1、14FTM06 AGMA Technical Paper High Contact Ratio Gearing: A Technology Ready for Implementation? By C.D. Schultz, Beyta Gear Service 2 14FTM06 High Contact Ratio Gearing: A Technology Ready for Implementation? Charles D. Schultz, Beyta Gear Service (The statements and opinions contained herein are th
2、ose of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association.) Abstract Todays competitive industrial gear marketplace demands products with excellent reliability, high capacity, and low noise. Surface hardened ground tooth gearing pre
3、dominates but the legacy tooth forms handicap further improvements in capacity and noise generation. Vehicle and aircraft equipment use tooth forms not found in the standard tables to achieve better performance at little or no increase in cost. This paper will propose adopting these high contact rat
4、io forms to industrial use. Copyright 2014 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 October 2014 ISBN: 978-1-61481-098-8 3 14FTM06 High Contact Ratio Gearing: A Technology Ready for Implementation? Charles D. Schultz, Beyta Gear Service Dis
5、cussion I first became aware of deeper than standard tooth forms in 1979. The venerable company had been through tough times but its staff of engineers and designers came up with some creative solutions in the effort to remain competitive. When competitors started to shift to carburized gearing and
6、invest in gear grinding equipment, the owners did not have the cash to follow suit. Some clever engineer decided to use teeth that were 20% deeper than standard and nitride them. The rating methods then in effect gave them competitive power densities with only the purchase of custom cutting tools. T
7、he 1.2 addendum combined with the 25 degree pressure angle did not result in true high contact ratio geometry (see Figure 1). Poor tool life, especially when cutting hard pre-nitriding blanks, made for some production challenges. Coming from a through hardening background I was very skeptical but ov
8、er time found the tooth form provided good results in the field. Replacing the special hobs wasnt possible in the reduced order volume of the early 1980s, however, and we did not use the 1.2 addendum system in new design standard products. My next exposure to high contact ratio gearing came eleven y
9、ears later during a tour of the Saturn automobile plant in Spring Hill, Tennessee. The Society of Automotive Engineers (SAE) organized the event and we were keen to see the compact, integrated gear manufacturing cell that had been set up to produce all the components needed for a front wheel drive t
10、ransaxle. It was an impressive achievement in 1990 to begin with raw forgings at one end of the line and have complete carburized, hardened, and ground helical gears ready for assembly at the other end. General Motors spent plenty of money on the project and it challenged the best equipment builders
11、 in the world to participate. The gear line included an automated inspection station after the gear grind operation. While watching the charting of parts in the cue, I noticed that the teeth were much deeper than “normal” but did not think to ask our guide a question about it. The equipment supplier
12、 gave out sample charts and when we debriefed back at our office we tried to run the geometry shown on it through our gear analysis software. The home brewed code “blew up” at the dimensions entered and when we dug into the error codes it was found to have exceeded the “allowable” profile contact ra
13、tio of 1.99. We didnt at first understand the significance of this limit in conventional gear design but after scouring our engineering library we came across a great paper by Leming 1 that explained things very well. Despite the many advantages of high contact ratio gearing that Leming pointed out,
14、 we put the concept aside and continued to design products with “standard” teeth. Conventional 20 degree rack 1.2 addendum rack Figure 1. Deeper than standard tooth form 4 14FTM06 A couple years later, though, one of our salesmen asked us to help a potential customer resolve a noise problem with his
15、 equipment. Our firm had a well-deserved reputation as a supplier of high quality ground tooth gears and we went to work reviewing a consultants telephone book thick report on the customers “problem.” Unfortunately, the solutions suggested were things we had tried before without much success and we
16、told the salesman we did not think the project was worth pursuing. This salesman was a very persistent man and he refused to take no for an answer. Under the guise of giving the client a tour of our facility, he arranged for a couple of engineers to meet with my boss and me. We explained our dismal
17、prognosis for quieting his gearbox and figured we were done with the matter. These engineers were just as persistent as our salesman and they knew we wouldnt be able to resist a well-argued challenge. Especially after they told us their project motto was “We wont fail because we didnt spend enough m
18、oney.” During the brainstorming that followed the Saturn tour, the Leming article came up. While I went to retrieve the reference book with the Leming paper in it, my boss committed to me designing a set of high contact ratio gears in less than a week. There was, after all, a three day weekend comin
19、g up and there would be fewer distractions. Six days later we met again and reviewed the proposed design. We had no way of predicting the possible noise reduction but the geometry worked out and we were ready to make drawings. The customer started expediting delivery of prototypes before the review
20、meeting was over. We thought perhaps two weeks after the hobs arrived, maybe eight to ten weeks total. This was not acceptable and the customer promised to use his influence to get the hobs made more quickly. The next day, when the drawings were done, he called back to report that there could be no
21、rush hob delivery. What other options were there? Jokingly reminding him of his project motto, we suggested wire cutting the parts. He didnt find the attempted humor funny and asked for blanks to be ready for his pick-up in two days. Said blanks were back to us three days later with Q9 quality teeth
22、 cut in them using tooth plots we provided. The sample gearbox was put on test two weeks later and the results were excellent. Noise reduction goals were easily met with no tooth modifications required. Knowledgeable observers could not let go of the long thin teeth appearing to be so delicate. Sure
23、ly those skinny teeth will break, they insisted. Upon the completion of the sound tests, the prototype gearbox was subjected to the same breakage test used many years earlier to approve the previous gearbox for production. It was still running flawlessly after completing the test three times. The co
24、nventional gearbox seldom survived extended testing. A modified version of the high contact ratio gearbox has now been in production for over 20 years. Tooling budgets and production schedules prevented me from using high contact ratio tooth forms often while a gear company engineer. We managed to p
25、urchase a few HCR hobs for specific projects where there simply was not enough room for conventional gears to transmit the load but, regrettably, there was not the will to implement this technology in a widespread way. Now that I have my own consulting firm I hope to change that situation and assist
26、 clients in developing HCR geared products. The history of high contact ratio gearing The official “history” of high contact ratio gears begins with aircraft gearboxes in World War II. Lemings excellent summary of the development work on aircraft systems was published in 1977 but there is also some
27、unofficial history dating back much further that bears study. We take the “standard” involute tooth forms for granted as they were adopted long before any of todays working engineers were born. The 14-1/2 degree “full depth” involute was the first to gain official recognition in April of 1921, but e
28、ven back then there was an effort to switch to 20 degrees, first at stub depth and shortly thereafter at full depth, to meet increasing load requirements for automobiles and trucks. A “composite” 14-1/2 degree system which combined an involute and cycloidal form into a single reference rack was also
29、 adopted in the 1920s, a recognition that not everyone was completely sold on the involute system either. So where did the “standard” form come from? If you look at old photographs or drawings you will see a variety of tooth proportions, especially prior to the widespread use of hobbing and shaping
30、machines in the late 1880s. Many gears had cast teeth and there is some evidence that the 14-1/2 degree system became popular in part because the sine of 14-1/2 degrees is 0.25 and that makes it easier to draw the tooth shape into the pattern than other pressure angles. A more plausible reason, base
31、d upon my limited foundry experience, is that 14-1/2 degree teeth have wider top lands which would be easier to maintain in the foundry conditions of that time. 5 14FTM06 In research for this paper I purchased a reprint of the American Machinist Gear Book. 2 Originally published in 1915 (before AGMA
32、 was founded), this volume is a time capsule of our trade. Six different involute tooth systems are described as a prelude to discussing the need for a “standard” tooth form (see Table 1). Wilfred Lewis 1900 speech to the American Society of Mechanical Engineers (ASME) is quoted at length. When he s
33、tarted in gears in 1870 cycloidal teeth were predominant. By 1875 he was sold on the advantages of the involute system but he didnt like the 14.5 and 15 degree systems proposed. He went with 20 degrees as “I did not at the time have the courage of my convictions that the obliquity should be 22.5 deg
34、rees or one-fourth of a right angle.” I mention this as evidence that there is nothing magic about the tooth forms we have settled on as “standard.” Using Lewis dates, we have a time line of involute teeth coming into common use in 1875, a committee being assigned to adopt a standard form in 1891 wi
35、th ASME, AGMA being formed in 1914, and the 14.5 degree full depth tooth not being enshrined as standard until the 1921 AGMA Annual meeting. Even in 1921 there was enough debate so that the 20 degree stub, composite cycloidal/involute rack, and 20 degree full depth form were put “on track” for later
36、 standardization. It is reasonably safe to say that the 14.5 degree form was not selected for its dynamic characteristics as the 1921 debate recognized the more favorable sliding characteristics of the 20 degree stub system along with its purported greater strength. I say “purported” based upon some
37、 instances I observed many years later where shaker screen gears were actually found to resist tooth breakage better at 14-1/2 degrees than even 25 degrees. This puzzled us until we discovered the profile contact ratio was 2.47 with the legacy tooth form and only 1.63 with the supposedly stronger 25
38、 degree tooth. The same part with 20 degree full depth teeth had a 1.93 profile contact ratio and it too suffered tooth breakage in the field. This situation points out the need to avoid single tooth contact entirely when designing HCR sets; the profile contact ratio has to remain over 2.00 at all t
39、imes regardless of tip relief or center distance fluctuation. Many pressure angle and tooth depth systems were in use prior to “standardization” and they continued to be popular long after the 1920s. None had an addendum that exceeded the familiar 1/transverse diametrical pitch until Buckingham 3 (S
40、ection 2, Spur and Internal Gears) proposed a 1.35/NDP system for instrument gears (see Figure 2). I confess to using this book for many years and not noticing this gear tooth system until I started researching this paper. Buckingham does not discuss profile ratio in his presentation despite develop
41、ing the rack offsets needed to use the tooth form on spur pinions down to 5 teeth. Table 1. Existing tooth “standards” in 1915, per American Machinist Gear Book (pp. 23-24) Pressure angle Addendum Dedendum Whole depth Brown tooth height based on p. - Examples: 2/2.5, 2.5/3, 3/4, 4/5, 5/7, 7/9, 8/10,
42、 10/12, 12/14, 14/18. Conventional 20 degree rack diagram Buckingham 1.35 addendum rack diagram Figure 2. High contact ratio tooth form 6 14FTM06 This is not to say that high contact ratio gears were not used prior to 1935. One example of very non-standard tooth proportions that I am personally fami
43、liar with dates to the 1895 vintage Hulet unloading machines. These revolutionary devices caused an amazing reduction in the cost of unloading bulk products from the holes of ships on the Great Lakes and are considered national landmarks in Cleveland, Ohio and Superior, Wisconsin. The drive mechanis
44、m used “finger gears” to allow for a big change in center distance (on the order of 1 inch). Finger gears (see Figure 4) were so named because they looked like fingers. The pressure angle was very low, around 8 degrees, but the whole depth was on the order of 5 inches divided by the nominal DP. We w
45、ere contracted to make spare pinions using our 1916 vintage gear milling machine. As I recall, the tooth space was so deep and narrow we had to use three different milling cutters get the shape and, because of accuracy limitations of the technology, hand file the transitions to get relatively smooth
46、 operation. Most of the manufacturing techniques currently in use were available 100 years ago. The machines were far less accurate and they were a great deal slower. Metallurgy and heat treating were not as sophisticated; bearings were of much lower capacity and quality. Every aspect of machinery w
47、as slower and our predecessors, being very practical people, reserved gear grinding for applications where it was the only way to get the gearbox to work. The 14-1/2 degree full depth form was still adequate for most applications in 1921 but designers could see that the 20 degree form, first in stub
48、 depth and later in full depth, offered advantages for the future. My purpose in bringing this topic into the discussion of high contact ratio teeth is simply this: The old answers were based on old conditions. We have different conditions in effect today. Many of the old technology and cost limitat
49、ions are no longer in effect. We are under great commercial pressure to produce lighter, more compact, longer lasting gearboxes at lower prices. The design rules have to change to help us respond to those commercial pressures. Design concerns with HCR teeth Since the publication of Lemings paper, high contact ratio (HCR) gears have been used in many aircraft, defense, and vehicle applications. They have yet to be featured in “catalog” gearboxes despite the following advantages: - Increased durability rating - Increased strength rating - Reduced noise levels Figure 3
