滾動(dòng)軸承習(xí)題及思考題

由于軸承安裝情況與受載情況的復(fù)雜性，計(jì)算軸承的徑向力與軸向力時(shí)不要死記公式，而是要學(xué)會(huì)根據(jù)具體情況進(jìn)行具體分析，步驟為：

*根據(jù)Fr求出Fr1和Fr2。*按表13－7估計(jì)Fd1和Fd2的值，它們的方向視軸承安裝方向而定。注意把派生軸向力的方向與外加軸向載荷Fae的方向一致的軸承標(biāo)記為2，另一端的軸承標(biāo)記為1。*由于軸承最終必須處于平衡狀態(tài)，所以Fd1和Fd2的值最后有一個(gè)要變化到F‘d，以便與Fae一起達(dá)到軸向力的平衡。當(dāng)Fae＋Fd2>Fd1則Fd1應(yīng)增大到F‘d1，使F‘d1＝Fae＋Fd2，而Fd2則不變。當(dāng)Fae＋Fd2<Fd1

則Fd2應(yīng)增大到F‘d2，使F‘d2＝Fd1－Fae，而Fd1則不變。

*兩端軸承所受的軸向力Fa1和Fa2如下：當(dāng)Fae＋Fd2>Fd1時(shí)，為

Fd1＝F‘d1，F(xiàn)a2＝Fd2；當(dāng)Fae＋Fd2<Fd1時(shí)，為

Fa1＝Fd1，F(xiàn)a2＝F

‘d2。另外，對(duì)于接觸角為150的軸承（70000C型），計(jì)算當(dāng)量動(dòng)載荷時(shí)會(huì)有一個(gè)迭代的過(guò)程。因?yàn)閄、Y系數(shù)的確定與比值Fa/Fr有關(guān)，而軸向力的確定與判斷系數(shù)e有關(guān)，e的確定又與比值Fa/C0有關(guān)。所以對(duì)于一個(gè)具體的軸承，無(wú)法通過(guò)一次計(jì)算確定e和A的值，也就不能確定X、Y的值。這是可以初選一個(gè)e值可在0.38

e0.56的范圍內(nèi)選擇，例如選e=0.5。有了初選的e值，就可根據(jù)力分析和表13－7估計(jì)出Fa，再由比值Fa/C0和表13－5確定新的e值和對(duì)應(yīng)的X、Y值，這時(shí)完成了一輪迭代。如果新的e值與初選的e很接近，則X、Y值已確定；否則，按新的e再確定Fa，進(jìn)行迭代，一般反復(fù)迭代一、二次就能滿(mǎn)足要求?！?3-8滾動(dòng)軸承例題分析

設(shè)根據(jù)工作條決定在軸的兩端反裝兩個(gè)角接觸球軸承。已知軸上齒輪受切向力Ft=2200N，徑向力Fr=900N，軸向力Fa=400N，齒輪分度圓直徑d=314mm，齒輪轉(zhuǎn)速n=520rpm，運(yùn)轉(zhuǎn)中有中等沖擊載荷，軸承預(yù)期計(jì)算壽命L’h=15000h。設(shè)初選兩個(gè)軸承型號(hào)均為7207C，試驗(yàn)算軸承是否可達(dá)到預(yù)期計(jì)算壽命的要求。32020021解：1.求徑向載荷

先求兩處徑向載荷垂直和水平分量

Fr2VFr1VFr2HFr1HFteFaeFreFaeFreFteFd=eFr求總徑向載荷

2.求兩軸承的計(jì)算軸向力Fd1和Fd2

查表得7207C軸承的基本額定動(dòng)載荷與基本額定靜載荷為

C=30500NC0=20000N對(duì)于70000C型軸承，內(nèi)部軸向力Fd=1.14FrFd=0.68FrFd=eFrFd=Fr／(2Y)70000B(a=40o)70000AC(a=25o)70000C(a=15o)角接觸球軸承圓錐滾子軸承其中e為判斷系數(shù)，按下表13-5選取21FaeFreFteFd2Fd1軸承類(lèi)型相對(duì)軸向載荷Fa/Fr

≤eFa/Fr>e名稱(chēng)代號(hào)f

0Fa/C0r

Fa/C0

XYXY判斷系數(shù)e調(diào)心球軸承10000—

—1(Y1)0.65(Y2)(e)調(diào)心滾子軸承20000—

—1(Y1)0.67(Y2)(e)推力調(diào)心滾子軸承29000—

—11.211.2圓錐滾子軸承30000—

—100.4(Y)(e)深溝球軸承60000角接觸球軸承0.1722.300.190.3451.990.220.6891.710.261.0301.550.281.380—100.561.450.302.0701.310.343.4501.150.385.1701.040.426.8901.000.440.0151.470.380.0291.400.400.0581.300.430.0871.230.460.120100.441.190.470.1701.120.500.2901.020.550.4401.000.560.5801.000.56—

—100.410.870.68—

—100.350.571.1470000AC

α=25?70000Bα=40?

70000C

α=15?表13-5徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)Y因?yàn)镕a未知，初選e=0.4

0.40Fd1=eFr1Fd2=eFr2于是

Fa1=Fae+Fd2Fa2=Fd2=605.05NFa1/C0=1005.05/20000=0.0503Fa2/C0=605.05/20000=0.0303重新查表選取判斷系數(shù)e

內(nèi)部軸向力:=0.4×875.65=350.26N

=0.4×1512.62=605.05N=400+605.05=1005.05N軸承類(lèi)型相對(duì)軸向載荷Fa/Fr

≤eFa/Fr>e名稱(chēng)代號(hào)f

0Fa/C0r

Fa/C0

XYXY判斷系數(shù)e調(diào)心球軸承10000—

—1(Y1)0.65(Y2)(e)調(diào)心滾子軸承20000—

—1(Y1)0.67(Y2)(e)推力調(diào)心滾子軸承29000—

—11.211.2圓錐滾子軸承30000—

—100.4(Y)(e)深溝球軸承60000角接觸球軸承0.1722.300.190.3451.990.220.6891.710.261.0301.550.281.380—100.561.450.302.0701.310.343.4501.150.385.1701.040.426.8901.000.440.0151.470.380.0291.400.400.0581.300.430.0871.230.460.120100.441.190.470.1701.120.500.2901.020.550.4401.000.560.5801.000.56—

—100.410.870.68—

—100.350.571.1470000AC

α=25?70000Bα=40?

70000C

α=15?表13-5徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)Y0.029沒(méi)有相同的值0.05030.400..0580.43Fa/C0表中沒(méi)有與計(jì)算結(jié)果相同的Fa1/C0值，采用線性插值法求e0.0580.43(0.0290.4)線性插值的原理α角的正切值為對(duì)邊比鄰邊0.0503e1

α重新查表選取判斷系數(shù)e

重新計(jì)算軸向力

Fd1=e1Fr1=0.422×875.65=369.52N

Fd2=e2Fr2=0.401×1512.62=606.56Ne1=0.422e2=0.401Fa1=Fae+Fd2Fa2=Fd2=606.56NFa1/C0=1006.56/20000=0.05033Fa2/C0=606.56/20000=0.03033兩次計(jì)算Fa2/C0結(jié)果相差不大，故取

重新計(jì)算軸向力e1=0.422e2=0.401Fa1=1006.56NFa2=606.56N=400+606.56=1006.56N3.求軸承的當(dāng)量載荷P1和P2

查下頁(yè)表并插值可求得徑向載荷系數(shù)X和軸向載荷系數(shù)Y軸承類(lèi)型相對(duì)軸向載荷Fa/Fr

≤eFa/Fr>e名稱(chēng)代號(hào)f

0Fa/C0r

Fa/C0

XYXY判斷系數(shù)e調(diào)心球軸承10000—

—1(Y1)0.65(Y2)(e)調(diào)心滾子軸承20000—

—1(Y1)0.67(Y2)(e)推力調(diào)心滾子軸承29000—

—11.211.2圓錐滾子軸承30000—

—100.4(Y)(e)深溝球軸承60000角接觸球軸承0.1722.300.190.3451.990.220.6891.710.261.0301.550.281.380—100.561.450.302.0701.310.343.4501.150.385.1701.040.426.8901.000.440.0151.470.380.0291.400.400.0581.300.430.0871.230.460.120100.441.190.470.1701.120.500.2901.020.550.4401.000.560.5801.000.56—

—100.410.870.68—

—100.350.571.1470000AC

α=25?70000Bα=40?

70000C

α=15?表13-5徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)Y采用線性插值法求Y1對(duì)軸承1

X1=0.44Y1=1.3271.300.43(1.400.4)1.400.401.300.43表中沒(méi)有e=0.422αY10.422

軸承2

X2=1Y2=0軸承工作時(shí)有中等沖擊載荷，查表取表13-6載荷系數(shù)

載荷性質(zhì)載荷系數(shù)fP無(wú)沖擊或輕微沖擊1.0~1.2中等沖擊1.2~1.8強(qiáng)烈沖擊1.8~3.0應(yīng)用舉例電機(jī)、汽輪機(jī)、通風(fēng)機(jī)、水泵等機(jī)床、車(chē)輛、動(dòng)力機(jī)械、起重機(jī)、造紙機(jī)、選礦基、冶金機(jī)械、卷?yè)P(yáng)機(jī)等碎石機(jī)、軋鋼機(jī)、鉆探機(jī)、振動(dòng)篩等1.2~1.8軸承的當(dāng)量載荷:

P1=fp(X1Fr1+Y1Fa1)P2=fp(X2Fr2+Y2Fa2)=1.5×(0.44×875.65+1.327×1006.56)=2581.49N=1.5×(1×1512.62+0×606.56)=2268.93Nfp=1.54.驗(yàn)算軸承壽命∵P1〉

P2所以按軸承1的壽命計(jì)算所選軸承滿(mǎn)足壽命要求。13-4一農(nóng)用水泵，決定選用深溝球軸承，軸頸直徑d=35mm，轉(zhuǎn)速n=2900r/min。已知徑向載荷Fr=1810N，軸向載荷Fa=740N，預(yù)期計(jì)算壽命L‘h=6000，試選擇軸承型號(hào)。解：1求比值Fa/

Fr=

740/1810=0.41查表13-5，X=0.56，Y=1.65相對(duì)軸向載荷f0Fa/C0r=14.7×740/15200=0.716，對(duì)應(yīng)e值在0.26和0.28之間2初選軸承型號(hào)：6207，C=25500N，C0=15200NP=XFr+YFa=2234.6NL=8545h驗(yàn)算Y＝1.55+(1.71-1.55)*(1.03-0.716)/(1.03-0.689)=1.6973L=4714hP=XFr+YFa=2269.6N選軸承型號(hào)：6307，C=33200NC0=19200N相對(duì)軸向載荷f0Fa/C0r=14.7×740/19200=0.56656，對(duì)應(yīng)e值在0.22和0.26之間.查表13-5，X=0.56P=XFr+YFa=2352.72NL=9345.67hY=1.71+(1.99-1.71)*(0.689-0.56656)/(0.689-0.345)=1.8113-5根據(jù)工作條件，決定在軸的兩端選用α=250的兩個(gè)角接觸球軸承，如圖示。軸頸直徑d=35mm，工作中有中等沖擊，轉(zhuǎn)速n=1800r/min，已知兩軸承的徑向載荷分別為Fr1=3390N，F(xiàn)r2=1040N，外加軸向載荷Fae=870N，作用方向指向軸承1，試確定其工作壽命。解：對(duì)于70000AC型軸承Fd=0.68Fr1FaeFr2Fr1Fd2Fd12正裝Fd1=0.68Fr1=0.68×3390=2305.2NFd2=0.68Fr1=0.68×1040=707.2N按Fa1=Fae+Fd2=1577.2N<Fd1，F(xiàn)a1=

Fd1=2305.2NFa2=Fd1－Fae

=1435.2NFa1/Fr1=0.68,e=0.68,查表13-5，X=1，Y=0Fa2/Fr2=1.38,查表13-5，X=0.41，Y=0.87P1=XFr=3390NP2=XFr+YFa=0.41×1040+0.87×1435.2=1675N查表（國(guó)家標(biāo)準(zhǔn)）：7207AC軸承的C=3050