【正文】 (17) Profile angle in the involute intersection point, deg. ν1(5c) ν2Proportional base tooth thicknesses mb1(4) mb2Use Table 2 to identify remaining equationsαwA/εαBGear z2Tell Us What You Think . . . Visit to? Rate this article? Request more information? Contact the authorsor panies men? tioned? Make a suggestionOr call (847) 4376604 totalk to one of our editors!thicknesses ma1= ma2= . An example of aspur gear mesh with a high contact ratio is shownin Figure 9.Spur gears (contact ratio εα≥ ) with a minimum possible number of teeth (Ref. 2) areshown in Figure 10. The minimum possible number of teeth for helical gears is not limited bytransverse contact ratio and could be as few asone (Ref. 6). An example of a helical gear with thenumber of teeth z1= z2= 1 is shown in Figure 11.Involute Gears with Asymmetric Tooth ProfileOpposite flanks (profiles) of the gear tooth arefunctionally different for most gears. The workload on one profile is significantly higher and/oris applied for longer periods of time than on theopposite one. The asymmetric tooth shape acmodates this functional difference.The design intent of asymmetric teeth is toimprove performance of main contacting profilesby degrading opposite profiles. These opposite profiles are unloaded or lightly loaded, and usuallywork for a relatively short period. The improvedperformance could mean increasing load capacityor reducing weight, noise, vibration, etc. Degree of asymmetry and drive profile selection for these gears depends on the application.Asymmetric profiles make it possible to managetooth stiffness and load sharing while keeping adesirable pressure angle and contact ratio on thedrive profiles.Direct design of gears with asymmetric teeth isconsidered in detail in other articles (Refs. 7 and8), covering topics such as analysis and synthesisof asymmetric gearing, area of existence, andapplications. Examples of gears with asymmetrictooth profiles are shown in Figure 12. Gears withasymmetric teeth should be considered for gearsystems that require extreme performance, likeaerospace drives. They are also applicable formass production transmissions where the share ofthe tooling cost per one gear is relatively insignificant. The most promising application for asymmetric profiles is with molded gears and powdermetal gears. Molded gear tooling usually requiresa custom shape, so the asymmetric profile doesnot significantly affect cost.SummaryDirect gear design is an alternative approach totraditional gear design. It allows analysis of awide range of parameters for all possible gearbinations in order to find the most suitablesolution for a particular application. This optimum gear solution can exceed the limits of traditional rack generating methods of gear design.Direct gear design for asymmetric tooth profilesopens additional reserves for improvement ofgear drives with unidirectional load cycles thatare typical for many mechanical AcknowledgmentsThe authors express deep gratitude to Gear Technologytechnical editors Robert Errichello of Geartech, located inTownsend, MT, and Dan Thurman for their help in preparing this article.References1. Groman, . “The Zones of Involute Mesh,” VestnikMashinostroeniya, 1962, Issue 12, pp. 12–17 (in Russian).2. Vulgakov, . Theory of Involute Gears,Mashinostroenie, Moscow, 1995 (in Russian).3. Colbourne, . The Geometry of Involute Gears,SpringerVerlag, New York, 1987.4. ANSI/AGMA 1006A97, “Tooth Proportions for PlasticGears,” Appendix F “Generating Gear Geometry WithoutRacks,” AGMA, Alexandria, VA, 1997., ., . Kapelevich, and . Kleiss. NewOpportunities with Molded Gears, AGMAFall TechnicalMeeting, Detroit, October 3–5, 2020, (01FTM9) , . and . Kapelevicich. “Expanding therange of involute helical gearing,” VestnikMashinostroeniya, 1982, Issue 3, pp. 12–14 (in Russian).Translated to English, Soviet Engineering Research, Vol. 2,Issue 3, 1982, pp. 8–9., . “Geometry and design of involutespur gears with asymmetric teeth,” Mechanism andMachine Theory, 2020, Issue 35, pp. 117–130., ., Q. Lian, and . Kapelevich.“Asymmetric modified gear drives: reduction of noise,localization of contact, simulation of meshing and stressanalysis,” Computer Methods in Applied Mechanics andEngineering, 2020, Issue 188, pp. 363–390.Figure 12—Spur gears with asymmetric teeth: 12a)a generator gear drive with αw= 41H11034, εα= fordrive flanks and αw= 18H11034, εα= for coast flanks。/ 176。/50 40176。/ 176。/ 176。/30 39176。/ 176。/ 176。/10 176。/ 176。 b) z1= 4, z2= 6, αw= , εα= 。, εα= )。, εα=)。This paper presents an alternative method ofanalysis and design of spur and helical involutegears. IntroductionModern gear design is generally based onstandard tools. This makes gear design quite simple (almost like selecting fasteners), economical,and available for everyone, reducing toolingexpenses and inventory. At the same time, it iswell known that universal standard tools providegears with less than optimum performance and—in some cases—do not allow for finding acceptable gear solutions. Application specifics, including low noise and vibration, high density ofpower transmission (lighter weight, smaller size)and o