# Relationship between diametral pitch and module

### Chapter 7. Gears

Pitch – metric module – diametral pitch – circular pitch – tooth thickness – tooth depth – base pitch Below are the ratios between the different systems: m = Gears can couple power and motion between shafts whose axes are parallel, For the metric rack it is 1 module, and for the inch rack it is 1 diametral pitch. . A geometric relationship can be derived (2, 12)* for the form of the tooth profiles to. DIAMETRAL PITCH (P) is the ratio of the number of teeth to the pitch diameter. . The approximate relationship between center distance and backlash change.

Pitch point divides the line between the line of centers and its position decides the velocity ratio of the two teeth. The above expression is the fundamental law of gear-tooth action.

## Elements of Metric Gear Technology

In this case, the motion transmission between two gears is equivalent to the motion transmission between two imagined slipless cylinders with radius R1 and R2 or diameter D1 and D2. We can get two circles whose centers are at O1 and O2, and through pitch point P. These two circle are termed pitch circles.

The velocity ratio is equal to the inverse ratio of the diameters of pitch circles. This is the fundamental law of gear-tooth action. The fundamental law of gear-tooth action may now also be stated as follow for gears with fixed center distance Ham The common normal to the tooth profiles at the point of contact must always pass through a fixed point the pitch point on the line of centers to get a constant velocity ration.

The two profiles which satisfy this requirement are called conjugate profiles. Sometimes, we simply termed the tooth profiles which satisfy the fundamental law of gear-tooth action the conjugate profiles.

Although many tooth shapes are possible for which a mating tooth could be designed to satisfy the fundamental law, only two are in general use: The involute has important advantages -- it is easy to manufacture and the center distance between a pair of involute gears can be varied without changing the velocity ratio. Thus close tolerances between shaft locations are not required when using the involute profile.

We use the word involute because the contour of gear teeth curves inward.

Gears have many terminologies, parameters and principles. One of the important concepts is the velocity ratio, which is the ratio of the rotary velocity of the driver gear to that of the driven gears. The number of teeth in these gears are 15 and 30, respectively. If the tooth gear is the driving gear and the teeth gear is the driven gear, their velocity ratio is 2.

### Elements of Metric Gear Technology | SDPSI

This involute curve is the path traced by a point on a line as the line rolls without slipping on the circumference of a circle. It may also be defined as a path traced by the end of a string which is originally wrapped on a circle when the string is unwrapped from the circle. This is part of abrasive wear and the following causes are possibilities.

Abrasion Wear Wear that looks like an injury from abrasion or has the appearance of lapping. Below are some of the causes. Adhesion Wear Wear commonly occurring between metals in sliding contact. Wear reduction is related to type, pressure, speed, distance and lubrication. A minute portion of the material in contact welds adheres and the wear mechanism comes from peeling off of these by shearing force.

Spalling This refers to the symptom of relatively large metal chips falling off from the gear surface due to material fatigue below the surface from high load. The gear surface's concave part is large and the shape and the depth are irregular.

Because the applied shear force exceeds the material's fatigue limit, fatigue cracks appear and grow leading to possible breakage of the tooth.

Excessive Wear Wear from the gear surface being subjected to intense repeated metal to metal contact which occurs when the oil film is thin and the lubrication is insufficient relative to the load and surface roughness of the gear.

This condition tends to occur when operating at very low speed and high load. To assist, Table is offered as a cross list. The one major exception is that metric gears are based upon the module, which for reference may be considered as the inversion of a metric unit diametral pitch. Gear Dimensions Terminology will be appropriately introduced and defined throughout the text. There are some terminology difficulties with a few of the descriptive words used by the Japanese JIS standards when translated into English.

One particular example is the Japanese use of the term "radial" to describe measures such as what Americans term circular pitch.

This also crops up with contact ratio. What Americans refer to as contact ratio in the plane of rotation, the Japanese equivalent is called "radial contact ratio".

This can be both confusing and annoying. Therefore, since this technical section is being used outside Japan, and the American term is more realistically descriptive, in this text we will use the American term "circular" where it is meaningful. However, the applicable Japanese symbol will be used. Other examples of giving preference to the American terminology will be identified where it occurs. It is intended as a broad coverage written in a manner that is easy to follow and to understand by anyone interested in knowing how gear systems function.

### Basic Gear Terminology and Calculation | KHK Gears

Since gearing involves specialty components, it is expected that not all designers and engineers possess or have been exposed to every aspect of this subject.

However, for proper use of gear components and design of gear systems it is essential to have a minimum understanding of gear basics and a reference source for details. For those to whom this is their first encounter with gear components, it is suggested this technical treatise be read in the order presented so as to obtain a logical development of the subject.

Subsequently, and for those already familiar with gears, this material can be used selectively in random access as a design reference.

## Basic Gear Terminology and Calculation

Figure Basic Geometry Of Spur Gears The fundamentals of gearing are illustrated through the spur gear tooth, both because it is the simplest, and hence most comprehensible, and because it is the form most widely used, particularly for instruments and control systems.

The basic geometry and nomenclature of a spur gear mesh is shown in Figure The essential features of a gear mesh are: The pitch circle diameters or pitch diameters. Size of teeth or module. Pressure angle of the contacting involutes Details of these items along with their interdependence and definitions are covered in subsequent paragraphs.

Precision instruments require positioning fidelity. Figure Figure 2.