Calculation of gear

The gears are primarily used to transmit rotary motion, but using appropriate gears and gear parts can transform flat reciprocating rotary and viceversa.En a lot of machines there is the transmission of rotary motion from one shaft to another. The gears or gear wheels are one of the best means to achieve this objective. Gears are mechanical systems that transmit rotational movement from one shaft to another by successively smaller contact cams called teeth. The teeth of a sprocket may be cylindrical or helical design and manufacture of these elements is something truly remarkable, and its importance is that machine elements are very frequent and extensive use and not how complicated it can become warns analysis and proper design. Below is designing a spur gear transmission, which is vital for proper functioning of the system that has coupled a concrete mixer and a ball mill. The spur gears are the simplest type of gear and running there. They are generally used for small and medium speeds; at high speeds, if not rectified, or has been corrected their carved, produce noise whose level depends on the speed they have.

Classification gear

Parallel axis gears.

Parallel shaft gears are the simplest type of common and gear, connected parallel axes and can transfer large amounts of power with high efficiency.

Internal gear teeth

In this type of gear teeth they are oriented inside instead of pointing outward. The resistance of an inner teeth gear is greater than the equivalent of one of external teeth.

Among its advantages it is that they operate at a shorter distance between centers with external pinion of the same size. This allows a more compact design but can not be used when the number of sprocket teeth is approximately the number of gear teeth.

Basics Spur Gear.

This work is focused on the design of helical gears, but it is essential to know that their basic nomenclature refers to having spur gears, it is therefore described its basic features in this chapter, this in order to understand more easily terminology helical gears. Note that in this chapter the analysis of forces to spur gears is not described, only the analysis of forces and parameters for the design of helical gears will be described, but it will in later chapters.

Basic nomenclature of spur gears.

Spur gears are used to transmit power and angular movement between parallel axes, are the easiest gears to analyze is why, its study is necessary to understand some other types of gears. The properties of the teeth straight, single and gears are described together. The terms and symbols adhere to the standards of the American Gear Manufacturers Association (AGMA) for its acronym in English.

Pitch diameter (D) and Step

Step circumference or pitch circle is a theoretical circle in which usually all the calculations for the design of spur gears are based. Its diameter is the pitch diameter. When there is a link between two gears (pinion and gear) it is worth mentioning that during the meshing pitch circles of each gear remain tangent. Symbol to indicate the pitch diameter of the pinion and the gear pitch diameter were used. Well will refer the number of teeth of each gear to the pinion tooth number is represented as and for engagement will be represented as. We should note that the pitch diameter is somewhere inside the tooth height, so can not be measured directly, it must be calculated based on other properties that will be described below.

I pass.

The distance between adjacent teeth and tooth size are controlled by the pitch of the teeth. There are three types to indicate the step that are commonly used in the gears: circular, diametral pitch module and metric happened.

Properties of the gear tooth.

When designing or inspecting gear teeth must consider several special properties, some of which are specified in Figure 1.13. Then define some

Addendum, or head height (a): The radial distance from the pitch circle to the outside of the tooth.

Dedendum, or standing height (b): This is the radial distance from the pitch circle to the bottom of the tooth space.

Or light radial clearance (c): The radial distance from the outside of the tooth to the bottom of the gap between the opposite gear teeth when the tooth is fully engaged. The radial clearance is defined as:

c = b – a

Outside Diameter (DO): The diameter of the circle enclosing the outside of the gear teeth.

DO = D + 2a

Root diameter (DR): Also called bottom diameter is the diameter and containing the bottom of the tooth space, which is the circumference of root or root circle. The root diameter is sometimes called center line and is expressed by the following equation:

DR = D – 2b

Overall height (ht): Also called a total depth and is the radial distance from the outside.

ht = a + b

Working depth (hk): The radial distance a gear tooth is inserted into the space between the respective gear teeth. Note that:

hk = a + a = 2a

Tooth thickness (t): The arc length measured on the pitch circle, from one tooth to another. Sometimes this is called thick circular and its theoretical value is half the circular pitch. That is:

t = p / 2

Space between teeth: Arc length is measured from the right side of a tooth to the left side of the next. Theoretically it equals the tooth thickness, but for practical reasons becomes greater.

Face width (F): It is also called tooth length or width of the flank, it is the width of the tooth measured parallel to the tooth axis direction.

Chamfer: Also called the arc fillet is joining the involute tooth profile with the root of the tooth space.

Face: the surface of the tooth of a gear, from the pitch circle to the outer circle of the gear.

Edge: The tooth surface of a gear, from the root of the tooth space, including chamfer.

Center distance (C): The distance from the center of the pinion gear to the center, is the sum of the pitch radius of the two gears in mesh.

Note:

Backlash or clearance:

If the tooth thickness identical to the value of the gullet was made, as it is in theory, the geometry of the tooth should have absolute precision that worked teeth and no room to lubricate the surfaces of the teeth. To solve these problems, practical gears are manufactured with tooth space slightly larger than the tooth thickness and the difference is called play or clearance.

To provide the cutting game that generates the gear teeth can penetrate more in the model of engagement than the theoretical value, in either or both partners gears. You can also create the game to adjust the distance between centers to a value greater than the theoretical. The magnitude of the game depends on the desired accuracy of the gear pair and the size and pitch of them. Two types of clearance or play, this may be linear or angular.

Basic Law of the meshing (joint action) and speed ratio

For two gears engage and maintain a constant velocity ratio, they must satisfy the basic law of meshing. This law can be stated as follows: The shape of the teeth of a gear should be such that the common normal at the contact point between two teeth should always pass through a fixed point on the centerline.

When two gears are meshed satisfy this law says they produce joint action.

Speed ratio mentioned in connection with the fundamental law is defined as the speed ratio driven gear to the angular velocity of the drive gear. Or put another way, is the relationship between the angular velocity of output divided between the angular velocity at the entrance. According to the above speed ratio is less than 1 when the impeller and pinion is greater than 1 when the gear is who produces the momentum.

One can express the velocity ratio as follows:

Involute tooth gears

Almost all the gears are cut according to a involute curve for the combined action. There are only a few gear cut completely or partially in the form of cycloidal curves and capable of coacting obtain. However the number of gears is small, which is why only the properties of the involute curve is considered. Spur gears and helical gears are cut under this type of curve.

The involute curve can be graphically obtained by winding a rope around a cylinder and then trace the path followed by a point on the rope when it is unwound from the cylinder. When applied to the involute gears, the cylinder around which the rope is wound is defined as the base circle. A gear teeth are cut with involute curve between the base circle and addendum, while the part of the tooth between the base and dedendum circles is simply a radial line.

Action of the gear tooth.

To understand the action that occurs when two gears are meshed we refer to Figure 1.18. Line is the line along which must remain all contact points of two teeth and along which acts normal force exerted on a tooth other. This line is known as the line of action or the pressure line. At the crossing point, the line AB is perpendicular to the centerline O1O2. The angle between AB and DE is called pressure angle. Almost all the gears are cut with pressure angles of 20 ° and 25 °, although still build gear pressure angle of 14.5 °.

The pressure line is located by rotating the line perpendicular to the center line in the crossing point an angle equal to pressure in opposite to the direction of rotation of the drive gear steering angle.

It is also important to mention that the radii r1 and r2 are the radii of the circles as shown in Figure 2.12 are mutually tangent crossing point located on the center line O1O2 with this we can define the radii of the base circles and pinion gear as follows.

 rb1=r1*Cosø

rb2=r2*Cosø

And in general:

rb=r*Cosø

Where rb is the base circle radius in inches.

Length and contact ratio.

When they begin to engage the teeth of two gears the initial point of contact occurs when the tooth flank of the drive gear contacts the top driven gear. The contact ends when the top of the drive contacts the tooth flank of the driven tooth.

Because the tops of the teeth of a gear addendum circle corresponding to the contact between the teeth of two gears starts when the addendum circle of the driven gear intersects the pressure line and ends when the addendum circle of gear driving intersects the pressure line. The contact length can be geometrically obtained as shown in Fig. 1.19 and is given by the following equation:

When two gears are in mesh it is desirable that there is always at least one pair of teeth in contact. The method generally used to indicate how many teeth are in contact is the contact ratio. This ratio is defined as the length of contact between the base split step, wherein step spleen is defined as the distance on the base circle between corresponding points of adjacent teeth.

The basic step can be related to the circular pitch as follows:

 Pb=pCosø

And the contact ratio as shown:

Almost all the gears are designed with contact ratio 1.2 and 1.6. For example a ratio of 1.4 indicates that contact will always contact a pair of teeth and a second contact pair is 40% of the time.

Materials for the manufacture of gears.

The gears are manufactured in a variety of materials, both metallic and nonmetallic. The importance of the choice of material in the design of mechanical parts is important to the conditions in which the work piece, in the case of the gears is recommended that the material used for their manufacture will be the cheapest available and to ensure the proper functioning of this or at least that work is satisfactory. For this, the designer must decide which of several known criteria is the most important to solve your problem. For example if the main consideration is the high strength steel should be used instead of cast iron. If the wear resistance is the main aspect nonferrous material should be used instead of ferrous material. Well if noise reduction is desired, the non-metallic materials behave better than metal. The characteristics of some materials used in the manufacture of gears according to their general classifications are described.

Iron castings

The cast iron is one of the materials most commonly used in the manufacture of gears, low cost, ease of casting, good machinability, high wear resistance and good property for noise abatement make your selection is logical. The main disadvantage of iron as a material for emptying gear is its low tensile strength, which makes the gear tooth is weak to bending and is necessary to use a greater tooth height. The cast iron ASTM numbers to values between 20 and 60 and are very commonly used in gear. It is mentioned that the numbering corresponding to the AGMA cast iron has the same tensile strength as that given by ASTM. Nodular iron is another type of iron casting with added magnesium and cerium. This material has a high resistance to tension and holds the wear characteristics and machinability of ordinary cast iron.

Steels

Steel gears are usually made of carbon steel or alloy steel. They have the advantage over cast iron, are high strength without excessive cost. However they require heat treatment to produce a sufficient surface hardening to obtain satisfactory wear resistance. The treatment usually causes distortion in meshing, resulting in that the load is not evenly distributed across the face of the gear tooth. Because the alloy steel are subject to less distortion due to heat treatment carbon steel often given preference over carbon steels.

Gears often has hardened completely templándolos them in water or oil. If what is needed is a low degree of hardness complete curing may be cheaper process heat treatment.

Case hardening gears used requiring a hardened surface and which very accurately leg is not needed. This procedure results in the engagement a harder surface compared to the core is taken. The advantage of this procedure is that, while the engagement surface is hard and wear resistant, the core remains tough.

Some common methods to produce the hardening process are described below:

Carburizing (Figure 2.9a.): One of the most widely used methods for surface hardening of teeth, cut gear is placed in a carburizing medium is heated, the surface layer of the gear teeth absorbs carbon (diffusion) and after one or more hours at elevated temperature to keep the carbon has penetrated to give the required depth of hardened.

Nitrided (Figure 2.9a.): A surface hardening process applied to the wheels of alloy steel nitrided gear to receive subsidized treatment to give an average hardening. The area will not be nitrided should be covered with copper plates or other suitable material, is then placed in the nitriding furnace heating to 1000 ° F (538 ° C). 

Nitriding is performed by the ammonia gas which decomposes into atomic nitrogen and hydrogen on the steel surface. The atomic nitrogen slowly penetrates the surface of the make and combines with other elements to form nitrides of extraordinary hardness. A steel alloy exclusively of carbon can not be successfully nitrided.

Induction hardening (Fig 2.9b, c.): The gear is superficially hardened by tin frequency alternating currents. The process involves winding an induction coil around the part, generally the part is rotated inside the coil, within seconds teeth are brought above the critical temperature (deep red color), after this process the gear is removed from the coil and is given a temple controlled by means of a spray bath applied by a spray or canceled will be immersed in a busy bathroom. Before the disk induction hardening heat treated gear.

Flame hardened (Fig 2.9d.): Provides a shallow hardening is by using an oxyacetylene flame special burners. For even heating generally rotates the gear in the flame. The gear is semiendurecido and teeth are lowered and given the final finish before harden.

Non-ferrous metals

 Copper, zinc, aluminum and titanium are the materials used to produce alloys which are useful as materials for gears. Copper alloys such as brass are commonly used, these are very useful for increasing the corrosion resistance and when they have very high sliding speeds. Because of its ability to reduce friction these materials are widely used in worm gear reducers and auger. Aluminum alloys and zinc are used in the manufacture of gears by the die casting process.

Nonmetallic materials

For many years gears are manufactured with non-metallic materials. It was used rawhide materials, nylon, various plastics, etc. The advantages obtained with the use of these materials are noise-free operation, internal lubrication, and vibration damping shock and economy in manufacture. The main disadvantage is the low load-bearing capacity and low thermal conductivity which produces distortion in the teeth due to the heat that weakens the gear teeth.

Recently compounds have been used for the manufacture of gears as thermoplastic resins reinforced with glass fibers and lubricant additive materials. This composite has a high load capacity, low thermal expansion, high resistance to wear and fatigue. However the gears manufactured with plastic materials vary widely in their properties, which do not depend on the test method used. Therefore it is necessary to test each design to determine if their performance is consistent with the values of the properties of the materials used.