MODELLING, SIMULATION AND OPTIMIZATION OF DAMPING

Transcription

1 MODELLNG SMULAON AND OPMZAON O DAMPNG Jiří Vondřich Evžen hőnde Departent of Eectric Drives and raction acut of Eectrica Engineering zech echnica Universit in Prague Astract Modeing siuation and optiization of different sstes were an integra part of the design and construction of sstes he diagra docuenting a phenoena infuencing ehaviour of the sste arrangeent a set of dnaic equations and creating a siuation nuerica ode are the prerequisites for creating a functiona and credie siuation ode Viration in sstes has two effects irst the ver high pea acceerations can ean that the effective weight of the viration sstes increases severa-fod and this a cause its destruction Second peope near the sstes fee these acceerations which can e uncofortae or even dangerous A viration ass is used to protect the sstes fro stead-state haronic disturance Depending on the driving frequenc of the origina sste the virating ass needs to e carefu tuned that is to choose adequate vaues of stiffness daping and eventua ass so that otion of the origina ass is a iniu he tuneae viration asorer is advantageous priari in that reduces the apitude of virations in the sstes for eape unaanced rotors cran gear cearances in earings osciation of the oving driven parts transient oading diverging and coasting of driving otors etc he present artice wi discuss the ethod onine optiization of the viration and daping contro for sstes using a viration tuneae ass with daping he anases and Mata -fie for the auto-tuning contro have een used he ai of the paper is to acquaint the reader with the design of the incorporated asorer to the viration sste which aes the suppression of the viration of the sstes to a iniu possie he resuting vertica trajector and acceeration of the car od showed that asorption using a springs and dapers reduces the viration apitude of the car od ar od virations on uneven highwas affect car ifetie passenger cofort and in turn cause daage to the road Asorption sste reduces these negative infuences and considera iproves the driving properties of the car t is possie to change the paraeters of the springs whie driving and thus contro the driving properties and cofort Before the reaization of viration asorption in a echanica arrangeent it is iportant to carr out a nuerica soution he nuerica soution for car od asorption in cooperation with the Mata-Siuin progra is shown on ode of the car Mode of the Sste On the ig is shown the ode of the car with four degrees of freedo 3 4 he car is oving on uneven road dispaceent st s cos Ωt ro the road then acting on the ripe force t s Ω cos Ωt ψ cos Ωt s Ω ψ Ω ψ n the tie t is the force t aiu and then dispaceent ψ he force acting on the ripe fro the road is t cosωt

2 he reations aong the degree of freedo are ig φ 3 4 st igure : Mode of the car with tires oving on uneven road Miniize criterion Equation of otion of this sste is t t 6 We introduce now 7 hen equation of otion is 8

3 Equations of otion 8 are aso possie written in the for B A 9 B A When we introduce Lapace transforation we otain B A p he transfer function Gp then fro equations is B A p Where the transfer function has for A G p p When optiizing the response of an eisting sste it is conventiona to iniize the aiu response he iniize criterion is in a p G 3 he Siuin schee of the soution and optiization is shown on the ig igure :Siuin schee of the daping of the car

4 3 Resuts and concusion On the ig 3 is shown soution of the iniize criterion 3 of the transfer function igure 3: Apitude characteristic of the soution of iniize criterion he paraeters of the ode are g 3 5 g 4 3 g 9 g N - N - 3 Ns - 8 Ns - s Ω565 s - On the ig 4 are shown the dispaceents of four degrees of freedo 3 4 after using the iniize criterion 3 he aiu apitude of the dispaceent of the car od is 65 he aiu apitude of the dispaceent φ of the car od is rad he aiu apitude of the dispaceent 3 of the ae 3 is 35 he aiu apitude of the dispaceent 4 of the ae 4 is 35

5 igure 4: Dispaceents of the car od and dispaceents of the car aes 3 and 4 References [] Author Jiří Vondřich Departent of Eectric Drives and raction acut of Eectrica Engineering zech echnica Universit in Prague echnica 66 7 Prague 6 vondrich@fecvutcz Author Evžen hőnde Departent of Eectric Drives and raction acut of Eectrica Engineering zech echnica Universit in Prague echnica 66 7 Prague 6 thonde@fecvutcz