§5 蜗杆传动 (交错轴Σ=90°)

§7 蜗杆传动worm gearing（shaft angle交错轴Σ＝90°）§7－1 General considerations 概述§7－2 Choice of the parameters and geometricalcalculations for Archimedean worm gearing普通圆柱蜗杆传动参数选择和几何计算§7－3 Materials, types of failure and design criteria 蜗杆传动材料、失效和计算准则§7－4 Forces in worm gearing 受力分析§7－5 Strength calculations 强度计算§7－6 Heat balance calculation 热平衡计算Design example 习题课§7－1 General considerations 概述 Characteristics and applications特点和应用Types of the worm gearing分类回总目录一、Characteristics and applications 特点和应用1、Advantages①High speed ratio i→ Small overall size（Z＝1～4）结构紧凑For motion drives传递运动：Up to1000For power drives传递动力：8～80②Smooth and silent operation 平稳，噪音小（Continuous engagement between worm and worm gear蜗杆与蜗轮连续啮合）2、Drawbacks①Low efficiency 效率低）Usually P<50KW （Σ＝90°，Vs②High cost 成本高（The necessity of using expensive antifriction materials for the worm gear 蜗轮轮圈用贵重有色金属青铜制造）3、Applications应用二、Types 分类：1、Cylindrical worm gearing 圆柱蜗杆传动： By shape of the threads in an end section 按轴截面内螺旋线形状分：2、Enveloping worm gearing 环面蜗杆传动3、Cone worm gearing 锥蜗杆传动①Archimedean worm 阿基米德蜗杆（Ordinary 普通）②Involute worm 渐开线蜗杆③Convolute worm 延伸渐开线蜗杆（Straight-sided inthe section normal to the thread 法向直廓）三、Meshing features of the ordinarycylindrical worm gearing普通圆柱蜗杆传动啮合特点Central cross section中间平面（主平面）：A plane which is normal to the worm gear shaft and parallel to worm shaft通过蜗杆轴线并垂直于蜗轮轴线的平面Special features 特点：In the central cross section 中间平面内The tooth profile on worm is straight-sided蜗杆齿廓：直线The tooth profile on worm gear is in volute 蜗轮齿廓：渐开线Mesh between a straight-sided rack and an in volute gear为（直）齿条与渐开线齿轮啮合特点：中间平面内§7－2 C hoice of the parameters andgeometrical calculations forArchimedean worm gearing 普通圆柱蜗杆传动参数选择和几何计算 Choice of the parameters参数选择Geometrical calculations几何计算回总目录一、Choice of parameters 参数选择1、Modules模数m，Profile angle齿形角αIn a central cross section, modules andprofile angle are standardized中间平面内为标准值α＝20°m ——P84 表6－42、d 1，qd 1——The pitch diameter of a worm蜗杆中圆直径q ——The worm diameter factor蜗杆直径系数①Gear 齿轮d 1＝mZ 1If m and Z 1are determined ，d 1 is determined.②Worm 蜗杆d 1＝mZ 1/tg γ≠ mZ 1m ，if m and Z 1are determined ，d 1is indeterminate.③Number of the hobs cutting worm gears depends on the diameter d 1 In order to limit number of the hobs and standardize them, severalstandard diameters are specifiedd 1多，则加工蜗轮滚刀多为减少刀具数目，并便于实现标准化、系列化：对每一m 蜗杆规定几个标准d 1——P84 表6－4111mZ mq d q m d ≠==蜗杆直径系数3、i 、Z 1、Z 2①Z 1 the number of worm 蜗杆头数1，2，4，6P83：Z 1＝f （i ）②i Speed ratio 传动比★Z 1↓ i ↑ η↓★Z 1↑ η↑ i ↓加工难121221d d Z Z n n i ≠==③Z2＝i Z128≤ Z2≤100 (32~63 is optimal for power drives 一般32~63)★Z2<28, Stationery 则平稳性↓★Z2>100, 则d2=mZ2↑Longer distance between the bearings of the worm → 杆长↑→ Rigidity of worm 杆刚度↓④γ The pitch helix angle of the worm蜗杆导程角γ>33°ηIncreases slightly , Difficulties in manufactureη↑缓慢, 加工难γ<3.5°Self-locking 自锁γ=3.5°~33°qZ mq mZ d Z p tg γ1111x ===πππη低•二、Geometrical calculations几何计算•Application 传动功用、i →Z 1（Z 2＝i Z 1）•Strength conditions 强度条件，q q Z tg γ11- P78表4－5 Geometrical dimensions are calculated计算几何尺寸.§7－3 Materials, types of failure and design criteria 蜗杆传动材料、失效和计算准则Materials 材料Types of failure 失效形式Design criteria 计算准则Structure and manufacture of the worm and worm gear蜗轮蜗杆的结构及加工方法回总目录一、Materials 材料Requirements 要求：Not only have enough strength And the good antifriction is more important不仅要有一定强度，更重要的是要有良好的减摩性和耐磨性。

（Material pairs of low and high levels of hardness 软硬相配）1、Worm materials 蜗杆Usually：45Structurally improvement调质High velocities and heavy load高速重载：45、40Cr、20CrHardening淬火2、Worm gear materials 蜗轮High velocities and heavy load 高速重载Tin bronze 锡青铜ZCuSn10P1ZCuSn5Pn5Zn5Better seize-resistant lower strength higher cost 抗胶合能力强，机械强度低，价格高（σb <300MPa ）（V s ＝12～25m/s ）ZCuAl10Fe3Mn2ZCuAl8Mn13Fe3Ni2Lower seize-resistant ,Higher strength , Lower cost抗胶合能力差，机械强度高，价格低（σb >300MPa ）Usually ：Aluminum －Iron bronze 铸铝青铜（V s ＝2～8m/s ）Low velocities and light load低速轻载：）（V s<2m/sCast iron灰铸铁HT200HT150二、Types of failure 失效形式Similar to types of failure in the toothed gearing ：Fatigue pitting, Seizing, Abrasive wear , Plastic flow of material and tooth breakage与齿轮类似：点蚀、胶合、磨损、塑性变形、断齿Special features as below 特点如下：①Worm gear failure 蜗轮失效（Strength of the worm is more than the one of worm gear 蜗杆强度高于蜗轮）②Closed drives闭式传动：Tin bronze锡青铜：The principal types of failure are pitting 点蚀为主（Because it has good seize-resistant ability 抗胶合能力强）Aluminum-iron bronze and cast iron 无锡青铜和铸铁：The principal types of failure are seize 胶合为主③Open drive 开式传动：Breakage after severe wear 磨损→折断三、Design criteria 计算准则Closed drive 闭式传动①Designed according to contact fatiguestrength of the tooth surface按齿面接触疲劳强度设计②Checked according bending fatigue strengthof the tooth root按齿根弯曲疲劳强度校核③Heat balance calculation热平衡计算Open drive开式传动：Design according to bending fatigue strength 按弯曲疲劳强度设计四、Structure and manufacture of the worm and worm gear蜗轮蜗杆的结构及加工方法1、Structure结构①Worm gear蜗轮②Worm蜗杆2、Manufacture加工方法①Worm gear蜗轮②Worm蜗杆Worms are made integral with the shaft and are seldom made fabricated , the following types of the worm designs are used蜗杆通常与轴做成整体，很少做成装配式, 可分为：With tool escape有退刀槽Without tool escape无退刀槽Relationship between forces acting on worm and worm gear 各力间关系 Magnitude of forces 力的大小 Direction of forces 力的方向§7－4 Forces in worm gearing 受力分析⎪⎩⎪⎨⎧-=-=-=t2a1a2t1r2r1F F F F F F 一、Relationship between forces各力间关系）相差和处，01.0cos cos γ(cos γcos d 2T cos γcos F F F F αtg F F F )ηT T (d 2T F F d 2T F F n max 22n t2n n1n1t2r2r111222t2a111a2t1ααααi ===========二、Magnitude of forces 力的大小3相同）与相反，ω与与拇指指向相同方向③方向②回转方向：四指握拳右旋伸右手①旋向：左旋伸左手，（蜗杆主动）②同前和①t22a1t2a1a1t r F F F (:F :F F F ⎪⎩⎪⎨⎧三、Direction of forces 力的方向As before Worm driving Helix direction: left hand for left-hand helix gear and right hand for right-hand helix gear.Rotating direction: bending direction of four fingers.Direction of F a1: The same direction of thumbingContact fatigue strength of the tooth surface on worm gear 蜗轮齿面接触疲劳强度计算 Bending fatigue strength of the tooth root on worm gear蜗轮齿根弯曲疲劳强度计算§7－5 Strength calculations 强度计算一、蜗轮齿面接触疲劳强度计算Contact fatigue strength of the tooth surfaceIn the central cross section, the tooth profiles of the worm and worm gear are the same as that of involutes helical gear and rack. Hence, the strength calculations are done for the tooth profiles of their equivalent spur gear and rack .在主平面内，蜗轮蜗杆的啮合相当于一对渐开线斜齿轮与斜齿条的啮合→取其当量直齿轮与直齿条的啮合进行强度计算。