Gear

Introduction
Spur gears are the most basic type of gear. Their basically are a cylinder or disk, with teeth projecting radially, these teeth are not straight-sided in form, the edge these teeth straight and aligned parallel to the axis of rotation. They are used to change the speed of rotation from one shaft to another. Also they can be used to change the direction of rotation. In this text weare going to talk about the gear, what is his function, de geometric parameter of the gear and how get the tooth profile.
Function
The gears are devices that transmit mechanical power by applying a force to the teeth of another gear or device, Depending on their construction and arrangement, geared devices can change (increase or decrease) rotational speed while correspondingly change thetorque , or in a different direction, from the power source. To understand well what is the function of gears we should understand first the fundamental law of the gears, that more or less said that the relationship the angular speed between gears that work together is always constant.
The change of speed and torque is due to the difference of the diameters between two different gears.

Image 1: apair of torque reduction gears (teeth no shown)

Power1=T1ω1 Power2=T2ω2
Power1≈Power1 (Without mechanical losses)


The power of the output is almost the same as the power of the input. But the torque and the angular speed are change by the differences of diameters between the gears. This is the principle of work of the gear boxes.
Geometric parameters
An important concept that weshould know, before know the geometric parameters, is the Line of action. The line of action is the line along which the force is applied between the two gear teeth and this line is always changing during the period of engagement of a pair of teeth. For involutes gears the force between the teeth is always directed along the same line. In conclusion, the line of action is constant. This impliesthat for involutes gears that the path of contact is also a straight line, coincident with the line of action as is indeed the case.

Image 2: line of action (from http://www.roymech.co.uk/Useful_Tables/Drive/Gears.html)
A tooth system is defined by a unique pressure angle and set of tooth proportions. The larger pressure angle makes teeth with a much larger base, and this make the teeth muchstronger and allows the production of gears with fewer teeth. Any two gears in mesh with each other must be of the same pressure angle.
If you affect the pressure angle the result is that reduction in the danger of undercutting and interference. Reduction of slipping speeds increased loading capacity in contact, seizure and wear, increased rigidity of the tooting, increased noise and radicalforces.
Now we are going to speak the different parameters of the gear.
Pitch point (p). The point where the line of action crosses a line joining the two gear axes (show in image 2).
Circular pitch (p). The distance from one face of a tooth to the corresponding face of an adjacent tooth on the same gear, measured along the pitch circle.
Pitch circle. Is a circle, with center axis of the gear, andthe perimeter passing trough the pitch point.
Base circle diameter(DB). Is the diameter on from where the involute teeth profile is based.
Pitch diameter (D). is the diameter of a pitch circle. That is to two times the perpendicular distance from the axis to the pitch point.
Number the teeth (n). the number of teeth of a gear,
Standard number of teeth for gears
12 13 14 15 16 18 20 22 2425 28 30 32 34 38 40 45 50 54 60
64 70 72 75 80 84 90 96 100 120 140 150 180 200 220 250
Module(m). is equal to the pitch diameter divided by the number of teeth.
m=(D(mm))/n
Similar to the module of the gear, the diametral pitch (dp) is described as the number of teeth over de pitch diameter in inches.
dp=n/(D(inch))
Operating pitch diameter. Is the pitch diameter obtained from the...