📐 Involute Gear Geometry

Calculate complete gear geometry from basic design parameters (ISO 21771)

Input Parameters

z Number of Teeth

Positive = external gear

mn Normal Module [mm]

αn Normal Pressure Angle [°]

Standard: 20°

β Helix Angle [°]

0° = spur gear

x Profile Shift Coefficient

Positive = addendum modification

b Facewidth [mm]

ha* Addendum Factor

Standard: 1.0

hf* Dedendum Factor

Standard: 1.25

📂 Load Preset (실제 가공 기어 233개)

Key Results

Reference Diameter d

—mm

Tip Diameter da

—mm

Root Diameter df

—mm

Base Diameter db

—mm

Normal Tooth Thickness sn

—mm

Transv. Tooth Thickness st

—mm

Span W_k

—mm

Span W_k+1

—mm

Pin Dia (dp) / M over pins

— / —mm

Contact Angle αp

—°

Contact Ratio εα

—

Total Contact Ratio εγ

—

Angles & Pitches

Trans. Module mt

—mm

Trans. Pressure Angle αt

—°

Base Helix Angle βb

—°

Tip Press. Angle αta

—°

Form Diameter dFf

—mm

Transverse Pitch pt

—mm

Normal Pitch pn

—mm

Base Pitch pbt

—mm

Tooth Thickness at Tip sta

—mm

Gear Profile Visualization

— Tip circle (da) — Reference circle (d) -- Base circle (db) -- Root circle (df)

Heights & Depths

Addendum ha

—mm

Dedendum hf

—mm

Spacewidth et

—mm

Overlap εβ

—

📈 Tooth Profile Values

Tooth thickness, pressure angles, and spacewidth at key diameters

Values at Key Diameters

Location	Diameter d [mm]	αt [°]	αn [°]	st [mm]	sn [mm]	et [mm]
Calculate gear geometry first

Custom Diameter Check

Check Diameter [mm]

🔧 Flank Modifications

Profile and lead modifications — ISO 1328

Profile Modification (Profilmodifikation)

Cα Profile Crowning [µm]

Balligkeit in Profilrichtung (mid-ordinate)

Cα,a Tip Relief Amount [µm]

Kopfkantenentlastung — material removed at tip

Lα,a Tip Relief Length [mm]

Roll length from tip over which relief is applied

Cα,f Root Relief Amount [µm]

Fußkantenentlastung — material removed at root

Lα,f Root Relief Length [mm]

Roll length from root start

GearPro Workpiece → Profile tab:
These correspond to Profilwinkelkorrektur and Profilballigkeitskorrektur fields. Crowning Cα is the midordinate of the parabolic profile modification.

Lead Modification (Flankenlinie / Breitenmodifikation)

Cβ Lead Crowning [µm]

Balligkeit in Breitenrichtung (Flankenlinienballigkeit)

fHβ Lead Taper (Konizität) [µm]

Flankenlinienschiefheit — linear taper across face width

fHβ,off Lead Offset (Schieflage) [µm]

Schieflage — global bias of lead line

Cβ,a Lead End Relief (Drive) [µm]

Breitenkantenentlastung — Antriebsseite

Cβ,b Lead End Relief (Coast) [µm]

Breitenkantenentlastung — Gegenseite

GearPro Workpiece → Lead tab:
These correspond to Breitenballigkeitskorrektur (Cβ), Flankenlinienschiefheit (fHβ), and Breitenkantenentlastung fields.

Modification Summary

Symbol	Description	Unit
Cα	Profile crowning	µm
Cα,a	Tip relief	µm
Cα,f	Root relief	µm
Cβ	Lead crowning	µm
fHβ	Lead taper (Konizität)	µm
Schieflage	Lead offset	µm

🔗 Gear Pair Calculation

Center distance, gear ratio, and working pressure angle for meshing gears

Gear 1 (Pinion)

z₁ — Teeth

x₁ — Shift

Gear 2 (Wheel)

z₂ — Teeth

x₂ — Shift

Common Parameters

mn [mm]

αn [°]

β [°]

b [mm]

Pair Results

Gear Ratio u = z₂/z₁

—

Ref. Center Distance a₀

—mm

Working Center Distance aw

—mm

Working Pressure Angle αwt

—°

Sum of Shift Coeff. Σx

—

Pair Contact Ratio εα

—

Pair Total εγ

—

Gear Pair Visualization

📋 Complete Results

All calculated parameters in a printable table

All Parameters

Symbol	Description	Value	Unit
Calculate gear geometry first (Tab: Gear Geometry)

⚙ Grinding Parameters

연삭 공정 파라미터 계산

Grinding Wheel (SLS)

Wheel Diameter ds [mm]

Standard: 400mm

Peripheral Speed vs [m/s]

Table Speed nw [rpm]

Radial Infeed ae [mm]

Results

Wheel Speed ns

—rpm

Contact Arc lc

—mm

Spec. MRR Q'w

—mm³/mm·s

Lead pz

—mm

Machine Data Reference

Grinding wheel (actual)

D=399.89mm, B=60mm

Max peripheral speed

50 m/s

Dressing roll

AR1, AR2

Last workpiece

mn=5, z=38, αn=25°, β=15°, x=0.15

Wk measured

83.95mm (target) / 84.3mm (actual)

Profile crowning

0.003mm

Tip modification

0.015mm / 5mm

Generating Grinding Kinematics

창성 연삭 운동학 (Wälzschleifen)

Hub axis (Y)

Axial stroke — tooth lead

Table axis (C)

Rotation — synchronized with Y

Radial axis (X)

Infeed (ae per pass)

Shift axis

Diagonal shift (Bias Control)

Coupling Y↔C

EG_DrehHubFak (GUD variable)

Dressing speed

8 ~ 60 mm/min (VuAbrMin ~ Max)

Max infeed/dress

0.2mm (ZstRadMax)

Dress overlap

1.0mm (BahnStreckeEinlauf)

Grinding norm

DIN 3962 (messtolDIN3962)

Axis Configuration

B axis

Table rotation (Dreh)

C axis

Additional rotation

Y axis

Hub (axial stroke)

X axis

Radial (infeed)

Grinding spindle

Zylinderscheibe (Cylindrical)

📖 Formula Reference

Key equations used in this calculator (ISO 21771, DIN 3960)

Basic Geometry

Transverse module

mt = mn / cos β

Transverse pressure angle

tan αt = tan αn / cos β

Base helix angle

tan βb = tan β · cos αn

Reference diameter

d = mn · z / cos β

Base diameter

db = d · cos αt

Tip diameter

da = d + 2(ha* + x)mn

Root diameter

df = d − 2(hf* − x)mn

Tooth Thickness

Trans. tooth thickness

st = mt(π/2 + 2x·tan αn)

Normal tooth thickness

sn = st · cos β

At arbitrary dia. d*

st* = d*(st/d + inv αt − inv αt*)

Involute function

inv α = tan α − α

Span Measurement (Wk)

Base tangent length

Wk = mn·cos αn·[(k−0.5)π + z·inv αt] + 2x·mn·sin αn

Optimal k

k ≈ z·(αt/π) + 0.5

Contact Ratio

Trans. contact ratio εα

(√(ra²−rb²) − rb·tan αt) / pbt

Overlap ratio εβ

εβ = b·sin β / (π·mn)

Total contact ratio εγ

εγ = εα + εβ

Recommended

εα ≥ 1.2 (spur), εγ ≥ 2.0 (helical)

Gear Pair

Working pressure angle

inv αwt = 2(x₁+x₂)·tan αn / (z₁+z₂) + inv αt

Working center distance

aw = (z₁+z₂)·mt / (2·cos αwt / cos αt)

Reference center dist.

a₀ = (d₁ + d₂) / 2

🎮 3D Gear Visualization

Interactive 3D model — rotate, zoom, pan with mouse

3D Gear Model (Three.js)

🖱 Left: Rotate | Scroll: Zoom | Right: Pan

🔬 Tooth Profile Detail

Individual tooth geometry with dimensional annotations

Single Tooth Profile

🚨 Alarm Hotline

Machine diagnostics — search alarms by code or keyword, view weak points by machine series

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Search alarms across all machine series

Type an alarm code, keyword, or select a machine series to filter

Consumable Replacement Schedule

Part	Interval	Applicable	Note

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Search spare parts by name, part number, or machine series

Total Parts

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Critical

Parts Database

Part Number	Description	Series	Status	Lead Time
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📋 Service History

Track service records, maintenance logs, and case history

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Total Cases

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Escalated

Recent Service Records

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Each resolved case is automatically logged with machine, alarm, solution, and parts used.

How it works:
1. Customer reports issue via Sebastian bot
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3. Case auto-saved → searchable knowledge base
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📚 Technical Manuals

Machine documentation, PLC references, and service guides

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PLC Data Blocks

DB100, DB103, DB20, DB72, DB1100
Machine function references

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Siemens 840D Parameters

MD1201~1225, MD32200, MD35200
Machine data configuration

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Motor Specifications

ETEL TMA/TMB, IDAM RM/RI
SIEMENS 1FW series

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GearPro Software

V4.3.13 operation guide
Setup & configuration

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Table Torque Optimization

Motor parameters for all series
Cauer filter & acceleration tables

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Troubleshooting Guide

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