10.1 GEARCALC/ page 1


Figure 10.1: GEARCALC - Wizard page 1

10.1.1 Description

The ’Description’ field allows the design to be labelled with a code or brief description for reference purposes and documentation.

10.1.2 Normal pressure angle

φn{αn} is the standard or generating pressure angle. For hobbed or rack-generated gears, it is the pressure angle of the tool. For helical gears, φn is measured on the generating pitch cylinder in the normal plane. φn is standardized to minimize tool inventory:

φn (deg.)Application

14.5 Low Noise
20 General Purpose
25 High load Capacity

Low pressure angle: Requires more pinion teeth (Np{z1}) to avoid undercut. Gives larger topland for same addendum modification coefficient.

High pressure angle: Allows fewer pinion teeth without undercut. Gives smaller topland for same addendum modification coefficient.

10.1.3 Helix type

You can design spur, single–helical and double–helical gearsets.

Characteristics for spur gearsets are:

Characteristics for helical gearsets are:

Characteristics for double–helical gearset are:

10.1.4 Helix angle

ψ{β} is the standard or generating helix angle. The helix angle of a gear varies with the diameter at which it is specified. The standard helix angle is measured on the generating pitch cylinder.

For hobbed gears, the helix angle may be freely chosen because the hobbing machine can be adjusted to cut any helix angle. For pinion-shaped gears, the helix angle must correspond to the helical guides that are available for the gear-shaping machine.

ψ (deg.) Application

0 spur
10-20 single helical
20-40 double helical

Low helix angle: provides low thrust loads but results in fewer teeth in contact (smaller face contact ratio, mF and higher noise generation. For the full benefit of helical action, mF {εβ} should be at least 2.0. If mF < 1.0 the gear is a low contact ratio (LACR) helical gear and is rated as a spur gear. Maximum bending strength is obtained with approximately 15 degree helix angles.

High helix angle: provides smooth-running, quiet gearsets but results in higher thrust loads unless double helical gears are used to cancel internally generated thrust loads.

10.1.5 Required ratio

The gear ratio mG{u}of a gearset is defined as a number |mG| >= 1.0 and is the ratio of the tooth numbers of the mating gears.

mG = NG/Np

It is also the ratio of the speeds (high/low) of the mating gears:

mG = -np/nG

For internal gearsets the gears rotate in the same direction instead of opposite directions. As convention the tooth number of the internal gear is set to a negative value. Therefore the ratio for an internal gear set is negative. For an internal gearset the difference of the tooth numbers |NG|- NP should not be too small to avoid interference between the tips of pinion and gear teeth.

For the sizings in GEARCALC Wizard the ratio for internal gear sets has to be below mG < -2.

For epicyclic gear trains, the overall gear ratio is:

mGo   =  |ZG ∕ZS |    for a star gear

mGo   =  |ZG ∕ZS | + 1    for a planetary


ZG = no. of teeth in internal gear

ZS = no. of teeth in sun gear

Typical ranges for overall gear ratio:

mGo Application

1-5 offset gears
3-6 star gear epicyclic
4-7 planetary epicyclic

For gear ratios larger than those shown in the table, it is generally more economical to use multiple stages of gearing rather than a single gearset.

Star gear Epicyclic Ratios:

planet/sun gear ratio for mGo >= 3:

mG = (mGo-1)/2

planet/sun gear ratio for mGo < 3:

mG = 2/(mGo-1) planet is the pinion

internal/planet gear ratio:

mG = (2*mGo)/(mGo-1)

Note: star gears cannot have mGo = 1. A reasonable minimum ratio is mGo = 1.2.

Planetary Epicyclic Ratios:

planet/sun gear ratio for mGo >= 4:

mG = (mGo-2)/2 sun is the pinion

planet/sun gear ratio for mGo < 4:

mG = 2/(mGo-2) planet is the pinion

internal/planet gear ratio:

mG = (2*(mGo-1))/(mGo-2)

Note: planetary gears cannot have mGo = 2. A reasonable minimum ratio is mGo = 2.2.

10.1.6 Profile modification

You can make corrections to the theoretical involute (profile modification). The type of profile modification has an impact on the calculation of the scoring safety. The Distribution factor (or Force Distribution factor) XGam is calculated differently depending on the type of profile modification. There is a significant difference between cases with and without profile correction. The difference between profile correction ’for high load capacity’ gears and thise ’for smooth meshing’ however is not so important. The calculation procedure requires that the Ca (of the profile correction) is sized according to the applied forces, but does not indicate an exact value.

10.1.7 Stress cycle factor

The stress cycle factor can be determined dependent upon the expected application. The choice of critical service (Y N 0.8) or general applications (Y N 0.9) can be set from the drop-down list.

10.1.8 Calculation of tooth form factor

The point of force to be assumed by the calculation of tooth form factor for spur and LACR gears is defined here. The drop down list allows the definition of force applied at tip or at the high point of single tooth contact (HPSTC).

10.1.9 Reliability and The Reliability Factor

The reliability factor KR accounts for the statistical distribution of fatigue failures found in materials testing. The required design life and reliability varies considerably with the gear application. Some gears are expendable, and a high risk of failure and a short design life are acceptable. Other applications such as marine gears or gears for power generation, require high reliability and very long life. Special cases such as manned space vehicles demand very high reliability combined with a short design life.

Reliability R Application Failure Frequency

0.9 Expendable gears. Motor vehicles. 1 in 10
0.99 Usual gear design 1 in 100
0.999 Critical gears. Aerospace vehicles 1 in 1000
0.9999 Seldom used. 1 in 10000

10.1.10 Required safety factors

An extra margin of safety can be specified by assigning SF > 1.0 for the bending stress and SH > 1.0 for the pitting. Since pitting fatigue is slowly progressive, and pitted gear teeth usually generate noise which warns the gearbox operator that a problem exists, pitting failures are not usually catastrophic. Bending fatigue frequently occurs without warning and the resulting damage may be catastrophic.

The safety factors should be chosen with regard to the uncertainties in the load and material data and the consequences of a failure. Small safety factors can be used where the loads and material data are known with certainty and there are small economic risks and no risk to human life. However, if the loads and material data are not known with certainty and there are large economic risks or risks to human life, larger safety factors should be used. The bending fatigue safety factor is frequently chosen greater than the pitting safety factor (SF > SH) since bending fatigue may be catastrophic. However, SF should not be too large because it leads to coarse-pitch teeth which may be noisy and prone to scoring failures.

Choosing a safety factor is a design decision that is the engineer’s responsibility. It must be carefully selected accounting for the uncertainties in:

Consider the need to conserve material, weight, space or costs. Most importantly, consider: