All I need is one gear! (By: Kenneth Y. Maxon)
Many months' back, I was out hunting through a surplus store for that one of a kind part that would sit on my shelf, and have no practical uses whatsoever. When, to my surprise the perfect part, not a useless one, reached up and shouted 'buy me!' For those of us who build robots this is a normal monthly ritual! (Okay, Okay, -Weekly, -Daily) The parts I found were specialized twenty tooth stainless steel chain sprockets and as is the law regarding purchases from a junk dealer, they had exactly two of the three pieces I needed. So, I'll save some money and buy these two, as I'll easily be able to track down the third from a retail sales vendor later. Many of you reading probably know what is coming, but I was not able to track down the third piece. The following details the steps required to make the needed sprocket, including the CAD and manufacturing processes.
Going from bad to worse. It turns out that the twenty tooth sprockets I had purchased were 0.1475"-pitch. Had they been 0.25" pitch sprockets, merely contacting my local supply house and placing an order would have sufficiently rectified the situation. At this point the common choice should have been to buy three new 0.25" sprockets as a set and continue with the project. Unfortunately for me, I was not sitting down when the salesperson relayed the cost of the set of three stainless steel 0.25" pitch chain sprockets. To compound matters the larger 180-tooth sprocket was not stocked anywhere in the United States and would take up to nine weeks for production from the date ordered. So far, all the feed back on this avenue of the robot project was negative. The only saving grace came by quick interjection on the part of the sales man who assured me the chain required for 0.1475"-pitch was readily available from their warehouse. He also knew the name of a manufacturing firm who could custom design and manufacture any sprocket I needed.
I ordered the 0.1475" pitch chain and opted to make a custom sprocket. This decision, I reasoned, would allow me to add several features to the design that could be integrated right into the custom part. The sprocket / chain assembly is used to turn the large tower assembly on my long-term robot project. A substantial gear reduction is used to transmit a large amount of torque required to power the arm, which rides on the side of the tower mechanism. Even if I was able to purchase a sprocket, I would be required to machine out the center of the sprocket to allow all of the cables to pass through its center and up into the tower. (Fig. 1) Additionally I would need to provide a new bolt hole pattern to facilitate attachment to the tower base. Finally the custom sprocket option affords locating grooves to support a hardened steel race way for a thrust bearing. (Fig. 3 below shows a small cut section with the gear in place mated to the support ring. It also defines the spaces left open for the steel races.)
RESEARCH: In making the sprocket, I turned to several sources for information. First, parts catalogs available from several different retail parts suppliers that have engineering information in the back. These offer technical information on tooth spacing, flexion of chain under load information, and tooth strength information. Second, the machinist handbook, an invaluable reference, which has the definitive word on gears, screws, sprockets, cams, types and properties of steels and most other things mechanical. Finally there are several comprehensive references on mechanical / machine / mechanism design which have information usually in an easily readable form.
From this collective information I outlined three important factors in the design of my sprocket. First the shape of the tooth (profile) is important in determining how quite the chain will run. I.E. based on the size of the sprocket, whether or not the chain will engage and release properly, or the tooth will snag the chain as it leaves the sprocket. Unwanted chain noise causes large amounts of power loss, and vibration, an unwanted characteristic on a platform with many processors, sensors and socketed components. The second factor in tooth shaping (both profile and cross section) is how much strength the tooth can pull. Since chains stretch substantially during impact loading it is important that the leading tooth, (the first tooth fully engaged along the axis of force) can handle 90% of the force being applied. Like gears, the teeth of sprockets are commonly made in both 20 and 14-degree pressure angles and a 14-degree pressure angle results in a thicker and stronger tooth. Finally tooth cross sectional shape, (as opposed to profile/outline) determines how much angular miss-alignment between the chain approach vector and the plane of the sprocket. A tooth with a V-profile will tend to lock into a chain and pull it's centerline onto the sprocket while at the same time, sacrificing ultimate strength.
CAD LAYOUT: I laid out the primary circle for the sprocket in CAD with a radius based on the distance from the center of the sprocket to the center of a given chain pinion. Using a formula based on the circumference one can easily calculate the radius taking into account that the circumference divided by 0.1475" (distance between pitches) must equal 180 (number of teeth desired). Next I constructed two lines through the center of the sprocket. The first vertical and the second rotated by 2-degrees (1 tooth worth, 360/180). I continued by fully defining a single tooth (Fig. 2) and then rotating while copying it 179 times to finish the sprocket plan-form shape. I choose to use a 14 degree pressure angle which although noted for slightly rougher operation offered higher tooth strength. To offset the rough operation I implemented a curfing cut to alleviate the extended corners sticking out past the chain pinion centerline, and put small (0.005") fillets on contacting corner between the curf and pressure face. In the interest of keeping things simple, I constructed the sprocket shape in 2 dimensions, and then constructed only one vertical profile. This option lent itself to the production method I planned. (See below)
So why build a CAD model of something that could easily be sketched by hand? Simple, I planned to manufacture this sprocket with CNC (Computer Numerical Control) technology, and there are several programs on the market that can easily generate G-code from the CAD database. Of the more popular of these are MasterCAM, SurfCAM, CadKEY, BobCAD, Pro-E (with add in package), and AutoCAD (with add in package), SolidWorks (with add in package) and Catia. Additionally, several of the CNC packages like the Ah-Hah! system that actually interpolate the G-Code, provide functionality to create simple G-Code canned cycles and sequences. When working from my home I use a commercially available CAD package in conjunction with a custom written CNC package, tailored to the specifics of my milling machine setup. (G-code is a text description language that directs the CNC equipped milling machine in how to move the cutter through the material.) The methodology of CAD generation (flat plan-form vs. full 3-Dimensional model) lead quickly to the G-Code generation. Later I went back and constructed a full 3-Dimensional model to integrate into the rest of the robot model. This allowed me to do a spatial check with all of the other parts modeled into the system letting me know that the part would fit before I build it!
FABRICATION: I first generated programs to drill the eight bolt hole circular pattern holes into the 5"x5"x0.25" stock. After this I would mount a one half inch piece of stock into the machine, skim cut the top flat, and run the same program with a smaller drill bit. This would allow me to tap the holes and bolt my work piece down while I cut the profile and vertical contours. Use of eight #6-32 shoulder (stripper) bolts with a good tight fit to the hole they were put into affords a positional accuracy of about 0.001" between the bolt hole pattern and the external contour of the sprocket, insuring the sprocket will 'spin true'. Roughing would use a three-quarter inch end mill to remove the outside stock corners of the square stock, and circle boar out the center as well. Additionally, a three-quarters inch wide by 0.015" deep trough was cut into the sprocket face that would later center the steel race of the thrust bearing. Detailing each of the teeth ensued with an eighth inch end mill, the largest diameter that would fit into the bottom of each sprocket tooth. Something to keep in mind, when using a carbide end mill is that commonly they are 0.001" smaller in diameter than the size they are manufactured to. It is best to measure the size of the actual cutter one will use, and write the programs specifically for it. In this application I built in an error of + or - 0.005" into the tooth profile and cross section so small changes in tolerance were acceptable. A larger three-eighths inch ball end mill was used to cut the vertical profile onto all of the teeth at the same time. This was accomplished by moving the cutter down the tooth profile, and every two thousands of an inch (0.002") executing a circular interpolation taking the cutter all of the way around the sprocket. When finished, the part was flipped, and fastened into place using the same holes since the part was symmetrical. Then the vertical profiles were cut onto the other side. All in all the entire fabrication process took close to three hours (on production machinery) mostly related to the material removal rate vs. the flute loading rate of a one-eighth inch end mill. To do the same job on my machine out in my garage I would plan to spend an entire Saturday!
PUTTING IT ALL TOGETHER: Referring to the picture above, one can identify the drive motor (of which the NEMA-23 face plate is visible) which with the help of a 100:1 worm gear reduction, followed by my 180:20 chain-sprocket reduction provides a total reduction of 900:1. This driven from a 40oz-in stepper produces enough torque to slide a six-pack of diet coke along the floor (assumed quite smooth) when pushed by the end of the robot arm that rides along side this tower. All of the pinions and drive sprockets are bearing mounted to help keep the power / torque transmission losses as low as possible. (Some of these bearings are visible in the picture.)
You may have noted that much of this work I take on, because - well, it's fun and the process of making my robot is as fulfilling as the finished robot will be. In the picture below, you can locate the large 180 tooth custom sprocket (slightly out of focus) in the background, and the two $3.00 sprockets purchased at a surplus store in the foreground (with chain). An interesting note: The tooth shape chosen for my sprocket is, although harder and more time consuming to produce, approximately 20 percent stronger than those on the commercially produced sprockets. Just for kicks and giggles, call a gear specialty house, and ask them how much they would charge for a one off of the sprocket I've described but make sure you're sitting down... Now I look back and think about what it really cost me. Even if I take my time for the CAD and fabrication work at a good engineering wage of $65 an hour plus materials, I still saved a couple of hundred dollars and the time spent learning, only goes to improve myself. I guess that junk shop really did save me money :-)
-Enjoy, Kenneth Y. Maxon
Useful Related References on Sprockets:
Berg: B-98' Product Catalog: avail. Applied Industrial Technology (4th Ave. Seattle WA)
Pic: 97' - Product line Catalog: avail. Applied Industrial Technology (4th Ave. Seattle WA)
Brown Berring: 96' Gears selection guide: avail. Applied Industrial Technology (4th Ave. Seattle WA)
98' - Machinist Handbook: avail. Tower Books (8th St. Bellevue WA)
96' - Marks Mechanical Engineering Handbook: avail. Tower Books (8th St. Bellevue WA)