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).
Article from 'The Autocar' magazine discussing the principles and efficiency of worm gearing, with constructive criticism by an independent engineer.
| Identifier | ExFiles\Box 2\6\ B002_X 140 141 157-page139 | |
| Date | 9th December 1911 | |
| THE AUTOCAR, December 9th, 1911 238 R141 Without Prejudice. II. Worm Gearing. More Constructive Criticism by an Independent Engineer. PROBABLY on no mechanical subject is there more misconception than with regard to worm gearing. And the misconception is not confined to the Layman; it extends in general right through and beyond mechanical engineering circles, for not all technical writers even are exempt, as witness: 'The latter, for small hauling arrangements, has been used with considerable success, the efficiency of a well-designed worm gear, running in an oil bath, being well over ninety per cent. It has the advantages of smooth and noiseless running, and it is quite impossible for the load to overpower the motor and run back should the current supply, from any cause, fail.' This paragraph, which is from a well-known standard book on mining machinery, was quoted by the present writer some years ago, and characterised truly as sheer nonsense, but in his turn he was criticised by a self-styled consulting engineer as talking 'double-sheer' nonsense! In general one rarely gets, in the literature on the subject, beyond the theoretical conditions of efficiency. It is always pointed out that a large thread angle is the one essential contributing to the attainment of high efficiency, but this is only half the truth. A large thread angle is equivalent in a single thread worm to a large proportion between pitch and pitch diameter, and in a multiple thread worm to a large proportion between 'lead' and pitch diameter. It is much better to speak of lead in the case of a worm with two or more threads than 'pitch,' because pitch is properly the distance between corresponding points, on the centre lines, of adjacent teeth or threads. For example, in a single thread worm of 1in. pitch, the lead is also 1in., but with two threads the lead is 2in., and with three threads 3in., and so on, whereas all through the pitch remains constant at 1in.! It is not difficult to see why a small angle leads to low efficiency if one considers the elementary case of the wedge employed to raise a load. Fig. 1 shows a wedge of 1 in 10 rise, and fig. 2 a wedge of 1 in 1 rise. In both cases the weight lifted is 100 lbs. and the height of lift is one foot, so that the duty or the useful work performed is the same, namely, 100 ft.-lbs. But the work expended in the two cases is very different. Let it be assumed in the first place that the coefficient of friction is 0.33—one-third of the weight—then for fig. 1, the work expended in friction is equal to the frictional resistance (100/3 or 33 lbs.), multiplied by the distance 10ft. through which the force is exerted, that is, 330 ft.-lbs. Adding to this the useful work done, 100 ft.-lbs., the total input is 430 ft.-lbs. and the efficiency is 100/430 = 23.3%. Now for fig. 2. The work expended in friction is again equal to the frictional resistance, 33 lbs. multiplied by the distance, 1ft., through which the force is exerted, that is, 33 ft.-lbs. Adding the useful work as before, 100 ft.-lbs., the total is 133 ft.-lbs., and the efficiency is 100/133 = 75%. Hence a change from 1 in 10 to 1 in 1 has increased the efficiency more than three times. A gradient of 1 in 10 corresponds to an angle of about 6°, while 1 in 1 corresponds to 45°, which is the angle most writers speak of as giving the greatest efficiency in worm gear. But consider now the effect of a greatly reduced coefficient of friction; instead of 0.33 assume 0.033, which latter is a long way within the possibilities under conditions of good lubrication. Reverting to fig. 1, the frictional resistance is now 100 x .033 = 3.3 lbs.; the force is exerted through 10ft. as before, so that the work of friction is 10 x 3.3 = 33 ft.-lbs. The useful work is again 100 ft.-lbs.; the total work is 133 ft.-lbs., and the efficiency is 100/133 = 75%. That is to say, good lubrication with a low angle is equal to bad lubrication with a high angle. Reverting to fig. 2, the frictional resistance is unaltered at 3.3 lbs., but the force is only exerted through 1ft., so that the work expended in friction is 3.3 ft.-lbs. The useful work remains at 100 ft.-lbs., the total is 103.3 ft.-lbs., and the efficiency is 100/103.3 = 97%. That is, a sevenfold increase from 6° to 45° has only resulted in an increased efficiency of some 22%. The first deduction from this consideration is that practically perfect conditions of lubrication are at least as essential as a high thread angle. The second is that the enhancement of efficiency is by no means proportional to the increase in thread angle. That leads to the question, Is 45° worth while? The writer thinks it is not. Take fig. 3. The angle is 30°, corresponding to a rise of 1 in 1.75, and assume, as before, a coefficient of friction of 0.033. The frictional loss is 3.3 x 1.75 = 5.8 ft.-lbs. The useful work 100 ft.-lbs., the total 105.8 ft.-lbs., and the efficiency is 100/105.8 = 94.5%. That is, a 30° angle may give an efficiency within 2½% of the 45° angle. A further increase of 5° to 35° thread angle raises the efficiency 1% to 95.5%, all under the assumed condition of 0.033 coefficient of friction. So far the argument has been on purely theoretical lines. The following are actual examples of successful worm gears built by a Swiss machine tool firm—the real originators of high efficiency commercial worm gears. The three gears thus quoted were made as nearly alike as mechanically possible with progressively different thread angles for the specific purpose of bringing out the influence of thread angle on efficiency and capacity. They were tested with the results noted: A.{Mr Adams} Two thread worm, 10° angle. Worm 1in. pitch, 2in. lead, 3.56in. pitch diameter. Wheel 43 teeth, 13.3in. pitch diameter. Maximum efficiency, 82%, at 3.5 h.p. [DIAGRAMS] Fig 1: Wedge diagram. Weight 100 lbs, height 1ft, base 10ft, ANGLE 6° Fig 2: Wedge diagram. Weight 100 lbs, height 1ft, base 1ft, ANGLE 45° Fig 3: Wedge diagram. Weight 100 lbs, height 1ft, base 1.75ft, ANGLE 30° Caption: Figs. 1, 2, and 3. | ||