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附 錄
Influence of Front Double wishbone Independent Suspension Performance on Front Rubber Bushing Stiffness of Lower Control Arm
Liu Xintian，Hung Hu ,Wang Jichang，Zhao Lihui，Gao Hui，WangYansong
Abstract--Front double wishbone Independent suspension is built according to hard point parameters of a car. After the rubber bushing stiffness of lower control arm is changed．The suspension performance is analyzed and discussed with multibody dynamic and Suspension Kinematics theory. The conclusion can be drawn as follows：when wheels are hoping, All the stiffness of lower control arm have no effect on camber angle，caster angle and kingpin_incl_angle，and torsion stiffness of rubber bushing has heavy effect on toe angle，but axial，radial stiffness have no effect ,While steering，all the stiffness of lower control arm rubber bushing have no effect on camber angle and toe angle，torsion stiffness has affects on camber angle ,axial stiffness has a little and radial stiffness has heavy , axial and torsion stiffness have none on kingpin_ incl _angle，but radial stiffness has heavy．During the analyze of traction force and brake force ,torsion stiffness of lower control arm rubber bushing has no effect on camber angle, kingpin_ incl_ angle and toe angle , axial stiffness has a little, and radial stiffness heavy , According to the curve of caster angle VS brake force, radial and axial stiffness of rubber bushing have a little affects on caster angle, but torsion stiffness none
Keywords-Front Double Wishbone Independent Suspension, rubber bushing, stiffness
I. INTRODUCTION
Double wishbone independent suspension is widely used on automobile now. Two wishbones have equal length or not. Equal length of double wishbone independent suspension is Not usually used now , Unequal length of double wishbone independent suspension can keep good road ability and reduce the interference between suspension and steer bar ,with reasonable structural parameters and Proper arrangements to make the parameter of wheel spin and wheel location floating in Permissible range. therefore, it is widely used in front suspension of car and small truck. Front double wishbone independent suspension is regard as research object using multi—body dynamics and Suspension Kinematics theory to analyze and discus the influence of suspension performance by axial , torsion , radical stiffness of rubber bushing.
II THE MODEL OF THE MULTI—BODY DYNAMICS
Multibody dynamics theory is the subject that study on the movement rule of the object in system . It is composed of multi_rigid_body dynamics and multi_fexible_body dynamics:
Where q,, are system’s system position,speed,acceleration vector, is langrange multiplier, t R denote the time , M denote inertia matrix of mechanical system, deonte constraint jaclbian matrix, Q denote outside force vector , denote location constraint equation.
;
;
Where v(q,t)is speed right side, is accleration right side.
Initial condition
q(0)=
(0)=
Putting the initial condition into(2)and (3), the rigid movement can be calculated by above functions
III FRONT DOUBLE WISHBONE INDEPENDENT SUSPENSION MODEL
Figure 1, front double wishbone independent suspension model
According to the suspension key hard point value of a certain car,front double wishbone independent suspension Kinematics model is built as shown Figure 1 .The characteristics of location parameters are analyzed in some operating conditions. During the analysis, axial ,torsion, radical stiffness of rubber bushing is respectively increasing to 5 times of original, and then comparison and analysis with the original.
IV THE INFLUENCE OF WHEEL LOCATION PARAMETERS BY LOWER CONTROL ARM FRONT BUSHING STIFFNESS
When front rubber bushing stiffness of lower control arm is changed，the influence of wheel location parameters are discussed separately under the conditions of wheel hop, steering, traction force and braking force.
A. Wheel hop
Camber angle VS wheel travel
Caster angle VS wheel travel
Kingpin_incl_angle VS Wheel travel
Toe angle VS Wheel travel
Figure 2.The curve of rubber bushing stiffness of lower control arm, wheel location parameters and wheel travel.
In fig 2, the four curves are under the conditions of unchanging lower control arm rubber bushing stiffness and radial，axial，torsion stiffness increasing 5 times(the changes of lower control arm rubber bushing stiffness are also like this in fig.3,4 and 5). In fig.2 while wheels is hoping ,according to the curve of camber angle vs wheel travel , caster angle vs wheel travel and kingpin_incl_angle vs wheel travel ,the conclusion is drawn that radial ,axial and torsion stiffness of rubber bushing has no the toe angle ,Radical stiffness of rubber bushing has heavy on the toe angle, but axial and torision stiffness have a little from the curve of toe angle vs wheel travel.
B Steering analyze
Camber angle VS Steering angle
Caster angle VS Steering angle
Kingpin_incl_angle vs steering angle
Toe angle vs steering angle
Figure 3.The curve of rubber bushing stiffness of lower control arm ,wheel location parameters and Steering angle
In fig.3,While steering ,according to the curve of Camber angle VS Steering angle and Toe angle VS Steering angle ,radial ,axial and torsion stiffness of rubber bushing has no effect on camber angle and toe angle .In the curve of caster angle VS Steering angle, torsion stiffness of rubber bushing has no effect on caster angle ,radical stiffness has a little but axial stiffness heavy .Axial and torsion stiffness of rubber bushing has no effect on kingpin_ incl_ angle ,but axial stiffness has heavy by the curve of kingpin_incl_angle VS Steering angle.
C brake force analyze
Caster angle vs brake force
Kingpin_incl_angle vs brake force
Toe angle vs brake force
Figure 4. The curve of rubber stiffness of lower control arm ,wheel location parameters and brake force
In fig.4,when braking ,according to the curve of Camber angle VS Brake force, kingpin_incl_angle VS Brake force and Toe angle VS Brake force，torsion stiffness of rubber bushing has no effect on the camber angle, kingpin_incl_angle and toe angle ,axial stiffness has a little, but radial stiffness heavy .In the curve of caster angle VS Brake angle ,radial and axial stiffness of rubber bushing have a little effect on caster angle ,but torsion stiffness has none.
D traction force analyze
Camber angle vs traction force
Caster angle vs traction force
Kingpin_incl_angle vs traction force
Toe angle vs traction force
Figure 5. The curve of rubber bushing stiffness of lower control arm, wheel location parameters and traction force
In fig.5, while braking，according to the curve of Camber angle VS Traction force，kingpin_incl_angle VS Traction force and Toe angle VS traction force ,torsion stiffness of rubber bushing has little effect on the camber angle, kingpin_ incl_ angle and toe angle，axial stiffness has a little，but radial stiffness heavy. In the curve of caster angle VS Traction angle，radial and axial stiffness have a little effect on caster angle, and torsion stiffness has none.
V. CONCLUSIONS
Using multi-body dynamics and suspension Kinematics theory to analyze the influence of wheels location parameter. when the radial, axial and torsion stiffness of lower control arm front ,rear rubber bushing is changing . when wheels hop，according to the analyze result of radial，axial，torsion stiffness of lower control arm front rubber bushing ,all the stiffness of lower control arm have no effect on camber angle，caster angle ,caster angle and kingpin _incl_ angle ,and torsion stiffness of rubber bushing has heavy effect on toe angle, but axial radial stiffness have no effect .while steering, all the stiffness of lower control arm rubber bushing have no effect on camber angle and toe angle , torsion stiffness has no on caster angle, axial stiffness has little and radial stiffness has heavy ,axial and torsion stiffness have none on kingpin _ incl _ angle, but radial stiffness has heavy. In the analyze of traction force and brake force, torsion stiffness of lower control arm rubber bushing has no effect on camber angle , kingpin_ incl _ angle and toe angle ,axial stiffness has a little, and radial stiffness heavy. According to the curve of caster angle VS brake force, radial and axial stiffness of rubber bushing have a little affects on caster angle ,but torsion stiffness none.
下控制臂橡膠襯套剛度對(duì)雙橫臂獨(dú)立懸架影響
摘要-前雙橫臂獨(dú)立懸架的建立是根據(jù)汽車硬點(diǎn)參數(shù)，對(duì)性能進(jìn)行了分析，并與多體動(dòng)力學(xué)和懸架運(yùn)動(dòng)學(xué)進(jìn)行了理論探討。可以得出如下結(jié)論:當(dāng)車輪需要運(yùn)轉(zhuǎn)時(shí)，所有的下控制臂的剛度并沒(méi)有影響外傾角，后傾角和主銷內(nèi)傾角，橡膠襯套和扭轉(zhuǎn)剛度對(duì)前束角產(chǎn)生很大影響，而軸向，徑向剛度沒(méi)有任何效果。然而在轉(zhuǎn)向時(shí)，所有的下控制臂襯套并無(wú)外傾角和前束角的影響，及扭轉(zhuǎn)剛度對(duì)彎度角的影響，軸向剛度，徑向剛度相對(duì)較大，軸向和扭轉(zhuǎn)剛度對(duì)主銷內(nèi)傾角無(wú)影響，但徑向剛度較大影響。在分析牽引力和制動(dòng)力的時(shí)候，下控制臂扭轉(zhuǎn)橡膠襯套剛度沒(méi)有對(duì)車輪外傾角，主銷內(nèi)傾角和前束角產(chǎn)生影響，對(duì)軸向剛度影響的卻很少，徑向剛度大，根據(jù)后傾角與制動(dòng)力曲線，徑向和軸向橡膠襯套剛度對(duì)施力者有一個(gè)小角度的影響，但扭轉(zhuǎn)剛度不變。
關(guān)鍵詞--前雙橫臂獨(dú)立懸架，橡膠襯套，剛度
I、簡(jiǎn)介
如今，雙橫臂獨(dú)立懸架被廣泛用于汽車行業(yè)中。等長(zhǎng)橫臂和不等長(zhǎng)橫臂，現(xiàn)在等長(zhǎng)的雙橫臂獨(dú)立懸架通常不是很常用，不等長(zhǎng)的雙橫臂獨(dú)立懸架可以保持良好的能力和減少道路懸掛之間的干擾，如果能夠設(shè)置合理的結(jié)構(gòu)參數(shù)和適當(dāng)安排，就可以以使車輪打滑和車輪定位參數(shù)在允許范圍內(nèi)浮動(dòng)。因此，它被廣泛應(yīng)用于汽車和小卡車前懸架等。前雙橫臂獨(dú)立懸架被做為研究對(duì)象，運(yùn)用多體動(dòng)力學(xué)和懸架運(yùn)動(dòng)學(xué)理論來(lái)分析懸浮軸，扭轉(zhuǎn)，橡膠襯套剛度性能影響的激勵(lì)方面等內(nèi)容。
II、多體運(yùn)動(dòng)學(xué)分析
根據(jù)多體運(yùn)動(dòng)學(xué)研究物體運(yùn)動(dòng)規(guī)律:
；
；
初始條件
q(0)=
(0)=
III、前雙橫臂獨(dú)立懸架模型
依據(jù)某懸架關(guān)鍵點(diǎn)的重要性，建立前雙橫臂獨(dú)立懸架運(yùn)動(dòng)學(xué)模型如圖1所示.在某些工況下分析，尋找位置參數(shù)的特點(diǎn)。在分析過(guò)程中，軸向，扭轉(zhuǎn)，橡膠襯套剛度分別比原來(lái)相比增長(zhǎng)了5倍，然后比較，并與原有的數(shù)據(jù)分析。
圖a 前雙橫臂獨(dú)立懸架模型
IV、下橫臂對(duì)車輪定位參數(shù)的影響
當(dāng)橡膠襯套控制臂的剛度改變時(shí)，對(duì)車輪定位參數(shù)的影響進(jìn)行了車輪下單獨(dú)跳，轉(zhuǎn)向，牽引力和制動(dòng)力的條件等方面的討論。
A. 輪跳
車輪外傾角與車輪跳動(dòng)
主銷后傾角與車輪跳動(dòng)
主銷內(nèi)傾角與車輪跳動(dòng)
車輪前束角與車輪跳動(dòng)
在圖2中，在四條曲線下不變的情況下控制臂襯套剛度橡膠和徑向，軸向，扭轉(zhuǎn)剛度增加5倍（下控制臂襯套剛度也像3，4和 5那樣）。根據(jù)彎度角曲線與車輪跳動(dòng)，圖2所表達(dá)的是主銷的后傾角與車輪跳動(dòng)和主銷內(nèi)傾角與車輪跳動(dòng)曲線關(guān)系，所以得出的結(jié)論是徑向，軸向和扭轉(zhuǎn)橡膠襯套剛度均沒(méi)有對(duì)前束角產(chǎn)生影響。然而橡膠襯套剛度對(duì)前束角影響大，但有軸向和扭轉(zhuǎn)剛度時(shí)車輪前束角與曲線有跳動(dòng)趨勢(shì)。
B 轉(zhuǎn)向分析
車輪外傾角與轉(zhuǎn)向角
主銷后傾角與轉(zhuǎn)向角
主銷內(nèi)傾角與轉(zhuǎn)向角
車輪前束角與轉(zhuǎn)向角
圖b曲線車輪定位參數(shù)及轉(zhuǎn)向角剛度
根據(jù)傾角與轉(zhuǎn)向角曲線和前束角與轉(zhuǎn)向角, 轉(zhuǎn)向時(shí), 徑向，軸向和扭轉(zhuǎn)橡膠襯套剛度對(duì)外傾角和前束角沒(méi)有影響。在后傾角與轉(zhuǎn)向角曲線中，橡膠襯套剛度并連桿機(jī)構(gòu)造成影響，剛度小，但軸向剛度比較大。軸向和扭轉(zhuǎn)橡膠襯套剛度沒(méi)對(duì)主銷內(nèi)傾角產(chǎn)生影響，而軸向剛度由主銷內(nèi)傾角與轉(zhuǎn)向角曲線共同決定。
C 制動(dòng)力分析
后傾角與剎車力
主銷內(nèi)傾角與制動(dòng)力
車輪前束角與剎車力
圖c下控制臂剛度，車輪定位參數(shù)和剎車力曲線
在圖4，根據(jù)傾角與制動(dòng)力曲線，剎車時(shí)，主銷內(nèi)傾角與制動(dòng)力和前束角與制動(dòng)力，扭轉(zhuǎn)橡膠襯套剛度對(duì)外傾角沒(méi)有影響，主銷內(nèi)傾角和前束角，軸向剛度小，但徑向剛度較大。徑向和軸向橡膠襯套剛度對(duì)傾角影響不大，扭轉(zhuǎn)剛度也影響不大。
D 牽引力分析
主銷內(nèi)傾角與牽引力
后傾角與牽引力
主銷內(nèi)傾角與牽引力
車輪前束角與牽引力
圖d 曲線 下控制臂，車輪定位參數(shù)和牽引力剛度曲線
在圖5中，根據(jù)傾角與牽引力曲線，當(dāng)制動(dòng)時(shí)，主銷內(nèi)傾角與牽引力和前束角與牽引力，對(duì)扭轉(zhuǎn)橡膠襯套剛度的傾角影響不大，主銷內(nèi)傾角和前束角，軸向剛度小，但徑向剛度較大。，徑向和軸向剛度的傾角影響不大，對(duì)扭轉(zhuǎn)剛度也沒(méi)有影響。
V.結(jié)論
使用多體動(dòng)力學(xué)和懸架運(yùn)動(dòng)學(xué)理論，分析了車輪定位參數(shù)的影響，當(dāng)徑向，軸向和下控制臂扭轉(zhuǎn)剛度在受控制之前，橡膠襯套正在發(fā)生變化。根據(jù)徑向分析結(jié)果，當(dāng)車輪跳動(dòng)時(shí)，下控制臂扭轉(zhuǎn)剛度在橡膠襯套變動(dòng)之前，所有的下控制臂的剛度并沒(méi)有產(chǎn)生外傾角的變化，包括后傾角，主銷后傾角和內(nèi)傾角，橡膠襯套剛度扭轉(zhuǎn)效應(yīng)對(duì)前束角有明顯影響，但軸向，徑向剛度則對(duì)其沒(méi)有任何效果。然而當(dāng)轉(zhuǎn)向時(shí)，所有的下控制臂襯套剛度橡膠不會(huì)對(duì)外傾角和前束角產(chǎn)生影響，對(duì)軸向剛度沒(méi)有影響，對(duì)徑向剛度影響較小，軸向和扭轉(zhuǎn)剛度對(duì)主銷角度無(wú)影響，但對(duì)徑向剛度影響較大。在分析的牽引力和制動(dòng)力時(shí)，下控制臂扭轉(zhuǎn)橡膠襯套剛度對(duì)外傾角沒(méi)有影響，對(duì)主銷內(nèi)傾角和車輪前束角而言，軸向剛度對(duì)其影響較小，但徑向剛度對(duì)其影響較大。根據(jù)后傾角與制動(dòng)力曲線，徑向和軸向橡膠襯套剛度對(duì)驅(qū)動(dòng)者有一個(gè)小角度的影響，但對(duì)扭轉(zhuǎn)剛度沒(méi)有影響。
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