ZHOU Yu-qing (周玉清), MU Yong-min(母勇民), LIU Jian-shu(劉建書),2, ZHANG Yun (章 云)

1 Xi’an Institute of Modern Control Technology, Xi’an 710069, China 2 Department of Automation, Tsinghua University, Beijing 100084, China 3 School of Mechanical Engineering, Xidian University, Xi’an 710071, China

Rapid Evaluation for Feed-axis Lubrication Condition Based on Soft Sensor

ZHOU Yu-qing (周玉清)1,2*, MU Yong-min(母勇民)1, LIU Jian-shu(劉建書)1,2, ZHANG Yun (章 云)3

1Xi’anInstituteofModernControlTechnology,Xi’an710069,China2DepartmentofAutomation,TsinghuaUniversity,Beijing100084,China3SchoolofMechanicalEngineering,XidianUniversity,Xi’an710071,China

Stribeck effect is regarded as the most important feed-axis friction characteristics. According to the relationship between friction and lubrication, a rapid technology for feed-axis lubrication condition evaluation of computer numerical control (CNC) machine tools based on soft sensor is proposed. To obtain its state information, the static friction force, Coulomb friction force, and viscous coefficient are used as the key parameters of the soft sensor for tread analysis. Then the various amplitude and velocity triangular wave test curve, and a precise nonlinear model identification method are presented. The results of the experiments analysis show that this method is feasible and reliable for evaluating feed-axis lubrication condition, which lays the foundation for on-line condition monitoring and reliability evaluation for feed-axis lubrication of machine tools.

machinetoolfeedaxis;softsensor;lubricationcondition;Stribeckeffect;reliability

Introduction

Feed-axis lubrication condition has a great influence on the reliability of computer numerical control (CNC) machine tool.The feed-axis mechanical parts will suffer from some problems, such as pitting, corrosion, wear, and crack in the bad lubrication state. As a result, serious Stick-slip phenomenon will be produced under low-speed and heavy-load condition[1]. And the bad lubrication state may lead to the part oscillations of feed-axis control system. Besides, it will result in motion error or accident standing, and shortens life expectancy[2]. Therefore, it is necessary to investigate on rapid technology for feed-axis lubrication condition evaluation of machine tool, and then estimate the lubrication state of the mechanical parts correctly[3-7].

To solve the above-mentioned problems, the information of lubrication state should be known in advance. Now, some sensors such as vibration, temperature, acoustic emission (AE), and oil sample have been used to obtain the lubrication state information[8]. These methods can work accurately based on the technology of Ferro graphic analysis, spectra analysis, physical and chemical properties of oil samples, magnetic Cypriot technology, image processing,etc. However, they still possess such inherent limitations as high cost, inconvenience mounted, and high bandwidth. Thus, it is not proper to be used as the lubrication state observation method of machine tool feed axis. Soft sensor has been widely used in industry fields[9]. And Stribeck effect is regarded as the important friction characteristics of feed axis. According to its relationship between the friction and lubrication, Coulomb friction force and viscous coefficient can be used as the key parameters of the soft sensor for tread analysis. Besides, these key parameters can be identified by the information coming from the built in-sensors such as motor current hall sensors and encoder[10]. And it is simple, and no extra sensors are needed, which facilitates online monitoring of feed-axis state through net. As a result, a kind of rapid technology for feed-axis lubrication condition evaluation of CNC machine tool based on soft sensor is proposed in this text.

1 Test Principle

1.1 Stribeck effect

Stribeck effect consists of three phases: boundary friction, mixed friction, and viscous friction. According to Stribeck model, the relationship between the friction and velocity in the steady-state movement can be expressed as Eq. (1).

(1)

wherev,Fc,Fs,σ, andvsare instantaneous velocity, Coulomb friction, static friction, viscous friction coefficient, and Stribeck boundary velocity, respectively.

1.2 Feed-axis lubrication condition evaluation principle

Stribeck effect is used mainly in the field of high-precision CNC machine tool nonlinear control and seldom to assess the state of lubrication[11-14]. However, some experimental results show that the greater the value of static friction force is, the worse the feed-axis lubrication condition will be, and the bigger the Stick-slip error will be; the smaller the value of viscous friction coefficient is, the better the feed-axis lubrication condition will be, and the few the Stick-slip error will be[15]. Therefore, if Stribeck model parameters are obtained, then the static friction, Coulomb friction, and viscous friction coefficient can be used as the key parameters of the soft sensor (see Eq. (2) and Figs.1 and 2) for trend analysis to reflect feed-axis lubrication condition, which can help the user to make relevant decisions.

Fig.1 Stribeck model

Fig.2 Tread analysis of lubrication state

(2)

whereσt i,Fcti, andFstiare the measured values at the certain time, respectively.

2 Parameters Identification of Soft Sensor

Evidently, parameters identification of the soft sensor is the important step for the tread analysis of feed-axis lubrication state, which is on the basis of the obtained state information.

2.1 Methods to obtain state information

Because the feed axis consists of some built-in sensors such as motor encoder, hall current sensors, and grid scale, the state information can be obtained through the special original equipment manufacturer (OEM) soft or the special testing system.

For the feed-axis control systems including servo amplifiers and servo motor, the mathematical torque can be simplified as follows:

(3)

whereT,J, andLare alternating current (AC) servo motor output torque, the total moment of inertia, and the pitch of the ballscrew, respectively. The total disturbance torque is composed of two parts: cutting torqueτcand friction torqueτf.

T=τf.

(4)

As shown in Eq. (4), the feed-axis friction force can be obtained under constant speed and no-load test condition.xis the feedback position by the grid scale or motor encoder. Supposing the sampling period isPand the sampling total number isN, the instantaneous velocity can be expressed as Eq. (5). Similarly, the instantaneous accelerationajis written as Eq.(6).

(5)

(6)

2.2 Parameters identification

2.2.1 Traditional Stribeck parameters identification

Traditional Stribeck parameters identification are based on Eq. (4). To separate the parameters, the constant speed and no-load test in short travel must be carried out ranging from 20 to 40 groups. Although the method works well, it is very cumbersome and time-consuming. As a result, it doesn’t meet the requirements of the user in the industry field.

2.2.2 Rapid parameters identification

As shown in Eq. (7), if we use the various velocity that changes with the test travel, and record the feed-axis servo motor output torque, the position feedback by motor encoder or grid scale, then calculate the instantaneous velocity and instantaneous acceleration according to Eqs. (5) and Eq. (6) so that the Stribeck parameters can be identified as fast as possible. Although the method is rapid and simple, two key problems must be solved: firstly, the test velocity must be planned reasonably; secondly, there are unknown nonlinear parameters such asFc,Fs,σ,vsandJmust be identified accurately.

(7)

(1) Testing route planning

The used various velocity test curves are triangular wave, square wave, sine, chirp curve, and so on. In this text,the various velocity and amplitude triangular wave test curve as shown in Fig.3 and Eq. (8) is selected, which is easy to program.

(8)

wherei=0, 1, 2, …，N-1,P,V,T,Vmax, andγiare the maximum test travel, the maximum test velocity, the sampling period， the maximum feed-axis velocity, and the tune coefficient, respectively.

Fig.3 Various amplitude and velocity triangular wave test curve

(2) Nonlinear model identification

The parameters are obtained by the least square method (LSM). The Eq. (7) can be written as Eq. (9).

(9)

Based on the LSM, some equations can be expressed as follows:

A=B-1H.

(10)

In Eq. (10), we can obtain the values of the parameters.

3 Experiment Research

3.1 Experimental platform

The experimental platform isY-axis of a milling machining center named VTM180. For each linear axis, it is driven by a servomotor, a reducer, and a ballscrew, and the pitch of ballscrew is 0.016 m. The using numerical control system is Siemens 840D with closed-loop position control.

3.2 Experimental analysis

With a travel of 0.12 m and 8 different velocities, the rapid identification experiments of Stribeck model parameters aboutY-axis were carried out (see Fig.4(c)). To verify the proposed rapid identification method, the traditional identification experiments are also comparatively implemented, and the velocity range -10-+10 m/min is divided into 28 groups (see Table 1). Furthermore, motor output torque and the feedback position by the line scale are collected simultaneously with the sampling frequency 83.33 Hz in rapid or traditional experiments.

The parameters are separated using the proposed rapid identification method in Section 2. Based on the feedback position, motor output torque and sampling frequency, the instantaneous velocity (see Fig.4(b)), the instantaneous acceleration (see Fig.4(c)) and torque (see Fig.4(d)) are obtained, respectively. According to Eqs. (9) and (10), the static frictionFs, Coulomb frictionFcand viscous friction coefficientσare identified. AndFs=Fc=4.45 N·m,σ=19.08 N·s. Furthermore, as shown in Fig.4(d), the calculated torque has been obtained, and the calculated torque using Eq.(7) matches well with the measured motor output torque, which shows the effectiveness of the proposed identification method.

Figure 4(e) shows the Stribeck friction curves ofY-axis on the basis of the rapid and traditional identification methods (see Table 1). For the result of traditional experiments, it describes clearly three friction phases, whereHS(-10--1.12 m/min) andFG(+1.12-+10 m/min) are the vicious frictions,SF(-1.12-+ 1.12 m/min) is the mixed and boundary friction. But the mixed friction phaseSCandEFare too small to be seen, the reason lies in that hydrostatic slide is used as the feed axis in this machine tool. From the results of rapid experiments, since the phases of the planned velocities are few, only the boundary friction (pointsEandD) and the viscous friction (GEandHD) can be observed. However, the identified Stribeck curves through rapid and traditional experiments are very similar, which shows that it is feasible and effective to use the proposed rapid identification method to separate the parameters.

Table 1 Velocities and measured motor output torque in traditional identification experiments

(a) Measured travel

(b) Instantaneous velocity

(c) Instantaneous acceleration

(d) Measured torque and calculated torque

(e) Identified curves

(f) Evaluation for Y-axis lubrication conditionFig.4 Key parameters identification of Stribeck effect and evaluation for Y-axis lubrication Condition

To effectively track the dynamic variation of the lubrication state of theY-axis, the tests were performed for every certain space of time, and the lubrication trend is analyzed based on the two main parameters static friction torque and viscous friction coefficient, by which the early lubrication fault can be found. Figure 4(f) shows the measurement result for a machine tool carried out for every week in about three months. It can be seen that the static friction torque varies between 4.01-5.13 N·m and the viscous friction coefficient changes between 16.73-24.36 N·s, and both variations are little, which implies that the lubrication states are stable during this time.

4 Conclusions

Based on the theoretical and experimental analysis, a new rapid evaluation method for the feed system lubrication state of CNC machine tool is investigated, and the following conclusions are made.

(1) The proposed method is simple, and no extra sensors are needed, which facilitates online monitoring of the machine tool state through net. The feasibility and the effectiveness of the proposed approach have been verified by experiments.

(2) The rapid evaluation results of lubrication state are greatly influenced by the velocity and the displacement, that is, the evaluation result is more accurate if the travel is shorter and the velocity is adjusted more precisely.

[1] Yeh S S, Sun J T. Friction Modeling and Compensation for Feed Drive Motions of CNC Milling Machines[J].JournaloftheChineseSocietyofMechanicalEngineers, 2012, 33(1): 33-49.

[2] Yang Z J, Chen C H, Li G F,etal. Research on Reliablity Analysis for Machine Tools [C]. 2013 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE), Dalian, China, 2013: 173-177.

[3] Munzinger C, Fleischer J, Broos A,etal. Development and Implementation of Smart Maintenance Activities for Machine Tools [J].CIRPJournalofManufacturingScienceandTechnology, 2009, 1(4): 237-246.

[4] Huo F, Poo A N. Precision Contouring Control of Machine Tools[J].InternationalJournalofAdvancedManufacturingTechnology, 2013, 64(1/2/3/4): 319-333.

[5] Tsutsumi M, Tone S, Kato N,etal. Enhancement of Geometric Accuracy of Five-Axis Machining Centers Based on Identification and Compensation of Geometric Deviations[J].InternationalJournalofMachineToolsandManufacture, 2013, 68(5): 11-20.

[6] Law M, Altintas Y, Phani A S. Rapid Evaluation and Optimization of Machine Tools with Position-Dependent Stability[J].InternationalJournalofMachineToolsandManufacture, 2013, 68(5): 81-90.

[7] Verl A, Frey S, Heinze T. Double Nut Ball Screw with Improved Operating Characteristics[J].CIRPAnnals—ManufacturingTechnology, 2014, 63(1): 361-364.

[8] Ebersbach S, Peng Z, Kessissoglou N J. The Investigation of the Condition and Faults of a Spur Gearbox Using Vibration and Wear Debris Analysis Techniques[J].Wear, 2006, 260(1/2): 16-24.

[9] Reda S, Cochran R J, Nowroz A N. Improved Thermal Tracking for Processors Using Hard and Soft Sensor Allocation Techniques [J].IEEETransationsonComputers, 2011, 60(6): 841-851.

[10] Zhou Y Q, Tao T, Mei X S,etal. Feed-Axis Gearbox Condition Monitoring Using Built-in Position Sensors and EEMD Method [J].RoboticsandComputer-IntegratedManufacturing, 2011, 179(4): 785-793.

[11] Huang S N, Tan K K. Intelligent Fusion Modeling and Compensation Using Neural Network Approximations [J].IEEETransactionsonIndustrialElectronics, 2012, 59(8): 3342-3349.

[12] Zhou Y, Peng F Y, Wang G X. A Study on the Dynamic Characteristics of the Drive at Center of Gravity (DCG) fFeed Drives[J].TheInternationalJournalofAdvancedManufacturingTechnology, 2013, 66(1/2/3/4): 325-336.

[13] Hanifzadegan M, Nagamune R. Switching Gain-Scheduled Control Design for Flexible Ball-Screw Drives[J].JournalofDynamicSystems,Measurement,andControl, 2013, 136(1): 71-75

[14] Gordon D J, Erkorkmaz K. Accurate Control of Ball Screw Drives Using Pole-Placement Vibration Damping and a Novel Trajectory Prefilter[J].PrecisionEngineering, 2013, 37(2): 308-322.

[15] Mei X S, Tsutsumi M, Tao T,etal. Study on the Compensation of Error by Stick-Slip for High-Precision Table [J].InternationalJournalofMachineToolsandManufacture, 2004, 44(5): 503-510.

Foundation item: National Natural Science Foundation of China (No. 51305324)

1672-5220(2014)06-0843-04

Receiveddate: 2014-08-08

* Correspondence should be addressed to ZHOU Yu-qing E-mail: zhouyuqing66@aliyun.com

CLC number: TP182 Document code: A