軸及軸承計(jì)算

1、2021/8/141N212319321462860對(duì)2點(diǎn)取矩1932146286021936410舉例：舉例：計(jì)算某減速器輸入軸危計(jì)算某減速器輸入軸危險(xiǎn)截面的直徑。已知作用在齒險(xiǎn)截面的直徑。已知作用在齒輪上的圓周力輪上的圓周力Ft=17400N, 徑徑向力，向力， Fr=6140N, 軸向力軸向力Fa=2860N,齒輪分度圓直徑齒輪分度圓直徑d2=146 mm,作用在軸右端帶作用在軸右端帶輪上外力輪上外力F=4500N（方向未方向未定）定）, L=193 mm, K=206 mm。設(shè)設(shè)a-a截面直徑為截面直徑為70mm，試校試校核其強(qiáng)度。核其強(qiáng)度。L/2LKFtFrFaFFaFrF1vF2v

2、解：解：1) 求垂直面的支反力和軸向力求垂直面的支反力和軸向力LdFLFF222ar1vN4287212364101vFvrvFFF12d212潘存云教授研制daa2021/8/142潘存云教授研制N930348034500MavMavF1HF2HMaHF1FF2F2) 求水平面的支反力求水平面的支反力N480319320645001FLKFF87002/t2H1HFFF3) 求求F力在支點(diǎn)產(chǎn)生的反力力在支點(diǎn)產(chǎn)生的反力1F2FFFF4) 繪制垂直面的彎矩圖繪制垂直面的彎矩圖2/193. 04287aVM2/2VaVLFMmN4142/193. 02123aVM2/=1VaVLFMmN2055)

3、 繪制水平面的彎矩圖繪制水平面的彎矩圖2/193. 08700 aVM 2/1HaHLFMmN840FtFL/2LKFtFrFaFFAFaFrF1vF2v12=Fad2aad2021/8/143MaMavMavF1HF2HMaHF1FF2FM2F6) 求求F力產(chǎn)生的彎矩圖力產(chǎn)生的彎矩圖7) 繪制合成彎矩圖繪制合成彎矩圖考慮F可能與H、V內(nèi)合力共面228404144632aH2aVaFaMMMMmN1400206. 04500aVMKFM2FmN927a a 截面截面F力產(chǎn)生的彎矩為：力產(chǎn)生的彎矩為：2/193. 04803aVM2/1FaFLFMmN463MaF228402054632aH2a

4、VaFa)(MMMMmN1328 MaFtFL/2LKFtFrFaFFAFaFrF1vF2v12=Fad2aad2021/8/144潘存云教授研制潘存云教授研制MaMavMavF1HF2HMaHF1FF2FM2F8) 求軸傳遞的轉(zhuǎn)矩求軸傳遞的轉(zhuǎn)矩9)求危險(xiǎn)截面的當(dāng)量彎矩求危險(xiǎn)截面的當(dāng)量彎矩MaF22ae)( TMMM2Ma2/146. 0174002T2/2tdFTmN1270T扭切應(yīng)力為脈動(dòng)循環(huán)變應(yīng)力，扭切應(yīng)力為脈動(dòng)循環(huán)變應(yīng)力，取折合系數(shù)取折合系數(shù): =0.6 22e)12706.0(1400TMmN1600mN9272F2 MMFtFL/2LKFtFrFaFFAFaFrF1vF2v12=F

5、ad2aad2021/8/14510)校核軸危險(xiǎn)截面處的強(qiáng)度校核軸危險(xiǎn)截面處的強(qiáng)度 MPa6 .46701 .01016003331.0dMWMeeca選選45鋼，調(diào)質(zhì)，鋼，調(diào)質(zhì)，b =650 MPa, -1b =60 MPa ca -1b ，強(qiáng)度足夠。強(qiáng)度足夠。2021/8/146滾動(dòng)軸承例題分析滾動(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個(gè)角接觸球軸承。已知軸上齒輪受切向力Ft=2200N，徑向力徑向力Fr=900N，軸向力軸向力Fa=400 N，齒輪分度圓直徑齒輪分度圓直徑d=314 mm，齒輪轉(zhuǎn)速齒輪轉(zhuǎn)速n=52

6、0 rpm，運(yùn)轉(zhuǎn)中有中等沖擊運(yùn)轉(zhuǎn)中有中等沖擊載荷，軸承預(yù)期計(jì)算壽命載荷，軸承預(yù)期計(jì)算壽命Lh=15000 h。設(shè)設(shè)初選兩個(gè)軸承型號(hào)均為初選兩個(gè)軸承型號(hào)均為7207C，試驗(yàn)算軸試驗(yàn)算軸承是否可達(dá)到預(yù)期計(jì)算壽命的要求。承是否可達(dá)到預(yù)期計(jì)算壽命的要求。32020021解：解：1. 求徑向載荷求徑向載荷 先求兩處徑向載荷垂直和水平分量 320+2002/200=-1dFFFaereVrNFFFVrreVr62.674=12-teHrFF320+200200=1NFFFHrteHr85.135312-Fr2VFr1VFr2HFr1HFteFaeFreFaeFreFteN38.225=5202/31440

7、0200900=-N15.84622005202002021/8/147Fd=eFr21211+=HrVrrFFF求總徑向載荷求總徑向載荷 2H2r2V2r2rFFF2. 求兩軸承的派生軸向力求兩軸承的派生軸向力Fd1和和Fd2 查表得查表得7207C軸承的基本額定動(dòng)載荷軸承的基本額定動(dòng)載荷與基本額定靜載荷為與基本額定靜載荷為 C=30500 N C0=20000 N對(duì)于對(duì)于70000C型軸承，型軸承，派生派生軸向力軸向力 Fd=1.14FrFd=0.68FrFd=eFrFd=Fr(2Y)70000B( =40)70000AC( =25)70000C( =15)角接觸球軸承角接觸球軸承圓錐滾子

8、軸承圓錐滾子軸承其中其中e為判斷系數(shù)，按下表為判斷系數(shù)，按下表13-5選取選取 21FaeFreFteN65.875=15.846+38.225=22N62.151285.135362.67422Fd2Fd12021/8/148軸承類型軸承類型 相對(duì)軸向載荷相對(duì)軸向載荷 Fa / Fr e Fa / Fr e 名名 稱稱 代代 號(hào)號(hào) f 0Fa / C0r Fa / C0 X Y X Y 判斷系數(shù)判斷系數(shù)e 調(diào)心球軸承調(diào)心球軸承 10000 1 (Y1) 0.65 (Y2) (e) 調(diào)心滾子軸承調(diào)心滾子軸承 20000 1 (Y1) 0.67 (Y2) (e) 推力調(diào)心滾子軸承推力調(diào)心滾子軸承

9、 29000 1 1.2 1 1.2圓錐滾子軸承圓錐滾子軸承 30000 1 0 0.4 (Y) (e)深溝球軸承深溝球軸承 60000角接觸球軸承角接觸球軸承0.172 2.30 0.190.345 1.99 0.220.689 1.71 0.261.030 1.55 0.281.380 1 0 0.56 1.45 0.302.070 1.31 0.343.450 1.15 0.385.170 1.04 0.426.890 1.00 0.440.015 1.47 0.380.029 1.40 0.400.058 1.30 0.430.087 1.23 0.460.120 1 0 0.44 1

10、.19 0.470.170 1.12 0.500.290 1.02 0.550.440 1.00 0.560.580 1.00 0.56 1 0 0.41 0.87 0.68 1 0 0.35 0.57 1.14 70000AC =2=2570000B = =40 70000C =1=15表表13-5 徑向動(dòng)載荷系數(shù)徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)與軸向動(dòng)載系數(shù)Y因?yàn)橐驗(yàn)镕a未知，初選未知，初選e=0.4 0.409Fd1=eFr1 Fd2=eFr2 于是于是 Fa1= Fae +Fd2 Fa2= Fd2 =605.05 N Fa1/C0= 1005.05/20000 =0.0503 Fa2/C

11、0= 605.05/20000 =0.0303 重新查表選取判斷系數(shù)重新查表選取判斷系數(shù)e 派生派生軸向力軸向力:=0.4875.65=350.26 N =0.41512.62=605.05 N =400+605.05=1005.05 N 21FaeFd2Fd1由于由于 Fae +Fd2 =400+605.05 =1005.05 N Fd1=350.26 N1端是壓緊端端是壓緊端(反裝時(shí)向左壓右端壓緊）反裝時(shí)向左壓右端壓緊）10軸承類型軸承類型 相對(duì)軸向載荷相對(duì)軸向載荷 Fa / Fr e Fa / Fr e 名名 稱稱 代代 號(hào)號(hào) f 0Fa / C0r Fa / C0 X Y X Y 判斷

12、系數(shù)判斷系數(shù)e 調(diào)心球軸承調(diào)心球軸承 10000 1 (Y1) 0.65 (Y2) (e) 調(diào)心滾子軸承調(diào)心滾子軸承 20000 1 (Y1) 0.67 (Y2) (e) 推力調(diào)心滾子軸承推力調(diào)心滾子軸承 29000 1 1.2 1 1.2圓錐滾子軸承圓錐滾子軸承 30000 1 0 0.4 (Y) (e)深溝球軸承深溝球軸承 60000角接觸球軸承角接觸球軸承0.172 2.30 0.190.345 1.99 0.220.689 1.71 0.261.030 1.55 0.281.380 1 0 0.56 1.45 0.302.070 1.31 0.343.450 1.15 0.385.17

13、0 1.04 0.426.890 1.00 0.440.015 1.47 0.380.029 1.40 0.400.058 1.30 0.430.087 1.23 0.460.120 1 0 0.44 1.19 0.470.170 1.12 0.500.290 1.02 0.550.440 1.00 0.560.580 1.00 0.56 1 0 0.41 0.87 0.68 1 0 0.35 0.57 1.14 70000AC =2=2570000B = =40 70000C =1=15表表13-5 徑向動(dòng)載荷系數(shù)徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)與軸向動(dòng)載系數(shù)Y 0.029 沒(méi)有相同的值0.0

14、503 0.40 0.058 0.43Fa / C0表中沒(méi)有與計(jì)算結(jié)果相同的表中沒(méi)有與計(jì)算結(jié)果相同的Fa1/C0值，采用線性插值法求值，采用線性插值法求e0.058 0.43(0.029 0.4 )422. 0=)40. 043. 0 (029. 0058. 0029. 00503. 0+4 . 0=-1e線性插值的原理線性插值的原理401. 0=2e同理可求得角的正切值為對(duì)邊比鄰邊0.0503 e1 40. 043. 00.029058. 0=-40. 0029. 0503. 0=tan-1e11重新查表選取判斷系數(shù)重新查表選取判斷系數(shù)e 重新計(jì)算重新計(jì)算派生派生軸向力軸向力 Fd1=e1F

15、r1 =0.422875.65=369.52 N Fd2=e2Fr2 =0.4011512.62=606.56 N e1=0.422 e2=0.401 Fa1= Fae +Fd2 Fa2= Fd2 =606.56 N Fa1/C0= 1006.56/20000 =0.05033 Fa2/C0= 606.56/20000 =0.03033 兩次計(jì)算兩次計(jì)算 Fa2/C0 結(jié)果相差不大，故取結(jié)果相差不大，故取 重新計(jì)算軸向力重新計(jì)算軸向力 e1=0.422 e2=0.401Fa1= 1006.56 NFa2=606.56 N =400+606.56=1006.56 N 123. 求軸承的當(dāng)量載荷求

16、軸承的當(dāng)量載荷P1和和P2 422. 0149. 165.87556.1006111eFFra222=401. 0=62.151256.606=eFFra查下頁(yè)表并插值可求得徑向載荷系數(shù)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)和軸向載荷系數(shù)Y 13軸承類型軸承類型 相對(duì)軸向載荷相對(duì)軸向載荷 Fa / Fr e Fa / Fr e 名名 稱稱 代代 號(hào)號(hào) f 0Fa / C0r Fa / C0 X Y X Y 判斷系數(shù)判斷系數(shù)e 調(diào)心球軸承調(diào)心球軸承 10000 1 (Y1) 0.65 (Y2) (e) 調(diào)心滾子軸承調(diào)心滾子軸承 20000 1 (Y1) 0.67 (Y2) (e) 推力

17、調(diào)心滾子軸承推力調(diào)心滾子軸承 29000 1 1.2 1 1.2圓錐滾子軸承圓錐滾子軸承 30000 1 0 0.4 (Y) (e)深溝球軸承深溝球軸承 60000角接觸球軸承角接觸球軸承0.172 2.30 0.190.345 1.99 0.220.689 1.71 0.261.030 1.55 0.281.380 1 0 0.56 1.45 0.302.070 1.31 0.343.450 1.15 0.385.170 1.04 0.426.890 1.00 0.440.015 1.47 0.380.029 1.40 0.400.058 1.30 0.430.087 1.23 0.460.

18、120 1 0 0.44 1.19 0.470.170 1.12 0.500.290 1.02 0.550.440 1.00 0.560.580 1.00 0.56 1 0 0.41 0.87 0.68 1 0 0.35 0.57 1.14 70000AC =2=2570000B = =40 70000C =1=15表表13-5 徑向動(dòng)載荷系數(shù)徑向動(dòng)載荷系數(shù)X與軸向動(dòng)載系數(shù)與軸向動(dòng)載系數(shù)Y采用線性插值法求采用線性插值法求Y1對(duì)軸承對(duì)軸承1 X1 =0.44 Y1 =1.327 4 . 0422. 01.4=4 . 043. 04 . 13 . 1-1Y1.30 0.43(1.40 0.4 )327. 1=)40. 0422. 0 (4 . 043. 04 . 13 . 1+4 . 1=-1Y 1.