inverse kinematics, an algorithm for the C-axis path optimization is developed using the weighted S-curve. Incorporated singular domain detection with the C-axis angle correction, the algorithm can easily be programmed and embedded into the CNC (computer numerical control) system as a postprocessing module and works in real-time. Then, an offline feedrate scheduling method is proposed by considering the drive and geometric accuracy constraints, allowing the rapid yet smooth movement in the neighborhood of singularity to be achieved. Additionally, it is found that the orientation accuracy can be improved by setting adequate cone angle and feedrate value. The results of both simulations and experiments on a prototype machine show that the C-axis can follow the non-singular tool trajectory well with relatively high rotary speed to pass through the singular domain, thereby verifying the effectiveness of the proposed approach.

Jerk-Continuous Feedrate Optimization Method for NURBS Interpolation

Feedrate scheduling is one of the most critical technologies in CNC machining, requiring a reasonable balance between efficiency and quality. This paper proposes a jerk-continuous feedrate smoothing (JCFS) method to generate a low-vibration and smooth feedrate profile for non-uniform rational B-spline (NURBS) interpolation. Firstly, the segmentation concept is introduced to subdivide the entire trajectory into segments to accommodate curvature changes of the NURBS curve, accelerating the acceleration/deceleration process. Secondly, a length threshold-based curve segment classification method is proposed to overcome the complexity of the traditional acceleration and deceleration algorithms. The curve segments are divided into long, medium, and short types, and the length threshold calculation model is derived. Next, to avoid computational complexity for engineering applications, a model is established for the first time to calculate the actual maximum feedrate for different types of segments. Finally, the horizontal-8-shaped and butterfly-shaped NURBS curves are simulated and analyzed. The simulation results indicate that the machining quality is steadily improved while several key indicators remain within the given tolerances. Compared with the traditional method, the proposed method reduces the computational and interpolation time by 17.2% and 22.8%, respectively, demonstrating the feasibility and effectiveness of the method.

Chatter suppression with productivity improvement by scheduling a [formula omitted] continuous feedrate to match spindle speed variation

Available spindle speed variation (SSV) methods, which are used to suppress regenerative chatter through disrupting the phase relationship between the inner and outer modulation on the machined surface, are usually performed in conjunction with the periodically varying feeds per tooth from the originally given constant feedrate. This article presents a new feedrate scheduling algorithm to match the SSV so that feed per tooth can be maximized during the whole machining. Concretely, a sinusoidal profile of feedrate is scheduled to match the designed SSV, meanwhile, the C3 continuous condition is guaranteed within all kinematic constraints. The feedrate is scheduled as two parts, i.e. a jerk continuous acceleration profile with the constant feedrate and a continuous sinusoidal profile above the constant feedrate. The continuity of the junction between these two parts is achieved through scheduling a gradually varying sinusoidal profile. To guarantee the kinematic constraints, the derivatives of the sinusoidal amplitude variation are obtained by the properties of trigonometric functions. As a result, a constant feed per tooth, which actually corresponds to the maximum of the periodically varying feeds per tooth associated with all existing SSV methods, is obtained, while the speed still periodically varies. It proves that the proposed scheduling algorithm can improve the machining efficiency since the feed per tooth is kept at the maximum level in most machining periods, and this is a great advancement over all existing SSV methods. Experiments confirm that chatter can be well suppressed with the significantly reduced machining time by using the proposed method.

A jerk-limited heuristic feedrate scheduling method based on particle swarm optimization for a 5-DOF hybrid robot

Compared with machine tools, five degrees-of-freedom (DOFs) hybrid robots have been widely concerned in the manufacturing of large complex surface parts due to their characteristics of high flexibility and large workspace. It is of great significance to schedule the time-optimal feedrate that satisfies the high-order constraints (e.g., jerk or jounce) in the toolpath and joint systems to achieve the high-precision and high-efficiency machining of the robot. To overcome the complexity of five-axis feedrate scheduling and improve the optimality of machining time, this paper proposes a jerk-limited heuristic feedrate scheduling (HFS) method with near-optimal time. Firstly, the analytical equations between all constraints and the parametric feedrate are derived, and the mathematical model for control points optimization of the parametric feedrate profile expressed by a B-spline curve is established. Then, combined with the global search particle swarm optimization (GSPSO) algorithm, a proposed moving window planning method optimizes a small number of control points so that the feedrate curve has enough rising space. Subsequently, to obtain the near time-optimal feedrate, the local search PSO (LSPSO) algorithm within the moving window is developed to locally adjust the non-uniformly inserted control points. Compared with the existing methods, the HFS method is beneficial to further optimize the machining time with a faster computation speed, and ensure the stability of the robot machining. Finally, simulations and experiments on the developed TriMule-800 hybrid robot verify the effectiveness of this method.

NURBS Interpolator with Scheduling Scheme Combining Cubic and Quartic S-shaped Feedrate Profiles Under Drive and Chord Error Constraints

Traditional S-shaped feedrate profiles only account for the initial and end feedrates during scheduling; they fail to consider whether the feed rate should continuously satisfy the constraints of the chord error in the processing step. To overcome this problem, this paper proposes a feedrate scheduling scheme that processes S-shaped quartic feedrate profiles at the initial stage followed by S-shaped cubic feedrate profiles to ensure machining quality and efficiency. First, the scheme traverses the feedrate points that satisfy the chord error to determine a slope suitable for the jerk of S-shaped quartic feedrate profile, in order to ensure that the increase in the feedrates does not exceed its constraints. Second, an iterative method is used to optimally allocate processing time between the S-shaped cubic and quartic feedrate profiles to optimize processing efficiency. Finally, a method for determining the new maximum feedrate under feedrate interference is discussed. Simulations and experiments are performed to verify the effectiveness of the proposed method relative to other methods. The results reveal that, when using the proposed approach, the processing and running times of the computer are reduced by 39.48% and 118.34%, respectively, as compared with those of other methods. • Combining S-shaped quartic and cubic feedrate profile, and then calculating the optimal time allocation between them. • Ensure that the speed, acceleration and jerk meet the given constraints. • The method avoids the problem when the profile is complex the maximum feedrate can’t be updated and reduces the caculation. • The problem of low machining efficiency caused by uniform motion near the minimum feedrate point is avoided.

Generalised NURBS interpolator with nonlinear feedrate scheduling and interpolation error compensation

Current nonuniform rational B-spline interpolating methods encounter problems pertaining to the interpolating error, feedrate profile, and machining efficiency; the optimal feedrate profile may not be obtained owing to the complex kinematics of multi-axis machine tools with hybrid structures. To address these problems and obtain an optimal feedrate profile with minimum machining time, this paper establishes a generalised representation for the nonlinear feedrate scheduling model, with static and dynamic feedrate constraints, through a numerical convex transformation. Based on the generalised model representation, a time-optimal feedrate profile can then be solved globally for both series- and parallel-structured mechanisms without problems caused by profile linear simplification or imprecise feedrate evolution. Considering the feedrate fluctuation problem caused by the difference between the theoretical arc length of the curve interpolation and the actual tool path, this paper proposes a novel co-lateral triangle deviation (CTD)-based parameter compensation interpolation algorithm. With the CTD calculation, which is related to the actual feed motion in real time, the proposed interpolation algorithm can determine the interpolating compensation distance for each interpolating segment and obtain the interpolation points using a second-order Taylor series expansion with a minimal interpolating error. Carried on a hybrid mechanism with complex kinematic constraints, the experimental and comparison results validated the effectiveness of the proposed method in feedrate scheduling and feedrate fluctuation reduction.