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Bevel gear terminology
Bevel gear drawings, catalogues and standards share a vocabulary that is mostly cones and angles. Every term below is shown on the drawing of one pair, with its value, so the words and the numbers can be read together.
The pair is a straight bevel, 20 and 40 teeth, outer module 5 mm, face width 25 mm, shaft angle 90°, dimensioned by the designer to ISO 23509. Where a value differs between the two members it is written pinion / wheel.
The cone
A bevel gear is a gear on a cone. Everything is measured from the pitch apex, along the cone (cone distances) or across it (diameters), and the tooth gets smaller in proportion towards the apex.
| Term | Meaning | Example |
|---|---|---|
| Pitch cone and pitch apex | The imaginary cones that roll on each other without slipping. Their common tip is the pitch apex; in a pair both apexes coincide. | - |
| Shaft angle Σ | The angle between the two gear axes - the sum of the two pitch angles. | 90° |
| Pitch angle δ | Half the apex angle of a pitch cone. For Σ = 90°, tan δ1 = z1/z2. | 26.565° / 63.435° |
| Outer cone distance Re | Along the pitch cone, from the apex to the heel. The same for both members. | 111.803 mm |
| Inner cone distance Ri | From the apex to the toe: Re minus the face width. | 86.803 mm |
| Mean cone distance Rm | From the apex to the middle of the face - where ISO 23509 calculates. | 99.303 mm |
| Face width b | The length of the teeth along the pitch cone. | 25 mm |
| Heel and toe | The outer, large end of the tooth and the inner, small end. Drawings dimension the heel. | - |
Size and module
A bevel tooth has a different size at every point along the face, so a module always belongs to a place. The two in use are the outer one at the heel, met, and the mean normal one, mmn; mistaking one for the other changes the pair's size by more than ten percent here.
| Term | Meaning | Example |
|---|---|---|
| Number of teeth z | Pinion first: the pinion is the smaller member. | 20 / 40 |
| Outer transverse module met | Pitch diameter at the heel divided by the tooth number. | 5 mm |
| Mean normal module mmn | The module at mid-face, normal to the tooth - the one ISO 23509 works in and a spiral bevel is specified by. | 4.441 mm |
| Pitch diameter de | The pitch cone's diameter at the heel: z · met. | 100 / 200 mm |
| Outside diameter dae | Over the tooth tips at the heel - the blank's largest diameter. | 113.085 / 202.652 mm |
| Circular pitch pet | From one tooth to the next along the pitch circle at the heel: π met. | 15.708 mm |
| Pressure angle α | The flank's angle at the pitch point, from the generating tool's profile. | 20° |
The tooth
The pinion's addendum is longer than the wheel's: the profile shift has moved part of the working depth from the wheel to the pinion, which strengthens the pinion and keeps it clear of undercut. The whole depth, the working depth and the clearance stay the same for both.
| Term | Meaning | Example |
|---|---|---|
| Addendum hae | From the pitch cone out to the tip, at the heel. | 7.315 / 2.965 mm |
| Dedendum hfe | From the pitch cone in to the root, at the heel. | 4.075 / 8.425 mm |
| Whole depth he | Addendum plus dedendum. | 11.390 mm |
| Working depth hwe | The depth both members' teeth share - whole depth less clearance. | 10.280 mm |
| Clearance c | The gap between one member's tip and the other's root. | 1.110 mm |
| Profile shift xhm1 | How much of the working depth moves from the wheel to the pinion (long and short addendum). | +0.435 |
| Circular thickness se | Tooth thickness along the pitch circle at the heel, before backlash. | 9.757 / 5.951 mm |
| Normal backlash jen | The play between the flanks of a meshing pair, normal to them. | 0.160 mm |
Angles and the blank
A blank is turned to cones, not cylinders, so its drawing is mostly angles. The face angle is what the turner sets; the mounting dimension is what the assembler sets, and getting it wrong moves the contact pattern.
| Term | Meaning | Example |
|---|---|---|
| Addendum angle θa | Between the pitch cone and the face cone. | 4.309° / 2.087° |
| Dedendum angle θf | Between the pitch cone and the root cone. | 2.087° / 4.309° |
| Face angle δa | The face (tip) cone's angle: δ + θa. The angle the blank is turned to. | 30.874° / 65.522° |
| Root angle δf | The root cone's angle: δ - θf. | 24.478° / 59.126° |
| Back cone distance rv | Along the back cone, from the pitch circle to the axis: de / (2 cos δ). The tooth at the heel is drawn on this cone. | 55.902 / 223.607 mm |
| Pitch apex to crown X | Axially, from the pitch apex to the crown - the outer tip corner. The mounting dimension. | 96.729 / 47.348 mm |
Spiral bevel terms
A spiral bevel adds three terms. The mean spiral angle βm is the angle between the tooth and the cone generatrix at mid-face; it is not the same along the face - made spiral with a 35° mean spiral angle and a 114.3 mm cutter, the 20/40 pair above runs from 32.6° at the toe to 37.8° at the heel. The cutter radius rc0 is the radius of the cutter head that cuts the curved tooth, from ISO 23509 Table E.1. The hand of spiral says which way the tooth curves seen from the apex; the two members of a pair are always of opposite hand. How these change the pair is in straight vs spiral bevel gears.
See every one of these on your own pair.
Open the designerQuestions
What is the heel and the toe of a bevel gear?
The heel is the outer, large end of the tooth and the toe the inner, small end, nearer the cone apex. Bevel gears are usually dimensioned at the heel.
What is the difference between m_et and m_mn?
m_et is the outer transverse module, at the heel; m_mn is the mean normal module, at mid-face and normal to the tooth. ISO 23509 works in m_mn, and spiral bevel gears are specified by it.
What is the mounting distance of a bevel gear?
The axial distance from the pitch apex to a reference face on the gear - on the drawing, from the apex to the crown, the outer tip corner. It fixes where the gear sits along its shaft.