November 2009 Institute Mihajlo Pupin Presenter: Svetlana B. Despotović, Dipl.El.Ing. High Performances Signal Generator Implemented On Two Axes Hydraulic Pulsator EUROCON 09, May 18-23, St. Petersburg Authors: S.Despotović, Ž.Despotović, S.Sudarević

Introduction Specific realization of two axe hydraulic vibration exciter (hydraulic pulsator, or vibrator) Driving system based on hydraulic servo drive and high performances signal generator (based on Direct Digital Synthesis - DDS) Possibility of choosing different excitation types: sine, triangle wave or stochastic Frequency range (0.1 – 31.5) Hz; Amplitude range (0 - 50) mm Cognition of vibration transmission across the human body and its influence on psycho-physiological abilities is very important for automotive design There two aspects for vibration influences on human body research: - Aspect of health (fatigue, ride comfort, professional diseases appearance) - Aspect of mechanical vibration transmission across the human body (biodynamic)

Pulsators (vibrators) work on hydraulic principle, due to significant mass load They are realized like hydraulic platform with excitation opportunity over two independent directions (two axes) or one line direction (one axis) Compound movement is required, i.e. simultaneously excitation over two axes Driving system should be designed to ensure continual amplitude tuning and vibration frequency over both or a single direction

There are several parts in this configuration: - Electrical energy supply - Hydraulic part - System for measurement - PI servo controllers - Control module Hydraulic Pulsator Control System

Direct Digital Synthesis Method (DDS) DDS is a method of producing an analog waveform (usually sine wave) at a given frequency. The frequency depends on two variables: the reference clock freq. and the binary number, programmed into the freq. register (provides the main input to the phase accumulator) If a sine lookup table is used, the phase acc. computes a phase (angle) address for the table, which outputs the dig. value of amplitude (that corresponds to the sine of that phase angle) to the DAC Sine wave with fixed freq: a constant value (phase increment, established by binary number/tuning word) is added to the phase acc in each reference clock cycle Larger phase increment produces higher frequency; smaller phase increment generates a slower waveform

Operation Modes of Hydraulic Pulsator There are three modes of hydraulic pulsator operation: - NO SWEEP (the sine or triangle wave is generated with the same amplitude and frequency over the whole time range) - SWEEP (the sine or triangle waveform is generated over the chosen frequency range, with selected step and the same amplitude during the total time of working. After some time, which is software determined, frequency will be changed from to, or from to ) - STOCHASTIC (the only excitation type is a sine wave. The stochastic signal is produced from the sum of a sine functions at the same time interval, which depends on the resolution frequency, and resolution frequency is finer if the frequency range is smaller; time interval for addition the sine function can be 2.5 ms, 5ms or 10 ms. All sine functions have the same amplitude, different frequencies and the random initial phases. Because of that fact, the resulting signal will be random, i.e. stochastic)

Touch panel (menu for choosing parameters):

Different Signal Generation D ifferent signals for platform driving - two lookup tables: for sine (and stochastic) and triangle wave generation Resolution for triangle signal in the case of SWEEP/NO SWEEP is 0.1Hz Resolution for sine (in the case of SWEEP/NO SWEEP) and stochastic signal is 0.01Hz (and better) One complete sine cycle – locations in sine lookup table. Period of resolution freq. is 100s, so interrupt will be occurred on each 2.5ms. One complete triangle cycle – 4000 locations in triangle lookup table. Period of resolution freq. is 10s, so interrupt will be occurred on each 2.5ms. Frequency(0.1 – 31.5) Hz Amplitude(0 - 50) mm Total time of working(0 – 999) min Required ranges for values of interest:

Sinusoid functions are added at the same time interval, from 2.5ms to 10ms, depending on resolution freq. (fres) in some required ranges: Frequency range [Hz] Number of sine (0.10 – 0.125)11 (0.125 – 0.16)10 (0.16 – 0.20)10 (0.20 – 0.25)12 (0.25 – 0.315)14 (0.315 – 0.40)20 (0.40 – 0.50)11 (0.50 – 0.63)14 (0.63 – 0.80)18 (0.10 – 31.5)31 If fres=0.01Hz, then will be only 3 sine functions in the first interval (0.1, 0.11, 0.12)Hz, and it is not enough, so we need a better (smaller) resolution. Attainable number of sine functions is restricted by two factors: Speed of processor (max 50 sine func. per channel, or 21 which is quite enough) 10ms (corresponds resolution freq. of Hz) is the maximal time due to motor features If fres=0.0025Hz, it will be 11 sine functions generated in the first interval (0.1, , 0.105, , 0.11, , 0.115, , 0.12, , 0.125)Hz

It is decided that different freq. ranges have different resolution frequencies:

Random Initial Phase Generation The flowchart presented below is used for random initial phase generation initial_phase0 is obtained from uControllers timer

Amplitude Scaling MAX5322 DAC with 12-bits resolution Provides (0 - 10) V on its output All values of interest are mapped on a number range ( ), because of the symmetry The amplitude resolution is always 0.1 mm, so the number corresponds to it For stochastic signal, which consists of n sinusoidal functions, amplitude of every signal is decreased by n times

Experimental Results Oscilloscopic records of set and realized values for sine and triangle stationary wave oscillation over two axes (horizontal and vertical). CH1 – reference signal; CH2 – realized signal: (Sine; vertical axe; 40mm; 0.1Hz) (Sine; horizontal axe; 40mm; 0.1Hz) (Triangle; vertical axe; 3mm; 10Hz) (Triangle; vertical axe; 40mm; 0.1Hz)

System responses in frequency (upper) and time (below) domain, on different stochastic excitations: Amplitude = 40mm Frequency range = ( )Hz Sum of 11 sine functions Amplitude = 40mm Frequency range = ( )Hz Sum of 21 sine function

Amplitude = 3mm Frequency range = ( )Hz Sum of 21 sine waves Amplitude = 1mm Frequency range = ( )Hz Sum of 21 sine functions Attained stochastic signals correspond to initial excitation in amplitude and in frequency

Conclusion Desirable signals were generated from signal generator Amplitude values near 40mm are possible in frequency range ( )Hz Smaller amplitudes correspond to greater frequency ranges A DDS method, used for different waveforms generation is software implemented The overall presented system is installed in the Department for Motor Vehicles and Motors at the Faculty of Mechanical Engineering, University of Kragujevac, Serbia Presented system is used on studies which are given in reference [8]: Demic S.M., Lukic, K.J, "Human Body Under Two-Directional Random vibration", Journal of Low Frequency Noise, Vibration and Active Control, Vol. 27, No. 3. (September 2008), pp