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1、 Chapter 11 Worm Gears 11.1 Worm Gears and Worms; Nomenclature, Materials11.2 Main Parameters and Geometrical Calculations 11.3 Force Analysis11.4 Stress Analysis and Design 11.5 Structural Design of Worm and Gears11.6 Lubrication and Heat Dissipation 11.1 Worm Gears and Worms; Nomenclature, Materia

2、lsWorm gearing is often used in situations requiring large reduction ratios or transmission between 90nonintersecting shafts, and often in low-power situations since that friction losses can be high due to sliding between worm threads and the gear teeth.Common reduction ratios of worm gearing range

3、from 4 to 100. Worm gearsets can be produced to provide ratios ranging from 1 to 360. In gear trains of dividing mechanisms reduction ratio reaches 600-1,000.Sketch of worm gear arrangement for cylindrical (single-enveloping) worm, giving standard nomenclature. Shown for double threaded worm.Worm sh

4、aft support bearings are typically subjected to radial loads and high thrust loads, and so with worm wheel bearings. If a rotating worm is constrained axially by thrust bearings, the worm gear is caused to rotate about its own axis, as the worm threads slide sidewise against the gear teeth. This sim

5、ulates the kinematic behavior of a linearly advancing rack engaged with a conjugate spur or helical gear. In the wormset, a bronze gear is usually paired with a hardened steel worm. High-tin bronze ZQSn10-1 and ZQSn5-5-5 Tin-free bronze ZQAl9-4 and 10-4-4 gray cast iron HT150.Worms are ordinarily ma

6、de from carbon or alloy steel .Worms of steel 15Cr, 15CrA, 10Cr, 20CrV are casehardened to surface hardness of . Worms of steel 40, 45, 40Cr and 40CrNi are hardened to . The materials of a worm-gear combination6256CR5045CR11.2 Main Parameters and Geometrical CalculationsThe plane passing through the

7、 axis of the worm and perpendicular to the axis of the wheel is called the main plane.In the section of the main plane, an Archimedean worm gives a contact between an involute wheel and a straight-sided rack. A basic requirement of a properly designed worm gearset is that the axial pitch of the worm

8、 must be equal to the circular pitch of the gear.The mating elements in the axial section of an Archimedean worm are identical to a rack of rectilinear contour with an angle of .For the module of a worm gear m we take the worm axial module equal to the circumferential module of the wheel. 402To insu

9、re proper contact between the worm and the gear teeth, the gear hob typically has the same basic cutter shape used for the worm. Worms may be manufactured with a single thread or with multiple threads. The number of threads on the worm is often referred to as the number of starts. The pitch diameter

10、 of a worm is not a function of its number of threads. The reduction ratio of a worm gear-set is not equal to the ratio of gear and worm pitch diameters, but equal to the ratio of the number of stars on the worm and teeth number on the gear.1221ZZnnimZpZlaw11111tandlw The lead, the axial advance of

11、any point on the worm thread for one revolution of the worm, is The mean worm lead angle 2 For the usual case, where the worm shaft is 90 to the gear shaft, the lead angle of the worm is equal to the helix angle of the worm gear:Table 11.1 gives formulae for determining the main geometrical proporti

12、ons of a worm gear with an Archimedean worm Correction of the worm gearIn a worm gear only the wheel is corrected while the size of the worm remains the same. The correction of the gear changes only the diameter of the worm pitch cylinder while the diameter of the wheel pitch cylinder does not chang

13、e.Sliding velocity vs at pitch point C, issincos212221vvvvvs11.3 Force Analysis 12222atFdTFtan121arrFFF111222)tan(dTFFFttacoscos2coscoscoscos2221dTFaFFtnannKFThe design load is used in calculating the strength of the gear. 11.4 Stress Analysis and DesignA common empirical design approach is to assum

14、e that tooth bending fatigue is less serious than surface durability when defining an acceptable design. Further, the surface durability criterion typically employed in practice is assumed to embody both surface fatigue and adhesive/abrasive wear parameters.We take the formula (10-4) as the initial

15、relation for calculating the active profiles in the same way as that for gears. Stress analysis2cossin222dcoscos/222dTFncos/31. 11dLc HEEHZmdKTZddKTZ2212221299222219HEZZKTmd The design calculations: Allowable surface stresses are assigned for the material of the wheel rim depending on the material o

16、f the worm running with it.When the wheels are made from cast iron or bronze with ultimate strength MPa the main failure mode on the gear surface is seizure. Therefore, allowable stresses are assigned depending on the combination of contacting materials and the velocity of sliding.Table11.3 gives ex

17、perimental values of H for thoroughly run-in and liberally lubricated gears. In other gears the tabulated values should be decreased approximately by 30%.Allowable surface stresses300BIf the wheel are made of bronze with ultimate strength B300 MPa the load-carrying capacity of the gear is limited by

18、 contact fatigue.The values of for some materials of wheels running with steel worms are given in Table11.4. 0HHNHK8710NKHN 0HWorms are usually made integral with the shaft. Typical designs of worm are shown in Fig. 11.6. Worm gears are made solid (Fig.11.7, a) or composite (Fig.11.7, b, c) with a b

19、ronze rim.The rim of a worm wheel is fitted onto the wheel center with interference (Fig.11.7, b) Another method of fastening the rim of a worm wheel to its center by means of flanges is employed if the wheel is large in diameter (Fig.11.7, c). 11.5 Structural Design of Worm and GearsFig.11.7 Typica

20、l structure of worm gears1) Efficiency of wormset 11.6 Lubrication and Heat Dissipation)tan(tan)96. 095. 0(For approximate calculations the full efficiency of worm gearscan be determined from Table 11.5. The magnitude of at different conditions can be obtained from Table 11.6.If the worm gear cannot

21、 hack-drive the worm, the wormset is said to be self-locking. 2) Self-locking conditionThe low lead angles required for effective self-locking imply the use of a single-thread worm and produce low efficiencies. Self-locking conditionThe lubrication and cooling issues become more important for worm gear sets with

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