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1、第7章 圓柱齒輪公差與配合應(yīng)用Chapter 7 Cylindrical gears tolerance and fit application,基本要求 Basic requirements,目的：了解圓柱齒輪的公差標(biāo)準(zhǔn) Aim:To understand tolerance standards of Cylindrical gear 初步掌握： Grasp preliminarily: 1.應(yīng)用要求、加工誤差 Application requirements and manufacturing error 2.評(píng)定指標(biāo) Evaluation index 3.圖樣標(biāo)注 Label

2、s of pattern 4.齒輪精度設(shè)計(jì) Design of gear accuracy 操作技能：評(píng)定指標(biāo)的檢驗(yàn) Manipulative skill:The test of evaluation index.,特點(diǎn) Traits 1 結(jié)構(gòu)緊湊 Compact structure 2 恒定的傳動(dòng)比 Constant transmission ratio 3 傳動(dòng)效率高 High transmission efficiency 4 可實(shí)現(xiàn)平行軸、相交軸和交錯(cuò)軸之間的傳動(dòng) It could realize the transmission between parallel axles, i

3、ntersectant axles and interlaced axles 5 使用壽命長 Long working life 6 維護(hù)保養(yǎng)簡單 Sample to maintain,作用：傳遞空間任意兩軸（平行、相交、交錯(cuò)）的旋轉(zhuǎn)運(yùn)動(dòng)，或?qū)⑥D(zhuǎn)動(dòng)轉(zhuǎn)換為移動(dòng)。Founction:To transmit the revolving movements of any two axles(parallel,intersectant and interlaced) in space.And to convert turn to shift.,缺點(diǎn)：要求較高的制造和安裝精度，加工成本高、不適宜遠(yuǎn)距離傳動(dòng)

4、。 Disadvantages:It needs higher accuracies of manufacture and installment. Conversion cost is high and it is not suitable for long distance transmission.,齒輪傳動(dòng)的類型 Types of gear drive,傳動(dòng)齒輪：轉(zhuǎn)速較高，功率較大 （汽車 飛機(jī)等變速裝置） Drive gear:Higher rotation rate and power(Speed variators in automobiles and airplanes) 動(dòng)力

5、齒輪：轉(zhuǎn)速不高，傳遞扭矩（礦山機(jī)械 起重機(jī)械） Power gear:The speed of revolution is not high and it transmits torque(mining machine and hoisting machinery) 分度齒輪：精確回轉(zhuǎn)（精密機(jī)床 儀表中的分度裝置） Dividing gear:Precise rotation(precision machine tool and dividing device in instrumentation),,齒輪傳動(dòng)機(jī)構(gòu)組成 The form of gear transimission mechan

6、ism,齒輪副、軸、軸承、箱體pair of gears, axles, bearings and boxes,失效形式 failure mode,輪齒折斷 tooth breakage,1.由于多次重復(fù)的彎曲應(yīng)力和應(yīng)力集中造成的疲勞折斷；The fatigue fracture which is caused by oft-repeated bending stresses and stress concentration. 2.由于突然嚴(yán)重過載或沖擊載荷作用引起的過載折斷。The overload break which is caused by sudden severe overloa

7、d or impact load. 直齒輪：齒寬較小的往往發(fā)生全齒折斷,齒寬較大的直齒輪或斜齒輪則容易發(fā)生局部折斷。 Straight gear:The gears with smaller breadth of tooth often emerge whole tooth fracture while the straight gears or helical gears with bigger breadth of tooth are easy to emerge local break.,一、 輪齒的失效形式,失效形式,,齒面點(diǎn)蝕 Tooth surface pitting,原因：由于在

8、齒面嚙合處脈動(dòng)循環(huán)變接觸應(yīng)力長期作用下，當(dāng)應(yīng)力峰值超過材料的接觸疲勞極限，經(jīng)過一定應(yīng)力循環(huán)次數(shù)后，先在節(jié)線附近的齒廓表面產(chǎn)生細(xì)微的疲勞裂紋。隨著裂紋的擴(kuò)展，將導(dǎo)致小塊金屬剝落，產(chǎn)生齒面點(diǎn)蝕。Reason:Because of the long term effect of pulsating cyclic variable contact stress on meshing point of tooth surface.When peak stress exceeds materials contact fatigue limit, hairlike fatigue cracks will a

9、ppear on tooth profile surface around nodel line after certain number of times of stress cycle.With the extending of flaws. Scrap metal will peel off to produce tooth surface pitting. 點(diǎn)蝕不良影響：影響輪齒正常嚙合，引起沖擊和噪聲，造成傳動(dòng)的不平穩(wěn)。 Harmful effects of pitting:Influencing the normal engagement of gear teeth,causing

10、 concussions and noise,creating un-stationary transmission.,一、 輪齒的失效形式,失效形式,,齒面膠合 Tooth surface bonding,高速重載傳動(dòng)中，常因嚙合區(qū)溫度升高而引起潤滑失效，致使齒面金屬直接接觸而相互粘連。當(dāng)齒面相對(duì)滑動(dòng)時(shí)，較軟的齒面沿滑動(dòng)方向被撕下而形成溝紋。On high speed and heavy load transmission.The raise of meshing zones temperature usually causes lubrication losing efficacy to

11、lead to the direct contacts of tooth surface metal and adhesions of each other.When tooth surfaces slither relatively, softer tooth surfaces are torn-out on glide direction to form grooves.,傳動(dòng)精度 transmission accuracy 齒側(cè)間隙---齒輪副合理性 backlash in circular tooth---The rationality of gear pairs.,1-1.齒輪的應(yīng)用

12、要求 Application requirements of gears,7.1 應(yīng)用要求及加工誤差 Application requirements and processing errors,傳遞運(yùn)動(dòng)的準(zhǔn)確性 The accuracy of transfer motion 傳遞運(yùn)動(dòng)的平穩(wěn)性 The stability of transfer motion 載荷分布的均勻性 The homogeneity of load distribution,,要求從動(dòng)輪與主動(dòng)輪運(yùn)動(dòng)協(xié)調(diào)，應(yīng)限制齒輪一轉(zhuǎn)內(nèi)傳動(dòng)比的不均勻性。Requiring the coordination of driven whee

13、l and action wheels movement.We are supposed to restrict the uneven movements of gears in one round.,1.傳遞運(yùn)動(dòng)的準(zhǔn)確性 The accuracy of transfer motions.,要求:齒輪在轉(zhuǎn)過一個(gè)齒距角的范圍內(nèi)，其最大轉(zhuǎn)角誤差應(yīng)限制在一定的范圍內(nèi)。 Requirement:The maximum angular error should be restricted in a certain range within the range of that gear turning a

14、round one angular pitch. 一個(gè)齒距角內(nèi)瞬時(shí)傳動(dòng)比沖擊、振動(dòng)和噪聲 Instantaneous transmission ratio within one angular pitchconcussion, shake and noise.,2.傳動(dòng)的平穩(wěn)性 The stability of transfer motion,3.載荷分布的均勻性 The homogeneity of load distribution,輪齒嚙合過程中，工作齒面沿全齒高和全齒長上保持均勻接觸，并且接觸面積盡可能的大。In the engagement process of gear teet

15、h.Working flanks of teeth are kept in even contact on whole teeth height and whole teeth length and contact areas should be as bigger as possible.,引起應(yīng)力集中，造成局部磨損，輪齒折斷，影響齒輪的使用壽命 Causing stress concentration to lead to concentrated wear and tooth breakage so that influencing working lifes of gears.,齒輪傳

16、動(dòng)過程中，非接觸面之間一定要有合理的間隙。There must be reasonable clearance between non-contact surface in the process of gear transmission.,4.齒輪副側(cè)隙的合理性 Rationalities of backlashes of gear pairs,1.貯存潤滑油 store up lubricating oil 2.補(bǔ)償齒輪的變形 compensate the distortions of gears 3.制造和安裝誤差所引起的尺寸變動(dòng) size changes which are cause

17、d by Manufacturing and installation errors,不同齒輪的傳動(dòng)精度要求 Transmission accuracy requirements of different gears,加工方法：rocessing methods: 按齒廓形成原理 仿形法 According to tooth profiles forming principlesform cutting method 展成法 generating method,7.2 加工誤差的來源與分類 The origins and classifications of mismachining t

18、olerance,滾齒機(jī) hobbing machine,誤差來源 Sources of errors,工藝系統(tǒng)：機(jī)床、夾具、刀具、齒坯本身 Process system:machine tool, fixture, cutter and gear blanks themselves.,安裝、調(diào)整 Install and adjust,,1 幾何偏心 ej Geometric eccentricity,1 齒輪加工誤差來源 The sources of errors in gear machining,2 運(yùn)動(dòng)偏心ey ek +分度蝸輪加工誤差 Eccentric motion ey ek +

19、mismachining tolerances of dividing worm wheel,1分度蝸輪dividing worm wheel 2 蝸桿worm 3 滾刀hobbing cutter 4 齒坯gear blanks,Gears with eccentric motions,3 機(jī)床傳動(dòng)鏈的高頻誤差 High frequency errors of Machine tool transmission chains,原因：分度蝸桿的安裝偏心和軸向躥動(dòng),導(dǎo)致蝸輪（齒坯）轉(zhuǎn)速不均勻 Reasons:The installation eccentricities and axial dr

20、ifting of indexing worms contribute to inhomogeneous speeds of worm gears(gear blanks). 結(jié)果：加工出的齒輪有齒距偏差和齒形偏差 Results:Processed gears have pitch deviations and profile deviations.,4滾刀的安裝誤差和加工誤差I(lǐng)nstallation errors and mismachining tolerances of hobbing cutters,滾刀偏心 ed Eccentricity of hobbing cutter,2.

21、齒輪加工誤差的分類The classifications of gear machining errors, 按表現(xiàn)特征可分為4類：It could be divided into four classes acording to performance characteristic,齒廓誤差 齒距誤差 Tooth profile error Pitch error 齒向誤差 齒厚偏差 Tooth alignment error Tooth thickness deviation,齒廓相對(duì)于工件的旋轉(zhuǎn)中心分布不均勻 Tooth profile is irregularly distribute

22、d to rotating center of the workpiece.,齒廓不是理論的漸開線 Tooth profile is not theoretical involute.,齒面沿齒輪軸線方向的形狀和位置誤差 Tooth flanks form and position errors along gear axis.,齒厚相對(duì)于理論值在整個(gè)齒圈上不一致 Tooth thicknesss inconformity to theoretical value on whole gear ring., 按方向特征可分為3類 It could be divided into three cl

23、asses according to directional features.,徑向誤差 切向誤差 軸向誤差 Radial errors Tangential errors Axial errors,齒高方向 齒厚方向 齒向方向 Tooth height direction Tooth thickness direction Direction of tooth, , 按周期或頻率特征可分 According to cycle or frequency characteristic,it could divided into,長周期誤差 Long cycle error,短

24、周期誤差 Short cycle error,,傳遞運(yùn)動(dòng)的準(zhǔn)確性 The accuracy of transfer motion,工作平穩(wěn)性 Work stability,以齒輪一轉(zhuǎn)為周期 Regard gears one turn as cycle,以齒輪一齒為周期 Regard gears one tooth as cycle,,,,圓柱齒輪傳動(dòng)公差 Transmission tolerances of cylindrical gears,GB/T10095.1-2001GB/T10095.2-2001,傳遞運(yùn)動(dòng)準(zhǔn)確性的評(píng)定指標(biāo) The evaluation indexes of tran

25、sfer motion accuracy 傳遞運(yùn)動(dòng)平穩(wěn)性的評(píng)定指標(biāo) The evaluation indexes of transfer motion stability 載荷分布均勻性的評(píng)定指標(biāo) The evaluation indexes of load distribution homogeneity 影響側(cè)隙的單個(gè)齒輪因素 Single gear factor which influences sideshake,7.3 單個(gè)齒輪的評(píng)定指標(biāo) The evaluation criteria of single gear,-1 傳遞運(yùn)動(dòng)準(zhǔn)確性的檢測項(xiàng)目The inspection item

26、s of transfer motion accuracy,切向綜合總偏差（F i） Tangential general deviation 齒距累積總偏差（Fp） Cumulative pitch error 徑向跳動(dòng)（Fr） Radial runout 徑向綜合總偏差（Fi） Radical general deviation 公法線長度變動(dòng)（Fw）The changes of base tangent length,單項(xiàng)評(píng)定指標(biāo) Single evaluation index,齒輪一轉(zhuǎn)范圍內(nèi)，測頭在齒槽內(nèi)與齒高中部雙面接觸，測頭相對(duì)于齒輪軸線的最大變動(dòng)量稱齒圈徑向跳動(dòng)。Within g

27、ears one turn range, gauge head is contacted in double sides with tooth height middle part within tooth space.The maximum variation that gauge contains toward gear axis is called gear ring radical runout.,Fr主要反映由于齒坯偏心引起的齒輪徑向長周期誤差。Fr mainly reflects the gear radical long term error which is caused by

28、 the eccentricity of gear blanks 可用齒圈徑向跳動(dòng)檢查儀測量，測頭可以用球形或錐形。 It could tested by gear ring radical runout detector. Gauge head could use sphere or taper.,-2 傳動(dòng)工作平穩(wěn)性的檢測項(xiàng)目 The inspection items of driving work stability,一齒切向綜合偏差 f i Tooth tangential and general deviation 一齒徑向綜合偏差 f i Tooth radical and

29、general deviation 齒廓偏差 Tooth profile deviation 基圓齒距偏差 fpb Base circle pitch deviation 單個(gè)齒距偏差 fpt Single pitch deviation,-3 載荷分布均勻性的檢測項(xiàng)目 The inspection items of load distributions homogeneity,螺旋線偏差：在端面基圓切線方向上測得的實(shí)際螺旋線偏離設(shè)計(jì)螺旋線的量 Helix deviation:The tested amount that actual helix deviates from designe

30、d helix on the tangential direction of end face base circle. （1） 螺旋線總偏差F 在計(jì)值范圍內(nèi)，包容實(shí)際螺旋線跡線的兩條設(shè)計(jì)螺旋線跡線間的距離Helix total deviation F Within the range of values,the distances between two designed helix path lines which include helix path lines. （2） 螺旋線形狀偏差 ff 在計(jì)值范圍內(nèi)，包容實(shí)際螺旋線跡線的兩條與平均螺旋線跡線完全相同曲線間的距離 Helix sha

31、pe deviation ff Within the range of values,the distances between two curves which are same as average helix path lines and including actual helix path lines. （3） 螺旋線傾斜偏差fh 在計(jì)值范圍的兩端與平均螺旋跡線相交的設(shè)計(jì)螺旋線跡線間的距離 Helix incline deviation fh Within the range of values,the distances between designed helix path li

32、nes that both ends are intersectant with average helix path lines.,,-4 影響側(cè)隙的單個(gè)齒輪因素 Single gear factors that influence sideshakes,1 齒厚偏差fSnTooth thickness deviation齒厚的上偏差（ESnS）The upper deviation of tooth thickness 下偏差（ESni）Lower deviation,,,一般都為負(fù)值 Commonly to be negative value,2 公法線長度偏差 Base tangen

33、t length deviation,7.4 齒輪副評(píng)定指標(biāo) The evaluation indexes of gear pairs,1 軸線的平行度誤差 The parallelism errors of axes 2 中心距偏差 The deviations of centre-to-centre separations 3 接觸斑點(diǎn) Contact spot 4 齒輪副的側(cè)隙 The sideshake of gear pair,4 齒輪副側(cè)隙 The sideshake of gear pair,齒輪副的最小極限側(cè)隙應(yīng)根據(jù)齒輪工作時(shí)的溫度和潤滑條件確定，與齒輪的精度等級(jí)無關(guān)。The

34、 minimum limit sideshake of gear pair should be ascertained by gears working temperature and lubrication condition.It has nothing to do with the gears accuracy class.,高溫工作的傳動(dòng)齒輪，為保證正常潤滑，避免發(fā)熱卡死，要求有較大的側(cè)隙；There should be biggish sideshake for drive gear working in high terperature.That is to ensure norm

35、al lubrication and preventing the gear from fever and jammed 而需正反轉(zhuǎn)或讀數(shù)機(jī)構(gòu)的齒輪，為避免空程，則要求較小的側(cè)隙。There should be lesser sideshake for the gears to prevent idle stroke which need positive inversion or reading mechanism., 側(cè)隙獲得方法 The methods to obtain sideshake,1.基齒厚制:即固定齒厚的極限偏差，通過改變中心距的基本偏差來獲得不同的最小極限側(cè)隙，此方法

36、用于中心距可調(diào)的機(jī)構(gòu)。Base gear thickness:Fix gear thicknesss limit deviations.Obtaining different minimum limit side gaps through changing the basic deviations of centre-to-centre separations. This method is used for the mechanisms of which centre-to-centre separations are tunable. 2.基中心距制:即固定中心距的極限偏差，通過改變齒厚的

37、上下偏差來得到不同的最小極限側(cè)隙，國標(biāo)采用后一種. Base centre-to-centre separation distance system:Fix centre-to-centre separations limit deviation.Obtaining different minimum limit side gaps through changing the upper and lower deviations of gear thickness. Chinese Standard adopts the latter.,jbnmin,jbnmin = jbn1 + jbn2,工

38、作溫度 潤滑方式 圓周速度 Working temperature Lubrication method Peripheral speed,補(bǔ)償溫升引起的變形Compensate the distortions caused by temperature rise,保證齒輪工作面的正常潤滑 Ensure the normal lubrication on gears working surface,最小法向極限側(cè)隙 The minimum limit sideshake on normal,Jbn2取決于潤滑方式和齒輪工作的圓周速度Jbn2 lies on lubricating method

39、 and the working peripheral speed of gear,7.5 漸開線圓柱齒輪精度設(shè)計(jì) The precision design of involute cylindrical gear,齒輪精度等級(jí)的確定 The ascertainment of gears accuracy class 齒輪副側(cè)隙、齒厚極限偏差的確定 The ascertainment of backlash of gear pair and limit deviation of tooth thickness 齒坯精度和齒輪表面粗糙度 Precision of gear blanks an

40、d roughness of gear surfaces 圖樣標(biāo)注 Pattern annotation,GB/T 10095.1-2001 漸開線圓柱齒輪精度第1部分 輪齒同側(cè)齒面偏差的定義和允許值The accuracy of involute cylindrical gear Part1 The definitions and allowable values of tooth flank tooth surface deviations GB/T 10095.2-2001 漸開線圓柱齒輪 精度第2部分 徑向綜合偏差與徑向跳動(dòng)的定義和允許值The accuracy of involute

41、 cylindrical gear Part2 The definitions and allowable values of radial integrated deviations and radial runout GB/Z 18620.14 指導(dǎo)性技術(shù)文件 Technical guidance document,分度圓直徑：510000mm standard pitch diameter 法向模數(shù)：0.570mm normal modulus 齒寬：41000mm tooth width,標(biāo)準(zhǔn)適用范圍 The scope of applications for standards,13

42、個(gè)精度等級(jí) Thirteen accuracy classes 0 、1 、2 3 5 6 8 9 12,待用inactive,高精度等級(jí) High accuracy classes,中等精度等級(jí) Middle accuracy classes,最低精度等級(jí)The lowest accuracy classes,7 GB/T10095.2（1）2001,一、漸開線圓柱齒輪精度等級(jí) The accuracy classes for involute cylindrical gears,1.齒輪精度等級(jí)的選擇 The selection for gear precision grade,根據(jù)用途

43、、使用要求、傳遞功率、圓周速度及其它技術(shù)要求而定，同時(shí)考慮切齒工藝及經(jīng)濟(jì)性。According to applications, operating requirements, transmitted power, peripheral speed and other technical requirements thus thinking about cutting process and economy.,選擇原則 Selection principles,選擇方法 Selection methods,1）計(jì)算法 computation technique 依據(jù)齒輪傳動(dòng)用途的主要要求，

44、計(jì)算確定出其中一種使用要求的精度等級(jí)，再按其他方面要求，作適當(dāng)協(xié)調(diào)，來確定其它使用要求的精度等級(jí).According to the main requirements of gear drive applications,calculating and ascertaining one usage requirements accuracy class.Then according to other requirements of other aspects and making proper coordination to ascertain the accuracy classes of

45、other usage requirements.,當(dāng)對(duì)傳遞運(yùn)動(dòng)準(zhǔn)確性沒有特別要求時(shí)，第公差組的精度常比第公差組低一個(gè)等級(jí)。When there are no special requirements for the accuracy of transfer motion.The precision accuracy of No.1 Tolerance group is usually lower by one class to No.2 Tolerance group 當(dāng)所傳遞的功率不特別大時(shí)，第公差組一般采用和第公差組相同的精度等級(jí)。When the transmission power

46、is not very high. No.3 Tolerance group usually adopts the same accuracy classes as No.2 Tolerance group. 齒輪副中兩齒輪對(duì)應(yīng)公差組的精度采用同級(jí)，也允許不同級(jí)。The corresponding tolerance groups that are of two gears in gear pairs also adopt different classes.,齒輪圓周線速度第公差組的精度等級(jí) Gears circumferential line velocity The accuracy c

47、lasses of No.2 Tolerance group,No.1 Tolerance group,No.2 Tolerance group,No.3 Tolerance group,The accuracies of transfer motions,The stabilities of transmissions,The homogeneities of load distributions,2）類比法 The methods of analogue 依據(jù)以往產(chǎn)品設(shè)計(jì)、性能試驗(yàn)以及使用過程中所積累的經(jīng)驗(yàn)、可靠的技術(shù)資料，經(jīng)過與所設(shè)計(jì)的齒輪在用途、工作條件及技術(shù)性能上作對(duì)比后，選定其精

48、度等級(jí)。According to the accumulated experiences and reliable technical data from past products design, performance test and use procedure.Choosing the accuracy classes after comparing with the designed gears on applications, working conditions and technical functions.,各種機(jī)械采用齒輪的精度等級(jí) The adoptted gears a

49、ccuracy classes for different machines,2.齒輪精度等級(jí)標(biāo)注 The label for gears accuracy class,,-0.330 -0.495,（ ）GB/T10095.22001,例：7-6-6 G M GB/T10095.22001,7 F L GB/T10095.22001,表示齒輪第、、公差組的精度分別為7級(jí)、6級(jí)、6級(jí)。The precision accuracy of the tolerance groups , and for gears are respectively as class7,6 and 6.,齒厚上、下偏

50、差代號(hào)分別為、。Gears upper and lower deviation codes are respectively as and .,二.齒厚極限偏差代號(hào) The code for limit deviation of tooth thickness,齒厚極限偏差的數(shù)值=齒距極限偏差（fpt）的倍數(shù) The numerical value of limit deviation of tooth thickness =The multiple of transverse pitch limit deviation,國標(biāo)規(guī)定:14種齒厚極限偏差的數(shù)值，大寫的英文字母表示。National

51、 standard:14 kinds of numerical values for limit deviation of tooth thickness and indicated by capital letters in English.,三.齒輪坯的精度和齒輪面粗糙度 Precision of gear blanks and Roughness of gear surface,齒坯公差 Tooth blank tolerance,齒坯基準(zhǔn)面徑向和端面跳動(dòng)公差 Radial and end face run out tolerances for gear blanks basic fac

52、e,齒輪表面粗糙度 Roughness of gear surface,齒面的表面粗糙度對(duì)齒輪的傳動(dòng)精度(噪聲和振動(dòng))、表面承載能力(點(diǎn)蝕、膠合和磨損)和彎曲強(qiáng)度(齒根過渡曲面狀況)等都會(huì)產(chǎn)生很大的影響。 Gears surface roughness would exert big effects on gears transmission accuracy(Noise and vibration), surface carrying capacity(corrosive pitting, glue together and wear and tear)and bending strength(Fillet surface condition).,單位：m,四、圖樣標(biāo)注例 The examples for pattern annotation,