DAO NG V TING N T VEHICLE VIBRATION AND NOISE

VEHICLE VIBRATION AND NOISE

Chapter1:General conception A vehicle is a complex vibration system with multi DOF ( Digree Of Freedom) and corresponding types of natural vibration. to be affected by many excitation sources. Resonance The system has the steady-stead vibration amplitude. The excitation frequency approaches the natural frequency. The number of resonance zones equal to the number of DOF

1VEHICLE VIBRATION AND NOISE

Study only mechanical vibration in low frequency from 0 to 300Hz. Mechanical vibrations of Engine and transmission have higher 300Hz frequency and create noises.The basic object to complete a vehicle is trying to reduce the steady-state peaks of resonance vibration.

Vehicle vibration and noise The solutions to reduce vibration: Reduce excitation intensity; Move the natural frequency out of the excitation frequency; to Equip accordant dampers; Falsify natural frequencies of mechanic details. Vehicle dynamic system is considered as a completation.

VEHICLE VIBRATION AND NOISE the subiect has 8 chapters: Chapter 1:presentation. Chapter 2: vibration excitation souces of vehicle system. Chapter 3: Characteristics of spring and damper. Chapter 4: Vehicle vibration system. Chapter 5: Basic conception of noise. Chapter 6: Vibration and noise of Wheels. Chapter 7: vibration and noise of a car body. Chapter 8: Standars of noise.

Vehicle Vibration and noiseChapter 2: Vibration excitation souses2.1 Roughness of a road.

Figure 2.1 Harmonic roughness of a road in X dimention

Vehicle Vibration and noise- Harmonic type of Roughness: With amplitude 0 , wave-length L we have the Equation describing roughness in X dimension: = 0 sin 2X/L = 0 sin 2X = 0 sin X Here, = /L [1/m] is length frequency, = 2/ L [rad/m] is length angle frequency) and = 2. With Base length of vehicle is ( one track model), We have the Relations between front and rear axes): 1 = 0 sin 2X 2 = 0 sin 2(X ) [1]

Vehicle Vibration and noise If velocity Vx = const then the change of roughness depending on time is wrote: 0 (t) = 0 sin 2ft = 0 sin t Here, = 2 V/L is Angle frequency of moving; f = V/L is moving excitation frequency

Figure2.2: Dependence of Harmonical roughness frequency fon wave-length L and velocity V.

7Vehicle Vibration and noiseReal roads have really random roughness. Its mathematic descriptions are random functions

Figure 2.3 Describing of road roughness in (X,Y) plane

Vehicle Vibration and noise2.2. Eccentricity of the wheel:

Figure 2.7: Describing an eccentricity of the wheel

If having a eccentricity (It is a difference between rotation centre and geometrical centre of the wheel ), Cz = const is normal stiffness, Zk is normal displacement from static position, amplitude of roughness is we have the equation of normal force as a following) Fz = Cz ( zk - cos ) [19]

Vehicle Vibration and noise Here, ( zk - cos ) is a normal deformace of the wheel and is a rolling angle from base position. After a circle of rolling, rolling radius is changed approximatcally by the function r = r0 - . Cos. If the real velocity of wheel centre is V then the angle velocity of the wheel is a following: k = d/dt = V /( rl0 + zk - cos) [20] It is clear that, is not constant so with a eccentricity the normal and tangential forces are changed on time Consider (zk ) = 0 , the influence of eccentricity with normal force change will be: Fz = - Cz sin V/r0 . t [21]

Vehicle Vibration and noiseChapter 3: Suspension Suspension springing and damping operate chiefly on the vertical oscillations of the vihecle. Driving comfort (loads on passengers and cargo) and operating safety (distribution of forces against the road surface as wheel-load factors fluctuate) are determined by the suspension.3.1 Kinematic relation:. Spring and damper are assembled between Sprung mass and Unsprung mass usually by a mechanism, we consider independence suspension in Fg. 3.1, 3.2

Vehicle Vibration and noise

Kinematic transmission of suspension

Vehicle Vibration and noise If point 1 is moved a value u1 by a force F1 then a spring will have a press F2 and a displacement u2. By Vitual Work Principle we have a following equation: F1.du1 F2.du2 = 0 [3.1] Here, relation F2 = f(u2) is dependent on spring characteristics. The relation between u1 and u2 is dependent on kinematics of suspension mechanism, generally u2 = (u1). Therefore, we have the relation beween force F1 and displacement u1: F1 = f [(u1)] du2/du1 [ 3.2] A Fitness of the suspension with displacement u1 is then C1 = dF1/du1 = { f[ (u1)] } [3.3]

Vehicle Vibration and noise In a simple case, when kinematic ratio between u1 and u2 is const ( u2 = u1, = const), susbtituting in 3.3 we have the relation C1 = 2C2 For Torsion bar we have similar relations: F1du1 m2 d2 = 0 [3.4] here m2 = f(2) and 2 = (u1). When linear kinematic relation m2 = Ct 2, 2 = . u1 ( = const) then C1 = const = Ct . 2 .

Vehicle Vibration and noise Similarly, in the case of damper depending on moving speed. If suppose damper force F2 = f(u2) then the relation between 1 and 2 is: u2 = (u1) or 2 = [ (u1)] = (1 , u1). The force F1 is provided by the equation: F1 = f[( 1, u2) ] [3.5]A differential (dF1 /d1 )u1 = (k1)u1 is called a damper coefficient of the system with displacement u1 and we have: K1 = dF1/d1 = d/d1 { f[ (u1 u1)] } [3.6] When u2 = u1 and damper charactericstics is linear F2= k22 then we have k1 = 2 k2) .

Vehicle Vibration and noise3.2 Steel springs: Steel springs usually used on vehicle are Leaf spring, Coil spring and Torsion bar .A. Leaf spring Figure 3.3:Siffness of the simetric spring: C = 4nbh3E / L*3 [3.7a] Stiffness of the nonsimetric spring: C = nbh3E( l1* + l*2 ) / 4 l1* l2* [3.7b] L : total length of loaded spring. L* Length of a free spring . l0* = 2/3 l0 l 1* = l1 - l0*/2 l2* = l2 l0*/2

16Vehicle Vibration and noise

Vehicle Vibration and noiseB. Coil springs: Siffness of the coil spring : C = Gd4 / 8nD3 with D is average diameter, d is a diameter of spring wire, n is sum of spring rings, G elactic modyn of material. Stiffness wil be constant when keeping constant parameters of the formular.

Vehicle Vibration and noise3.3 Air springs: Gas in air springs usually is air for changed mass spring and is nitrogen for constant mass spring.

Vehicle Vibration and noiseA.L thuyt c bn v phn t n hi kh( theory of air spring): A Space on a piston is fully charged by gas, in the base position(Z = 0)the spring has a volum V0, absolute pressure P0 and be loaded by a force Fz0 = (p0 pmt).S, with pmt is atmosphere pressure. If moving the piston then pressture in cylinder is changed by multivariable function p.Vn = const with n is depend on temperature. With moving frequency f = 1 Hz then n =1.33, when f = 10 Hz then n = 1.37 Affer a working time the temperature of gas is equal to the temperature of the atmosphere and we can consider n = 1

Vehicle Vibration and noise When a sping is pressed then volume V = V0 S.z, with z is pressed displacement. The pressed force is equal to: Fz = [ P0V0n /(V0-S.z)n - Pmt].S [20]. Momentary fittness of the spring is equal to: C = dFz/dz = np0V0nS2 /(V0 S.z)n+1 [21a]. And the fitness at the first moment Z = 0 is: C0 = np0S2 /V0 [21b]. Substituting p0.S = (Fz0 +pmtS) in [21b] we have: C 0 = n(Fz0 + pmtS)S /V0 [21c] Fz0 is base load on the spring.

In one-DOF system with air spring: In the base state there are Fz0 = gM0 and p0, V0, S. When changing of load by Fz1 then the air pressure will be increased into p1 = (Fz1 + Spmt)/S.In the case of constant air mass the volume of air is changed isothermally into V1 = p0V0/p1 = V0 (Fz0 +pmtS)/(Fz1 + pmtS).

Vehicle Vibration and noise Fittness of the spring at the Fz1 load in vibration will be: C1 = n(Fz1 + pmtS).S/ V1

Fittness ratio in loads Z1 and Z2 is: C0 /C1 = V1/V0 [( Fz0 + pmt .S) / (Fz1 + pmt .S)] = [(Fz0 + pmt .S) / (Fz1 + pmt .S)]2 The ratio of The natural angular frequencies will be: 0 / 1 = [ (c0/M0 )/c1/M1 ]1/2 = . ( Fz1/Fz0 )1/2 (Fz0 /Fz1)1/2 [22] So we can say that when increasing of load then the natural angular fryquency of system will be increased( To be against a linear spring). If p0 >> pmt then the increasing is proporsional with square root of the vibration mass.

In case of changing of load but The air volume is maintained constantly (of cause the air mass will be increasing) then V0 =V1. and we have: C0/c1 = ( Fz0 + pmt .S) / (Fz1 + pmt .S) The ratio of The natural angular frequencies will be: 0 / 1 = [( Fz0 + pmt .S) / (Fz1 + pmt .S)] (Fz1/Fz0]1/2 1 [23] So we can say that when increasing of load and maintaining of constantly volume then the natural angular fryquency of system will be nearly constant.

Vehicle Vibration and noiseHydropneumatic spring Diagram of a hydropneumatic spring is plotted in the figure 3.6: the piston forcing on liquid and transmiting pressure to the air space. The air mass is not changed in operating and the area of the piston is constant. The operating pressure in static load is relatively great about from 2 to 10 Mpa.

Vehicle Vibration and noise The weakness of this spring is having a very big raising of stiffness when increasing of static load. In this case there is no problem for a car (no truck) when the ratio beween noload mass and fullload mass about 1.3 1.7 or a fullload natural frequency is biger only 1.3 times than a noload natural frequency. In the case of trucks when the rear axle load can be changed 3 or 4 times they usually use a anti-press spring ( Fig. 3.7). Piston has 2 faces Sh and Sd with correlative air pressure and volumes ph , pd, Vh, Vd. the Force on the spring is determined: Fz = phSh pdSd (Sh Sd) pmt [24]

Vehicle Vibration and noise The moment fitness of the spring is: C = n( ph.S2h /Vh - PdS2d /Vd) [25] We consider the case when Vd , Vh =const: In the base state the spring is forced by Fz0 and pressure is ph0,pd0 . If the load is increased to Fz1 then the spring is moved a displacement z1 and we can write a equilibrium equation Ph1 =[ Vh0 / ( Vh0 Sh.z1)]Ph0 , Pd1 = [Vd0 / ( Vd0 + Sd z1)]Pd0 . From a calculated value z1 we can calculate volumes Vh1 = Vh0 Sh. z1 ; Vd1 = Vd0 + Sd z1 and the stiffness of the spring C1 = Fz1/z1.

Vehicle Vibration and noiseC. Air spring: Theoretically we can have an any characteristics of the air spring. Practically, Characterictics of this spring is determained by test and supplied by manufactory. Can control the hight of the spring when changing load by changing internal air mass while the volume is not changed. This control is an advantage by opinion of keeping of constant natural frequency under load.

Vehicle vibration and noise3.4 Hydrolic damper:

Figure 3.10:Schema of fluid flow. Figure 3.11: Fluid flow between piston and cylinder a: non-eccentric b:eccentric

Vehicle vibration and noise Hydrolic damper consumes kinetic energy of vibration system and changes it into heat. The basic problem of damping contruction is how to achieve a suitable characteristics this is relation between damping force and damping speed. a. Basic theory: If fluid in cylinder is pressed throught narrow slots then to be pressure difference between two spaces of the cylinder p = W2 . Here is resistance coefficient, is fluid density ( about 900 kg/m2), W [m/s] is fluid speed in slots. If Q = v.S [m3/s] is fluid flow pressed throught slot with v[m/s] called damping speed, S called cross section area then W = Q/Ss with Ss is slot area.

Vehicle vibration and noise If the flow is tranquil we have relations for 2 cases: The slot is non- eccentric: p= ( 12l)/(s3d) . Q [29a] The slot is eccentric: p= ( 24l)/(5s3d) . Q [29b] d is diametr of flow, s is dimention of slot (s 1.

Vehicle vibration and noiseIn the special case when 2 / a. b = 1 then the vibration of two axles are independent each other, so if having a force on the front axle then there is not a force on the rear axle and each other.From it we can divide into two independent vibration of two axles. The natural frequency of this moving is: 1 = ( C1 / MT.b)1/2 , 2 = ( C2 / MT .a)1/2 [4.16]Vertical moving is determined: Z1,2 = A sin 1,2 t

Vehicle vibration and noiseThe angular frequencies[rad/s] defined above are used as basic parametrs of the system. In the case when 2/ a.b 1 then they are signed as *1, *2 and to be called the partial natural angular frequencies of the suspension. The same is vibration frequency f*1 = *1 / 2 ; f*2 = *2 /2. [ Hz]. If 2 / a b = 1, the vibration of two axles are independent we describe a damping of the front and rear axles by aperiodic coefficients: 1 = 2 =