THEORETICAL METHOD FOR DETERMINING PARAMETERS OF THE VACUUM BOOSTER (VB) IN AUTOMOBILE BRAKE SYSTEMS

Аннотация

Nowadays, with the increase in the number of vehicles, the demand for traffic safety is also rising. One of the ways to reduce the number and consequences of traffic accidents is to improve the technical condition of the vehicle's braking system. As a result, the use of tuning services (modification of components) is becoming more common, especially in vehicles. For instance, analyzing and selecting boosters, and determining the feasibility of installing them intoother vehicles, has become a current andsignificant issue. Keywords:Vacuum booster, membrane surface, pushrod Introduction: Today, to ease the driving process for the driver, boosters are being widely used. To theoretically justify the parameters of the vacuum booster (VB), mathematical calculations were conducted to determinetheVB membrane surface and radius. Figure1.Vacuumbooster diagram 1 - diaphragm; 2 - buffer of rod; 3 - push rod; 4 - atmospheric chamber; 5 - vacuum chamber; 6 -rod; 7-return spring ofthevalve body. Theforce at thevacuum chamber entrance (at theboosterpush rod) isdetermined as follows [1]: Р = Р *U (1) T p p Where: P –force onthebrake pedal, N(P <500 N) p p U –transmission ratio ofthebrake pedal (U =3.2) p p Theforce at thevacuum booster rod(output ofthevacuum chamber) is calculated as: P =P +P (2) r T M Where: P –force generated bythe boostermembrane, N m 34 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue07(2025) P =(ρ -ρ )*S (3) m a b m Where: ρ –pressure ontheleft sideofthe membrane, MPa a ρ –pressure ontheright sideofthe membrane, (0.065 +0.003MPa) b S –membrane surfacearea (0,32m²) a During braking, the force between thetireand theroad is calculated as: (4) Where: M –vehicle mass, kg a g–gravitational acceleration (9.81 m/s²) φ–coefficient ofadhesion Therolling resistance momentof thecar wheel is: (5) Where: r –wheel radius, m w Forceapplied tothebrake pad: Pʹ= (6) Where: μ–friction coefficient r –distance from thewheel axletothe brake pad, m d Pʹ= (7) Forceonthebooster rod is calculated as: =Pʹ/ (8) Thetransmission ratio ofthemaster brake cylinder is: (9) From theformula above, thesurface areas ofthe masterand working cylinders are: (10) Where: d ,d –diameters oftheworking and mastercylinders w.c m.c Equating formulas (2) and (8): (11) Substituting formulas (1), (3), (7), (9) into (11), the membrane surface area (S ) of the vacuum m boosteris determined as: 35 INTERNATIONAL MULTIDISCIPLINARY JOURNAL FOR RESEARCH & DEVELOPMENT SJIF2019:5.2222020:5.5522021:5.6372022:5.4792023:6.5632024:7,805 eISSN:2394-6334 https://www.ijmrd.in/index.php/imjrd Volume12,issue07(2025) (12) From this formula, theradius ofthevacuum boostermembrane is calculated as: (13) Table:Vehicle Mass andVB Radius № Vehicle Mass VB Radius 1. 1072 0.31 2. 1460 0.36 3. 1650 0.38 4. 2100 0.43 5. 2880 0.50 Figure2.Graph ofvacuumbooster membrane radiusas afunctionof vehiclemass Using formula (13), the VB radii of different light vehicles can be calculated, and graphs relating membrane radius to vehicle mass can be constructed. Based on theoretical calculations with different vehicle masses, VB membrane radii were determined using formula (13), and a graph was constructed from thetable above. Thus, using the above method, the vacuum boosters in light vehicles’ braking systems were theoretically analyzed and mathematical parameters were derived. With this method, parameters of vacuum boosters (membrane surface area, membrane radius, and pressure difference) ofvarious light vehicles can alsobe recalculated byaltering these variables.