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Backlash Detection in CNC Machines Based on Experimental Vibration Analysis

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Backlash Detection in CNC Machines Based on Experimental Vibration Analysis Backlash Detection in CNC Machines Based on Experimental Vibration Analysis S. Ali A. Moosavian Ebrahim MohammadiAsl Department of Mechanical Engineering Department of Maintenance K. N. Toosi Univ. of Technology Mapna Turbine Manufacturing Co. (TUGA) Tehran, Iran Karaj, Tehran, Iran [email protected] [email protected] Abstract—Exploiting backlash free mechanisms and 5]. Information about the size of the backlash is also needed. In gearboxes, the stiffness of servo axes in CNC machines can be the case of known backlash, a backlash compensating improved. In fact, the rigidity of these axes will be increased, so controller can guarantee exact output tracking. When the that different types of feed-forward control can be implemented. backlash characteristics are unknown, adaptive laws have been Furthermore, backlash free mechanisms facilitate designing proposed to update the controller parameters and to guarantee foolproof systems without challenging with the instability and bounded input-output stability, [6-7]. nonlinear behavior of backlash. However, any mechanical failure and looseness causes backlash which in turn may lead to severe Introducing a smooth inverse function of the backlash and vibrations. So, backlash detection and exploiting efficient using that in the controller design with back stepping preventive maintenance (PM) to prevent interrupt in the technique, a backlash compensator has been proposed, [8]. For production line is of interest. In this paper, first a simple model the design and implementation of this controller, no knowledge for mechanical system of a CNC servo axis, and its control system is assumed on the unknown system parameters. Backlash will be presented. This reduced order system for speed control compensators have been also proposed using dynamic will be detailed. Next, the bandwidth of vibration frequencies due inversion by the fuzzy logic, [9]. The classification property of to backlash is estimated and behavior of a servo axis with various fuzzy logic systems makes them a natural candidate for the backlashes is simulated. Then, to encapsulate the role of backlash rejection of errors induced by the backlash, which has regions in different conditions, performance response of five in which it behaves differently. An adaptation algorithm can be mechanically different axes with different servo gains in various developed to estimate the backlash parameter online, and under CNC machines are empirically investigated. These experimental certain conditions a fuzzy compensator with the adaptation frequencies of vibration obtained in completely different CNC machines (small, medium and heavy size) are compared with algorithm guarantees that the backlash output converges to the those estimated. Simulation and experimental results show that desired trajectory, [10]. Extending the dynamic inversion the frequency of vibration in a servo axis with backlash is not technique to discrete-time systems by using a filtered affected by the value of backlash, while the position control gain prediction, and using a neural network for inverting the dictates this frequency. Finally, an experimental equation will be backlash nonlinearity in the feedforward path, an algorithm has developed that estimates this frequency for various CNC been proposed for backlash compensation that guarantees machines. bounded tracking errors, and also bounded parameter estimates, [11]. Keywords—Backlash, CNC machines, Vibration Analysis. In industrial CNC machine tools, to have an accurate I. INTRODUCTION finished surface, both exact positioning and smooth movement with low contour deviations are demanded. On the other hand, Backlash causes inaccurate motion, and extraordinary progress in providing high speed milling and grinding spindles vibration which imposes severe limitations on the quality of (with the aim of exploiting ceramic/ hydrostatic bearings), and control. This will damage the power transmission train parts, improvement in cutting materials have facilitated producing thus various techniques have been suggested for backlash high quality finished surfaces with high speed servo axis. detection and estimation, [1-2]. Simple models of mechanical Backlash free mechanisms (like double nut screws, double backlash found in the control system literature ignore the pinion gearbox, etc.) have perfect linear dynamics, and enable impact behavior that dominates motion at low amplitudes. As a us to fulfill all aforementioned demands. However, in the case result, such models can not characterize the low-amplitude of small backlash that is rising from worn mechanical parts, an limit cycle oscillations that occur in closed-loop control uncontrolled nonlinearity will impose to the system that distorts systems. Therefore, a more realistic model of mechanical the dynamic behavior of the axis and disturbs its expected backlash should incorporate visco-elastic contact forces smooth movement. In this paper, first a reduced order model of between the two masses, [3]. On the other hand, for backlash the mechanical system of a servo axis will be introduced, and compensation, high-performance controllers require high- an ordinary CNC control system will be reviewed. The quality measurements of the current state of the power train, [4- response of speed and current control for the mechanical 978-1-4244-1676-9/08 /$25.00 ©2008 IEEE RAM 2008 vibration will be discussed. Next, based on the experimental results of five mechanically different axes (with different servo τ l 1 v2 gains), a simple model of backlash is illustrated and the bandwidth of vibration frequency due to backlash is estimated. Jl s Then, the effect of value of backlash on a servo axis is simulated and the experimental frequencies of vibration in cs τ − various CNC machine tools (small, medium and heavy size) are s compared with the estimated frequencies. δ 1 1 k ks II. AXIS MECHANICAL MODEL r s τ Backlash between mechanical parts may take place due to d τ − m ω v1 failure or looseness, wear, etc., which imposes nonlinearity to 1 m 1 the system. Basically, in a critical condition backlash leads to Jm s kr vibration when desired acceleration is zero (speed is constant) and movement is not affected by the gravity. The result would Figure 1. Axis model block diagram be wasted surface finish, broken cutting tool, damaged ω = ξ = mechanical elements of axis, which in turn increases backlash. n ks Jl and cs (2 ks Jl ) Therefore, detection, and control of backlash becomes significantly essential especially for CNC machine tools that III. AXIS CONTROL SYSTEM the default assumption is a backlash free mechanical The software of the investigated CNC machine tools is mechanism. Siemens SINUMERIC 840D that implements a cascade control In a CNC machine, each axis composed of different system including three main parts: position controller (P), mechanical parts like coupling, gears, lead screw, etc. that have speed controller (PI) and current controller (PI), where actuator different mechanical properties. All of these elements can be is a permanent magnet synchronous motor (AC servo motor). modeled as a set of springs and dampers, while the more Fig.2 shows the simplified block diagram of a servo axis closed elements we take the more resonance frequencies will exist. loop control system. Various parameters and signals in this However, in most cases the servo axis can be modeled based on block diagram are defined as: the lower resonance frequency, and the other elements can be x : setting position from interpolator ignored or assumed to be rigid. In Fig.1 a reduced order of d mechanical model is illustrated where: xact : axis actual position measured by direct encoder τ : load torque l e : following error τ d : reaction of axis on motor τ k : position control gain m : motor torque v J m : moment of inertia of the motor including its gears or kr : ratio between motor speed and axis speed coupling nset : setting speed of motor J l : moment of inertia of the load nact : actual speed of motor measured by motor encoder v1 : velocity of axis obtained from motor side ksp : speed controller proportional gain v2 : velocity of axis directly obtained Tsi : speed controller integrator time k s : stiffness of axis τ set : setting torque cs : damping of axis iset : setting current k r : ratio between motor speed and axis speed i : actual (measured) current δ : amount of backlash act ω : speed of motor Also the servo axis is equipped with two encoders that are m known as measuring system 1(motor encoder), and measuring Equation of motion for this model (without backlash) is: system 2(direct encoder). Direct encoder is directly connected to the axis and provides the exact position of the axis whether there is backlash or not. The value of direct measuring system τ = + Jl × ω − M (s) τ m (J m M (s)).s. m l (1) is utilized for position feedback in position controller. The k 2 k r r other encoder is located inside the motor and it is used as a feedback for speed controller. However, in most CNC machine 1 + 2ξ(s ω ) tools according to the kinematics of the axis, the difference Where: M (s) = n , + ξ ω + ω 2 between motor encoder and direct encoder should be in a 1 2 (s n ) (s n ) limited tolerance to assure a safe motion. τ d τ τ − ω xd nset set iset d-q axis iact m m + 1 1 1 kvkr ksp PI Current kt − − Tsi s kt controller J m s x n act act From Direct Encoder From Motor Encoder Figure 2. Closed loop position control system in a servo axis The controllers of the cascade control are to be designed to Frequency responce of closed loop speed controller provide higher cross frequency in each inner loop with respect 20 to its outer loop. For tuning the servo gain of the speed and current controller an attempt should be done to keep the 0 amplitude of speed (also current) controller at 0dB over the -20 Amplitude widest frequency bandwidth. In practice, the cross frequency of -40 speed and current controller should reach about 200-300HZ -60 and 500-100HZ, respectively, [12].
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