Creation of Gears

This article is reproduced with the permission.Masao Kubota, Haguruma Nyumon, Tokyo : Ohmsha, Ltd., 1963. Gears are wheels with teeth and are sometimes called toothed wheels. Gears are mechanical components that transmit rotation and power from one shaft to another, if each shaft possesses appropriately shaped projections (teeth) equally spaced around its circumference such that as it rotates, the successive tooth goes into the space between the teeth of the other shaft. Thus, it is a machine component in which the rotary power is transmitted by the prime mover’s tooth surface pushing the tooth surface of the driven shaft. As an extreme case, when one side is a linear motion (this can be thought as rotational motion around an infinite point), it is called a rack. There are many ways to transmit rotation and power from one shaft to another such as by rolling friction, wrapping transmission, etc. However, in spite of a simple structure and a relatively small size, gears have many advantages such as certainty of transmission, accurate angular speed ratio, long lasting and minimal loss of power.

From small clocks and precision measuring instruments (motion transmission applications) to large gears used in marine transmission systems (power transmission applications), gears are used widely and are ranked as one of the important mechanical components along with screws and bearings. There are many types of gears. However, the simplest and most commonly used gears are the ones used to transmit specific speed ratio between two parallel shafts at a defined distance. In particular, gears with their teeth parallel to the shafts as shown in Figure 1.1 called spur gears are the most popular.

[Figure 1.2 Pitch Cylinders] When two shafts intersect, the references for carving teeth are the cones in rolling contact. These are the bevel gears as shown in Figure 1.3 where the base cone on which teeth are carved is called the pitch cone. (Figure 1.4). When the two shafts are not parallel and non-intersecting, there are no true rolling contacting curved surfaces. Based on the type of gears, teeth are created on a pair of reference contacting rotating surfaces. In all cases, it is necessary to set the tooth profile such that the relative motion of the contacting pitch surfaces matches the relative motion of the meshing of the teeth on the reference curved surfaces. When gears are considered as rigid bodies, in order for two bodies to maintain a set angular speed ratio while in contact at teeth surfaces, without running into each other or separating, it is necessary for the common normal components of speed of the of the two gears at the contact point to be equal. In other words, at that instant, there is no relative motion of the gear surfaces in the direction of the common normal, and the relative motion exists only along the contact surface at the point of contact.

Now, using the method as before, from the imagined meshing of gear A with the imaginary gear C, obtain the tooth form FA as the envelope of tooth form FC. Designate the contact line of tooth surfaces FA and FC as IAC. Similarly, obtain the contact line IBC and tooth surface FB from the imaginary meshing of gear B and the imaginary gear C. Thus, the tooth surfaces FA and FB are obtained by the mediation of FC. In this case, if the contact lines IAC and IBC match, gears A and B are in line contact, and if IAC and IBC intersect, gears A and B will have a point contact at that intersection. That means, with this method, it is possible to lead to point contact tooth forms as well as line contact tooth forms.
However, there are limits to geometrically obtained tooth forms as explained above, especially when the tooth bodies of surfaces FA and FB invade each other, or when those areas cannot be used as tooth forms. This invasion of one tooth body into another is called interference of tooth profiles.
As clear from the above explanation, there are theoretically many ways to produce tooth forms which create specified relative motion. However, in reality, consideration for the gear mesh, tooth form strength and difficulties of tooth cutting will limit the usage of these kinds of tooth forms to just a few.

Free Gear Technical Data available in PDF format

KHK offers for free the “Gear Technical Data” book in PDF format. This book is very useful for learning about gears and gearing. In addition to the types of gears and gear terminology, the book also includes sections regarding tooth profile, calculations of dimensions, strength calculations, materials & heat treatment, ideas about lubrication, noise, etc. You can learn a lot about gearing from this book.

Why is it difficult to obtain needed Gears ?

There is no standard for the gear itself

Gears have been used worldwide since ancient times in many applications and are representative components of machine elements. However, as far as the precision class of gears, there are industrial standards in various countries such as AGMA(US), JIS(Japan), DIN(Germany), etc. On the other hand, there are no standards with regard to factors which ultimately specifies [the gear itself] such as its form, size, bore diameter, material, hardness, etc. As a result, there is no unified approach but it is a collection of the actual gear specifications decided by the individual designers that suits the design of their machines or those decided by the individual gear manufacturers.

There is a diversity of gear specifications

As mentioned above, there is a diversity of gear specifications. With the exception of very simple gears, it is not an overstatement to say that there are as many kinds as there are places where gears are used. For example, among many gears, when the pressure angle, tooth pitch and number of teeth specifications are matched, there are many other specifications that define gears such as bore size, face width, heat treatment, final hardness, surface roughness after grinding, existence of shaft, etc. It can be said that the possibility of two gears being compatible is low. This is one of the reasons why (when a gear breaks, for example) it is difficult to obtain a replacement gear.

Cannot obtain the desired gears

Sometimes it occurs that you cannot obtain a replacement gear for a worn out or broken one at the place the machine is being used. In this case, most of the time, there is no problem if there is a manual or a parts list for the machine that contains the drawing necessary for the gear’s manufacture. There is also no problem if it is possible to contact the machine’s manufacturer and that the maker can supply the needed gear. Unfortunately, in many cases :
 – The machine’s manual does not show the drawing of the gear by itself
 – It is not possible to obtain only the gear from the machine’s manufacturer, etc
For such reasons, it is difficult to obtain the needed gear. In these cases, it becomes necessary to make the manufacturing drawing of the broken gear. This is often difficult without specialized technical gear knowledge. The situation is often similarly difficult for gear manufacturers due to insufficient data for the gear. Also, to create the drawing from the broken gear requires great deal of engineering manpower and this raised the question of who will be burdened with this cost.

When only one gear is needed, the production cost is high

When the machine using a gear is mass produced, then so is the gear which is made to a certain production lot size, spreading the unit cost of the gear by taking advantage of the economy of scale. On the other hand, users utilizing the machine after it has been manufactured and when one or two gears need replacement, they often face a high production cost making the final repair cost at times very expensive. In short, the difference in the two production methods (mass production or small lot production) has a large effect on the cost of the gear. For example, a purchase of 300 gears in one shot for a new machinery production project (making 300 gears in one lot) compared to buying one replacement gear later (with the production lot of 1 piece) has a tremendous difference in manufacturing unit cost. This is the same situation at the design stage of a new machine when one gear is needed for the prototype with the same high cost.

Possibility of using standard gears

When designing a new machine, if the specifications of the gears used can be matched to those of the gear manufacturer’s standard gears, the problems mentioned above can be solved. By this method :
You can avoid the step of designing new gears during the design of a machine
You can utilize 2D/3D CAD models, printable part drawings, strength calculations, etc. provided by the gear maker
Even if you need only one gear as a trial, the standard gears are normally mass produced by the gear maker and are reasonably priced
These are some of the conveniences you can take advantage of. Also, when a gear in a machine in use needs replacement, if its specifications are similar to those of a gear maker’s, it may be possible to interchange it with a standard gear by itself or a standard gear with a secondary operation. In this situation also, it may be possible to avoid the inconvenience of doing the following tasks