Hardware-in-the-loop simulation for estimation of position control performance of machine tool feed drive

Journal Pre-proof Hardware-in-the-loop simulation for estimation of position control performance of machine tool feed drive

Namhyun Kim, Hyunjung Kim, Wonkyun Lee PII:

S0141-6359(19)30288-0

DOI:

https://doi.org/10.1016/j.precisioneng.2019.08.010

Reference:

PRE 7005

To appear in:

Precision Engineering

Received Date:

16 April 2019

Accepted Date:

25 August 2019

Please cite this article as: Namhyun Kim, Hyunjung Kim, Wonkyun Lee, Hardware-in-the-loop simulation for estimation of position control performance of machine tool feed drive, Precision Engineering (2019), https://doi.org/10.1016/j.precisioneng.2019.08.010

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Journal Pre-proof

Hardware-in-the-loop simulation for estimation of position control performance of machine tool feed drive Namhyun Kima, Hyunjung Kima, and Wonkyun Leea,*

a

Department of Mechanical Engineering, Chungnam National University, Daejeon

34134, Korea (e-mail: [email protected], [email protected], and [email protected])

*Corresponding author: [email protected]

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Abstract One of the most important measures for improving the performance of a machine tool is to set its controller parameters appropriately. The setting of these parameters is typically done by an expert when the machine tool is initially installed. Although parameter tuning is crucial when there is a change in the operation conditions, it is a challenge faced by non-experts as improper settings can result in critical problems in the machine tools. Simulation software, which estimate the control performance and identify appropriate parameters, can be used for the easy customization of these parameters. However, it is difficult to accurately model a commercial controller owing to its complex structure and several unreleased functions. This paper proposes a novel method that utilizes Hardware-In-the-Loop (HIL) simulation for estimating the position control performance of machine tool feed drives. HIL improves the simulation accuracy by integrating a real commercial controller into the simulation loop. The simulation error caused by the inaccuracy of the controller model is out of existence in the HIL simulation. The procedure of configuring the HIL simulation, from modeling and parameter identification of the machine tool feed drives, to organizing data exchange between the real controller and feed drive model, is extensively explained. The accuracy of the proposed HIL simulation is experimentally evaluated and applied for the estimation of position control performance, based on the controller parameters. The estimation of step response, failure mode, and effect analysis, as well as the evaluation of the control algorithm, are also performed using the HIL simulation. The results demonstrate that the HIL simulation can not only be used for the estimation of control performance but also for performance enhancement of machine tools. Keywords: HIL simulation, full-closed feedback; motion control unit; failure mode and effect analysis; gain tuning; feed drive model

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1. Introduction Precision metal cutting using a machine tool is a traditional and fundamental process in the manufacturing industry, especially for mold manufacturing. The application of this type of machine tools has increased rapidly since the early 2000s because the metal parts machined by the metal cutting process are commonly used for the final product [1]. The speed and accuracy of the machining process plays a major role in determining the productivity of the manufacturing process. To achieve high-speed machining with high accuracy, the position control performance of the machine-tool feed drive is required to be supported. The dynamic behavior of this drive greatly depends on how a motion controller is designed [2]. Appropriately setting of the controller parameters (e.g., controller gains, feedback control algorithm, filters, and optional functions) is a major contributor to the enhancement of machine tool performance [3]. Generally, a machine tool builder sets the controller parameters by considering the machining application and dynamic behavior of the feed drives as the final step of machine tool building. The initial set of controller parameters is not adjusted throughout the life of the machine tool. The machine tool is generally used for various machining applications, which have different machining conditions. Forced vibration or chatter, which causes serious deterioration in machining quality, is generated when the resonance frequency of the feed drive system, including the feedback control loop, is close to the frequency of the force generated by the cutting process or a self-oscillation of the driving parts [4]. These problems can be avoided by adjusting the controller parameters, as they are crucial in the determination of the frequency response characteristics of the feed drive system [5]. Moreover, during the lifetime of a machine tool, the deterioration of feed drive parts, such as a ball screw and a Linear-Motion (LM) guide, causes a change in its dynamic behavior. In addition, the structural deformation of the machine tool caused by continuous disturbance forces or changes in the environment alters the dynamics of the feed drive system [6]. For this, the controller parameters should be reset to maintain the performance of the machine tool. However, it is a challenge for the non-experts to identify suitable parameters for machine tools under varied conditions. The setting of inappropriate parameters can cause machine tool

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failure and deterioration of position control performance [7]. Simulation-based techniques for estimating the characteristics of the control system and utilizing the results for parameter tuning are a potential solution for the aforementioned problems. Younkin proposed a simulation technique to predict the performance of machine tool feed drives [8]. Procedures for modeling a commercial numerical controller and feed drive dynamics, including the effects of friction and backlash, were proposed, and the model was evaluated by comparing the transient response of the simulation result with that of real feed drives. Jeong et al. proposed a modelbased motor current prediction method [9]. A Computerized Numerical Control (CNC) and a feed drive system were modeled at the component level and combined to estimate the complex nonlinear dynamic behavior of the feed drives. The accuracy of the proposed method was verified by comparing the simulated driving current, position, and velocity to those of the actual feed drives. Pandilov et al. analyzed the influence of changing the controller parameters on the feed drive performance by using a virtual model of machine tools [10]. A simplified motion controller model composed of proportional-proportional-integral control loops and a multibody dynamic model of the feed drive system were used for the simulation. The position accuracy and dynamic stiffness were simulated and evaluated using the model. Sztendel et al. proposed a method to improve the dynamic performance of a 5-axis CNC machine tool based on a Software-In-the-Loop (SIL) simulation platform [11]. A motion controller and feed drive were modeled and operated in real-time to estimate the dynamic performance of the CNC machine tool. The aforementioned research demonstrated that the simulation model can be used to estimate the control performance and subsequently adjust the controller parameters. However, the reliability of the simulation result is highly dependent on the accuracy of the simulation model. Machine tool components can be divided into three parts, namely the controller, actuator, and auxiliary, for simulation modeling [12]. The actuator includes feed drives and a spindle, which exhibit complex dynamic behavior. Various studies for examining the modeling and parameter identification of the actuator have been proposed [13]. The auxiliary represents the parts of the machine tool in addition to the controller and actuator, such as the cutting-oil supplication system, chiller, and safety devices. It is modeled in a simple

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form owing to its insignificant impact on simulation accuracy. The controller contains a Programmable Logic Controller (PLC), a Numeric Control Kernel (NCK), and a Motion Control Unit (MCU) [14]. A PLC generates on/off signals to control the auxiliaries (e.g., pump, chiller, and LED). An NCK generates the reference position for each axis from the part program entered by an operator. It contains various functions to improve the tracking and contouring performances by adjusting the reference position. An MCU generates the driving command of each axis for eliminating the error between the reference and the actual positions. It contains various filters and control algorithms to improve the stability and accuracy of the feedback control [15]. These functions, filters, and control algorithms in the NCK and MCU are not released in detail because they are the core technologies of the controller. Thus, the controller model has limited accuracy as compared to the other available models for machine tool parts. This paper proposes a HIL simulation-based framework for estimating the position control performance of machine tool feed drives. Real controller hardware replaces the controller model to improve the simulation accuracy by eliminating the inaccuracy of the controller model [16, 17]. A feed drive system composed of a rotary motor, coupling, support bearings, a ball screw, LM guides, and a table is modeled considering the complicated dynamic characteristics caused by nonlinear friction, deflection of the coupling, and the ball screw. The feed drive model is implemented using a real-time computer connected to the controller. The accuracy of the HIL simulation is demonstrated by comparing the tracking performance of the feed drive system testbed with the simulation result. The HIL simulation is utilized to estimate the position control performance of the machine tool feed drive in accordance with the various controller gains. Furthermore, special situations expected to occur during signal transmission between the controller and feed drive are artificially generated using the HIL simulation to test the performance of the controller. Section 2 describes the construction and verification of HIL simulation in detail. In Section 3, various tests using verified HIL simulation are performed. The position control performances (e.g., step responses, performance of the full-closed feedback control algorithm, and failure mode and effect) in accordance with the

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various controller parameters are compared and discussed. Finally, Section 4 concludes the paper. 2. Construction of the HIL simulation This section explains the configuration and verification of the HIL simulation. The dynamic behavior of the feed drive system, including nonlinear friction and deflection of the coupling and ball screw, was modeled. A feed drive testbed was constructed and utilized to identify the feed drive model parameters. The procedure of modeling and parameter identification of the feed drive system is described in detail below. 2.1. Configuration of the HIL simulation Fig. 1 shows the configuration of the HIL simulation. The command voltage generated by a commercial motion controller (Clipper, Delta Tau) is gathered using the Analog-to-Digital Converter (ADC) of a real-time computer (Micro Lab Box, dSPACE). The position of the feed drive is simulated in real time based on the feed drive model and command voltage measured by the ADC. The position is converted into an incremental encoder signal with a resolution of 1 µm and transmitted to the controller through the digital Input Output (IO) of the real-time computer. The sampling and calculation frequency of the real-time computer is set at 80 KHz, which means that the allowable feed drive velocity of the proposed HIL simulation is 80 mm/s. 2.2. Feed drive modeling Fig. 2 shows the feed drive system used in conventional machine tools. Its dynamic behavior is modeled as follows: 𝑀𝑠𝑥 = 𝑢 ― 𝐹𝑓,

(1)

where 𝑀𝑠 denotes the total mass of the feed drive system, which contains the mass moment of inertia of the rotating parts (e.g., motor, support bearings, and ball screw) and the mass of the moving parts (e.g., table, ball screw nut, and LM guide blocks);

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𝑥 and 𝐹𝑓 represent the table position and the total friction force generated at the rolling contact components (e.g., bearing, ball screw, and LM guide).Then 𝑢 denotes the driving force generated by the motor that is derived as follows: 2𝜋 , 𝐿𝑏

𝑢 = 𝑉𝑡𝑐 × 𝐾𝑑 ×

(2)

where 𝑉𝑡𝑐 and 𝐿𝑏 represent the torque command voltage generated at the motion controller and the lead of the ball screw, respectively. 𝐾𝑑 is a parameter of the motor drive that represents the torque to voltage ratio. In this study, 𝐾𝑑 is set as 0.0637 Nm/V. The driving torque is converted to the driving force using the ball screw lead. The Stribeck curve model is utilized to estimate the friction force as follows [18]:

{ 𝑥 + {𝐹

)}

(when 𝑥 ≥ 0)

)}

(else)

(

|𝑥|

(

|𝑥|

𝐹𝑓 = 𝜇𝑣𝑝𝑥 + 𝐹𝑐𝑝 + (𝐹𝑠𝑝 ― 𝐹𝑐𝑝)exp ― 𝑣𝑠𝑝 , 𝐹𝑓 = 𝜇𝑣𝑛

𝑐𝑛

+ (𝐹𝑠𝑛 ― 𝐹𝑐𝑛)exp ― 𝑣𝑠𝑛 ,

(3)

where 𝜇𝑣𝑝, 𝐹𝑐𝑝, 𝐹𝑠𝑝, and 𝑣𝑠𝑝 indicate the viscous friction coefficient, Coulomb friction, break-away friction, and Stribeck velocity, respectively, when 𝑥 is positive, and 𝜇𝑣𝑝, 𝐹𝑐𝑝, 𝐹𝑠𝑝, and 𝑣𝑠𝑝 show the viscous friction coefficient, Coulomb friction, break-away friction, and Stribeck velocity respectively, when 𝑥 is negative. The disturbance force, including the inertial and friction forces, induces the torsional deflection of the coupling and ball screw. The disturbance force also causes an axial deflection of the ball screw. The deflection of the coupling and ball screw affects the actual position of the table. Therefore, the deflection of the coupling and ball screw are modeled and applied to the feed drive model. The total torsional deflection of the coupling and ball screw is calculated by dividing the driving torque by the torsional stiffness as follows: 𝐿𝑏

𝜃=

(𝑀𝑠𝑥 + 𝐹𝑓) ∙ 2𝜋 𝑘𝑡

,

(4)

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where 𝑘𝑡 represents an equivalent torsional stiffness of the coupling and ball screw, which can be calculated as follows: 𝑘𝑡𝑐 ∙ 𝑘𝑡𝑏

𝑘𝑡 = 𝑘𝑡𝑐 + 𝑘𝑡𝑏,

(5)

where 𝑘𝑡𝑐 and 𝑘𝑡𝑏 denote the torsional stiffness of the coupling and ball screw, respectively. The axial deflection of the ball screw is calculated by dividing the driving force by the axial stiffness of the ball screw, 𝑘𝑎𝑏, as follows:

𝛿𝑏 =

𝑀𝑠𝑥 + 𝐹𝑓 𝑘𝑎𝑏

.

(6)

The torsional and axial stiffness of the ball screw depends on the position of the ball screw nut to which the driving torque is applied. Thus, the torsional and axial stiffness of the ball screw are expressed as follows: 𝑘𝑡𝑏|𝑓𝑢𝑙𝑙

𝑘𝑡𝑏 = (𝐿𝑡 ― 𝑥),

(7)

and 𝑘𝑎𝑏|𝑓𝑢𝑙𝑙

𝑘𝑎𝑏 = (𝐿𝑡 ― 𝑥),

(8)

where 𝑘𝑡𝑏|𝑓𝑢𝑙𝑙 and 𝑘𝑎𝑏|𝑓𝑢𝑙𝑙 are the full length of torsional and axial stiffness of the ball screw, respectively, and 𝐿𝑡 represents the travel length of the feed drive system. Consequently, the change in the table position caused by the deflection of the coupling and the ball screw is calculated by combining Eqs. (4) − (8) as follows: 𝛿𝑡 = (𝑀𝑠𝑥 + 𝐹𝑓) ∙ [𝐶1 ∙ (𝐿𝑡 ― 𝑥) + 𝐶2],

(9)

where

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1

𝐶1 = 𝑘𝑡𝑏|𝑓𝑢𝑙𝑙 ∙

𝐿𝑏 2

( ) 2𝜋

1

+ 𝑘𝑎𝑏|𝑓𝑢𝑙𝑙,

(10)

and

1

𝐶2 = 𝑘𝑡𝑐 ∙

𝐿𝑏 2

( ).

(11)

2𝜋

2.3. Parameter identification The parameters of the feed drive model are identified experimentally by using the feed drive testbed. The feed drive with a stroke of 150 mm is composed of a ball screw (BNK1004, THK) with a diameter of 10 mm and a lead of 4 mm, and a set of LM guides (SSR15XW, THK). The feed drive is driven by a permanent magnet synchronous motor (SGM7J, Yaskawa) equipped with a 20-bit incremental encoder and a servo drive (SGD7S, Yaskawa). A linear scale (Tonic, Renishaw) with a resolution of 0.1 μm is used to measure the actual table position. Urea-based grease (AFA, THK) with a dynamic viscosity of 20 mm2/s is used to lubricate the ball screw and the LM guides. The commercial motion controller used for the HIL simulation is also used for the feed drive testbed. The torque command voltage generated by the motion controller is gathered using the ADC from the real-time computer. Four friction model parameters (𝜇𝑣, 𝐹𝑐, 𝐹𝑠, and 𝑣𝑠) are identified based on a genetic algorithm and the experimentally obtained Stribeck curve [19]. Fig. 3 shows the Stribeck curve of the feed drive system. The friction force is measured during reciprocal motion at 26 constant velocities in a range of 1 and 50 mm/s. The velocities are increased in steps of 0.5, 2, and 5 mm/s in the sections of the boundary (1 to 6 mm/s), fixed (7 to 23 mm/s), and full-film (25 to 50 mm/s) lubrication, respectively. The average friction torque at each velocity is calculated from the torque command voltage and converted to a linear force based on the ball screw lead. The cost function of the genetic algorithm-based optimization is defined as follows [19]: 𝑁

𝐽𝑜 = ∑𝑖 =𝑠 1𝑒𝑠𝑠2(𝑉𝑆,𝑥𝑖) + 𝑚𝑎𝑥{|𝑒𝑠𝑠(𝑉𝑆,𝑥)|},

(12)

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where 𝑉𝑆 = [𝐹𝐶 𝐹𝑆

𝑣𝑆

𝜇𝑣],

(13)

and 𝑁𝑆 is the number of points composing the Stribeck curve. 𝑒𝑠𝑠 is the steady-state identification error at table velocity 𝑥, and is defined as follows: 𝑒𝑠𝑠(𝑉𝑆,𝑥) = 𝐹𝑠𝑠(𝑥) ― 𝐹𝑠𝑠(𝑉𝑆,𝑥),

(14)

where 𝐹𝑠𝑠 is the experimentally measured steady-state friction force and 𝐹𝑠𝑠 is the estimated steady-state friction force calculated using Eqs. (1) − (3). The MATLAB Global Optimization Toolbox is used to set the genetic operators and optional parameters. The maximum generation, the number of iterations before the algorithm halted, is set to 500 for identification of the sliding friction parameters. The fitness limit, the value of the cost function that ended the generation, is set to 70. Table 1 lists the identified friction model parameters. A series of experiments are performed to identify the total mass, 𝑀𝑠, and two deflection model parameters (𝐶1 and 𝐶2). The total mass is calculated using Eq. (1) based on the torque command measured during acceleration. Fig. 4 shows the change in the table position caused by deflection of the coupling and ball screw, 𝛿𝑡, with respect to the initial table position measured during the constant velocity motion. The velocity and acceleration of the table are set as 100 mm/s and 200 mm/s2, respectively, for all experimental conditions. The deflection is derived from the difference between the table positions measured by the linear scale and the rotary encoder. Two deflection model parameters, 𝐶1 and 𝐶2, are derived as ―8.644 × 10 ―8 𝑠2 and 1.035 × 10 ―7 𝑠2/m, respectively, by fitting the result in Fig. 4 to the first-order polynomials. 2.4. Verification of HIL simulation The accuracy of the HIL simulation is evaluated by comparing the following errors of the HIL simulation and the actual feed drive testbed during reciprocal motion at

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various conditions. The same part program and controller parameters are used for both the HIL simulation and the testbed. Fig. 5 shows the position and following error of the testbed and HIL simulation during reciprocal motion in accordance with various acceleration times, Ta, and target velocities, V. The peak and Root-MeanSquare (RMS) values of the following error are presented in Table 2. The result shows that the HIL simulation reflects the position control performance of the real feed drive testbed accurately. 3. Estimation of position control performance The application of inappropriate controller parameters or a control algorithm can lead to the deterioration of machine tool performance. For this, the proposed HIL simulation can be utilized to test the machine tool performance, without the occurrence of the aforementioned problems. This section describes the application of the HIL simulation for the estimation of position control performance. 3.1. Step response The proper setting of controller parameters with respect to the control system plays a key role in determining the performance of the position controller. Calculating the controller gains based on the dynamic model of the feed drive system is a traditional way of designing a control system [20]. However, this method is difficult to apply for tuning the commercial controller owing to the complexity of the feedback control system. The position and velocity control loops are usually operated in different devices with different cycle times. Moreover, various filters are applied to both input and output lines to protect the control system from external noise. Therefore, the experts set the controller parameters by considering the operation conditions of the machine tools. Changing the controller parameters requires expertise because improper gains can lead to serious problems in machine tools by deteriorating the stability of the control system. The HIL simulation is an effective method for testing the position control performance of the feed drives in accordance with the controller parameters. A step response is an important factor in the identification of the appropriate controller parameters, because it shows the position control performance in terms of the response speed, overshoot, and settling time of the control system.

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Fig. 6 (a) compares the step responses to the controller parameters using the HIL simulation. The best gains derived from the HIL simulation are applied to the feed drive testbed. Fig. 6 (b) compares the step responses of the HIL simulation with the feed drive testbed. The results demonstrate that the HIL simulation can be used to identify the appropriate controller parameters. 3.2. Failure mode and effect analysis Unpredictable accidents that occur during machining (e.g., collision and communication error) can lead to severe failures of machine tools. With regard to this, a commercial CNC controller exhibits a function of detecting and responding to the failure of protecting the machine tools from unpredictable accidents. However, it is difficult to test the aforementioned function because reproducing artificial failure during the machining process can severely damage the machine tools. In this case, HIL simulation can be used for estimating the manner in which the machine tool responds in the event of failure without damaging the machine tools. Two types of failures, i.e., collision and communication error, in position feedback signals are artificially generated in a virtual environment by adjusting the feed drive model. Fig. 7(a) shows the position, following error, and command voltage of the feed drive when a collision occurs. The driving current generated from the motor drive is set to zero during motion. The following error and command voltage are increased immediately after the collision occurs. The controller detects the failure and kills the control loop when the following error exceeds the following error limit. Fig. 7(b) shows the results when a communication error occurs in the position feedback signals. The encoder signals generated from the encoder model are set to zero during motion. Similar to the response of the collision, the following error and command voltage are increased until the controller recognizes the failure. Simultaneously, the feed drive moves by approximately 225 mm until the controller recognizes the failure, because the command voltage is applied to the motor drive consistently. 3.3. Feedback control system Figures 8(a) and (b) illustrate the semi and full-closed loops, respectively. These are the two common configurations of the feedback control system of the machine tool

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feed drives. In the semi-closed loop, the angular position of the motor measured by a rotary encoder is used to derive the position and velocity of the table. In this case, the change in the table position caused by the deflection of the coupling and ball screw is not recognized by the feedback control system. Therefore, the accuracy of the table position is degraded in a region where the deflection of the coupling and ball screw is large. In the full-closed loop, on the other hand, a separate detector is utilized to directly measure the actual table position, which is referred to as the position control loop, whereas the table velocity calculated from the angular position of the motor is used in the velocity control loop. The change in the table position caused by the deflection of the coupling and ball screw can be compensated in the full-closed loop. The HIL simulation is used to compare the performances of the semi- and full-closed loops. The change in the table position, 𝛿𝑡, is calculated using the deflection model derived in Section 2 and added to the angular position of the motor to derive the actual table position. Fig. 9 shows the position, deflection of the table, and following error estimated by the HIL simulation during sinusoidal motion with an amplitude of 50 mm and a period of 2π s. The peak value of the following error is reduced from 598.9 to 571 μm after the application of the full-closed loop. The result shows that the full-closed loop can achieve higher position accuracy when compared to the semi-closed loop. However, the performance of the full-closed loop can deteriorate when the reliability of the actual position measured by a separate detector is degraded, due to noise or time delay. The effect of time delay on position control performance is tested using the HIL simulation. An artificial time delay is applied to the feedback signal of a separate detector (i.e., actual table position) in the virtual environment. Fig. 10 shows the result of the HIL simulation when the time delay is increased in steps of 1.25 ms in the range between 0 and 5 ms. The result shows that the time delay on the feedback signal causes vibration during the full-closed loop. The position control performance of the full-closed loop becomes worse than that of the semi-closed loop when the time delay exceeds 2.5 ms. 4. Conclusion

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This paper proposes a method to estimate the position control performance of machine tool feed drives based on a HIL simulation. The configuration of the HIL simulation, from modeling of the feed drive components to data exchange, is explained in detail. The accuracy of the HIL simulation is evaluated experimentally to verify the proposed modeling procedure. The HIL simulation is utilized to estimate the step response, failure mode, effect analysis, and to evaluate the feedback control system. 1) The step responses of the feed drive with respect to various sets of controller parameters are compared, to show that the HIL simulation can be used to identify appropriate controller parameters without the risk of the feed drives becoming unstable due to improper gain setting. 2) The failure mode and effect analysis based on the HIL simulation shows that the HIL simulation can be used to test how the machine tool responds when extreme situations occur. 3) A comparison of the feedback control algorithm reveals that the HIL simulation can be used to test the application of a new control algorithm before applying it to real machine tools. The results show that HIL simulation can be applied not only to estimate control performance but also to improve machine tool performance.

Acknowledgments This work was supported in part by research fund of Chungnam National University and in part by Korea Institute of Machinery and Materials for the project, “Development of Technology for Mobile Platform-based Machining System” (No. NK210B).

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18. W. Lee, C.-Y. Lee, Y. H. Jeong, and B.-K. Min, Friction compensation controller for load varying machine tool feed drive. International Journal of Machine Tools and Manufacture, 96, pp. 47-54, 2015. 19. W. Lee, C.-Y. Lee, Y. H. Jeong, and B.-K. Min, Distributed component friction model for precision control of a feed drive system. IEEE/ASME Transactions on Mechatronics, 120 (4), pp. 1966-1974, 2015. 20. P. Van Den Braembussche, J. Swevers, H. Van Brussel, and P. Vanherck, Accurate tracking control of linear synchronous motor machine tool axes. Mechatronics, 6 (5), pp. 507-521, 1996.

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Analog voltage (torque command) 6

ADC

Velocity[mm/s]

5

4

3

Feed drive model

2

1

0 0

0.5

1

1.5

2

2.5

Time[s]

DAC Encoder interface

Digital voltage (Encoder signal)

Motion controller

Digital I/O

Encoder model

Real-time computer

Fig. 1. Configuration of HIL simulation.

Axial stiffness Torsional stiffness

x

Motor Coupling Bearing Nut Table Ball screw Bearing

(a)

Motion controller

Servo drive

Feed drive

(b) Fig. 2. Feed drive testbed: (a) schematic diagram and (b) photo.

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100 75

Friction (N)

50 25 Measured Estimated

0 -25 -50 -75

-100 -15

-10

-5

0

5

10

15

Velocity (mm/s)

Fig. 3. Stribeck curve of the feed drive system.

Fig. 4. Change in table position caused by the deflection of the coupling and ball screw.

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Fig 5. Comparison of the HIL simulation and the actual feed drive testbed during reciprocal motion with various conditions: (a)-(c) position and (d)-(f) following errors.

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(a)

(b) Fig. 6. Step responses of the feed drives: (a) HIL simulation results with respect to the various controller parameters, (b) comparison of feed drive testbed and HIL simulation result at Gain2.

21

12 23 34 45

Time 1 2 2(s) 3 34 45 12 23 34 45

12 23 34 45 12 23 34 45 3 34 45 1 2 2(s) Time

12 23 34 45 12 23 34 45 12 23 34 45

Time (s)

250250 200 250 250200 150 200 200150 250 250 100 150 150100 200 200 50 50 100 100150 150 0 0 50 50100 100 5 50 00 1 0 050 51.5 0 00 1 0 1.5 0 10 1 51.5 1 1.5 1.5 0.5 0.5 1 1.5 1 1 10 0 0.5 0.5 0.5 0.5 -0.5 0-0.5 0 5-0.50-0.5 0 00 1 010 0 1 5-0.5 10-0.5 0 01 57.5 7.5 10 10 5 5 7.5 7.5 10 10 2.5 5 2.5 5 7.5 7.5 0 0 2.5 2.5 -2.550-2.550 2.5 2.5 5-2.5-2.5 0 01 0 0 0 01 5-2.5-2.5 5 0 01

Position (mm)

Failure

Fol. error (mm)

20 20 15 20 20 15 20 10 10 20 15 15 15 5 5 15 10 10 10 0 10 50 5 5 0 0 50 0 1 1.5 0 00 1 0 1.5 0 10 1 1 1.5 1.5 1.5 0.5 0.5 1 1.5 1 1 10 0 0.5 0.5 0.5 0.5 -0.5 0-0.5 0 0 00 1 -0.50-0.5 010 0 1 -0.5 10-0.5 0 01 7.5 10 7.5 10 5 5 7.5 7.5 10 10 2.5 2.5 5 7.5 5 7.5 0 0 2.5 2.5 -2.550-2.550 2.5 2.5 0 01 -2.50-2.5 0 0 01 -2.5-2.5 0 01

Command (V)

Command (V)

Fol. error (mm)

Position (mm)

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Failure

12 23 1 2 Time 23 12 23

34 45 5

(s) 34 45 5 34 45 5

12 23 34 45 5 12 23 34 45 5 1 2 Time 2 3 (s) 34 45 5

12 23 34 45 5 12 23 34 45 5 12 23 34 45 5

(a)

Time (s)

(b)

Fig. 7. Position, following error, and command voltage of feed drive when the failure occurs at 5 s: (a) collision and (b) communication error.

Reference position

Position control loop

Velocity control loop

Motor

Velocity feedback Position feedback

(a) Reference position

Position control loop

Velocity control loop

Motor

Separate detector

Velocity feedback Position feedback

(b) Fig. 8. Two common configurations of the feedback control system of machine tool feed drives: (a) semi- and (b) full-closed loops.

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50

Position (mm)

0

50 -50 0

1 -1

1

1.5

2

2.5

0

0.5

1

0

0.5

1

-1 00

0.5

1

0 50

50 -50 0 0 0

0.5

1

1.5

2

(a)

0

3

3.5

Semi-closed loop Full-closed loop

2

2.5

3

3.5

1.5

2

2.5

3

3.5

1.5

2

2.5

3

3.5

4

2 2.5 2.53

33.5

3.5 4

Time (s) 0.5 0.5

11

(b) 1.51.5 2

Semi-closed loop Full-closed loop

0 1.6 -0.45 -0.5 -0.55 -0.6

50

3.5

1.5

0.5 0.4

0

2.5

Time (s)

10.6

-1

3

Semi-closed loop Full-closed loop

-50 -50 0 0

Fol. error (mm)

0.5

1 -50 0

Deflection (μm)

0

1.7

1.2

1.3 0.5

1.8

1.4

1

1.5

2

2.5

3

3.5

Time (s)

(c)

Fig. 9. HIL simulation result of semi- and full-closed loops during sinusoidal -50

motion: (a) position, (c) following error. 0 (b) 0.5deflection 1 1.5 of 2the table, 2.5 3and 3.5 4

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1 1 1 0 0 0 -1 -1 -1

1 1 1 0 0 0 -1 -1 -1

0 0 0

0 0 0

Fol. error (mm) 1 2 1Time 2(s) 1 2

3 3 3

delay 1.25[msec] delay 1.25[msec] delay 1.25[msec]

1 2 1 2 1Time 2(s)

3 3 3

delay 3.75[msec] delay 3.75[msec] delay 3.75[msec]

1 1 1

2 2 2

Time (s)

3 3 3

Fol. error (mm)

50 50 50 0 0 0 -50 -50 0 -50 0 0

Fol. error (mm)

Fol. error (mm)

Fol. error (mm)

Position (mm)

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1 1 1 0 0 0 -1 -1 -1

1 1 1 0 0 0 -1 -1 -1

1 1 1 0 0 0 -1 -1 -1

No delay No delay No delay

0 0 0

1 2 1Time 2(s) 1 2

3 3 3

0 0 0

1 2 3 1 2 3 1Time 3 delay2(s) 5.00[msec]

0 0 0

1 1 1

delay 2.50[msec] delay 2.50[msec] delay 2.50[msec]

delay 5.00[msec] delay 5.00[msec]

2 2 2

Time (s)

3 3 3

Fig. 10. Result of HIL simulation when the feedback signal of the actual position is delayed.

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Table 1. Identified friction model parameters.

Symbol (units)

Positive direction

Negative direction

𝐹𝑐 (N)

61.5

-59.2

𝐹𝑠 (N)

78.1

𝑣𝑠 (m/s) 𝜇𝑣 (N s/m)

1.02 × 10

-84.3 ―3

1.42 × 103

-9.83 × 10 ―4 1.48 × 103

Table 2. The peak and RMS values of the following errors.

Conditions

HIL Simulation

Testbed Peak (μm)

RMS (μm)

Peak (μm)

RMS (μm)

V=3.6mm/s, Ta=200ms

39.39

10.41

43.64

9.9

V=5.7mm/s, Ta=200ms

48.05

13.19

52.65

14.57

V=5.7mm/s, Ta=50ms

60.07

14.92

78.45

16.76

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• HIL simulation is used to estimate and evaluate the position control performance. • Configuration of the HIL simulation, from modeling to data exchange, is explained. • HIL simulation is used to find the appropriate controller parameters. • HIL simulation is used for failure mode and effect analysis in virtual environment. • HIL simulation is used to evaluate semi- and full-closed loops at various situations.

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