VALICALC / MECHANICAL ENGINEERING SUITE / DS12

Straight & Spiral Bevel Gear Drive Design Sheet

Choose actual integer teeth, outer transverse module and intersecting shaft angle. Pitch cone and mean-face geometry form a common preliminary basis; straight-bevel forces are calculated separately. Spiral manufacturing, force signs and strength require the actual process and hand data.

Verified mathematical models with explicit assumptions. Component capacity and applicability are shown as separate checks.

Labeled example inputs • SI calculations • Project revision 0 • No account or cloud upload

01 / ENGINEERING INPUTS

Define the operating point

Bevel subtype

Pinion teeth

Gear teeth

Outer transverse module

Intersecting shaft angle

deg

Actual face width along pitch cone

Straight pressure angle / spiral normal angle

deg

Pinion input RPM magnitude

rpm

Pinion input torque magnitude

N·m

Entered motoring efficiency assumption

User face width / cone distance limit (0 = unknown)

02 / CALCULATE → SELECT → RECALCULATE

Calculation & checks

Pinion pitch cone angle

26.56505 deg

Gear pitch cone angle

63.43495 deg

Outer cone distance

67.08204 mm

Mean cone distance

57.08204 mm

Outer pinion pitch diameter

60 mm

Outer gear pitch diameter

120 mm

Mean pinion pitch diameter

51.05573 mm

Mean gear pitch diameter

102.11146 mm

Mean transverse module

2.55279 mm

Output RPM

750 rpm

Output torque from entered efficiency

190 N·m

Input mechanical power

15.70796 kW

Output mechanical power

14.92257 kW

Loss from entered efficiency

0.7854 kW

Pinion nominal tangential force

3,917.28818 N

Pinion nominal radial force

1,275.25309 N

Pinion nominal axial force

637.62654 N

Original schematic; not a manufacturing drawing. Straight bevel · Mean-face station · Intersecting shafts. Actual dimensions and model checks are listed in the calculation record.

Intermediate values and comparisons - SI units
Member	Teeth	Cone angle (rad)	Outer pitch d (m)	Mean pitch d (m)
Pinion	20	0.463648	0.06	0.051056
Gear	40	1.107149	0.12	0.102111

Criterion-specific verification

PASSED · Intersecting pitch-cone consistency
Cone angles sum to the entered shaft angle; both outer cone distances match by the selected tooth ratio.
UNKNOWN · Entered face-width/cone-distance criterion
No universal width limit is imposed; use actual applicable geometry/process guidance. No positive applicable limit was supplied.
PASSED · Subtype force model
Unshifted straight-bevel nominal force magnitudes at the pinion mean station; application signs require your coordinate convention.
BLOCKED · Finished tooth / cutter / mounting geometry
Nominal pitch cones are not a generated Gleason/spiral manufacturing drawing.
BLOCKED · Full bevel contact / root rating
Applicable ISO 10300/AGMA data, material and process factors need independent validation. Spur stress is not reused.
UNKNOWN · Operating efficiency qualification
Efficiency is an entered motoring assumption; no material or product efficiency curve is supplied.

Method and calculation trace

tanδ1 = sinΣ/(z2/z1 + cosΣ); δ2 = Σ − δ1, solved by atan2 with conventional acute cone limits.

R = d1/(2sinδ1); mean station Rm = R − b/2; dm = douter Rm/R. Actual face width changes geometry and nominal straight-bevel forces.

Straight pinion Fr = Ft tanα cosδ1; Fa = Ft tanα sinδ1. Nominal pinion forces derive from input torque, not loss-adjusted output torque.

Spiral mode keeps nominal pitch-cone/module calculations usable and explicitly blocks process-dependent force/rating procedures.

Assumptions & scope

Conventional intersecting conical pitch surfaces require 0 < δ1,δ2 < 90°. No hypoid offset. Mean station is halfway along the entered face width; outside and mean module are distinct.

Finished tip/root and Gleason cutting geometry are not solved by these nominal pitch-cone calculations. Face-width applicability and cutting/mounting details must be reviewed.

Spiral mode exposes nominal pitch cones and mean module only. Cutter/process-specific generated tooth geometry, hand-dependent axial force, contact and ISO 10300/AGMA strength remain blocked.

Worked example

20/40 teeth, outer module 3 mm and 90° shafts give cone angles 26.565° and 63.435° and outer cone distance 67.082 mm. A 20 mm face reduces the pinion mean diameter to 51.056 mm. 1500 RPM input gives 750 RPM output; entered 95% efficiency gives 190 N·m output torque.

Calculation methods and sources

δ1 = atan2(sinΣ, z2/z1+cosΣ); δ2=Σ−δ1; R=d1/(2sinδ1); dm=douter(R−b/2)/R

Conventional intersecting, acute pitch cones; outside transverse module and halfway mean-face station. Spiral output is nominal cone geometry, not generated tooth surfaces.

KHK Gear Technical Reference, calculation of bevel dimensions; Tập 1 6.54–6.57 printed pp114–115 / PDF113–114.

Straight: Ft=2T/dmean; Fr=Ft tanα cosδ; Fa=Ft tanα sinδ

Straight pinion nominal magnitudes; actual force signs require application axes. Spiral hand/process forces and strength are blocked.

KHK Gear Technical Reference, gear forces §12; independent pressure-angle force resolution.

n out = n in/i; P out = ηP in; η total = Πη; T out = ηiT in

Serial passive motoring power flow; 0 < η ≤ 1. Rotation signs do not imply a reversible loss model.

Tập 1, 2.15–2.18 and 3.23–3.25; independent conservation-of-energy derivation.

Textbook references identify the method context. Historical numerical catalog, material and service-factor tables have not been copied or treated as current product ratings.

Related calculators and references

Existing component-selection Jobs → · All mechanical worksheets →

Common questions

Does this approve a real component?

No. The worksheet separates mathematical results from criterion-specific checks. Actual motor, belt, gear, shaft, bearing and joint capacity need applicable current source data and engineering review.

What changes after choosing a physical size?

The worksheet recalculates the outputs and geometry from the entered actual dimensions or discrete tooth/link count. Dependent checks are reevaluated; previously saved results are not restored as approvals.