Spur/helical/belt/chain arithmetic

Ideal drive ratio & forces

Inputs

Declared drive familySelect only the geometry label for the stated ideal-ratio arithmetic; no topology or component selection occurs.

Driver teeth / pitch measureN1—Driver tooth count or compatible pitch-diameter measure used only in the ratio.

Driven teeth / pitch measureN2—Driven tooth count or compatible pitch-diameter measure used only in the ratio.

Input speedn1Declared driver speed.

Input torqueT1Declared driver torque.

Transmission efficiencyη%User-entered overall efficiency from 0 to 100; this screen does not select it.

Driver pitch diameterd1Driver pitch diameter for pitch-line speed and tangential-force arithmetic.

Declared pressure angleφUser-entered pressure angle for the elementary radial force decomposition.

Declared helix angleβUse zero for non-helical/belt/chain models; this screen reports an elementary axial-force component only.

Results

Driven / driver ratio

—

Ideal output speed

600

Output torque with stated efficiency

124.2

Driver pitch-line speed

7.5398

Driver tangential force

1,125

Elementary radial force component

409.47

Elementary axial force component

301.44

i = N2/N1; n2 = n1/i; T2 = T1·i·η; v = πd1n1/60; Ft = 2T1/d1

A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.

Calculation snapshot

Ideal drive ratio & forces

Formula version 1.0.0

Conditions

Declared drive family	helical
Driver teeth / pitch measure	20
Driven teeth / pitch measure	60
Input speed	1800
Input torque	45
Transmission efficiency	92
Driver pitch diameter	80
Declared pressure angle	20
Declared helix angle	15

Calculated response

Driven / driver ratio	3 —
Ideal output speed	600 rpm
Output torque with stated efficiency	124.2 N·m
Driver pitch-line speed	7.5398 m/s
Driver tangential force	1,125 N
Elementary radial force component	409.47 N
Elementary axial force component	301.44 N

Method

i = N2/N1 · n2 = n1/i · T2 = T1·i·η · v = πd1n1/60 · Ft = 2T1/d1

Source

Shigley's Mechanical Engineering Design:

Boundaries

User-declared driver/driven geometry
Ideal ratio
User-entered efficiency
Simple helical force decomposition

This printout is a record of displayed inputs and deterministic formula output. It is not an approval, certification, or engineering conclusion.

Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion

Method

Formula, when it applies, and when it does not

Calculate a user-defined driven/driver ratio, output speed and torque, pitch-line speed, tangential force, and an elementary helical axial-force component.

i = N2/N1; n2 = n1/i; T2 = T1·i·η; v = πd1n1/60; Ft = 2T1/d1

When

User-declared driver/driven geometry
Ideal ratio
User-entered efficiency
Simple helical force decomposition

Don’t

This is an ideal user-declared drive-ratio screen. It uses a simple pitch-circle tangential-force relation and an elementary pressure/helix-angle force decomposition; axial force is reported only for the declared helical option. It excludes component selection, planetary topology, gear tooth strength, mesh stiffness, backlash, lubrication, heat, durability, manufacturing quality, belt/chain tension, vibration, dynamic load factors, bearing reactions, and system validation.

Shigley's Mechanical Engineering Design