IDENTIFICATION AND VERIFICATION OF DYNAMIC PARAMETERS FOR THE WELDING MANIPULATOR

Welding production lines are indispensable parts of the production processes in the automotive industry. In many cases, the production line operation is ensured by equipment with linear conveyors or robots, wherein linear guiding systems are basic elements of these manipulators. The failure of some linear guiding system may lead to significant production losses. Hence, the knowledge of their operating loads is necessary to determine very exactly. The objective of this article is to identify and verify the basic dynamic parameters of the welding manipulator, as a starting point for the operating loads calculation of linear guiding systems. This issue was solved by combining the measurement of kinematic values and MBS (Multi-body System) analysis in case of the concrete linear welding manipulator, which was the main part of the observed welding line. We have measured time values of acceleration in defined points of the manipulator and evaluated them by FIR (Finite Impulse Response) filter, FFT (Fast Fourier Transformation) analysis and ODS (Operating Deflection Shapes) analysis. The obtained frequency spectrum showed oscillation frequencies, which could be compared with frequencies of the manipulator dynamical model by different mass and stiffness parameters. In this way, the dynamic parameters of the welding manipulator can be identified and used for the next calculations and

In case of welding production lines, a prediction of linear guiding system failures in one of the first places is needed, because these parts enable in these lines the transport of car bodies for the welding process. Should they fail, the production must be stopped for a few days. This situation can lead to significant production losses. Therefore, the prediction of the failures is very necessary and the determination of the linear guiding systems loads is the main task for calculations and simulations on the welding manipulator mechanical model [2,3,16].
To identify these operating loads, it is necessary to have sufficient notions about the dynamical behaviour of the welding manipulator. In this article, the issue is solved as the planar motion of the manipulator.

MEASUREMENT
In Fig. 1 is displayed the 3D model of the welding manipulator with positions of two acceleration sensors (S-V and S-Z). The major parts of the manipulator are the cart, two socalled Z-axes and two clamping frames with car bodies.
The welding manipulator exercises a translation motion, which is provided by the stepper motor through a rack gear and linear guiding systems. The linear guiding systems connect the cart with the frame by means of guide profiles. However, the elastic construction parts and clearances of linear guiding systems cause oscillations of the manipulator against the mashing point of the rack gear. The rack gear, the stepper motor and linear guiding systems are placed on the cart of the manipulator. The clamping frames with the car bodies are connected to the cart through the Z-axis that enables their vertical translation motion.
Kinematics of the welding manipulator was measured by two three-axis acceleration sensors [12]. The first sensor S-V was situated close to the stepper motor that powers the manipulator. The second one S-Z was situated close to the car bodies clamping frame (Fig. 1). The knowledge of the kinematic parameters in two positions gives sufficient notions about the dynamic system behaviour of the welding manipulator [1]. 1 -cart, 2 -Z-axis, 3 -clamping frame, 4 -linear guiding system, 5 -rack gear, 6 -acceleration sensor S-V, 7 -acceleration sensor S-Z

Finite Impulse Response (FIR) filter
Measured data were evaluated by the FIR filter that enabled the identification of the system basic motion in each coordinate axis. Considering the Fast Fourier Transformation (FFT) analysis result, the FIR filter was used as a low pass filter with the cut-off frequency 3 Hz. The higher order of the filter was used for reaching the sufficient slope of the transition band.
Measured and filtered values are shown in Fig

FFT analysis
The results of the FFT analysis are shown in Fig. 8. Fig. 8 shows the results of the FFT analysis by previously introduced filtered signals. The basic oscillation frequency of the manipulator is around 1,2 Hz.

Operating Deflection Shapes (ODS) analysis
The ODS analysis was made for the operating frequency 1,2 Hz of the manipulator. Eight one-axis acceleration sensors were placed in the translational direction on the longer Z-axis and on the clamping frame. The result of this analysis is shown in Fig. 9.

MULTI-BODY SYSTEM (MBS) ANALYSIS
The basis for creating the dynamic model of the manipulator is its 3D model that provides its mass parameters. Kinematic, elastic and damping connections are assigned to the 3D model. The dynamic system of the manipulator has the kinematic excitation, where the acceleration values are given by the data of the stepper motor. The dynamic model with corresponding connections is shown in Fig. 10.

Elastic and damping parameters of the system
The vertical stiffness of the elastic connection may be calculated: , wherein is the torsion stiffness, moment of inertia about the axis, basic oscillation frequency (1,2 Hz) of the manipulator about the axis (Fig. 10), distance between elastic and damping connections and the rotational point and number of elastic and damping connections [4].
The vertical damping coefficient is: , wherein is relative damping coefficient. 57. Fig. 9. Operating deflection shapes of the manipulator

Kinematical excitation
For the kinematical excitation, the time function of the stepper motor velocity and its derivation may be used. This was reached by "the five point method" with equation: , wherein is new value of acceleration (velocity) and is last value of acceleration (or velocity).
The final acceleration function used for the kinematical excitation of the system is shown in Fig. 11. Fig. 11. Kinematical excitation of the manipulator dynamic system The maximum value analysed of the stepper motor acceleration was 1,5 m/s 2 .

COMPARISON OF MEASURED AND SIMULATED ACCELERATION VALUES
Results show the relatively sufficient matching between measured and simulated acceleration values. However, it should be noted that for the achievement of better results, it would be appropriate to solve the system as nonlinear. But in this case, it is necessary to know more input parameters.
The comparison of measured and calculated acceleration values is shown in the following figures. In Fig. 12 is shown the comparison between filtered acceleration values of the first sensor S-V in the translational direction and the acceleration as the simulated result of the MBS analysis in the same direction.

CONCLUSIONS
Nowadays, linear guiding systems are used in a wide range of applications, especially for enabling the linear motion of manipulators, robots, transporting parts etc. Usually, the linear guiding systems are present in the very important part of these machines. However, their operating load by the relative complicated dynamic behaviour is not well known, hence, the linear guiding systems might be overloaded, which can lead to their premature failure. Therefore, the knowledge of their operating load is strictly demanded. For the operating load calculation, it is first necessary to identify and verify the dynamical parameters of these machines with the help of the corresponding dynamic model to determine the values of the operating load.
This article illustrates the process of identifying dynamical parameters and their verifications. This process is based on the combination of the measurement and mathematical methods, which can be described in a few steps. First, the process uses measured acceleration values in two points of the moving part. They are evaluated by FIR and FFT. The evaluation of operating deflection shapes can be added for the visualisation of the part oscillation. In the second step, it is necessary to identify mass parameters and elastic and damping parameters of parts connection in the system. 3D modelling and its integrated functions can be used. The system movement can be calculated using the MBS analysis. Finally, the measured kinematical values are compared with the calculated ones. The dynamic parameters are correctly determined in the case of good accordance between the measured and simulated results.