From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Technical explanation of the design, forces, contact, lubrication, wear, and pitting in worm gear assemblies.
| Identifier | ExFiles\Box 136\5\ scan0321 | |
| Date | 1st September 1937 guessed | |
| 6 Worm Gearing—contd. Resultant force perpendicular to axis of worm wheel = √(S² + E²) The force (E) is equal in magnitude to the end thrust on the worm, but since its line of action is displaced from the axis of the worm by a distance d/2, it exerts journals loads ± E d/l on the worm shaft bearings in the axial plane which contains the common perpendicular to the shaft axes. Assuming the journal bearings of the worm shaft to be symmetrically disposed about the common perpendicular, these forces are added to, or subtracted from, S, the resultants are combined vectorially with ±E, and the journal loads are : Wormshaft bearings = √[(S ± E d/l)² + (±E)²] = ½√[E²(tan²ψa ± D/l)² + E²] Worm wheel shaft bearings √[(S ± E D/l)² + (±c)²] = ½√[E²(4R/D tan ψa ± D/l)² + c²] Bearings. Nearly all modern worm drives, whether in automobiles or otherwise, embody anti-friction bearings. It is, of course, essential that the gears be maintained as nearly as possible in their correct relative positions when under load, the only respect in which accuracy is unimportant being in the axial position of the worm. The axial position of the worm wheel rim must be maintained within limits of 0·002in. in automobile axles of normal type, and to do this not only must the thrust bearings be accurate, but the journal bearings must allow but little radial play, because the effect of the non-axial end thrust is to tilt the wheel in the plane containing its axis and the common perpendicular to the axes and thus to cause lateral movement of the rim relatively to the axis of the worm. To this end the ratio of bearing span to worm wheel diameter must not be too small. The worm shaft thrust bearing is subject to a combination of heavy axial load and high speed, and in the past, double ball thrust bearings have been used for the purpose. At high speeds, however, centri-fugal force on the balls produces a wedging effect on the races and the result has a tendency to over-heating. Present practice is to use a duplex ball bearing, to take thrust in either direction, with axially-free ball or roller bearings for journal loads. The less onerous thrust conditions on the worm wheel usually permit it to be mounted in a pair of double-purpose ball bearings, which must be carefully mounted with provision for fine adjustment of axial position. In conditions of relatively light loading, a similar bearing arrangement may be used for the worm shaft. Relative displacement of worm and wheel under load. When the gears are under load the forces exerted on each other and on the casing which supports their bearings inevitably produce distortion, and the result is that the conditions of contact between worm and wheel are disturbed. As previously, it is convenient to assume contact to be occurring only at the pitch point, and to resolve the resultant force there into three mutually perpendicular components. The component which acts along the common perpendicular to the shaft axes causes flexure of the shafts and stretch of the casing between the worm shaft bearing and the worm wheel shaft bearings. This results in an increase of centre distance between the gears and tends to cause the area of contact on the wheel teeth to be concentrated on the "leaving" side, i.e., the side of the worm wheel from which the worm threads emerge when the worm is driving the wheel. Actually this tendency is overwhelmed by that resulting from the force component which acts parallel to the axis of the worm wheel. The component parallel to the axis of the worm has no appreciable effect on contact conditions, because distortions which it produces result merely in an axial movement of the worm. The remaining force component is usually the most serious of the three, because it deflects the worm shaft by bending in a plane parallel to the worm wheel axis, bends the worm wheel about a diameter parallel to the worm axis and rocks it about the same diameter by virtue of radial play in the journal bearings which support the worm wheel shaft. On this account the area of contact on the worm wheel tooth—or the "tooth bearing"—moves towards the "entering" side of the tooth in spite of the opposite tendency of the first-mentioned force component. This is particularly disadvantageous because it is desirable that the "tooth bearing" under load should not extend quite to the entering side of the tooth. A fine wedge-shaped clearance diminishing in thickness in the direction in which the surface of the worm thread approaches the contact area is helpful in maintaining an oil film between worm and wheel, the hydrodynamic conditions being roughly similar to those in the clearance between a rotating shaft and a bearing bush. On the contrary, if the oil film which the worm brings with it towards the worm wheel tends to be scraped off, a heavy contact occurs at the very edge of the wheel tooth. To counteract this undesirable effect of deflection, the axial position of the worm wheel may be adjusted so that contact in the unloaded condition is towards the leaving side of the tooth. The amount of the offset has to be found by repeated trial ; there is no rigorous method of calculating it even when all the dimensions of the gears and their casing are known. Contact bearing. Worm gears are usually checked for general accuracy by setting them up at the correct centre distance on a testing fixture, lightly coating the worm with prussian blue or equivalent marking substance and running the gears together by hand rotation of the worm. The extent of the marking which then appears on the Fig. 10. Worm and differential unit for rear axle. 7 Worm Gearing—contd. is an indication of the distribution of contact. With perfect gears, correctly mounted, this "marking" would extend over the whole area of the tooth flank; in practice the marking often appears in detached areas, whose distribution shows the probable position and extent of the contact bearing when the initial high spots have been worn off. If the gears are to have an adequate "entry gap" when in operation, the light load marking should not extend quite to the "entering" side of the tooth. Accurate control of the contact bearing in this respect can be effected by giving the worm wheel generator special adjustments which call for a good deal of skill and experience. The accuracy of the gears having been checked on the testing fixture, special precautions must next be taken in fitting them into the axle casing (or other mounting) in which they have to work. The axial positioning of the worm (provided that it is of ample face width) does not demand any specially high degree of accuracy, but the method of supporting the worm wheel must permit of fine axial adjustment. Slight axial movement of the worm wheel in one direction causes the contact bearing to move (relatively to the wheel) in the opposite direction. The greater the lead angle of the worm the more sensitive are the gears in this respect. The contact bearing under load will inevitably differ from the light load marking because of the distortions already mentioned. The aim is therefore for a light-load bearing extending over about 70 per cent. of the available area of the tooth flank and concentrated towards the "leaving side." Given gears and mounting of normal rigidity, the effect of load-distortion is to move the contact area across the tooth until it is just short of the entering edge. Noise. Gears which become perfectly accurate when distorted by the loading on them would operate silently at any speed, apart from noise produced by the relative sliding of smooth surfaces. The ideal condition is unattainable in practice because even if it were possible to manufacture without error there would still be the difficulty of determining tooth shapes and dimensions which would change under load to the theoretically correct values. Even with this problem solved, there arises the impossibility of producing (say) a tooth shape which shall be correct under all possible values of loading. Deflection of loaded teeth of a worm wheel causes the angular position of the wheel to differ at any instant from that theoretically corresponding to the angular position of the worm. With the worm driving, the wheel lags behind the position it would occupy if there were no deflection. Consequently, commencement of contact between a wheel tooth and a worm thread is attended by an impact which, although it may not induce any serious dynamic stresses, can help to produce noticeable noise when it is repeated (say) 300 times per second. Impacts of this sort will occur at the tips of the worm wheel teeth unless arrangements are made to avoid them. This can be done by modifying the profile of the axial section of the wheel teeth so that the tips are slightly thinner than the theoretical amount, the light load marking then failing to extend quite to the throat of the wheel. The result is that the tip of the load-deflected tooth enters into contact with the worm thread with a wedgelike action instead of a hammer blow. The presence of an oil film between worm thread and wheel tooth is primarily arranged in order to avoid the rapid wear which would result from metallic contact, but its viscous resistance to sudden displacement causes it also to be useful as a means of reducing the severity of impact and the associated production of noise. In well-designed worm gears the contact conditions are such as to maintain an adequate oil film, and this is probably one reason for the quiet running characteristic of this type of gear. Another lies in the disparity between the hardness of worm and worm wheel, the former usually being of case-hardened steel precision ground with extreme accuracy and the latter of relatively soft bronze capable of accommodating itself (and any slight inaccuracies which it may possess) elastically, plastically, or by wear to the form of the worm. Lubrication of worm gears. The lubricant used for worm gears must fulfil two main requirements: (a) It must be capable of maintaining a film at each contact line under all loading conditions, because otherwise the direct sliding of metal-to-metal surfaces would produce excessive heat and rapid wear. (b) It must lead to a low coefficient of friction between the nominally contacting surfaces. The first of these demands a fairly high viscosity, the actual figure depending on the intensity of loading on the contact lines. In general, the higher the speed of the gears the lower the intensity of loading and therefore the less viscous the oil need be. As, of course, a desirable from the point of view of reduction of power loss by churning the oil not actually at points of contact. So far as automobile rear axle gears are concerned, a most difficult condition is that of full engine torque on first speed, and in this there is not much variation of rubbing speed between one class of vehicle and another. It is found, in fact, that one general oil specification is satisfactory for all ordinary rear axle worm drives. On the score of low coefficient of friction castor base oils have a distinct advantage over mineral oils and they are also capable of withstanding heavy loading. Their serious disadvantage is a tendency to deterioration and this makes their use inadvisable unless regular replacement can be guaranteed; for this reason, a mineral oil is normally to be recommended. In automobile rear axle worm drives a continuous supply of oil to worm and worm wheel is arranged by placing in the casing such a volume of oil as will ensure dipping of one or other of the gears in all circumstances. Liberal dimensions are desirable for the casing, both to obtain adequate external surface for cooling and to accommodate an ample quantity of oil, again to avoid over-heating. The types of oil recommended for worm gear lubrication maintain lubricating qualities at temperatures as high as 290 deg. F.{Mr Friese}, a figure which may be expected to be attained in a heavily loaded drive. Wear and pitting. Should it happen that worm gear lubrication is imperfect—by reason of failure of oil film owing to faulty contact or unsuitable oil, or of complete absence of oil—the worm wheel teeth suffer abrasive wear and bronze dust may be discovered in the sump. The first-mentioned cause of rapid wear is probably the most common of the three. It can arise from inadequate "entry gap," the oil film being, as it were, strangled at birth, and it is usually accompanied by excessive temperature rise. Difficulty of this sort may often be completely overcome by resetting the worm wheel and specially filing the teeth so as to prevent contact at the entering edge, the clearance thus formed facilitating the entrance of oil between thread and tooth. Even when the design, manufacture and mounting of worm gears are all correct, pitting of the worm wheel teeth is likely to occur if the tooth stresses reach the high figures which are common to-day. The appearance of pitting in the early stages of the life of a worm wheel is often regarded by the user with apprehension, but actually there is rarely need for alarm. It is nearly always found that after the initial development, the rate of extension of the pitted area falls rapidly away, and the gears continue to run without trouble. Even with extensive pitting, worm wheels can give excellent service and cases of failure from this cause are extremely rare. The actual mechanism of the phenomenon of pitting is not quite certain, but it seems probable that high local surface pressure causes rupture of the metal at the most highly stressed point, which lies at some distance below the surface. From this initial break, minute fissures extend to the surface and eventually a small piece of metal breaks right out. The splitting off of the fragment which originally occupied the pit is probably hastened by the entry of oil into the fissures and the generation there of hydrostatic pressure when the line of contact of tooth and thread passes over the mouth of the fissure. As tending to confirm this last point, it may be mentioned that during certain investigations into the subject, it was found that no pitting occurred unless oil were present. There is certainly no evidence to show that pitting can be regarded as an indication of inadequate lubrication. The relatively large maze particles which may fall from the worm wheel when pitting is in progress may naturally give rise to some alarm when they are subsequently found in the sump. Actually the only serious danger is that of their being carried into the contact zone or into the bearings and experience shows that with a sump of reasonable capacity this is a negligible risk. The length of service obtained from a worm drive is naturally dependent on the operating conditions and the magnitude of the stresses to which it is normally subjected. Experience with worm gears | ||