# All the answers you want to know about the straight bevel gear

#### What are the characteristics of the straight bevel gear mechanism?

Answer: 1) transfer the motion and power between two intersecting axes.

2) The gear distribution on the cone shrinks from the big end to the small end.

3) The large end face is the standard parameter face.

4) The tooth profile curve is spherical involute.

#### What are the correct Meshing Conditions for straight bevel gears?

Answer: M1 = M2 = m, α 1 = α 2 = α R1 = R2 (R is the taper distance) of large end face

#### What is the back cone, equivalent gear and equivalent number of teeth of the bevel gear?

Answer: the cone tangent to the graduation circle on the big end spherical surface of the bevel gear is called the back cone of the bevel gear, and the sector formed by the projection and expansion of the parallel conical generatrix of the big end surface of the bevel gear to the back cone is called the sector gear.

The straight cylindrical gear equivalent to the large end profile of the bevel gear is called the equivalent gear of the bevel gear, and its number of teeth is called the equivalent number of teeth.

#### What is the purpose of equivalent gear and equivalent number of teeth?

Answer: a pair of equivalent gears of bevel gear are used to study the meshing principle of bevel gear, such as coincidence degree and correct meshing conditions. A single equivalent gear is used to calculate the minimum number of teeth without undercutting and to select the tool number and calculate the bending strength of bevel gear when machining bevel gear with profiling method.

#### How to calculate the pitch circle diameter, transmission ratio and equivalent number of teeth of the bevel gear?

Answer: D = 2rsin δ; i12 = ω 1 / ω 2 = Z2 / Z1 = D2 / D1 = sin δ 2 / sin δ 1; zv = Z / cos δ

Typical examples and answers：

For example 1, a involute spur gear is known, and its parameters are m = 5 mm, ha* = 1, c* = 0.25, α = 200, z1= 10, Z2 = 20, X1 = 0.4249, and X2 = 0;

1) The calculation method is used to judge whether undercutting will occur when machining the pinion;

2) The radii of the base circle RB1 and Rb2, the radii of the top circle ra1, ra2 and the base pitch Pb of the two gears are calculated;

3) If the center distance of this pair of gears when meshing without backlash is a ‘= 76.95 mm, the overlap coefficient ε can be calculated by using graphic method. (Regulation: take the length scale μ L = 1 mm / mm)

Solution: 1) ∵ when Z1 = 10, xmin = < 17-z1) / 17 = < 17-10) / 17 = 0.418, because there is X1 = 0.429 > xmin = 0.418, there will be no undercutting.

2）rb1 = r1 cosα = mz1 / 2 cosα = 5×10 / 2 × cos200 = 23.49

rb2 = r2 cosα = mz2 / 2 cosα =5×20 / 2 × cos200 = 46.98 mm

ra1 = m (z1 / 2 + h*a + x1 >= 5×<10 / 2 + 1 + 0.4249）= 32.12 mm

ra2 = m (z2 / 2 + h*a + x2 ）= 5×<20 / 2 + 1 + 0） = 55 mm

pb = pcosα = πm cosα = 5×π×cos200 = 14.76 mm

3) Correctly make the center distance a ‘= 76.95 mm and the base circle and the tooth top circle of the two gears; correctly make the theoretical meshing line N1N2, find out the actual meshing line points, B1, B2 and measure b1b2 = 20.5 mm

Substituting formula: ε = b1b2 / Pb = 20.5 / 1.4.76 = 1.39k 