involute cylindrical gears and gear pairs DIN 3960

Calculating Gears: KISSsoft-Z

6.1 Z01 Gear Basemodule
Gear Geometry Calculation for Spur Gears According to DIN 3960.
Valid for: Internal and external teeth and spur and helical teeth.
 Tooth profile displacement (proposition for optimised layout area according to the MAAG
handbook, after compensating for specific sliding according to DIN 3992; in addition, the
profile displacement can be post-calculated from the base tangent length or from the
dimensions of the rollers)
 Reference profiles according to ISO 53, DIN 867, DIN 58400 or to free choice (for
precision engineering: interfering tools)
 Regarding tip relief, profile correction, tooth tip chamfer, tooth width chamfer, flank line
correction, etc.
 Control for undercut, pointed teeth, meshing disturbance, bottom clearance, ease of
installation, necessary involute and producable involute, etc.
 Calculating the control values for the base tangent length, the tooth thickness, the
measurement over balls for one and two balls, the measurement over rolls for one and two
rolls. The control measures are calculated for the upper and lower tolerance.
 Alternatively, the tooth thickness allowance can be determined.
o According to DIN 3967 (eg e25) (database provided).
o According to DIN 58405 (eg 8g) for precision engineering.
o From the nominal circumferential backlash or from the specified circumferential
backslash
 Users can construct various individual tolerance tables for tooth thickness
deviations if they do not want to work with the DIN 3967 standard. These tables are
processed automatically by the programme.
 For precision mechanics: tip circle (incl tolerances) with intersecting tool
 Calculating the circumferential backlash range (and normal backlash) of the gear wheel pair
regarding the tooth thickness deviation and centre distance tolerances.
 Calculating all relevant values such as overlapping, specific sliding, etc.
 Calculating and checking the effective overlapping and root diameter (regarding the tooth
thickness deviation)
 Specific gliding: Graphical representation of gliding around meshing point
 Gear wheel view: Graphic representation of gears wheels (front and axial section)
 Angles can be entered as decimal figures or in minutes and seconds.
 Input in modules in mm or as diametral pitch or circular pitch, transverse module or normal
module
 Different tooth qualities for single wheels

Materials and Milling Cutter Reference Profiles from Database

The user can define any materials and reference profiles in a special database. The programme
provides 50 different materials and 15 different milling cutters. Special materials and milling cutters
can be entered while using the programme, or they can be stored in corresponding files assisted by a
material managing programme (see pos. K07, page pageref). The programme considers all
hardening methods of DIN 3990. Additionally, stainless steel, aluminium, bronze, etc are supported.
Plastics with module Z14 (page pageref).
Base Module Calculating:
  gear wheel set

 single gear wheel

Calculating:
 Epicyclic gear (sun, planets, ring gears)
 Load distribution train (pinion, exchangeable wheels, wheel)
Option Z01a
 misalignment train (pinions, exchangeable wheels, wheel)

 double misalignment train (pinion, exchangeable wheel, wheel)

When working with planetary gears, the mountableness check can be

switched off (if division of planetary gear's centre is even). If switched off,
centres can be calculated with Option Z19g (page pageref). Speed of
planetary gear layout is free definable (2 of 3 speeds can be predefined:
speed of sun, rim and bridge).

Option Z01b Calculating

 rack (pinion paired with rack)
These options (Z01a, Z01b) contain an adapted input according to the chosen configuration and a
summarising output.
Option Z01x Extension of spur geometry: Layout of addendum modification
factor (optimum range, balanced gliding, etc), deep tooth form,
interfering tool, special print with all production tolerances DIN
 3961, ISO 1328, DIN 58405, BS 436; Calculation of addendum
modification factor from already found values; calculation of
effective overlapping (with measures).
Calculation of profile corrections of spur gears: Calculation
of points A through E of meshing line with their respective
involute lengths. Print-out of radii, diameters, involutes and
operating lengths for the involute check-diagram (for gear and its
respective counter wheel). The programme calculates also a
proposition for the tool to carry out profile corrections; data can
be re-used directly to calculate the tooth forms.
Layout of deep tooth forms: For deep tooth gears the
programme uses special reference profiles with bigger dedenda
and addenda. This function can also be activated in the fine
layout. In this case, the reference profile is calculated for every
solution in the output in such a way that a defined actual contact
ratio is achieved.
Increasing the interval of the minimal addendum
modification: The interval of normal addendum modifications
can be reasonably enlarged with this option. This is suitable for
helical gears, conical gears, worms, crossed helical gears.

6.2 Z02 Spur Gear Strength Calculation

According to DIN 3990, Dec. 1987 (latest issue)
Extensive, very detailed calculation according to the most accurate method (method B) which can
control all important values.
 Calculation of the general influence factors (DIN 3990, part 1) with dynamic factor,
longitudinal load distribution factor and transverse load distribution factor:
o Longitudinal load distribution factor for helical gear pairs according to method C2
with:
 Graphical representation of the load configuration
 Considering the support effect or load bearing control respectively
o Longitudinal load distribution factor for planetary trains according to method C1
o Longitudinal load distribution factor according to method B by exact recalculation of
the tooth trace deviation due to deformation with the shaft calculation.
 Calculating safety against tooth flank fracture (Hertzian stress, DIN 3990, part 2) according
to method B.
 Calculating safety against tooth root fracture (DIN 3390, part 3) according to method B;
optionally calculating tooth form and stress correction according to method C.
 Calculating safety against scoring (DIN 3990, part 4). Both calculation methods (flash and
integral temperature) are available according to method B.
 Materials according to DIN 3990, part 5.

Stress Calculation According to ISO 6336: The norm 6336 for

stress calculation was issued in 1996 and has replaced all
Option Z02a national norms. The calculation includes the general factors (part
2), the root safety (part 3), the materials (part 5) and the safety
against scoring (which is not part of the norm but a suggestion).
The norm ISO 6336 corresponds to DIN 3990, but includes some
distinct deviation, especially in the fatigue limit, whereby the
safety factors are slightly decreased.
 ISO 6336 varies from DIN 3990 especially regarding fatigue
resistance.

Extension of strength calculation: Graphic representation of

flash temperature course during meshing; Tooth friction and
Option Z02x
power loss; calculation of static tooth root strength (based on
DIN 3990).

6.3 Z13 Calculating According to AGMA Standards (US-

Norms)
Calculation according to the latest AGMA edition:
The strength-calculation of cylindrical gears is carried out according to ANSI/AGMA 2001-B88.
The standard is implemented in all details; the propositions for the dynamic load factor and
longitudinal load distribution factor from AGMA can be used in this calculation as well as the
propositions from DIN 3990. The geometry factors (tooth-root and tooth-flank) are calculated
according to ANSI/AGMA 908-B89. Pitting resistance power rating, contact load factor, bending
strength power rating and unit load bending strength are calculated and intermediate results are also
available. The calculation can be applied to all gear configurations (incl. planet gears, etc). Please
note that the AGMA does not permit calculating the tooth-root strength when applied to internal
gears.
The tooth tip factor Y has to be calculated (according to AGMA 908) for tip load (force application
on tip) or for HPSTC (application of force in single contact points), depending on kind and
accuracy of the teeth. Quality straight tooth gear wheels are calculated with HPSTC.
Tooth form factor Y by graphical method: AGMA offers a
calculation method for the tooth form factor Y of outer gears.
There are no calculation methods for inner toothing. According
Option Z13a to AGMA, inner toothings can only be constructed using
graphical methods. For this purpose, the exact tooth form is
drawn and the most important values are measured (eg root
radius etc).
KISSsoft can then calculate these items: First, the programme
calculates the tooth form and then determines the necessary
parameters (root radius, lever-arm, tooth-root width). The
method to determine the tooth form factor is a modified version
of the AGMA proposition. Analogue to the Obsieger procedure
(see Z19i, tooth-root calculation according to Obsieger, page
pageref), the programme defines the point of the tooth root
where the factor I (=Y/Kf*..) is minimal. The biggest strain lies
in this point.

6.4 Z14 Gears Manufactured from Synthetic Materials

Calculation of the safety factors for tooth roots and flanks of spur gears made of synthetic materials
(according to VDI 2545 / G. Niemann, Maschinenelemente II, 1985). This calculation method
considers the extreme influence of temperature on these materials. You can choose between oil or
grease lubrification or dry-run.
The calculation method calculates the local temperature on the tooth flank and root, and, taking into
account the number of load changes, issues the maximum permitted load. The calculation is done
for plastic/plast as well as for steel/plastic pairings. The check of the permitted deformation is also
carried out.
The following materials are included:
 moulded-laminated wood
 laminated plastic
 Polyamid (PA12 and PA66)
 Polyoxymethylen (POM)

All specific equalities of the materials are stored in text files (material strength depending on
temperature and number of load changes); you can easily enter your own materials.

6.5 Z03 Spur Gears Rough Layout

Automatic determination of the most important tooth parameters (centre distance, pitch, number of
teeth, face width). The user just has to enter the scheduled power rating and the required ratio. After
the pre-determination is done, an optimising run of the strength calculation is performed. The
minimum safety factors can be chosen beforehand.
In defining the range for b/mn-, b/a-, b/d ratio the user can easily find accurate dimensions. The
range of distance between axes and the module range - as important results - belong to the output.
The programme comes up with different solutions and gives a reasonable proposition. The fine
layout can be designed out subsequently.
The following can be designed by Z03: paired gears (inner an douter toothing), planetary trains.

6.6 Z04 Spur Gear Fine Layout (Geometry Variant

Calculation)
After the nominal ratio, axle distance and intervals for modules and helix angles have been entered,
the programme calculates and prints propositions for the number of teeth, pitch and other
modifications. The printout also contains the deviation from the nominal ratio, specific sliding and
contact ratios. This module also allows laying out planetary gear trains and gear sets using an
intermediate gear.
A rating according to different criteria (noise, accuracy of transmission, vibration, weight, strength,
etc) is carried out subsequently to the output of different geometric variants.
Important parameters can be limited if necessary (tip circle, root circle, min tooth number, tolerable
undercut, variants with specific gliding  3.0, etc).
Alternatively, in the case of planetary gears or helical gears with an intermediate gear, you can
calculate with a given axis distance or with a given internal gear wheel diameter.
In case of spur gear trains, the axis distance can be defined exactly or within an interval.
Additional strength-calculation for all variants: At the end of
the calculation using varying gear geometry, KISSsoft will
calculate, tabulate and print the values for the tooth-root and
Option Z04a
tooth-flank strength. This option can be applied to a single gear,
a pair of gears, planet-gears as well as to a gear-train with an
intermediate gear.
The Options Z04 and Z04a are valid for spur gear pairs, planetary trains and spur gear trains.

6.7 Z05 Tooth-Form Calculation

 Exact calculation of the tooth form, with the manufacturing process taken into account, eg
hub, rack-type cutter or pinion-type shaper cutter.
  with or without tooth thickness deviation
 Cutter (tool) can be defined with buckling root edge.
 representation of tooth form on screen
 print out of tooth form on paper
 saving the flank line in polar co-ordinates on disk
 check if manufacturing is possible (effective involute etc)

This module is very useful when internal gears are to be manufactured, since the manufacturing
process is calculated with all checks of contact problems, diminution of the transverse contact ratio,
beginning and end of the involute, etc.
Graphic representation of the tooth form on screen. Wheels can be represented individually or as
pairs:

The stepwise rotation on screen allows observing the rolling process. The x-y-coordinates of the
tooth profile are printed by the printer.
If module K05a is installed, the tooth form (of one or more teeth) and the gear wheel view in cross
and axis section can be transferred to the CAD.
Option Z05a Input of any cutter or tooth forms: Consisting of freely
definable elements (straight lines, circular arcs, elliptical arcs,
involutes). Additionally, the contact point line is calculated. This
option can also be used for the calculation of tooth forms which
are not involute types (eg gear pumps). The contour can also be
read from DXF or VDA format. Thus, the form can be defined in
 CAD or be read from a 3D-measuring system.
Reference profile calculation for gears with involute or
special profile: The reference profile is calculated from the data
of a given toothing or from different measured points of the
Option Z05c
toothing and then represented graphically (on screen, plotter or
CAD). The programme can analyse non-involute toothing as
well.
When the generated profile is displayed on screen, it can be used
to show the tool positions (small cuts) in order to check the
calculation. The reference profile can be calculated for frontal
and axial section.
Calculating the pairing gear with basic profile: For the
calculation of the tooth form from the counter wheel, the gear
Option Z05d pair (with number of gears etc) is defined as spur gears; gear 1
serves as the producing gear. The tooth shape of gear 2 can thus
be produced from gear one. The calculation is done in two steps:
Step 1: Calculation of tooth shape of producing gear. KISSsoft
calculates the producing gear, the tooth contour is enlarged to
allow for the second gear's deviation. After the calculation of the
first gear's tooth shape, this shape is recalculated as a tool (spur
gear), where the tip's length is increased. Additionally, the tip
will be rounded optimally.
Step 2: Calculation of the effective tooth shape (with deviation)
of gear 1 and calculation of wheel 2 (without deviation, it has
been taken into account in the first step) with the total computed
in step 1. This results in the effective tooth shape of gear 1 and 2.
The reference profiles of gears, which have been calculated this
way, can also be determined by activating option Reference
Profile Calculation.
Add-on for shape manufacturing: Calculation of tooth shape
considering
 Nominal deviation of tooth thickness
Option Z05e  Radial strain (tooth root and tip)
 Tangential strain (tooth thickness)

 Included steel body

The calculated contour produces the contour of the injection
casting form.
Calculation of the electrode for manufacturing the injection
casting form.
 Calculation as above, additionally regarding the spark
gap.

 Option Z05d allows calculating the hobbing cutter in

order to produce the electrode.
Option Z05f Circle shaped running in curve on tooth tip: From a diameter
to be defined, a running in curve into which an involute passes
tangentially is fixed at the tooth tip. The bending of this curve
increases steadily from arch to arch till the last arch passes into
the tip diameter. This modified tooth shape (Hybrid Tooth) has
great advantages if, in spite of inacurate manufacturing, there
 should be a noise reduced run of the gears. Normally, a running-
in curve is only used with deep drove toothing with a contact
ratio of over 2.1.
Head-modification of the calculated gear wheel with: no head-
modification, tip chamfer, running-in curve of arcs (according to
H. Hirn), running-in curve with progressive addendum
modification and head rounding, linear addendum modification,
progressive addendum modification; the course of the head-
modification can be adjusted with factors.
Additionally, KISSsoft contains a layout function which can give
appropriate propositions for the start (radius) of way-in curve
and amount of tip relief. This happens with calculation of the
profile correction.
Optimal tooth root rounding: The toothroot which comes
about through the chosen tools might not be rounded optimally.
Option Z05g
A too small radius in the root section often results in a high
notch effect and therefore in a lower tooth root strength.
The option Z05g calculates an ellipsis with the largest possible
radius in the root section from a definable diameter (mostly:
usable root circle) and then produces the respective
modifications for the tooth shape.
On the root circle diameter, too, you may leave a certain distance
to be defined, which can be very useful for special purposes, eg
if you use certain measuring instruments.
This option can be used for the following purposes:
1. The tooth shape is eroded subsequently: the tooth root
should be, regarding its strength, optimally
manufactured.

2. The gear is milled: the best possible root is to be laid out:

In order to do so, this option has to be activated;
additionally, the reference profile of the toothing will be
calculated from the tooth shape (Z05c), and the desired
tool will be produced.
Checking with the strength calculation: the programme
considers the best possible tooth rounding if the settings are
switched to Tooth shape calculation according to
Obsieger (Z19i, page pageref).
A layout function in the input window proposes the root circle as
a start for the modification, proposed for the curve length is 0.02
·module.
Cycloids and arcs in the tooth form calculation: can be
Option Z05h
defined directly in the tooth form interface.
Arc approximation: converting the tooth flank into arc
(according to H. Hirn): some eroding machines have problems to
work with polylines, which can be avoided by entering the data
Option Z05i
in arc. Annotation: the display of the tooth flanks in arc in
KISSsoft is not very aesthetic, but the data are correct (We are
working on this problem).
Option Z05j Displaying collision when rolling (spur gears): when rolling
(in the graphical display), the collision message can be activated.
 It selects in the drawing the points with squares where touch or
collision happens.
brown marked: touch (between 0.005 * module distance and
0.001 * module penetration)
red marked: collision (over 0.001 * module penetration)
Collisions on all meshing teeth are recognised and selected, the
option is very useful to analyse rolling of non-involute tooth
forms or of measured tooth forms (over a 3D-programme) with
the theoretical one-flank roll-check.
Displaying collision in rolling (worms/helical gears): same
Option Z05k
function as in Z05j (spur gears).

6.8 Z06 Face-Gear Calculation

Calculation module that calculates the geometry of face gears coupled with helical pinion gears. 2D
views with shape of tooth simultaneously on the inside, at the centre and on the outside. Checking
undercut and tooth tip is performed graphically in the two dimensional view, while head height can
be varied to prevent pointed tooth tip. 3D views with the possibility of exporting the files (Option
K05g). The shape of the tooth is calculated by simulating construction with a shaping cutter.
Calculation of strength is approximated using the corresponding bevel gear.

6.9 Z07 Bevel-Gear Calculation

Geometry calculations of spur, helical and spiral toothed bevel gears. Geometry and control
measures according to DIN 3971. The calculation only includes the geometry of bevel gears so far
as they are independent from helices. Refer to the calculation example in your manual. The outer,
middle and inner tip and reference diameter are calculated additionally for straight cut, skew cut,
Gleason and Klingelnberg toothed bevel gears.
Bevel gears with cycloidal spiral toothing: Geometry,
Option Z07a manufacturability and strength of bevel gears are calculated
according to the Klingelnberg method.
According to Klingelnberg's factory standard KN3028 (geometry
and manufacturing) and KN3030 (calculation of strength), a
complete calculation is carried out for bevel gears with cycloidal
spiral toothing:
 Machine types FK41B, AMK400, AMK635, AMK855,
AMK 1602 with all corresponding cutter heads, radii and
number of gears
 Shaft angles and angle corrections are freely definable
 Entire geometry with distance to machine, modules
(inner, middle, outer), angles of the teeth, waste-material
control, undercut space, calculation of the addendum
modification factor for compensated sliding, control of
reverse cutting, control and calculation of the necessary
tip reduction to the inner diameter, transverse contact-
and overlap-ratio, tooth form factor and stress correction
factor.
 Calculation of all tooth dimensions

 Calculation of Hertzian stress, of safety against tooth root

 fracture, as well as the safety against scoring (according
to the integral temperature criterion) with all adaptations
of the factory standard KN 3030.
Construction:
 Determining the main factors by a rough calculation (on
the basis of the power data and the rated transmission
ratio) with the possibility to influence the number of teeth
on the pinion, of the module, of the diameter (of the bevel
gear) and of the tooth width.
 Constructing the addendum modification factor for
o minimal necessary coefficient to avoid
undercutting

o compensated sliding

Hypoid bevel gears with a cycloidal spiral toothing:

Constructing geometry as well as manufacturability and strength
Option Z07b
of Hypoid bevel gears (bevel gears with off-centred axes)
according to the Klingelnberg method.
According to Klingelnberg's factory standard KN 3029
(geometry and manufacturing) and KN 3030 (calculation of
strength) a complete calculation is carried out for bevel gears
with cycloidal spiral toothing:
 Machine types FK41B, KNC40, KNC60, AMK855,
AMK1602 with all corresponding cutter heads, radii and
number of gears
 Shaft angles and angle corrections, pressure angle for
tension and compression flank are freely definable
 Entire geometry with calculation of the tooth angles, the
width of the teeth, distance to the machine, the modules
(inner, middle, outer), the angles of the teeth, waste-
material control, undercut space, calculation of the
addendum modification factor for compensated sliding,
control of reverse cutting, control and calculation of the
necessary tip reduction to the inner diameter, transverse
contact- and overlap ratio, tooth form factor and stress
correction factor, optionally for the tension or the
compression flank.
 Calculation of all tooth dimensions

 Calculation of Hertzian stress, of safety against tooth root

fracture, as well as the safety against scoring (according
to the integral temperature criterion for the equivalent
skew gear) with all adaptations of the factory standard
KN3030.
Construction:
 Determining the main factors by a rough calculation (on
the basis of the power data and the rated transmission
ratio) with the possibility to influence the number of teeth
on the pinion, of the modules, of the diameter (of the
bevel gear) and of the tooth width.
  Suggestion for suitable pressure angle for tension and
compression flank.
 Constructing the addendum modification factor for
minimal necessary coefficient to avoid undercutting.

 Calculating the spiral angle (middle of bevel gear)

through the module or vice versa.

Turning dimensions of bevel gears: All necessary dimensions

(tip and root diameter of the outer and inner bevel) are calculated
Option Z07c to produce the technical drawing of the bevel gear. In addition,
the tooth dimensions of the outer and inner bevel diameter are
calculated.

Gleason bevel gear toothing: Converting of the bevel gear

Option Z07d description into analogue data (according to DIN 3971 and DIN
3991) according to the Gleason method and vice versa.
The transverse and the normal modules of the outer bevel are
taken into account by including them in the middle bevel and the
additional properties of the bevel geometry of the Gleason
method are considered. This option allows therefore to calculate
strength and layout of bevel gears (according to DIN 3991)
which are produced according to the Gleason method.

Strength analysis according to ISO/DIS 10300: There is only a

preliminary draft for the strength analysis of bevel gears. We
Option Z07e
have implemented this algorithm into KISSsoft. However, the
norm is not yet compulsory.
Strength analysis according to ISO/DIS 10300: Strength
Option Z07f
analysis according to ISO 10300, only method D.
Strength calculation according to G. Niemann,
Option Z07g Maschinenelemente III, Springer; (Method of substitute toothed
spur gear). This method corresponds to DIN 3991.
Strength calculation for plastic gears according to G. Niemann
Option Z07h
and VDI2545
Calculation of bevel gear differential Static strength analysis
Option Z07i
of bevel gears and calculation of bevel gear differential.

6.10 Z08 Worm-Gear Calculation

 Calculating the geometry, efficiency, temperature safety, pitting safety, wear safety, safety
against tooth breaking and deflection safety of worm gear sets. The acceleration behaviour is
calculated, too. The calculation is done according to DIN 3996 or according to G. Niemann,
Maschinenelemente III. Various worm gear materials are supplied in an additional data base.
Flank shapes: ZA, ZE, ZH, ZI, ZK, ZN, ZC.
 Calculating worm geometry according to DIN 3975. Tooth thickness and control measures
(tooth width, roll and ball measures of worm gear) according to DIN 3960. Manufacturing
tolerances according to DIN 3971.
 Layout of tooth width, distance between axis, gradient angle, etc.
  Strength calculation according to draft of DIN 3996 (edition 1996) or according to G.
Niemann, Maschinenelemente III, Springer Verlag 1983, with:
efficiency, temperature security, safety against pitting, wear-safety, safety against tooth
fracture and bending.
Data for various worm-gear materials are included, calculations are also suitable for plastics.
 The initial torque under load is calculated, which can be of great importance regarding the
layout of drives.

Control dimensions for Worms and Worm Gears: For worms

with flank shapes ZA, ZI (or ZE), ZK, ZN, the control
dimensions are calculated with consideration of tooth thickness
Option Z08a
tolerances: three wire measure and tooth thickness for the worm,
measures over balls for the worm gear and the centre distance
without backlash.

For Worm Gear Dimensioning with Normal Module: see

Option Z19b
page pageref

6.11 Z09 Splines according to DIN 5480

The geometry and the control measures of splined shafts and hubs can be calculated according to
DIN 5480 (1986). The tolerance norm according to DIN 5480, page 14, is implemented entirely.
Strength can be analysed with the machine element programme (M02c).

6.12 Z10 Helical-Gear Calculation According to the FVA

Method
Gear geometry and strength are calculated according to the gear calculation method of
Forschungsvereinigung Antriebstechnik (FVA). The calculations are fundamentally done according
to DIN 3990, with consideration of all deviations; you will therefore get the same results with this
programme as with the FVA programme.
The FVA can be regarded as a reference-programme. If problems occur when using different
programmes and comparing the results of this calculations, the FVA-calculation can be used as a
reference.

6.13 Z12 Calculating Operating Backlash

The backlash during the acceptance test according to DIN 3967 (considering tooth deviation,
crossing of axes according to DIN 3964, form and position deviation) and the operating backlash
(considering the temperature differences between gears and housing) are calculated in addition to
the calculation of the theoretical backlash.

6.14 Z16 Torque Layout

The maximal torque is calculated for spur gears, bevel gears and worms to the extent where the
required safeties can be met (considering required life duration and nominal safety for tooth
fracture, pitting, scoring, for worms also wearing and temperature safety).
Option Z16a Torque layout for equi. design load: Any equi. design load (up
to 20 elements) can be defined; with frequency, power/torque
 and speed. All equi. design loads according to DIN 15020 (crane
design) are included. The calculation is based on DIN 3990, part
6 (February 1990), with Palmgren-Miner rule. For fatigue
strength, a modified stress-cycle diagram can be chosen
(deviation from DIN 3990):
 according to Miner
 according to Corten/Dolan

 according to Haibach

6.15 Z17 Calculating Screw-Gears

Calculating screw gears (helical gears with crossed axes) according to G. Niemann,
Maschinenelemente II, 1985. The existing version contains the calculation and controlling of the
geometry of screw gears with any axis angle. Manufacturing and control data is generated.
Option Z17a Strength calculation: developmental

6.16 Z18 Service Life Calculation

After input or confirmation of the required minimum safety-factors for tooth-root and tooth-flank
strength, the service life (in hours) is calculated (based on the given load) for all gears. The
calculation bases on the limited-life calculation according to DIN 3990 (Palmgren-Miner rule). For
fatigue strength, the modified stress-cycle diagram can be chosen (deviation from DIN 3990):
 according to Miner (DIN 3990)
 according to Corten/Dolan
 according to Haibach

At the same time, the service life of the system is issued (all gear wheels of the configuration).
Calculation of gear life with collective load: Any equi. design
loads (up to 20 elements) can be defined by the user with
Option Z18a frequency, power/torque, speed. All collective loads are included
(DIN 15020, crane design). The calculation is based on DIN
3990, part 6 (February 1994), with Palmgren-Miner rule.
Safety with load spectra: If the required lifetime, the power
rating, application factor (which is usually set to 1.0 if a load
spectra is used) and the applicable load spectra are defined, the
resulting safety factors for root and flanc are calculated. The
safety factors against scuffing will be calculated and reported
using the highest load of the load spectra.

6.17 Z19 Special Calculations

Option Z19a Gear geometry for backlash (for spur gears): The spur gear
geometry according to DIN 3960 is based on the calculation of
the (theoretical) backlash. Thus, the sum of the addendum
modification factors of the individual wheels over the centre
distance is determined. With this option, the addendum
modification factors can be entered independent of the centre
distance. This is very useful when examining the limiting
positions (backlash, overlapping) at greatly varying centre
 distances (eg with large centre distance tolerances).

Calculating worm with dimensioning via the normal module:

The geometry of a worm gear pair is normally calculated with
the axial module. With this option, the dimensioning can be
Option Z19b
accomplished alternatively with the normal module (tool
module). The tip- and root-diameter as well as the addendum
modification factor are particularly influenced.

Optimising the centre distance with regard to equalised

sliding: The centre distance between two gears is calculated in
Option Z19d such a way that the specific sliding of a gear pair (spur gears) is
equalised, while keeping the addendum modification factor of
one (selected) gear constant.

Representation of the specific sliding: The course of the

Option Z19e specific gliding during meshing (sliding and rolling velocity) can
be displayed graphically.

Sensible tooth alignment correction: The norm DIN 3990

requires sensible values for tooth alignment correction. This
Option Z19f
additional programme generates a suggestion for a reasonable
layout of the tooth alignment correction according to DIN 3990.

Calculating centres of planetary gears or intermediate gears:

For planetary gears: Calculating centres of planetary gears to
Option Z19g enable the mountableness (which is essential if planetary gears
cannot be arranged with a even numbered ratio because of their
conditions of tooth number).
For gears drives (3 gears): The programme calculates the
arrangement of all intermediate gears (mountableness taken into
account) from the centre distance between first and last gear.

Calculating the tooth form factor according to Obsieger: The

tooth form and the stress correction factor is calculated according
Option Z19i to DIN 3990 or ISO 6336 at the place of the tooth root where the
tangent angle is 30o. This is - foremost for inner gears - not very
accurate.
Obsieger (Periodical "Konstruktion" 32 (1980), p. 443-447) has
provided a better solution. The product of tooth form and stress
correction factor is calculated for all points in the foot area of the
actual tooth form. The strength calculation is done with the
maximum amount.
This method is very convenient, especially for special tooth
forms and inner gears. The calculation can also be used in the
strength analysis according to DIN 3990 and ISO 6336 as well as
in the layout function.

6.18 Z22 Hardness-Depth

Calculating the optimal hardness depth (for case-hardened or nitrided gears). Represented are the
stress contours perpendicular to the flank surface, and when displaying the hardening contours,
warnings are given if the behaviour is unsatisfactory.

6.19 Z23 Deformation of Gear Rims (for Internally Geared

Wheels)
The gear rings of internally geared wheels can be deformed by the tooth forces when the gear ring
has to be produced relatively thin for constructive reasons. This programme calculates the bending-
and tangential stresses for the conditions at the meshing point and between meshing points (of two
neighbouring planetary gears). It also calculates the radial deformation.

6.20 Z24 Contact Stiffness of Gear Pair

Different positions of teeth and their forms result in a continously changing contact stiffness during
rolling. The course of the contact stiffness is calculated from the actual tooth form and is
represented graphically. Moreover, the average variation of stiffness is calculated. This result is
important for the close examination of how frequencies are generated. The more the stiffness varies
the more frequencies are produced. This calculation is also included in the fine layout module
(Z04); the programme indicates the variation of stiffness for every variant.

6.21 Z25 Graphical representation of Hertzian pressure and

of tooth root stresses along the actual tooth flank
Displaying the hertzian stress and the tooth root stress based on the actual tooth form

6.22 Z26 Transport Volume of Gear Wheel Pumps

Automatic calculation (choose in Settings) based on the actual tooth form with print of report and
including the calculation function in the fine layout (Z04).

6.23 Z26a The Special Option of Gear Wheel Pumps

This Option allows a very detailed analysis of the gear pump. The change in important parameters
of a pump during contact are calculated and graphically displayed. The detailed analysis includes
parameters such as the enclosed volume (that which is trapped between two engaging tooth pair
contacts, fed-back volume), the volume with critical in-flow (oil stream should be continual if
possible), narrowest point between flanks of first tooth pair not engaging marking the boundary of
critical in-flow area, in flow velocity, oil flow (with Fourier analysis for evaluation of noise
potential), total volume under entry chamber pressure. Further important results from the analysis
are the change in torque on both gears, the change in Hertzian pressure sigH, sliding velocity vg and
the wear number sigH*vg. Hertzian compression at the point of tooth contact can be taken into
consideration for calculation of the forces, which can influence the result significantly. The pressure
experienced by the enclosed volume is dependent on the construction of the pump. This can be
defined through appropriate input, and has a considerable influence on the torque development.

6.24 Z27 Kinematic Based on the Actual Tooth form

Specific gliding, gliding speed, ratio, gliding factors

6.25 Z80 Tooth Profiles on Miscellaneous Roller Bodies

With this complex programme, the exact meshing can be calculated for absolutely freely definable
contact curves and tooth profiles. It is possible, eg to calculate the meshing of oval gears, to analyse
these on screen and to send the data to a machine tool (eg eroding, laser-cutter) via the included
interface (NC- or DXF-format). The tooth profile of the tool can be defined entirely unconstrained
or with KISSsoft tooth form calculation. A possible application is eg the calculation of the meshing
for a cam disc or a cam plate if the sliding conditions become too extreme for smooth rollers.

6.26 Z81 Pairing of Non-Circular Gears

For gears of arbitrary form (eccentric circles, ellipses, free definition) the paired non-circular gear is
calculated at a given centre distance. The condition that the transmission ratio must be a whole
number, is checked. The course of the instantaneous transmission ratio during a rotation as well as
both the contact curves are represented graphically and analytically. The meshing of both wheels
can be calculated and presented subsequently with programme Z80.

Dual Flank Measurement

The dual flank measurement procedure has become a very
practical measurement method.
This test method allows production quality to be easily and

quickly checked. Production times can be reduced by

utilizing the full allowable tolerance range.

Measurement per DIN 3960

Two gears are meshed with zero backlash. The gears are
then rotated and the variations in the center distance are
measured (a”).

(1) Gear to be checked

(2) Master gear
(3) Measuring slide
(4) Measuring gauge
(5) Base
(6) Direction of force
(7) Spring
(8) Force adjustment

Two flank working variation Fi’’

The two flank working variation Fi“ is the variation of the

center distance a“. It is the difference between the largest
and the smallest center distance for one revolution. (DIN
3960).

Two flank working error fi’’

The two flank working error fi“ is the largest variation of the
center distance for each single tooth and its corresponding
angular motion. (DIN 3960).

Working concentricity variation Fr’’

The working concentricity variation Fr“ is the cyclical portion

of the two flank working variation Fi“. This is measured by
placing a trend curve in the dual flank measurement chart.

The working concentricity variation Fr” is measured between

the highest and lowest points of the trend curve. (DIN
3960).
Method and apparatus for fabricating precision teeth
An approximately shaped or formed gear is fabricated in any desired way and is then corrected by
means of substantially ring-shaped rolls or rolling tools performing striking or hammering
operations in the tooth gaps of such gear. The rolls rotate in a planetary fashion in revolving rolling
or roller heads. Such rolling heads are advanced to a maximum radial penetration depth of the rolls
which is governed by a stop and are then retracted, if necessary. The advance or feed is preferably
performed by a hydraulic drive, the pressure of which is regulated electro-hydraulically by means of
a template or the like. The hydraulic drive acts against the action of a spring. The approximately
formed teeth, which are thus rolled in an overlapping manner, are produced by the addition of
material per tooth flank. Preferably, such material addition amounts to at least twice or three-fold
the summation pitch error according to DIN 3960 to 3962 (German Industrial Standard 3960 to
3962). The above-mentioned pressure-controlled advance or retraction undertaken against the
action of spring force is preferably accomplished along a maximum path or distance of 0.25 mm.
This distance is frequently smaller than 0.1 mm. Precision teeth are produced which frequently no
longer even have to be ground.