Search

Highlights • A novel transmission engaging model (TEM) is proposed to describe the friction force. • The TEM model provides a better understanding of friction engagement process. • A two-step identification process is proposed to identify the parameters of the TEM. • A full servo control system is simulated to validate the TEM. • The simulation and experimental results for the LuGre and TEM are compared. Abstract In this paper, a novel transmission engaging model is proposed by modifying the conventional LuGre model to describe microcontact behavior. The proposed model uses the bristle deformation stage, partial transmission engaging stage, and complete transmission engaging stage to characterize the friction force when the platform reverses its moving direction. The model retains the basic characteristics of the LuGre model. However, unlike the LuGre model, the model can explain why the friction force increases although the velocity of the moving platform remains constant in the experiment. The model can provide more accurate friction force estimations than the LuGre model can. Finally, the model is integrated with the servo dynamics model to estimate the position feedback, velocity feedback, and friction force. The experimental results show that the model has higher estimation accuracy than the LuGre model for the friction force, velocity feedback, and position feedback. [ABSTRACT FROM AUTHOR]

This paper develops a novel interpolation algorithm to compensate the error caused by elastic deformation which can achieve higher tracking accuracy even without the signal from the linear scale on the table. First, a dynamic model which considers flexural modes of a feed drive system, servo control loops, and friction effects simultaneously is constructed. Based on the dynamic model, the equation of elastic deformation is then derived. The equation is further simplified to form a formulation in computing the deformations which is mainly caused by inertial and viscous forces during motion. Experiments and simulations are conducted to validate both dynamic model and the simplified elastic deformation equation. Based on the simplified equation, a novel elastic deformation compensation interpolation (MEDCI) algorithm is proposed to generate the modified position commands such that the tracking errors caused by elastic deformation can be reduced. Experimental results on the linear trajectory demonstrate that the proposed algorithm could reduce the maximum elastic deformation error from 23.4 μm to 6.4 μm and the root mean square (RMS) error from 19.5 μm to 3.1 μm which correspond to 84.1% and 72.6% reduction, respectively. Furthermore, the MEDCI can achieve more than 10% reduction as compared to the results in published literature. [ABSTRACT FROM AUTHOR]

In this paper, an integrated dynamic acceleration/deceleration (IDAD) interpolation algorithm which combines the acceleration/deceleration before interpolation (ADBI) and acceleration/deceleration after interpolation (ADAI) is proposed. The IDAD scheme could confine the maximum contour error at the junction of a linear line (G01) block under consideration of the command and servo dynamic errors. The contour error formulation for the IDAD is derived analytically and then utilized for interpolation design. Because the error formulation could predict the command and dynamic errors analytically, the IDAD could adjust the connecting velocity of two blocks such that the overall contour errors are bounded within the given tolerance. The simulation results validate the proposed algorithm that can reduce the contour errors by 50 % but only an increase of 10 % machining time as compared to the integrated acceleration/deceleration (IAD) interpolation technique. [ABSTRACT FROM AUTHOR]

Feedrate scheduling with kinematic constraints is a challenging problem for five-axis machining. Linear and rotary drives of five-axis machine tools have different capabilities and limits. The main issue is that the feedrate profile generated by the existing five-axis feedrate scheduling method might violate kinematic constraints since the tangential and axial jerk could not be directly correlated due to nonlinear kinematics transformation. In this paper, a novel master-based feedrate scheduling (MBFS) approach with real-time and drive constraints is developed to generate smooth trajectories along five-axis linear toolpaths. Based on inverse kinematic equations, tooltip feed parameters are evaluated by a five-axis feed regulation formula (FFRF) such that axial velocities, accelerations, and jerks could be constrained within given limits simultaneously. The tooltip or rotary axis having the largest motion duration is selected to be the master, and the others are regarded as the slaves which move with the master synchronously. Rather than planning the feedrate profile using the curve parameter algorithm, linear and angular trajectories are planned by matching the same motion duration to realize time synchronization of five-axis motion. The local corner smoothing method is adopted to blend the velocities of the motion axes and generate cornering trajectories while satisfying corner position tolerance and drive constraints. Finally, experiments are conducted on a five-axis engraving machine to verify that the proposed method can satisfy the kinematic constraints, and improve tracking and contour accuracy. [ABSTRACT FROM AUTHOR]

Modern motion control adopts acceleration/deceleration before interpolation (ADBI) motion planning to eliminate path command errors. However, the individual velocity profiles might not be continuous at the junction of the blocks. Acceleration/deceleration after interpolation (ADAI) method may provide an alternative for solving the discontinuous problems, but it causes path command errors. In this paper, an integrated acceleration/deceleration interpolation (IAD) scheme which integrates the ADBI and ADAI modules is proposed. The ADBI provides a look-ahead function which plans the feedrate profiles based on chord errors, command errors, curvatures, and acceleration limits. Within the look-ahead function, the command error equation is utilized to determine the feedrate at the junction of adjacent blocks. Then the ADBI performs non-uniform rational B-spline (NURBS) interpolation using the planned feedrate profile and outputs the position points to the ADAI module. The ADAI module processes the points by a digital convolution technique such that the continuity of the block junction velocity is ensured. Finally, the IAD is applied to the multi-block NURBS interpolation to validate its effectiveness. Simulations and experiments are conducted to demonstrate the IAD scheme. It is shown that the IAD scheme can reduce the acceleration significantly at the junctions of the blocks under the given tolerance of the command error. Furthermore, the proposed algorithm can improve tracking and contour accuracies as compared to the hybrid multi-blocks look-ahead approach. [ABSTRACT FROM AUTHOR]

Abstract: A novel pendulum-type vibration isolation system is proposed consisting of three active cables with embedded piezoelectric actuators and a passive elastomer layer. The dynamic response of the isolation module in the vertical and horizontal directions is modeled using the Lagrangian approach. The validity of the dynamic model is confirmed by comparing the simulation results for the frequency response in the vertical and horizontal directions with the experimental results. An approximate model is proposed to take into account system uncertainties such as payload changes and hysteresis effects. A robust quantitative feedback theory (QFT)-based active controller is then designed to ensure that the active control can achieve a high level of disturbance rejection in the low-frequency range even under variable loading conditions. It is shown that the controller achieves average disturbance rejection of −14dB in the 2–60Hz bandwidth range and −35dB at the resonance frequency. The experimental results confirm that the proposed system achieves a robust vibration isolation performance under the payload in the range of 40–60kg. [Copyright &y& Elsevier]

Abstract: In this paper, a novel approach is proposed to analyze the inverse dynamics of a 3-PRS (Prismatic, Revolute, Spherical) parallel mechanism. The dynamic equations of the actuated legs and the moving platform are formulated in the joint and the task space, respectively. The reaction forces applied at the spherical joints are utilized to integrate the complete equations and a special decomposition is proposed for efficient calculation. By employing the Jacobian analysis, the constraint forces in the joint coordinates are recognized to be the internal forces for the moving platform and lead to the special decomposition. The proposed algorithm can provide higher computational efficiency as compared to the conventional approach. Computer simulations on tracking circular motion are performed to analyze the inverse dynamics of the 3-PRS mechanism and it is shown that the proposed decomposition of the reaction forces could be utilized to provide a deeper understanding for the interactions between the legs and moving platform. Since the closed-loop kinematic constraints are inherent for parallel manipulators, the proposed methodology could also be applied to other parallel mechanisms. In real-time control, the proposed algorithm with high computational efficiency might be utilized for dynamic compensation. [Copyright &y& Elsevier]

Abstract: Methodologies for planning motion trajectory of parametric interpolation such as non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, most of the algorithms were developed based on the constraints of feedrate, acceleration/deceleration (acc/dec), jerk, and chord errors. The errors caused by servo dynamics were rarely included in the design process. This paper proposes an integrated look-ahead dynamics-based (ILD) algorithm which considers geometric and servo errors simultaneously. The ILD consists of three different modules: a sharp corner detection module, a jerk-limited module, and a dynamics module. The sharp corner detection module identifies sharp corners of a curve and then divides the curve into small segments. The jerk-limited module plans the feedrate profile of each segment according to the constraints of feedrate, acc/dec, jerk, and chord errors. To ensure that the contour errors are bounded within the specified value, the dynamics module further modifies the feedrate profile based on the derived contour error equation. Simulations and experiments are performed to validate the ILD algorithm. It is shown that the ILD approach improves tracking and contour accuracies significantly compared to adaptive-feedrate and curvature-feedrate algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is proposed to generate a smooth and jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules: geometric, dynamics-based, and jerk-limited modules. The geometric module can detect the local maximum/minimum (max/min) curvatures, and divide a NURBS curve into small segments according to the information of sharp corners. The feedrates at the sharp corners are determined based on confined chord errors and curvatures of the curve. The dynamics-based module utilizes a dynamics feedrate modification equation (DFME) to estimate contour errors at the sharp corners and adjusts the feedrates at the locations of the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the segments’ length and the given jerk limit. Simulations are performed to verify real-time performance of the look-ahead algorithm. Experiments using a PC-based motion controller and an X–Y table are conducted to demonstrate that high-accuracy can be achieved with the proposed dynamics-based interpolator as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms. [Copyright &y& Elsevier]

This paper presents the direct kinematics solutions for a novel 3-PRS parallel mechanism. The geometric method is applied to formulate three coupled trigonometric equations. One algorithm for solving the three coupled equations is to use the Bezout’s elimination method which leads to a total of 64 solutions. By categorizing the 64 solutions into six groups and further examining the corresponding configuration for each group, the preferred solution to the direct kinematics problem can be obtained. The other approach for solving the coupled equations is to apply the optimization techniques with side and behavior constraints set by analyzing undesired configurations. This approach can obtain the preferred solution without checking all the possible solutions. Moreover, it can perform more efficiently than the elimination method. [Copyright &y& Elsevier]

• The novel servo-friction model is developed for predicting the quadrant protrusions. • The factors of quadrant protrusions under different motion conditions are analyzed. • The optimization to determine the quadrant error compensation parameters is proposed. • A new multi-square-pulse compensation method and its tuning algorithm are suggested. • The experimental results compensated by different approaches are discussed. The nonlinear phenomenon of friction causes significant tracking errors when a platform reverses its moving direction. These tracking errors can cause quadrant protrusion (QP) for circular motion. To solve this problem, the conventional approach is to inject a compensation signal during the period of velocity reversal to overcome the friction effect. The waveform of this compensation signal has not yet been investigated. In this paper, a novel multi-square-pulse compensation (MSPC) method is proposed based on minimization of QP to determine the optimal MSPC waveform. To implement MSPC, the waveform is first computed using an identified servo-friction model. MSPC signals for the trajectories with different velocities and accelerations (Vel/Acc) are discussed, and the performance is compared with that of conventional quadrant error compensation (QEC). To validate the novel MSPC algorithm, experiments were conducted on an XY table. To further improve the experimental results by considering modeling errors, MSPC incorporating a tuning algorithm, called MSPC_TA, is proposed. The experimental results with different Vel/Acc show that QPs can be reduced by 95% by using the MSPC_TA approach. [ABSTRACT FROM AUTHOR]

This paper presents an integrated servo-feed-drive model including the cutting force and structural effect to predict tracking errors in an end-milling process. Most conventional approaches consider the cutting force to be an equivalent torque to servo feed drive. However, in addition to acting as the equivalent torque to the servo feed drive, cutting forces also cause the machine table to vibrate. This paper considers the aforementioned cutting-force effects to predict tracking errors and then verifies the tracking errors using experimental results. Experiments are conducted on a 3-axis computer numerical control (CNC) machining center to validate the tracking errors predicted by the proposed servo-feed-drive model. For one case study, the peak-to-peak tracking errors from the experimental, proposed, and traditional models are 3 μm, 2.8 μm, and 0.5 μm, respectively, for the x-axis, and 2.1 μm, 1.7 μm, and 0.4 μm, respectively, for the y-axis. The experimental results illustrate that the tracking errors predicted using the proposed model are more accurate than those predicted using the traditional model without consideration of the transmission path. Therefore, it can be concluded that the proposed integrated model provides much accurate tracking-error prediction, and thus, the ball-screw and machine-table flexibilities should be considered. [ABSTRACT FROM AUTHOR]

vA generalized model that integrates the Navier- Stokes equation and coupling-of-modes (COM) model for biosensing SAW devices is developed in this paper. The SAW device is separated into three regions: interdigital transducer (IDT), substrate (delay line), and sensing regions. To evaluate the effects of metal thickness, mass loading caused by bioreaction, and different viscous fluid loading, the sensing region is further divided into three layers: piezoelectric substrate, metal layer, and fluid layer. In contrast to the conventional study, which is focused on the change of phase velocity, this model can evaluate the insertion loss and phase shifts under different sensing conditions. It can be shown that the integration of the COM model can provide guidelines for designing the bio-sensing device such as choosing the proper number of IDT, the width of the overlap, and the thickness of the metal layer. Furthermore, the generalized model can be utilized to evaluate the optimal thickness of the metal layer to achieve the maximum sensitivity. [ABSTRACT FROM PUBLISHER]

Abstract: Robustness issue is considered to be one of the major concerns in application of the iterative learning control in motion control systems. The robustness in servo systems is related to parameter uncertainties and noise accumulation. In this paper, both parameter uncertainties and noise are considered in derivation of the error dynamic equation of the ILC algorithm. Based on the error dynamics, the H∞ framework is utilized to design the robust learning controller. An optimization design process in selecting the proper learning gain and determining the learning function is proposed to ensure that both tracking performance and convergence condition are achieved. Simulations and experiments are conducted to validate the robust learning algorithm which can be applied efficiently to machine tools with the payload varying from 0 to 20kg. The experimental results demonstrate that the proposed method improves the tracking and contouring performances significantly when performing a complex NURBS curve on a three-axis milling machine. [Copyright &y& Elsevier]

Flank wear is the most common wear that happens in the end milling process. However, the process of detecting the flank wear is cumbersome. To achieve comprehensively automatic detecting the flank wear area of the spiral end milling cutter, this study proposed a novel flank wear detection method of combining the template matching and deep learning techniques to expand the curved surface images into panorama images, which is more available to detect the flank wear areas without choosing a specific position of cutting tool image. You Only Look Once v4 model was employed to automatically detect the range of cutting tips. Then, popular segmentation models, namely, U-Net, Segnet and Autoencoder were used to extract the areas of the tool flank wear. To evaluate the segmenting performance among these models, U-Net model obtained the best maximum dice coefficient score with 0.93. Moreover, the predicting wear areas of the U-Net model is presented in the trend figure, which can determine the times of the tool change depend on the curve of the tool wear. Overall, the experiments have shown that the proposed methods can effectively extract the tool wear regions of the spiral cutting tool. With the developed system, users can obtain detailed information about the cutting tool before being worn severely to change the cutting tools in advance. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a nonlinear dynamic analysis of a 3-PRS series-parallel mechanism with consideration of joint effects which includes flexibility, clearance and friction. The Newtonian approach is applied to derive the equations of motion of the 3-PRS mechanism. The Runge–Kutta method and contact verification criterion are combined to solve the nonlinear piecewise differential equations. The linearization technique is applied to determine the natural frequencies and their associated mode shapes. The simulation results show that the natural frequencies of the 3-PRS mechanism shift with the position of prismatic pairs and the physical interpretations are given by using the associate mode shapes. The effects of joint clearance and friction cause the natural frequencies to decrease and significantly affect the modes of which rotational motions are dominated. It is also shown that the dynamic response becomes larger as the joint clearances increase, and the joint contact forces become larger as joint clearances and friction coefficient increase. [Copyright &y& Elsevier]

Abstract: Modern motion control adopts NURBS (Non-Uniform Rational B-Spline) interpolation for the purpose of achieving high-speed and high-accuracy performance. However, in conventional control architectures, the computation of the basis functions of a NURBS curve is very time-consuming due to serial computing constraints. In this paper, a novel FPGA (Field Programmable Gate Array) based motion controller utilizing its high-speed parallel computing power is proposed to realize the Cox–de Boor algorithm for second and higher degrees NURBS interpolation. The motion control algorithm is also embedded in the FPGA chip to implement real-time control and NURBS interpolation simultaneously for multi-axis servo systems. The proposed FPGA-based motion controller is capable of performing the Cox–de Boor algorithm and the IIR (Infinite Impulse Response) control algorithm in about 46 clock cycles, as compared to the 1303 clock cycles by the traditional approach. Numerical simulations and experimental tests using an table verify the outstanding computation performance of the FPGA-based motion controller. The result indicates that shorter sampling time (10 μs) can be achieved for NURBS interpolation which is highly critical to the success of high-speed and high-accuracy motion control. [Copyright &y& Elsevier]

Flank wear is the most common wear that happens in the end milling process. However, the process of detecting the flank wear is cumbersome. To achieve comprehensively automatic detecting the flank wear area of the spiral end milling cutter, this study proposed a novel flank wear detection method of combining the template matching and deep learning techniques to expand the curved surface images into panorama images, which is more available to detect the flank wear areas without choosing a specific position of cutting tool image. You Only Look Once v4 model was employed to automatically detect the range of cutting tips. Then, popular segmentation models, namely, U-Net, Segnet and Autoencoder were used to extract the areas of the tool flank wear. To evaluate the segmenting performance among these models, U-Net model obtained the best maximum dice coefficient score with 0.93. Moreover, the predicting wear areas of the U-Net model is presented in the trend figure, which can determine the times of the tool change depend on the curve of the tool wear. Overall, the experiments have shown that the proposed methods can effectively extract the tool wear regions of the spiral cutting tool. With the developed system, users can obtain detailed information about the cutting tool before being worn severely to change the cutting tools in advance. [ABSTRACT FROM AUTHOR]

Flank wear is the most common wear that happens in the end milling process. However, the process of detecting the flank wear is cumbersome. To achieve comprehensively automatic detecting the flank wear area of the spiral end milling cutter, this study proposed a novel flank wear detection method of combining the template matching and deep learning techniques to expand the curved surface images into panorama images, which is more available to detect the flank wear areas without choosing a specific position of cutting tool image. You Only Look Once v4 model was employed to automatically detect the range of cutting tips. Then, popular segmentation models, namely, U-Net, Segnet and Autoencoder were used to extract the areas of the tool flank wear. To evaluate the segmenting performance among these models, U-Net model obtained the best maximum dice coefficient score with 0.93. Moreover, the predicting wear areas of the U-Net model is presented in the trend figure, which can determine the times of the tool change depend on the curve of the tool wear. Overall, the experiments have shown that the proposed methods can effectively extract the tool wear regions of the spiral cutting tool. With the developed system, users can obtain detailed information about the cutting tool before being worn severely to change the cutting tools in advance. [ABSTRACT FROM AUTHOR]

• A novel 2-DOF model with two LuGre friction models is proposed to describe the frictional behavior and elastic deformation of a feed drive system. • A quick identification method is designed to obtain parameters of spring, damping and frictional model. • The novel 2-DOF model is used to represent the nonlinear behavior of the feed drive system and to explain the special two-stage behavior of the motor torque. • The elastic deformation could be accurately predicted and validated by the simulation and experimental results. This study investigated the frictional behavior and elastic deformation of a feed drive system by using two LuGre frictional models. The LuGre models were used to describe frictional behaviors on two sliding surface bodies connected by a spring-damper component. To investigate the interaction between friction and elastic deformation during speed reversal, the feed drive system was divided into two parts: the motor-screw and nut-table. The forward path and sinusoidal path were designed to identify the parameters of the spring, damping, and the frictional model. A 2-degree-of-freedom model was combined with the two LuGre models to represent the nonlinear behavior of the feed drive system. The proposed model provided a clear physical interpretation of the conventional hysteresis frictional curve. Furthermore, comparisons between the simulation and experimental results revealed that the maximum prediction error of elastic deformation was approximately 0.91 μm, and the average simulated error of elastic deformation was approximately 0.36 μm, which indicated the accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

In the accepted paper, the authors' affiliation has been wrongly typeset as People's Republic of China, but this should read Taiwan. The correct affiliations are shown below. [ABSTRACT FROM AUTHOR]

Correction to: I Scientific Reports i https://doi.org/10.1038/s41598-021-97610-y, published online 7 October 2021 Hong-Tsu Young was omitted from the author list in the original version of this Article. The original article can be found online at https://doi.org/10.1038/s41598-021-97610-y. [Extracted from the article]