Spur-Gearing

Euler's “New Commentaries,” Vol. XI, St. Petersburg, about 1760. According to Willis the involute form was first suggested by Euler in his second Paper on “The Teeth of Wheels.”.

Camus on “The Teeth of Wheels,” translated by Hawkins G. I. . Second edition, published by J. S. Hodson, London, 1837.

Professor Robert Willis: Proc. Inst C.E., 1838, Vol. 2. [Page 357.] Also, “Principles of Mechanism.” Published by Parker, London, 1841.

Sang Edward : “New General Theory of the Teeth of Wheels.” Published by Black A. Black C. , London, 1852.

Cooper J. H. : Journal, Franklin Institute, 1879, Vol. 108, pages 15–16.

Walker John Others (Trans. Amer. Soc. Mech. Eng., 1885, Vol. 6, pages 862–3). Short notes as to maximum speeds and the relation thereto of pitch and workmanship, 6,000 feet per minute given as a maximum.

Grant G. B. (American Machinist, 31st October 1885, Vol. 8, pages 2–3) considers the curves for working surfaces of gear teeth and shows the involute to be superior to the epicycloid for efficiency. C. A. Smith (American Machinist, 1886, Vol. 9, page 6) criticizes Grant's article.

Lewis Wilfred : Amer. Soc. Mech. Eng., 1886, Vol. 7, pages 273–310, and American Machinist, 1886, Vol. 9, page 4. Experiments by Wm. Sellers and Co. on power transmission by gearing to ascertain the speeds and pressures liable to cause “cutting.” Also calculations for efficiency.

Brown and Sharpe Mfg. Co.: Practical Treatise of Gearing: First Edition, 1886.

Harkness W. : Proc. Amer. Assoc. Advance. of Science, 1886, page 183. Formulæ for strength, etc., of brass, wood, and iron teeth.

Reuleaux F. : Trans. Amer. Soc. Mech. Eng., 1887, Vol. 8, pages 45–85. Friction in toothed gearing and wear on teeth.

Couch A. B. Others : Trans. Amer. Soc. Mech. Eng., 1887, Vol. 8, pages 699–704. Discussion on data for working pressure on gear-teeth.

Longridge Michael : Annual Reports of Engine and Boiler Insurance Co., 1887–89. [Page 358.].

Sharp Archibald : “Wheel Teeth,” Proc. Inst. C.E., Vol. 113, 1892–3, and Vol. 121, 1894–5. [Page 358.].

Lewis Wilfred : Proc. Engineers' Club of Philadelphia, Investigation of the Strength of Gear-Teeth, January, 1893, Vol. 10. Also American Machinist, 1893, Vol. 16, pages 3–4. [Page 371.].

Reuleaux , “The Constructor,” 1893 Edition, page 146, quotes Tredgold as recommending 400 lb. per inch of width, but adds that pressures as high as 1,400 have been successfully used. He also shows that P × N/b ought not to exceed 28,000, and may be reduced to 12,000 or even 6,000. For wooden teeth he mentions 15/20,000, with an example given of 7,000 to 8,000 having run 26 1/2 years (page 147). [Page 371.].

Geyelin Emile : Proc. Engineers' Club of Philadelphia, April 1894 Vol. 11, page 142. [Page 374.].

Jones F. R. : Trans. Amer. Soc. Mech. Eng., 1897, Vol. 18, pages 766–794. Diagrams for relative strength of gear-teeth.

Mayo J. B. : Trans. Amer. Soc. Mech. Eng., 1898, Vol. 19, pages 109–118. A strength of gear chart.

Lecornu L. : Revue de Mécanique, 1898, Vol. 2, pages 24–42. Toothed gearing in England and America; line of action, form of teeth, efficiency, strength, etc.

Grant G. B. : A Treatise on Gear Wheels. Eighth Edition, 1899. Gives a bibliography and, after considering involute and cycloidal shapes as well as others, strongly advocates the universal adoption of the involute.

Lasche O. : Zeit. des Ver. deut. Ing., 1899, Vol. 43, page 1417. [Pages 361–9; and also Appendix II, page 390.].

Lewis Wilfred : “Interchangeable Gearing,” Proc. Engineers' Club of Philadelphia, Vol. 18, February 1901, page 51; and in American Machinist, 1901, Vol. 24, pp. 218–9. [Page 358.].

Christie (Proc. Engineers' Club of Philadelphia, Feb. 1901, Vol. 18, page 44, and in Iron Age, Vol. 67, 28th February 1901, page 19) gives an example 2,100 lb. per inch of face at 2,500 feet per minute. PN/b = 286,000. Carbon 0·86 per cent. Highest recorded velocity 3,900 feet per minute for mortise-wheels—680 lb. per inch of face, life short. He suggests that the product of speed by pressure divided by circular pitch—that is, Velocity × Load/Pitch, should not exceed 1,000,000. [Page 370.].

Graves E. : Proc. Engineers' Club of Philadelphia, 1901, Vol. 18, page 57. [Page 375.].

American Machinist, 1901, Vol. 24, page 689. Table of Strength of Gear-Teeth in terms of diametral pitch.

American Machinist: Vol. 24, page 1079, 12th October 1901. List of proportions and strength of spur-gear teeth adopted by Joseph Adamson and Co.

Bruce Robert A. Lieut R.N.V.R. (American Machinist, 1901, Vol. 24, pages 1140, 1269, and 1288) furnished an article advocating increased obliquity and shorter teeth. [Page 360.].

American Machinist: Vol. 25, 15th February 1902, page 145, “The Strength of Shrouded Teeth,” by Wilfred Lewis. A single shroud may add 10 per cent. and double shroud 30 per cent. to the strength of teeth, but the space occupied would be better employed in increasing the width of the face of the teeth.

Thornbery W. H. (Staffordshire Iron and Steel Inst., 1902) gives several different values varying from about 400 lb. to 800 lb. per inch of width on cast-iron teeth of 4-inch circular pitch. These give the very low stresses of 1,000 lb. to 2,000 lb. per square inch of material. [Page 374.].

Büchner : Zeit. des Ver. deut. Ing., 1902, Vol. 46, pages 159 and 278. [Page 364.].

Williams H. D. (American Machinist, 1903, Vol. 26, page 257) wrote a Paper on Measurements of Contacts, comparing the resistance to crushing of curved surfaces of different radii in contact.

Kent William : Mechanical Engineers' Pocket Book (Seventh Edition, 1904, pages 900–5). Several formulæ for calculating the strength of gear-teeth are compared and examples quoted of gearing running at high speeds up to 3,000 feet per minute.

Cheddie (American Machinist, 1905, Vol. 28, page 220) gives his ideas as to relative loads on cast-iron, gun-metal, cast-steel, and forged steel, in the ratios of 1, 1 1/2 and 2 1/2 respectively, with modifications for speed and shock as in “lifting machinery.”.

Leire G. J. : Machinery, 1905, July, page 565. [Page 374.].

Logue C. H. : American Machinist, 1907, Vol. 30, Part I, page 804. [Page 355 and Fig. 3.].

Burgess Frank : American Machinist, 1907, Vol. 30, Part I, pages 935–6. A long tooth gives a better movement than a short one.

Engineering: 21st February 1908, Vol. 85, page 241. Recommendation of the Wuest system for all cases where high reduction, high powers, or high speeds are encountered.

Humpage Thomas : “Manufacture of Spur-Gearing,” Inst. Mech. E., July 1908.

In Nicolson Smith's “Lathe Design,” published by Longmans, Green, London (1908), will be found, on pages 158–162, an extended reference to Stribeck, Bach, and Lasche's investigations.

Smith Robert H. : “Design and Waste and Wear of Wheel Teeth,” Society of Engineers, May 1908. [Page 361.].

Flanders R. E. (Trans. Amer. Soc. Mech. Eng., 1908, Vol. 30, page 921, and American Machinist, 1909, Vol. 32, page 307) advocates shorter teeth and increased pressure angle.

Litchfield N. : Trans. Amer. Soc. Mech. Eng., 1908, page 967. [Pages 370 and 375.].

Logue C. H. : American Machinist, 1908, Vol. 31, Parts I and II, pages 95 and 115. [Page 370.] Considers the effect of wear as well as strength when calculating the size of gear-teeth.

Revillon L. P. M. : Iron and Steel Inst., Carnegie Memoirs, 1908–9, Vol. 1, page 160. [Page 370.].

Iron Age: 30th April 1908, Vol. 81, page 1382. Manganese steel gear-wheels and pinions that lasted five times as long as ordinary steel, on travelling cranes.

Logue C. H. (American Machinist, 1909, Vol. 32, Part 1, page 917, and Vol. 32, Part 2, page 571) suggests varying the working stresses for the teeth of wheels according to the method of construction and presumed accuracy of workmanship, but the figures given seem to be only personal opinions unsupported by evidence either of a practical or a theoretical nature.

Livingstone R. : Electrician, 19th March 1909, page 892. [Page 368.].

Unwin W. C. : “Elements of Machine Design,” 1909, Part 1, page 41 [page 379] and page 399; when the whole load is assumed to come on one corner of the tooth, the safe load P is shown to increase as the square of the pitch.

Plessing R. (Zeit. des Ver. deut. Ing., 1910, Part 2, Vol. 54, page 1682), advocates increasing the pressure angle, and points out how this can be done with existing generating machines, and shows, by calculation, the required difference in diameter of base circle and side accordingly.

Steven J. D. : “Tooth Gearing,” Inst. Mech. E., July 1910.

Brackenbury H. I. : Trans. Amer. Soc. Mech. Eng., 1910, Vol. 32, pages 739 et seq. References to strength of gearing, etc., and also in discussion.

Lewis Wilfred : Trans. Amer. Soc. Mech. Eng., 1910, Vol. 32, page 803. Refers to investigation by a committee, and gives a summary of experiments.

Parsons C. A. Sir : Trans. Inst. Naval Arch., 1910, Vol. 52, pages 169–83. The use of helical spur-gearing in the application of the marine steam-turbine. Again in the same publication, 1911, Vol. 53, Part I, pages 29–36, and Part II, pages 79–95.

Schaefer Otto : Dingler's Polytechnisches Journal, 1910. [Page 376.].

Lewis Wilfred : Amer. Soc. Mech. Eng. and Inst. Mech. E. Joint Meeting, July 1910. Suggested interchangeable system of involute gearing with a pressure angle of 22 1/2°, and an addendum of 0·275 circular pitch.

Logue C. H. : American Machinist, 1910, Vol. 33, Part 2, pages 67, 139, and 527. Comments on gear efficiency. References to N.Y. Subway Gears. [Page 375.] A suggested modification in the Lewis formula, giving allowable increase in load for generated teeth.

Eden Rose Cunningham : “The Endurance of Metals,” Inst. Mech. E., October 1911.

Day P. C. : Trans. Amer. Soc. Mech. Eng., 1911, Vol. 33, pages 681–715. Herring-bone gears on the Wuest system. See also Page's Weekly, February 1912, Vol. 20, pages 237–9, and pages 341–4.

Rikli (Zeit. des Ver. deut. Ing., 1911, Vol. 55, page 1435): Tests of the efficiency of transmission by spur-gearing show that the loss is only about 2 per cent.

Flanders R. E. : Stevens Inst. Indicator, April 1911, Vol. 28, pages 141–59. Practical considerations in the design and construction of spur-gearing; involute versus cycloidal; cast versus cut teeth; standard versus special shapes; and some remarks on strength.

Wallwork: Engineering, 20th January 1911, Vol. 91, page 86. Testing appliances for reduction gears.

Page's Weekly: 29th December 1911, pages 1201 et seq. [Page 357.].

Betz W. C. : American Machinist, 1912, Vol. 37, page 322. Heat treatment of gears.

Millar H. T. : Machinery, 1912, Vol. 19, page 99. A logarithmic chart for finding the strength of gear-teeth.

Marx G. H. : Trans. Amer. Soc. Mech. Eng., 1912, Vol. 34, page 1376. [Pages 364 and 374.].

Drake C. W. (Electric Journal, June 1912, page 554) states that raw-hide may be run up to 2,000 or 3,000 feet per minute. [Page 374.].

White G. T. : Toothed Gearing. Published by Scott Greenwood, London, 1912.

American Society of Mechanical Engineers: “Standard Involute Gearing,” 1913, September Journal, page 1405. Report of a Committee. A majority of this Committee recommended a standard system ranging from a 12-tooth pinion to a rack, the angle of obliquity to be 22 1/2° with addendum 7/8 module (0·28 pitch) and dedendum 1 module (0·318 pitch).

Burgess (American Machinist), 1913, Vol. 36, page 113) shows the increased number of blows under a hammer test that alloy steels will sustain as compared with 0·3 per cent. carbon steel and cold rolled steel.

Electric Railway Journal (8th November 1913, Vol. 42, page 1021). Large users of gear-wheels under severe conditions, such as tramway companies and departments, are now giving considerable attention to the wear of gear-teeth under various conditions, and are keeping systematic records of measurements taken by special gear-tooth micrometers at regular intervals.

Parsons C. A. Sir (Inst. Naval Arch., 1913) states that greater attention is being given every year to accuracy in dividing or pitching out of gear wheels when being cut.

Mechanical Engineer, 19th December 1913, page 577: Modern hardened and lubricated gears are said to be able to carry 3,000 lb. per inch of width.

In the Electric Railway Journal (20th December 1913, page 1299) are given some particulars of tests on tool-steel wheels and pinions on the Memphis Street Railway. One set had already run 183,759 miles, and showed the wheel-teeth only polished and worn one-third perhaps as much as could ultimately be obtained as against a total life for soft or untreated wheels of 156,000 and pinions of 32,675 miles. (See Science Abstracts, B. 1914, Vol. 17, page 216.).

Gartside Vincent : Trans. Manchester Assoc. of Engineers, 1912–13, page 133. [Page 357.].

American Machinist, 1913, Vol. 38, pages 539–40. An editorial reference to discussion of Marx's Paper.

Stults W. R. : American Machinist, 1913, Vol. 38, pages 999–1000. Suggestive criticisms on Marx's Paper.

Electrical Review: July 1913, Vol. 73, page 84. Treatment of tramcar gear-wheels and pinions.

Parker J. H. : Off. Rep. Nat. Mach. Tool-Builders' Assoc., October 1913, pages 176–190. Heat treating and case hardening of gears for machine tools.

Gleason A. C. : Idem. Also in Iron Age, November 1913, Vol. 92, pages 1020–3. Also in Industrial Engineering, February 1914, pages 71–75.

Colburn G. L. : American Machinist, 27th November 1913, Vol. 39, pages 895–6. Testing strength of teeth by drop hammer.

Gleason A. C. : American Machinist, 1913, Vol. 39, page 1039. Six tables of strength of gear-teeth, hardened and soft. Also in Machinery, January 1914, Vol. 20, page 388. And in American Machinist, May 1914, Vol. 40, page 830, a description of a spur-gear testing machine at the Gleason works.

James F. W. : Mechanical Engineer, October 1913, Vol. 32, pages 409–10. A chart for determining horse-power of spur-gears.

Charles Fair in reply to the Discussion (Proc. Amer. Inst. Elect. Eng., 1914, February, page 320) gives 4,200 feet per minute for cloth gears and 5,000 feet per minute for “herring-bone” teeth.

Parker John (Trans. Amer. Soc. Mech. Eng., 1913, page 785) wrote on Gearing for Machine Tools, dealing with different materials and best methods of treatment for different conditions of service.

Converse T. V. (American Machinist, 1914, Part 1, Vol. 40, page 182) advocates increasing the angle of obliquity.

Lewis Wilfred : Trans. Amer. Soc. Mech. Eng., 1914, Vol. 36, pages 231–7. Gear testing machine. Also see American Machinist, July 1914, Vol. 41, pages 41–2.

Trumpy S. : American Machinist, 1914, Vol. 40, page 956. Letter as to the safe working stress for heat-treated gears.

Practical Engineer: July 1914, Vol. 50, pages 76 et seq. General discussion of Lewis formula and Marx's experiments.

Allen W. L. : “Recent Developments in Railway Motor Gearing,” Electric Journal, October 1914. Follows through the various materials used for railway gearing up to case-hardened steel, the cost of which is rather excessive, owing to the care necessary in the heat treatment. Also describes a new process of heat treatment by which a surface corresponding to that of case-hardened steel could be obtained at a much lower cost.

Parkinson J. Son : American Machinist, October 1914, Vol. 41, page 743. Gear testing machine described and illustrated.

Sawtelle E. S. : Electric Railway Journal, November 1914, Vol. 44, pages 1157–8. Tool-steel pinions and mild-steel gear-wheels.

Practical Engineer: March 1915, Vol. 51, pages 120–3. Strength of teeth in relation to shape.

Moore H. F. Seeley F. B. : “The Failure of Materials under Repeated Stress,” American Society for Testing Materials, June 1915. [Page 380.].

Ross A. A. : “Operating Conditions of Railway Motor Gears and Pinions,” General Electrical Review, pages 249–258, April 1915.

Marx Cutter : Amer. Soc. Mech. Eng., Sept. 1915, “The Strength of Gear-Teeth.” [Fig. 15, page 373.].

Suverkrop E. A. : American Machinist, 1915, Vol. 42, pages 725–730. Heat-treating equipment and methods.

Iron Age: 16th September 1915, Vol. 96, page 629. Heat treatment of gears.