Degree of gear loss

Symbol	H_v
Unit	-
Attribute-ID	vdi_2736_2014_degree_of_tooth_loss_according_to_Wimmer
Numeric ID	10600
Value Type	PMBoolean

The degree of tooth loss can be determined according to Ohlendorf or Wimmer.

Determination according to Ohlendorf (1 <= ε_α <= 2)

For transverse contact ratios between 1 and 2 (1 <= ε_α <= 2) the degree of tooth loss H_v is determined as:

$H_{v} = \frac{π \cdot (u + 1)}{z_{2} \cdot \cos (β_{b})} \cdot (1 - ε_{1} - ε_{2} + {ε_{1}}^{2} + {ε_{2}}^{2})$

u	Tooth ratio u = z2 / z1 ≥ 1
z₂	Number of teeth of the gear
β_b	Helix angle at the base circle
ε₁, ε₂	Tip contact ratio of pinion, gear

Source: VDI 2736:2014-06 Sheet 2

Determination according to Wimmer (0 < ε_α <= 3)

For transverse contact ratios between 0 and 3 (0 < ε_α <= 3) the degree of tooth loss H_v is determined as:

$H_{v} = \frac{π \cdot (u + 1)}{z_{1} \cdot u \cdot \cos (β_{b})} \cdot (a_{0} + a_{1} |ε_{1}| + a_{2} |ε_{2}| + a_{3} |ε_{1}| ε_{1} + a_{4} |ε_{2}| ε_{2})$

u	Tooth ratio [z₂ / z₁]
z_1/2	Number of teeth of pinion / gear
β_b	Base circle helix angle
ε₁, ε₂	Tip contact ratio of pinion / gear
a_0...4	Coefficients for the tooth loss factor

Table: Factors a₀ through a₄ for calculation of the geometric loss factor of a gear analogous to Wimmer

Transverse contact ratio	Location of the pitch point C	a₀	a₁	a₂	a₃	a₄
0 ≤ ε_α ≤ 1	Before the engagement area	0	0	0	1/ε_α	1/ε_α
	In the engagement area	0	0	0	1/ε_α	1/ε_α
	After the engagement area	0	0	0	1/ε_α	1/ε_α
1 ≤ ε_α ≤ 2	Before the engagement area	0	1	1	0	0
	In 1st dual-engagement area	0	1	-1	0	1
	In single-engagement area	1	-1	-1	1	1
	In 2nd dual-engagement area	0	-1	1	1	0
	After the engagement area	0	1	1	0	0
2 ≤ ε_α ≤ 3	Before the engagement area	0	1	1	0	0
	In 1st triple-engagement area	0	1	-1	0	2/3
	In 1st dual-engagement area	4/3	-1/3	-1	1/3	2/3
	In 2nd triple-engagement area	1	-1/3	-1/3	1/3	1/3
	In 2nd dual-engagement area	4/3	-1	-1/3	2/3	1/3
	In 3rd triple-engagement area	0	-1	1	2/3	0
	After the engagement area	0	1	1	0	0

Source: Wimmer, Albert: Lastverluste von Stirnradverzahnungen - Konstruktive Einflüsse, Wirkungsgradmaximierung, Tribologie; TU München, 2006