Chain and Sprocket Drive

The racecar must be driven by some kind of mechanical system. In this case, sprockets are attached to the transmission and floating shaft while power is transferred between them by a mechanical chain. Chain drives have several advantages to other methods, some of which are long life, constant ratios, and no slipping. Chains come in a wide variety of pitches, widths and strands so the final design choice is often obtained by searching through manufacturer’s catalogs. The same is true for sprockets, which come in a wide variety of diameters, pitches and widths. There are several factors such as temperature and working conditions that could be taken consideration, but are neglected due to the nature of the car’s use. A sprocket can be modeled as a polygon within a circle. The number of teeth on a sprocket is represented by corners of the polygon that touch the circular boundary. The flat spots between the corners represent spaces between the teeth. This is a model of the speed variation. It is important that the variation in speed be kept as low as possible. This is generally done by increasing the number of teeth. For this particular design given, the driver sprocket has 16 teeth, while the driven sprocket is said to have 46 teeth. The formula for speed variation is provided in the textbook on page 890.
[pic] (Equation 1)
[pic]([pic] (Equation 2)
[pic]([pic] (Equation 3)
Equations 2 and 3 indicate that speed variations are very small so this aspect of the design is acceptable. The next step is to take a second look at the polygon model of the sprocket. A 5/8” pitch chain specified within the design criteria so both the sprockets should have matching pitches to ensure proper meshing. Diametral pitch is defined as the number of teeth on a gear divided by the pitch diameter. To find the diameter of the sprockets, circumference is used therefore a factor of pi is required. The approximate diameters of both sprockets are found as follows. [pic]([pic] (Equation 4)
[pic] (Equation 5) [pic] (Equation 6)
Equations 5 and 6 indicate the theoretical diameters of the drive and driven sprockets to be about 3.1 and 9.1 inches, respectively. The amount of mechanical power remains constant as it flows through the system from the engine to the shafts. This means that the smaller sprocket encounters larger forces than the larger one, which means that it should generally be made of a tougher material. A suitable sprocket that met all the design parameters was found in the Renold catalog. The 16 tooth, 1 strand, Renold 269104 carbon steel item was selected as the drive sprocket, with teeth hardened to a Rockwell Hardness of Rc 50. This sprocket was listed as having a diameter that almost exactly matched the theoretical 3.1 inches. A similar process was used to select the driven sprocket. This time a suitable selection was found in the Martin catalog. The 46 tooth Martin 50B46 type B item was chosen, which also had a very close diameter to the theoretical approximation of 9.1 inches. This sprocket is made from finished carbon steel. The next step is to determine the center to center distance between sprockets to select a chain. This is purely an approximation. Several sources, including the textbook, indicated that this distance should be 30-50 times the value of chain pitch for optimum wear life. Taking the average value;
[pic]” (Equation 7)
This distance is used to calculate the expected length of the chain;
[pic] (Equation 8)
[pic]( L[pic](pitches of chain.)
Over time the chain tends to elongate due to excessive use. The maximum amount of allowed elongation is usually considered to be about 2% of the overall length. This is not taken into consideration given the short lifetime of the car and the small chain used. In larger systems this should not be neglected. The specified chain pitch is 5/8”. Both sprockets have single rows of teeth, meaning that the chain should consist of one strand of metal links. A suitable chain was found in the Renold catalog. The Renold number 110056 Synergy BS Transmission Simplex Chain was chosen, having an ISO part number ISO10B-1.

Torque is provided by the engine and is reduced through the transmission and again by the chain drive system before it reaches the rest of the car. The driving sprocket is about 3.1 inches in diameter so must be made of a stronger material than the 9.1 inch driven sprocket because of the forces involved. These diameters were calculated by the geometric relationship between diametral pitch and the sprocket polygon, and then compared to established company product catalogs. The chain was then selected as a single strand of links, having a pitch of 5/8”. Much was learned as a result of having researched these principles.