# Calculation of geometric dimension of involute standard spur gear

#### Geometric dimension calculation of standard spur gear

 Name Code Calculation formula Tooth shape angle α 20 ° for standard gear Tooth number z Determined by transmission ratio calculation Modulus m Determined by calculation or structural design Tooth thickness s s=p/2=πm/2 Alveolar width e e=p/2=πm/2 Pitch p p=πm Base pitch pb pb=pcosα=πmcosα Addendum height ha ha=ha*m=m Tooth root height hf hf=(ha*+c*)m=1.25m Tooth height h h=ha+hf=2.25m Index circle diameter d d=mz Diameter of addendum circle da da=d+2ha=m(z+2) Radicle diameter df df=d-hf=m(z-2.5) Base diameter db db=dcosα Standard center distance a a=(d1+d2)/2=m(z1+z2)/2

Normal tooth system ha  = 1, C  = 0.25

Short tooth system ha  = 0.8, C  = 0.3

When a pair of gears are engaged, the radial distance between the tooth top of one gear and the tooth root of another gear is indicated by C. The top clearance can avoid the teeth colliding with each other when a pair of gears are driven, and can store some lubricating oil. Standard center distance a = R1 + R2 = m (z1 + Z2) / 2

Example: a pair of standard spur gears are known to have a transmission ratio of i12 = 3, driving wheel speed n1 = 600r / min, center distance a = 168m m, module M = 4mm. Try to find the speed of driven wheel N2. What are the gear teeth Z1 and Z2?

Solution: transmission ratio i12 = N1 / N2 = Z2 / Z1

n2＝n1／i12＝600／3＝200r／min

i12＝Z2／Z1＝3

a＝m (Z1＋Z2) ／2＝168

Z2＝3Z1 Z1＝21

Z1＋Z2＝84 Z2＝63

#### Spur gear internal meshing and gear

Differences between inner gear and outer gear

1.The top circle of the internal gear is smaller than the graduation circle, and the root circle is larger than the graduation circle.

2.The tooth profile of the internal gear is concave, and the tooth thickness and the tooth width correspond to the tooth width and the tooth thickness of the external gear respectively.

3.In order to make the tooth profile of the internal gear top all involute, the tooth top circle must be larger than the base circle.

When the gear transmission shaft is required to be parallel, the rotation direction is the same, and the transmission structure is compact, the internal mesh and gear can be used

#### Spur gear drive

1.Correct engagement conditions

The condition of correct engagement of spur gears is that the modulus and pressure angle of the two gears are equal respectively

2.Continuous drive conditions

The former pair of teeth has not finished meshing, and the subsequent pair of teeth has entered meshing state.

Note: a single gear has a fixed dividing circle and dividing circle pressure angle, but no pitch circle and engagement angle. Only when a pair of gears are engaged, there is pitch circle and engagement angle. 