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1、4 蜗杆传动 worm gearing （shaft angle交错轴90）v41 General considerations 概述v42 Choice of the parameters and geometrical calculations for Archimedean worm gearing 普通圆柱蜗杆传动参数选择和几何计算v43 Materials,types of failure and design criteria 蜗杆传动材料、失效和计算准则v44 Forces in worm gearing 受力分析v45 Strength calculations 强度计算v46
2、 Heat balance calculation 热平衡计算v Design example 习题课vCharacteristics and applications 特点和应用vTypes of the worm gearing 分类41 General considerations 概述回总目录1、Advantages High speed ratio i Small overall size （Z14）结构紧凑 Smooth and silent operation 平稳，噪音小（Continuous engagement between worm and worm gear 蜗杆与蜗
3、轮连续啮合）For motion drives 传递运动：Up to1000For power drives 传递动力：880一、Characteristics and applications 特点和应用2、Drawbacks Low efficiency 效率低（90，Vs ）Usually P50KW High 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应用蜗杆传动应用二、Types 分类：v1、Cylin
4、drical worm gearing 圆柱蜗杆传动：v By shape of the threads in an end section 按轴截面内螺旋线形状分：v2、Enveloping worm gearing 环面蜗杆传动v3、Cone worm gearing 锥蜗杆传动 Archimedean worm 阿基米德蜗杆（Ordinary 普通）Involute worm 渐开线蜗杆 Convolute worm 延伸渐开线蜗杆（Straight-sided in the section normal to the thread 法向直廓）三、Meshing features of
5、the ordinary cylindrical worm gearing 普通圆柱蜗杆传动啮合特点vCentral 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-s
6、ided rack and an in volute gear 为（直）齿条与渐开线齿轮啮合Special features 特点：In the central cross section 中间平面内v特点：中间平面内蜗杆齿廓：直线蜗轮齿廓：渐开线为（直）齿条与渐开线齿轮啮合BACK42 Choice of the parameters and geometrical calculations for Archimedean worm gearing普通圆柱蜗杆传动参数选择和几何计算vChoice of the parameters 参数选择vGeometrical calculations
7、几何计算回总目录1、Modules 模数m，Profile angle 齿形角 In a central cross section,modules and profile angle are standardized 中间平面内为标准值 20m P84 表64一、Choice of parameters 参数选择2、d1，qd1The pitch diameter of a worm 蜗杆中圆直径qThe worm diameter factor 蜗杆直径系数 Gear 齿轮 d1mZ1 If m and Z1 are determined，d1 is determined.Worm 蜗杆
8、d1 mZ1/tg mZ1 m，if m and Z1 are determined，d1 is indeterminate.Number of the hobs cutting worm gears depends on the diameter d1 vIn order to limit number of the hobs and standardize them,several standard diameters are specified vd1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d1 P84 表643、i、Z1、Z2 Z1 th
9、e number of worm 蜗杆头数 1，2，4，6P83：Z1f（i）i Speed ratio 传动比Z1 i Z1 i 加工难 Z2i Z1 28 Z2 100 (3263 is optimal for power drives 一般3263)Z2100,则d2=mZ2 Longer distance between the bearings of the worm 杆长 Rigidity of worm 杆刚度 The pitch helix angle of the worm 蜗杆导程角33 Increases slightly,Difficulties in manufact
10、ure 缓慢,加工难3.5Self-locking 自锁=3.533低二、Geometrical calculations 几何计算Application 传动功用、iZ1（Z2i Z1）Strength conditions 强度条件，qP78 表45 Geometrical dimensions are calculated 计算几何尺寸.BACK43 Materials,types of failure and design criteria 蜗杆传动材料、失效和计算准则v Materials 材料 v Types of failure 失效形式v Design criteria 计算准
11、则 v 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：45 Structur
12、ally improvement 调质 High velocities and heavy load 高速重载：45、40Cr、20Cr Hardening 淬火 2、Worm gear materials 蜗轮v 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（b300MPa）Usually：AluminumIron bronze 铸铝青铜（Vs28m/s）vLow v
13、elocities and light load 低速轻载：Cast iron 灰铸铁HT200HT150（Vs300MPa）：Principal type of failure is seizure,H is independent of the number of stress cycles,but depends on sliding velocity.胶合为主，H与应力循环次数N无关而与相对滑动速度Vs有关。KKAKVK Steady load KA、KV、K Smaller values of KA、KV、K 见P80 表46及P80说明BACK二、Bending fatigue s
14、trength of tooth root on worm gear 蜗轮齿根弯曲疲劳强度计算 By analogy with helical gearing,but stress concentration factor stress concentration factor Ysa is not considered 按斜齿轮方法计算但不计应力修正系数Ysa The teeth of wormgears are taken from 20 to 40%stronger than those of helical gears弯曲强度与斜齿轮相比增大约40Strength increasing
15、 factor 强度增长系数1.4Tooth thickness grows(Their arched tooth shape results in so-called natural correction which occurs in all cross sections except the central one)The maximum allowable wear amount of the tooth root thickness is 20 允许齿根厚度最大磨损20 补偿轮齿磨损系数1.5F For checkingFor designNotes说明 YF,Form factor
16、 for worm gear teeth,selected according to the virtual number of teeth ZvZ2/cos3.YF齿形系数，根据ZvZ2/cos3查取 P82 表48Y Helix angle factor 螺旋角系数BACK46 Heat balance calculation 热平衡计算vEfficiency 效率123vHeat balance calculation 热平衡计算回总目录v一、Efficiency 效率123v1、1Efficiency in engagement 啮合效率（The sliding velocity be
17、tween tooth surfaces 齿面间相对滑动 Power losses 功率损失）vMesh loss power is principal loss power.It is computed approximately by efficiency formula for screws 最主要功率损失近似用螺旋面效率计算公式 Equivalent friction angle v当量摩擦角f（Pair of materials材料组合、Types of lubrication oils润滑剂、Vs.）Vs v The sliding velocity Vs 相对滑动速度2、2Eff
18、iciency in splashing about and mixing the lubricant 搅油效率（0.99）3、3Efficiency in bearing friction轴承效率（Rolling bearing 滚动轴承：0.99 Sliding bearing 滑动轴承:0.980.99）The pitch helix angle of the worm threads 导程角Rigidity of the wormBACK二、Heat balance calculation 热平衡计算（t7590）vThe heat balance 热平衡：In an unit tim
19、e,the amount of heat evolved by worm gearing equals to the heat removed by radiation from the free surface of the housing and by conduction through the foundation plate or frame 传动发热速率箱体散热速率Usually t020（Temperature of the surrounding air）环境温度 KdHeat transfer factor 传热系数1218W/m2（Larger values are use
20、d under favorable conditions of air circulation 通风良好取大值）AFree surface of the housing from which heat is removed（m2,散热面积）外壁与空气接触，内壁为油飞溅到或浸到的箱体表面积As a first approximation 初算时：Fins are located P1Power transmitted by worm 蜗杆传动功率（KW）If 若t1 7590,ThenA Fins are located 散热片Kd Fan are mounted 风扇 Water coolin
21、g is employed 循环水管Kd2028 W/m2 BACK习题课vPull-out device for heating-furnace in heat-treat workshop is shown in Fig.热处理车间加热炉拉料机构，如图所示。v已知：P电机2.1KW，n电机960rpm，i22.5，Lh13500h，Steady load载荷平稳，low-volume 小批量生产。回总目录一、Preliminary selection of garages of accuracy,materials,and Z1 初选材料、精度等级、Z1 1、Materials 材料：P7
22、5 表42 Worm gear 蜗轮 ZCuSn10P1 Sand casting 砂模 （Low-volume 小批量）表43 Worm 蜗杆 45 Structural improvement 调质 2、Grades of accuracy 精度等级 P74 表41 Take grade 8 取8级3、Z1:P76 倒数78行，i22.5 Z1 2 Z2 Z1i222.545（28，100）二、Preliminary determination of m,q and d1初定m、q、d1 P83:Z1=2 0.750.82 KKAKVK111.05 1.05 KA0.81.25 取KA1K
23、V11.1（Estimate 估计Vs1907.1)(Z2=2)三、Determination of the parameters of the worm gear 确定传动尺寸 d150mm d2mZ26.345283.50mm Check 校核V2（Vs）四、Check bending fatigue strength 弯曲强度校核 YF：根据ZvZ2/cos35/cos31484249.36 P82 表48 YF1.64Y：（Contact on both sides of the teeth双面受力）五、Heat balance calculation 热平衡校核Kd 1218W/m2
24、 Kd15W/m2 P12.1KWt020 1230.940.9920.92P83 表410BACK思考题思考题思考题思考题圆柱蜗杆环面蜗杆传动锥蜗杆传动阿基米德蜗杆渐开线蜗杆法向直廓蜗杆Intagral designBimmetallic designBolted designRimmedl design人有了知识，就会具备各种分析能力，明辨是非的能力。所以我们要勤恳读书，广泛阅读，古人说“书中自有黄金屋。”通过阅读科技书籍，我们能丰富知识，培养逻辑思维能力；通过阅读文学作品，我们能提高文学鉴赏水平，培养文学情趣；通过阅读报刊，我们能增长见识，扩大自己的知识面。有许多书籍还能培养我们的道德情操，给我们巨大的精神力量，鼓舞我们前进。