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  STUDYING SEMI ACTIVE SUSPENSION SYSTEM USING BALANCE CONTROL STRATEGIES TO IMPROVE RIDE COMFORT Assoc. Prof. Dr. Dao Manh Hun D!"#.$In.   Vu Van Tan  Automotive Engineering Department – Mechanical Engineering Faculty – University of Transport and Communications Summary:  The smooth motion is one important factor of the automobile quality. There are many measures to improve the smooth movement of the car, in which researchers in Vietnam and in the world interested in semi-active control of suspension system. This paper presents the content Balance control method applied to semi-active suspension system with two control regular are Balance Control "on-off" and continuous Balance control. I. INTRODUCTION uring road traffic, the road surface is the main source of e!citation causing vehicle vibration that influences driver and passengers. The study of suspension system is one of the most effective ways to improve ride comfort. Because of economical energy consumption and good ride quality, the semi-active suspension system is a een interest for many researchers.The semi-active suspension systems have been studied since #$%& '#(. )owadays they are quite  popular in modern vehicles. There are a variety of control algorithms for semi-active suspension systems, one of which is balance control strategy.  Figure 1: Semi-active suspension system in Cadillac SRX. II. CONTENT *n this part we consider a one-mass model +figure .a with e!citation ! & +t, spring rate  and damping factor c which has # degree of freedom.#  a)b) Figure 2: Passive model and Semi-active model using balance control strategy:a) Passive suspension system b) Semi-active suspension system. Vibration equation is given in the following form &. .. =++ d    F  F  !m +# "#ere: /    and / d  are spring force and damping force corresponding. -+ &  ! !  F     −= + -+  &..  ! !c F  d   −= +0The relations between  .. .  !m , /    and / d  in case of harmoni1ed e!citation are shown in figure 0.  Figure $: Relation bet"een %orce acting on t#e sprung mass &m' in case o% #armoni(ed e!citation:  : *amping %orce +F  d   ), ------- : Spring %orce +F     ) and : nertial %orce +   ..  !m  ). The amplitude of acceleration of sprung mass 2m3 in harmoni1ed e!citation depends on damping force and spring force due to the following equations '( 40,4 &&&&.. τ τ τ  +<<+ +<<+= t t t t t t m F  F  ! d   +4  τ τ τ τ  +<<+ +<<+ −= &&&&.. 40,4 t t t t t t m F  F  ! d   +5 "#ere:  t &  is the time during which the spring force is 21ero36 τ    is the frequency of vibration.uring vibration, one would lie to have small  ..  ! , however in accordance with the equations 4, 5 and figure 0, the rise of damping force causes increment of amplitude of the acceleration in one part of the cycle of vibration. 7fter that the amplitude of ..  !  will be reduced if /    and / d  have the same magnitude. 8hen increasing the e!citing frequency, it is dominated by damping force / d .  a!he"a# S$ and S$ San!ar '( proposed balance control strategy using active damper +/igure .b which can be hydraulic damper with throttle, friction damper, 9: damper, ;: damper, electromagnetic damper <.This strategy maintains that the damping force increases the acceleration of sprung mass when the damping force and spring force have the same sign. The -state active damper +=n - =ff, at the 2off3 state when damping force and spring force act on the same direction +  &--++ .&.&  >−−  ! ! ! ! , and vice versa at 2on3 state when +  &--++ .&.&  ≤−−  ! ! ! ! . Therefore the damping force is against the spring force and the strategy is called Balance Control '(. %$&$ Continuous 'alance Control  *n order to maintain the equality of damping for and spring force at the 2on3 state >−−≤−−−− = &--++& &--++-+ .&.&.&.&&  ! ! ! !  ! ! ! ! ! !   F  S/ +>amping coefficient for active damper +/igure 4 >−−≤−−−−−= &--++& &--++ -+ .&.&.&.&.&.&  ! ! ! !  ! ! ! !  ! ! ! ! C  S/ +% 0   Figure 0: #e value o% C  S/  "it# respect to -+ &  ! ! −  and -+ .&.  ! ! − . 8hen the relative velocity -+ .&.  ! ! − is very small, the damping coefficient is closed to infinity, which cannot happen for the real damper. Therefore the damping coefficient for active damper   C ?7 must continuously vary within the interval +C ma! , C min  according to the manufacturer@s desire. The value of C ?7  can be determined as the following >−−≤−−−−−= &--++ &--++, -.+min,ma! .&.&.min.&.&ma!.&.&min  ! ! ! !C   ! ! ! !C   ! ! ! ! C C  S/ +A*n this case, the value of damping force is plotted as seen in figure 5.4   Figure : *amping %orce F  S/  "it# respect to -+ &  ! ! −  and -+ .&.  ! ! − in case o% continuous balance control. %$%$ ()n*off+ 'alance Control  The 2on-off3 balance control is studied to simplify the woring of the damper '(. *n the two states, the active damper is controlled at ma!imum state or minimum state or high and low state correspondingly. *n this case, the damping force is determined as >−−≤−−− = &--++& &--++-+ .&.&.&.&.&.  ! ! ! !  ! ! ! ! ! !C   F  onS/ +$ "#ere:  C =n  is the damping coefficient of damper 2on-off3 at the 2on3 state.The relation between damping force in 2on-off3 balance control and -+ &  ! ! − and -+ .&.  ! ! − is shown in figure >.  Figure 3: *amping %orce F  S/  "it# respect to -+ &  ! ! −  and -+ .&.  ! ! − in case o% &on-o%%' balance control. %$,$ Simulation and evaluate semi*active suspensions system using 'alance Control$ a. E%c!&!n sourc's( ?tudy the e!citing source from road-surface irregularities as impulse unit +stepped and sine unit and random case +ighway anoi  Dangson '%( +/igure%.  Figure 4: Road pro%iles. ).   E*a#ua&!on cr!&'r!a &.&#mac&.>m&.&#m b Deft trace:ight trace 5
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