[SEL] OT gear making in brief

[Richard Strobel]

Thanks for the advise gang.  I have quite a few options now.

On another note, check this baby out.  This I believe was originally peddled 
or treadled.  "Didn't make any mistakes with that one, I'll bet."


http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&rd=1&item=3778985788&ssPageName=STRK:MEWA:IT

and another pix.

http://www.lathes.co.uk/senecafalls/page7.html

sic 'em
Rick




----- Original Message ----- 
From: "Richard Allen" <linstrum55 at yahoo.com>
To: "Stationary Engine List" <sel at lists.stationary-engine.com>
Cc: "Richard Allen" <linstrum55 at yahoo.com>
Sent: Saturday, January 29, 2005 7:29 AM
Subject: [SEL] OT gear making in brief


> Making gears, brief summary
>
> Gear tooth geometry for the most part is a nightmare from the
> perspective of a mathematician, but a piece of cake for a machinist. I
> have my feet planted in both fields and have looked at gear tooth
> design from both perspectives. From a real-world practical standpoint I
> could care less about the actual mathematics of a gear tooth shape
> because knowing the math of its shape is not necessary for generating
> that shape, just as I don't have to have any knowledge of parabolic
> curve equations to be able to throw a rock!
>
> The way that the commonly used involute gear tooth shape is generated
> is done quite simply by the interaction of two mating parts rotating in
> the way in which they are to be used. The result is that the correct
> and exact curved surfaces on the gear teeth are formed naturally. It is
> nowhere near as simple for a mathematician to figure this out and then
> draw a picture, and in their words, the machinist's method is "elegant"
> compared to theirs. The name of the shape is "involute", but unlike the
> parabolic curve or the circle where there is only one such shape for
> each of those (and consequently makes them unique), the involute curve
> is actually a whole series of curves that gradually transition in
> one-tooth increments from the truly straight-sided triangular teeth
> (with the tips cut off) of the flat rack gear to the theoretical
> minimum two-toothed pinion gear whose pair of opposed teeth have highly
> curved contact surfaces that engage the teeth of a flat gear rack. The
> flat gear rack can be thought of as a gear with lots of teeth and a
> huge diameter, and in fact on gears with a very great number of teeth,
> the teeth are very nearly the same shape as the triangular rack gear
> teeth. By the way, one-tooth gears exist and are quite common, they are
> called single-helix worms and they run on a worm gear, but that is
> cheating because the profile of the worm tooth is the same as a flat
> gear rack tooth! A single helix worm is considered a one-tooth gear
> because its mating gear advances one tooth per revolution of the worm.
> Worms can have more than one helix, though, just like a threaded rod
> can have more than one helix cut on it (multiple helix threaded parts
> are most commonly used for the screw lids on jars where the engagement
> has to be great but the number of turns to unscrew it needs to be few
> to save motion).
>
> Gear teeth can be any form you want as long as it is physically
> possible for them to mesh. A common everyday non-involute example we
> all know is where the teeth are roughly pyramidal on one of the gear
> wheels and circular humps on its mating part, which in practice is the
> ordinary bicycle sprocket gear and roller chain. The roller chain is
> just a long flexible gear and when made into a perfect circle it still
> works just fine with its sprocket gear, it fits equally well both
> inside and outside! Another non-involute form is the so-called silent
> chain used for the timing gear train of engines and also for the
> transfer-case gearing in a lot of four-wheel-drive vehicles. The silent
> chain tooth shape and method of construction are extremely simple, as
> well as rather amazing and efficient in operation, and I think highly
> underutilized.
>
> Involute gears are made by several methods, but the only one that does
> not involve specially shaped cutters is by shave-cutting the teeth
> using a cutting tool that is a flat gear rack in profile (gear rack, as
> in the rack-and-pinion gearing used for a lot of steering mechanisms).
> This is highly desirable because the involute curve of a tooth is
> different for different numbers of teeth. A cutter with the profile for
> a ten-tooth gear is useless for cutting a gear with eleven teeth
> because the teeth are different shapes. The only time a specific tooth
> profile cutter becomes practical for gears with different number of
> teeth is when the number of teeth on a gear becomes very large, which
> is when tooth shape begins to approach the flat-sided pyramid shape of
> the flat gear rack. For gears with large numbers of teeth a cutter can
> be used for a specific range of teeth, one size cutter say for gears
> with 24 and 25 teeth,  another for 26, 27, and 28 teeth, another for
> 29, 30, 31, and 32 teeth, etc., the range increasing as the number of
> teeth gets larger. For shave cutting with a gear rack-shaped cutter,
> the round gear blank is first "gashed", which is where the blank is
> indexed for the number of teeth it will have by removing most of the
> metal between the teeth by sawing or milling. Next, with the gear blank
> laying on its side while the gashed slots are rotated in perfect time
> with the rack-shaped cutter teeth, the gashed blank is fed under the
> rack-shaped cutter, which is also laying on its side. When the
> rack-shaped cutter moves down, its teeth mesh at full depth into the
> slots gashed into the blank, and the excess metal between the blank
> teeth is shaved off by the sharpened side of the rack. The rack is
> moved the same way you would drag a comb down the side of a round
> biscuit of soft clay so its teeth scrape grooves into it. The gashed
> blank is fed in another tiny increment while also being rotated in
> time, and then the rack-shaped cutter moves down again, taking off
> another small shaving. After the gashed blank has been fed one complete
> revolution in time with the rack-shaped cutter, while also having
> dozens or even hundreds of downward strokes performed to shave off
> unwanted material, it now has its teeth properly formed with the
> involute curve. There were no special levers, arms, linkages, cams, or
> any other mind-boggling Rube Goldberg contraptions used. The gear
> rack-shaped cutter will cut every and all number of gear teeth on any
> size gear using that size and shape of tooth profile. All that is
> needed for generating the involute curve are a rack-shaped cutter,
> which is extraordinarily simple to make, and a method for timing the
> rotation between the gashed biscuit blank and the cutter. Another gear
> cutting method based on the rack is gear hobbing using a cutting tool
> called a hob. The hob is a round cutter with gear rack-shaped teeth
> that cuts by being rotated instead of being moved linearly and is the
> same basic design shape as a thread-cutting tap. A hob that is
> positioned correctly with an accurately-gashed gear blank is
> self-timing in very thin gears and automatically rotates the gear blank
> as it is fed in from the side, the angled teeth grabbing and rotating
> the work piece as it turns. The flat gear rack teeth can have any
> amount of truncation and angle of triangle you want, within reason set
> by the physical limitations of the parts that mesh with it. Half of the
> angle between the legs of the triangular rack teeth is one definition
> of the gear tooth pressure angle, and the angle most commonly used for
> gears with large numbers of teeth is 14.5 degrees. Gears with few teeth
> use 20° or 25° to avoid thin tooth roots from gear tooth tip motion
> that requires clearance that "undercuts" into the root of the gear
> tooth. The 14.5° angle was very specifically chosen because the sine of
> 14.5 degrees is extremely close to 0.25 (0.25038 to be exact), making
> the measurement calculations for machining the gear rack very easy (in
> fact, the 14.5° gear tooth pressure angle is in reality 14.478° because
> the actual sine value used is 0.25000, not 0.25038, but in the real
> world that value in its application is so close to 14.5° that there is
> no meaningful difference between the two angles). A pressure angle of
> 20° is also very common in gears with a large number of teeth,
> especially in German machinery, or for gears made from very soft
> materials. As the pressure angle is increased the force pushing the
> gears apart increases, so if the squat blunt teeth of a shallow
> pressure angle are used, then a great deal of force is generated
> pushing the gears apart and it unnecessarily tears up the bearings
> supporting the gears. A pressure angle of 30° is occasionally found,
> and it is the result of the gears being hobbed using an ordinary
> threading tap! The thread tap-hobbed 30° pressure-angle teeth are very
> blunt and come to sharp points, which are only good for light torque
> loads.
>
> Sprocket gears used with roller chains are another example where the
> shape of one of the parts is used to generate the other. Sprockets are
> cut by advancing a round cutter into a gear blank that is rotated in
> time with it. The round cutter travels the same path as a roller in the
> roller chain and therefore cuts out the shape of its contact path.
>
> The silent chain used for timing in a lot of engines is an example
> where there are no special curves or oddball calculations needed! The
> geometry of the links eliminates all of that. Another feature that is
> peculiar to silent chain is that the lengthening of pitch from wear is
> self-compensating because as the chain is re-tensioned it climbs
> outward on the gear teeth, where the pitch is greater. Because of this
> they are good where rotational velocity needs to be very uniform,
> making it perfect for running camshafts that have the ignition timing
> attached. They are also good for tank tracks where high speed
> chattering from a mis-matched pitch between the track and drive
> sprocket caused by excessive wear would be a problem.
>
> Hypoid and other gears with compound curved teeth and odd-angle contact
> seem to be a real puzzler about how they are cut, but again the motions
> needed to form the contact paths are generated while being cut by
> timing the cutters with the rotation of the gear blanks.
>
> Standardized gear tooth sizes are determined by making the generator
> flat gear rack with tooth spacings specified by using a formula based
> on pi-inches. One pi-inch is simply 3.14159 inches long. A gear with 20
> teeth per pi-inch has the teeth 0.1571 inches apart, or 1/20 of an inch
> multiplied by pi.  A gear with three teeth per pi-inch has them 1.0472
> inches apart. Instead of calling them teeth per pi-inch it is
> abbreviated as a 20-pitch, 9-pitch, or 3-pitch, etc., gear. All gears
> with the same size pitch number will all fit each other. So a gear with
> 127 teeth will fit a 50 tooth gear if they both have the same pitch
> number.
>
> The only special calculations that need to be made for the machining
> operations generated by the natural functions of gear tooth contact
> paths are for making adequate clearance and minimizing backlash. The
> final operation in some gearing is by selecting the gears that fit
> together the best because things like minor differences from one
> cutting tool to the next can amplify differences that make selected fit
> necessary in spite of careful measurement and good machine shop
> practice. That is why straight cut spur gears are a favorite where
> noise is of no concern since their simplicity in both design and
> manufacturing methods produce very precise parts where little or no
> matching needs to be done to ensure a good fit. Helical and hypoid
> gears introduce angles where the set-up measurements are based on their
> tangents, and tiny errors of 1/10,000 inch will introduce
> angle-amplified cutting errors of up to 0.020-inch that are totally
> unavoidable, even by the best equipment and operators. This is where
> custom fitting of parts becomes necessary, and is why automobile
> differentials with hypoid ring and pinion gears must be in custom
> matched sets.
>
> There is still a lot more to gears and their designs, but this covers
> most of the real basics. Simple spur gears can be cut in a home
> workshop on an ordinary lathe with some special attachments.
>
> Rich Allen
>
> _______________________________________________
> SEL mailing list
> SEL at lists.stationary-engine.com
> http://www.stationary-engine.com/mailman/listinfo/sel
>