Design and implementation of a linear jerk filter for a computerized numerical controller

The proposed filter is placed in front a buffered digital differential analyzer, and is formed by combining three modified moving average filters. It can export the position commands to ensure smooth and accurate motion of a tool with a linear jerk change. These output commands can guarantee contour accuracy despite the error in the chord height. The acceleration and jerk can be designed simply by specifying the number of registers. The filter can be implemented using three circular buffers to simplify the arithmetic and reduce the computation time. The high precision motion commands are confirmed by installing the filtering algorithm in a digital signal processor of a computerized numerical controller. The radius of the command trajectory does not become distorted at high speed 30 m/min. The commands filtered by the linear jerk filter stabilize the beginning and end of the actual motion of the machine table.     

A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk

In this paper, the problem of optimal feedrate planning along a curved tool path for 3-axis CNC machines with the acceleration and jerk limits for each axis and the tangential velocity bound is addressed. It is proved that the optimal feedrate planning must be “Bang–Bang” or “Bang–Bang-Singular” control, that is, at least one of the axes reaches its acceleration or jerk bound, or the tangential velocity reaches its bound throughout the motion. As a consequence, the optimal parametric velocity can be expressed as a piecewise analytic function of the curve parameter u. The explicit formula for the velocity function when a jerk reaches its bound is given by solving a second-order differential equation. Under a “greedy rule”, an algorithm for optimal jerk confined feedrate planning is presented. Experiment results show that the new algorithm can be used to reduce the machining vibration and improve the machining quality.     

An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control

Parametric interpolation has been widely used in CNC machining because of its advantages over the traditional linear or circular interpolation. Many researchers focused on this field and have made great progress in the specific one, NURBS curve interpolation. These works greatly improved the CNC machining with constant feedrate, confined chord error and limited acceleration/deceleration. However, during CNC machining process, mechanical shocks to machine tool caused by the undesired acceleration/deceleration profile will dramatically deteriorate the surface accuracy and quality of the machined parts. This is, in most occasions, very harmful to machine tools. In this paper, an accurate adaptive NURBS curve interpolator is proposed with consideration of acceleration–deceleration control. The proposed design effectively reduces the machining shocks by constraining the machine tool jerk dynamically. Meanwhile, the constant feedrate is maintained during most time of machining process, and thus high accuracy is achieved while the feedrate profile is greatly smoothed. In order to deal with the sudden change of the acceleration/deceleration around the corner with large curvature, a real-time flexible acceleration/deceleration control scheme is introduced to adjust the feedrate correspondingly. Case study has been taken to verify the feasibility and advantages of the proposed design.     

A newly developed corner smoothing methodology based on clothoid splines for high speed machine tools

Continuous linear commands are widely executed in computer numerical control (CNC) machining. The tangential discontinuity at the junction of consecutive segments restricts the machining efficiency and deteriorates the surface quality. Corners of linear segments have been successfully blended by inserting parametric splines. There still exists challenges when the common methods are employed in the line-segment commands due to part of the following restrictions: (1) the stringent computation for iteratively calculating the arc-length; (2) the unwanted feedrate fluctuation; (3) the oversize contour deviation for separately completing curve fitting and velocity planning.A novel smoothing method based on a clothoid pair to synchronously accomplish planning of geometry blending and speed scheduling is proposed, the spline parameter of which is arc-length-parameterized. The arc-length, curvature extreme, and geometric shape of the transition curve are analytically expressed by the transition length. On these bases, the transition curve and the velocity profile are concurrently constructed based on the predefined approximation error, the reachable velocity, and normal kinematic constraints in the look-ahead stage. Then, a real-time interpolation scheduling is developed to overcome the crossing difficulties between the linear and parametric segments. Compared with existing methods, the proposed method can analytically calculate the length of transition curves for the arc-length-parameterized expression form. Furthermore, the feedrate fluctuation is eliminated in the fine interpolation. Moreover, the overlarge contour derivation produced by corner smoothing is significantly avoided. It is friendlier to the CNC system for the on-line executing smooth motion since more computing resources can be released to handle other tasks, smoother motion can be achieved and higher contour accuracy can be obtained. The experimental results also demonstrate its practicability and reliability.     

An FPGA-based low-cost VLIW floating-point processor for CNC applications

In the high-speed free-form surface machining, the real-time motion planning and interpolation is a challenging task. This paper presents the design and implementation of a dedicated processor for the interpolation task in computerized numerical control (CNC) machine tools. The jerk-limited look-ahead motion planning and interpolation algorithm has been integrated in the interpolation processor to achieve smooth motion in the high-speed machining. The processor features a compactly designed floating-point parallel computing architecture, which employs a 3-stage pipelined reduced instruction set computer (RISC) core and a very long instruction word (VLIW) floating-point arithmetic unit. A new asynchronous execution mechanism has been employed in the processor to allow multi-cycle instructions to be performed in parallel. The proposed processor has been verified on a low-cost field programmable gate array (FPGA) chip in a prototype controller. Experimental result has demonstrated the significant improvement of the computing performance with the interpolation processor in the free-form surface machining.     

复杂曲面笔式加工的直接插补算法

复杂曲面笔式加工时的工具轨迹是位于曲面上的自由曲线轨迹．针对此类形式的轨迹，给出一种复杂曲面笔式加工时的自由曲线型刀轨的直接插补算法，即对位于曲面上以投影方式形成的任意自由曲线形式的刀轨进行插补计算，生成控制机床运动的指令．该方法的实现扩充了CNC系统的轨迹控制功能，提高了复杂曲面的加工效率．仿真和试切的结果证明算法可行而且有效．该算法也可以应用到整体曲面加工中．     

The feedrate scheduling of NURBS interpolator for CNC machine tools

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G⁰ continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor–corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.     

A CNC machine tool interpolator for surfaces of cross-sectional design

A machining strategy for milling a particular set of surfaces, obtained by the technique of cross-sectional design is proposed. The surfaces considered are formed by sliding a Bezier curve (profile curve) along another Bezier curve (trajectory curve). The curves are located in perpendicular planes. The method employs a three-axis CNC milling machine equipped with suitable ball-end cutter and is based on the locus-tracing concept. The algorithm described, utilizes a real-time CNC interpolator providing the highest possible accuracy, of which the milling machine is capable. The surface quality is controlled by keeping the distance between scallops within a programmed value. Finally, the whole machining task can be programmed in a single block of the part program.     

数控机床上下料机器人运动控制轨迹优化研究

运动轨迹优化是工业机器人研究的一个重要领域.七段S型曲线是从传统的梯形加减速算法基础上发展而来的,尽管S型速度曲线控制算法提高了加减速过程中的稳定性,使运动过程中的速度变化连续,有较好的平滑性,但其加加速度仍存在阶跃变化问题,导致加速度存在明显的拐点,容易造成机器人在运动过程中发生冲击或振动.在上述研究的基础上,将多项式速度曲线控制算法与S型速度曲线控制算法相结合,提出了一种改进的S型速度曲线控制算法,通过优化加加速度,使其速度、加速度连续变化,曲线平滑性更好.在新代机械手臂控制系统下,对改进后S型速度曲线控制算法进行试验,证明所提出的算法在加减速过程中能够获得更加平滑的速度和加速度.     

NURBS曲线实时插补中的速度规划算法

大多数现有的NURBS曲线实时插补算法并未考虑速度方向的变化给各运动轴带来的影响,这会导致加工过程中单轴速度的剧烈变化.提出一种能保证各运动轴平稳运行的速度规划算法,它在满足精度要求的前提下,通过控制切向加速度和加加速度进行速度平滑,并根据各运动轴的当前速度和机床的实际性能再次调节进给速度,保证了机床的平稳运行.模拟实验证实了该算法的有效性.     

FPGA implementation of higher degree polynomial acceleration profiles for peak jerk reduction in servomotors

Acceleration profile generation for jerk limitation is a major issue in automated industrial applications like computer numerical control (CNC) machinery and robotics. The automation machinery dynamics should be kept as smooth as possible with suitable controllers where trajectory precision ensures quality while smoothness decreases machinery stress. During the operation of commercially available CNC and robotics controllers, small discontinuities on the dynamics are generated due to the controller position profiler which is generally based on a trapezoidal velocity profile. These discontinuities can produce undesirable high-frequency harmonics on the position reference which consequentially can excite the natural frequencies of the mechanical structure and servomotors. Previous works have developed jerk limited trajectories with higher degree polynomial-based profiles, but lack one or both of computer efficiency for on-line operation and low-cost hardware implementation. The present work shows a low cost, computationally efficient, on-line hardware implementation of a high-degree polynomial-based profile generator with limited jerk dynamics for CNC machines and robotics applications to improve the machining process. The novelty of the paper is the development of a multiplier-free recursive algorithm for computationally efficient polynomial evaluation in profile generation and a low-cost implementation of the digital structure in field programmable gate array (FPGA). Two experimental setups were prepared in order to test the polynomial profile generator: the first one with the servomotor at no load and the second one for the servomotor driving a CNC milling machine axis. From experimental results it is shown that higher degree polynomial profiles, compared to the standard trapezoidal speed profile improve the system dynamics by reducing peak jerk in more than one order of magnitude while precision is maintained the same and on-line operation is guaranteed.     

Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system

In this paper, the time-optimal feedrate planning problem under confined feedrate, axis velocity, axis acceleration, axis jerk, and axis tracking error for a high-order CNC servo system is studied. The problem is useful in that the full ability of the CNC machine is used to enhance the machining productivity while keeping the machining precision under a given level. However, the problem is computationally challenging. The main contribution of this paper is to approximate the problem nicely by a finite-state convex optimization problem which can be solved efficiently. The method consists of two key ingredients. First, a relationship between the tracking error and the input signal in a high-order CNC servo system is established. As a consequence, the tracking error constraint is reduced to a constraint on the kinematic quantities. Second, a novel method is introduced to relax the nonlinear constraints on kinematic quantities to linear ones. Experimental results are used to validate the proposed method.     

Local asymmetrical corner trajectory smoothing with bidirectional planning and adjusting algorithm for CNC machining

The linear motion command (G01) is a widely used command format in CNC machining. However, the tangential direction discontinuity at the corner junction will cause velocity fluctuations and excite the structural vibration of machine tools. Corner smoothing methods with controlled tolerance are used to obtain continuous smooth motion. Typically, most methods generate a symmetrical cornering trajectory around the angle bisector, and the trajectory generally decelerates first and then accelerates, which limits the velocity increase. In this paper, a novel local asymmetrical corner trajectory smoothing method is proposed, which can realize accelerated/decelerated cornering transition. The proposed method can obtain the analytical solution in one step, which is different from two-step geometric-based corner path smoothing, and can generate the same cornering trajectory in back-and-forth parallel toolpath. In addition, this paper proposes a bidirectional planning and adjusting algorithm for the situation where smoothed cornering paths are close to each other or even overlap. The algorithm can generate a jerk-limited trajectory by coordinating the cornering error of adjacent corners, while respecting the user-specified tolerance. Experimental results demonstrate the effectiveness of the proposed method in contour accuracy and cycle time for CNC machining along short-segmented toolpath.     

An adaptive real-time NURBS curve interpolation for 4-axis polishing machine tool

The non-uniform rational B-spine (NURBS) curve interpolation is a key technology of the advanced computer numerical control (CNC) system. NURBS curve interpolation can realize a high-speed and high-precision machining, and it can also avoid some inevitable deficiencies of the linear and circular interpolation functions which are generally used in traditional NC system. Before the interpolation, some calculation tasks are finished, which will decrease the amount of calculation during interpolation and increase the interpolation efficiency. Further, an adaptive NURBS curve interpolation with real-time and flexible S-shaped curve acceleration/deceleration (ACC/DEC) control method is added to the interpolation algorithms. The NC machining simulation conducted with the MATLAB software and the NURBS curve interpolation experiments performed on the 4-axis polishing machine tool demonstrate the validity and correctness of the adaptive real-time NURBS curve interpolation algorithm in the CNC system.     

Linear and angular feedrate interpolation for planar implicit curves

In multi-axis CNC machining, a cutting tool combines translation and rotational movements with respect to a workpiece. This entails CNC interpolation to take angular feedrates defining the speed of the rotational movement into account, while current interpolations are overwhelmingly based on linear feedrates defining the speed of the translation movement. This paper considers linear and angular feedrate interpolations of 2D tool paths for multi-axis machining. A 2D tool path is identified by a position curve assumed to be a 2D implicit curve and a tool orientation curve based on the implicit curve. The paper will relate the angular feedrate to the linear feedrate along the tool paths. The result is then used to develop the angular feedrate interpolation from the linear feedrate interpolation. Detailed interpolation schemes for such hybrid feedrates as a constant linear feedrate with constrained angular feedrate (CLCA) and a constant angular feedrate with constrained linear feedrate (CACL) have further been constructed. A corrected interpolation scheme is further present to augment the initial interpolation. Example interpolations including a quadric curve, the nodal cubic and a quartic curve are carried out to illustrate the feasibility and effectiveness of the proposed approach.     

Automated surface subdivision and tool path generation for -axis CNC machining of sculptured parts

As an innovative and cost-effective method for carrying out multiple-axis CNC machining, -axis CNC machining technique adds an automatic indexing/rotary table with two additional discrete rotations to a regular 3-axis CNC machine, to improve its ability and efficiency for machining complex sculptured parts. In this work, a new tool path generation method to automatically subdivide a complex sculptured surface into a number of easy-to-machine surface patches; identify the favorable machining set-up/orientation for each patch; and generate effective 3-axis CNC tool paths for each patch is introduced. The method and its advantages are illustrated using an example of sculptured surface machining. The work contributes to automated multiple-axis CNC tool path generation for sculptured part machining and forms a foundation for further research.     

基于Adams-Bashforth-Moulton预估校正法的NURBS插补算法研究

针对传统的基于连续微小线段的插补方法在复杂零件型面加工中具有插补误差大和速度波动大等不足,对NURBS曲线的插补原理、插补参数计算、速度波动等方面进行了研究,结合加工弓高误差、法向加速度、法向加加速度等约束条件进行了速度规划,提出了一种基于Adams-Bashforth-Moulton(ABM)预估校正法的NURBS曲...     

Motion pattern analysis of parallel kinematic machines: A case study

This paper looks at the “five-axis machines” for machining operations. These machines have five (or six at maximum) degrees of freedom (dof). The output motion must have at least three translational and two rotational dof. This output motion pattern can be obtained with different structural topologies: serial, parallel, hybrid and with serial and/or parallel manipulators working in co-operation. The latter allows higher motion ranges in rotational and translational dof. Moreover, it provides a good stiffness, a highly valued requisite in applications like machining. Manipulators of this type are characterized by their kinematics to be integrated in the CNC, which requires the study of the relative motion between their modules. This motion is usually complex, and in certain cases presents kinematic relations not evident. This work presents a methodology to solve the motion pattern out of the direct and inverse kinematics of the relative motion between the modules of which the manipulator is composed. On the one hand, the spindle is mounted on a parallel module. On the other hand, the working table is mounted on a serial module. This methodology was applied to the Hermes parallel manipulator in combination with rotary and linear tables. As a result, a series of considerations regarding other possible combinations between modules was made and a new machine is proposed.     

Torsional displacement compensation in position control for machining centers

In a CNC machining center, each axis of an XY table is linked to a motor through a ballscrew. Since the stiffness of the ballscrew is finite, there exists a torsional displacement resulting in a difference between the position of the motor and the corresponding position of the table. For more precise position control of the table, methods using measuring instruments such as a laser interferometer can be used, but this is too expensive to be implemented in a commercial CNC machining center. In this paper, a method is proposed to reduce the error of the table's position without directly measuring the position of the table. The method consists of a torsional displacement feedback algorithm and an estimation of the torsional displacement. The proposed method is tested in a CNC machining center and shows significant reduction in the error of the table position.     

数控系统连续微段重构与插补算法研究

针对目前微段加工研究中采用的非重构微段加工方法存在的加工轨迹与设计曲线轮廓误差较大,轮廓加工精度较低,及微段节点处速度方向不连续,因此加工表面质量不高,加工过程机床振动较大的问题。在计算机数控（Computerized Numerical Control,CNC）中采用实时曲线重构与插补算法进行连续微段加工以实现对曲面的高速高精度加工。微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足加减速要求的可以直接递推的插补样条曲线的重构条件。应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到um级精度的同时,加工速度提高了2~2.4倍。实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内进行整体加减速速度规划,提高加工效率,而且加工轨迹的进给速度的衔接平滑,轨迹光滑,表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了平衡了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度。