Calculation of differential bevel gears in KISSsoft · 2020. 12. 10. · KISSsoft Release 2020 provide both models as sample for the users. The kinematic (speed and torque) of the

/ July 2020 / Calculation of differential bevel gears / Dipl. Ing. Jürg Langhart1

Calculation of differential bevel

gears in KISSsoft

Webinar for:

KADKRAFT SYSTEMS Pvt Ltd, IN-Chandigarh

Presenter:

KISSsoft AG, Dipl. Ing. Jürg Langhart


1. Differential bevel gears in a system

2. Differential bevel gears as a component

3. Strength calculations, static and ISO 10300

4. Specific properties of forged bevel gears

compared to milled bevel gears

5. Design of tip and root alterations

6. Design and sizing of differential bevel gears

7. Contact analysis of differential bevel gears

8. 3D models and re-engineering

9. Conclusion


Forged bevel gears are typically

applied in differential gearboxes of

vehicles, to allow different speeds

between the wheels.

This applies for classical rear axles as

well as for the new e-drive axles.

KISSsoft Release 2020 provide both

models as sample for the users.

The kinematic (speed and torque) of

the differential bevel gears depend on

the speed difference between the

axles.

The speed ratio can be controlled in

KISSsys in the user interface.

1. Differential bevel gears in a system - Applications


The speed can be controlled in

KISSsys in the user interface.

Same speed on both wheel axles

there is no relative motion between the

differential bevel gears, pure static

application (see report, n1,2 = 0 rpm).

Faster speed on the left or right

wheel

there is relative motion between the

differential bevel gears, rolling

application (see report, n1 = 565 rpm).

1. Differential bevel gears in a system - Kinematics


Looking at the differential casing as a

subsystem, the designer wants do find

the optimum between the components

shafts and gears.

Example: the pinion shaft diameter

affects the shaft bending and gear

safety:

Diameter of pinion shaft: 14 mm

→ max. displacement: 76 μm

Diameter of pinion shaft: 16 mm

→ max. displacement: 50 μm

➔ shaft bending is reduced by 33%,

what means lower gear misalignments.

1. Differential bevel gears in a system – Design optimization


In KISSsoft, the differential bevel gears

are handled as gear pairs with several

strands (means pinions).

The bevel gear geometry is

represented by the parameters from the

ISO geometry standard, means a tooth

shape which is nominal rectangular.

To make the shapes of the forged bevel

gears in KISSsoft represented more

realistic, tip and root alterations can be

applied. The strength calculation is not

affected by this (*).

In 2D, both the tip and root alterations

are visible. In 3D, only the tip

alterations are represented.

2. Differential bevel gears as components


Analytical calculations are leads to low

safety numbers as the calculation is too

conservative (neglecting the positive

effect of the webbing).

In KISSsoft, the static calculation and

rating standards like ISO 10300, AGMA

2003, DIN 3991 are available for fast

rating and DOE calculation.

The contact analysis allows for rating of

the Hertzian pressure, including the

crowning, webbings, etc. for estimation

of Hertzian pressure.

For a final rating, the analysis by FE

methods is recommended.

3. Strength calculations - Overview


The static calculation in KISSsoft

provides a safety number for root

bending load only.

Therefore, the highest root stress is

calculated, based on the highest acting

force and lever arm.

The root bending stress is compared

with the static material properties as

tensile strength and yield point.

3. Strength calculations - static


Sample for static calculation

Torque on diff. casing T_diff: 2400 Nm

Number of strands n: 2

Highest circumferential force Ft1, Ft2:

T_diff = number of strands *(Ft1*l1 + Ft2*l2)

Material properties:

Yield point σs: 850.00 (N/mm²)

Tensile strength σb: 1200.00 (N/mm²)

Safety against yield point [Ss=σs/σF] 0.80 0.78

Safety against tensile strength [Sb=σb/σF] 1.13 1.10

3. Strength calculations - static


The strength rating according to the

standards allows the calculation against

• Root bending

• Hertzian pressure

• Scuffing

• Flank fracture

The torque is valid for a gear pair. The

torque of the differential casing is to be

divided by the number of strands

(between 2 and 4) and by the number

of side gears (always 2).

As the webbing achieve a large

strengthening effect, the safety number

for root bending are possibly in the

range of 0.3 to 0.6.

3. Strength calculations - ISO 10300


Sample for ISO calculation

Torque on diff. casing T_diff: 2400 Nm

Number of strands: 2

Output torque gear 2 T2: 600 Nm

Material properties:

Endurance limit root σFlim: 430.00 (N/mm²)

Endurance limit flank σHlim: 1500.00 (N/mm²)

Root safety [SF] 0.398 0.416

Flank safety [SH] 0.431 0.440

Safety of the hardened layer [SEHT] 0.366 0.372

Safety against tooth flank fracture [SFFB] 0.373 0.373

Safety factor for scuffing (intg.-temp.) [SSint] 1.336

Safety factor for scuffing (flash-temp) [SB] 0.970

3. Strength calculations - ISO 10300


The forging process has many more

degrees of freedom in the design than

for conventional, milled bevel gears.

On the other hand, there are a number

of additional restrictions, which the

engineer has to consider, and also the

calculation software has to be able to

consider these points.

Webbings, no jamming of gears

KISSsoft calculates the root alteration

based on tip alterations of the counter

gear, and the required tip clearance.

Rounding radius at the tip

4. Specific properties of forged bevel gears compared to milled bevel gears

Source: mav.industrie.de

in the tab ‘Modification’, the tip rounding radius is entered.


Demoulding of parts is required

the transverse pressure angle at root

form circle must be greater than 0 (or

any experience value).

No interference when rolling

the distance of active diameter to form

diameter must be greater than 0 (or any

experience value).

Minimum root radius

a minimum root radius based on a tool

radius can be entered.

Tooth thickness at tip form circle

for avoiding through hardening, a

minimum thickness is required.

4. Specific properties of forged bevel gears compared to milled bevel gears


Root alterations are a result of the

forging process and lead to higher

bending strength.

Tip alterations are applied due to space

constraints and to avoid jamming with

root alterations.

A disadvantage is the reduced contact

area and the increased Hertzian

pressure.

In KISSsoft, there are two possibilities

for sizing the alterations:

- sizing of tip alterations based on

space constraints

- sizing of root alterations based on

minimum webbing thickness, etc.



Sizing of tip alterations

In the tab ‘Modifications’, the tip

alteration can be sized according to the

given space constraints.

The tip alterations at inner side are

typically determined by entering the

distance from crossing point to blank

(yhaki).

Optionally, the gear body can be

expanded to the front side, to have a

straight face.



Sizing of tip alterations

In the tab ‘Modifications’, the tip

alteration can be sized according to the

given space constraints.

The tip alterations at outer side are

typically determined by entering the

modified outer diameter of the bevel

gears (dae_mod)

Optionally, the gear body can be

expanded to the outer side, to have a

straight face.



Sizing of root alterations

In the ‘module specific settings’, the

root alteration can be sized according

to the given design constraints:

- required distance between bore and

webbing at toe


washer

- maximum pressure of thrust washer


webbing at heel

The webbings at the outer side follow to

a specific algorithm by considering di,

max pressure, daAS, sBfAS.



The design criteria of differential bevel gears are similar as

for other gears.

• high root strength, which is achieved by max. root radius,

high pressure angle, low number of teeth, etc.

• high contact ratio to reduce the noise excitation, which is

achieved by high addendum and dedendum height, low

pressure angles, etc.

• others as efficency, weight, etc.

All the solutions need to fullfill the feasibility resp. geometrical

requirements by the forging process, as explained before!

6. Design and sizing of differential bevel gears


The sizing of forged differential bevel

gears with KISSsoft fine sizing

functionality is a great help, as it is:

- fast: using the analytical standards

- repeatable: independent of user

- complete: checks every combination

of design parameters

The fine sizing creates, depending on

the settings, huge number of solutions.

Each of the solutions has individual root

and tip alterations, as per the design

requirements.

6. Design and sizing of differential bevel gears - Calculation


The solutions are shown in KISSsoft in

table and graphical display.

Many filtering options eliminate

solutions which do no fulfill the

geometrical requirement.

The table allows a fast ranking

according to the preferred criterias. The

graphic allows a setup of 3 parameters.

The post processing by a separate data

file is possible too. Herewith, based on

application- and company-specific

experiences, the best macro geometry

can be found.

6. Design and sizing of differential bevel gears - Evaluation


The contact analysis in KISSsoft allows

the rating of:

• Hertzian pressure

• Transmission error

• Root stresses

• Meshing stiffness

• etc.

It takes the tip and root alterations into

account, which is the reduced contact

area.

Also micro geometry and misalignment

can be applied, so that a realistic

contact calculation is performed.

The webbings are not considered.

7. Contact analysis under load (LTCA)


The tolerances of the forging process

lead to variation in the results.

These variation has typically to be

checked by the engineer to simulate

the expected range of results in

transmission error, hertzian pressure,

etc. (robustness check).

The robustness is checked in KISSsoft

by the modification sizing tool.

Here, the tolerances for e.g. crowning,

profile crowning, helix angle, etc. are

entered and all the combination are

calculated.

7. Contact analysis under load (LTCA) – robustness calculation


KISSsoft provides the 3D models as

basis for the CAD modelling, FE

analysis, etc.

The 3D models are available as volume

models (STEP) or skin models (single

tooth, etc.)

Also the measurement grids are

available in the Gleason and

Klingelnberg format.

8. 3D models


Forged differential bevel gears have

different definition for profile shift and

tooth thickness allowance than

conventional manufactured bevel

gears.

The models can be adjusted, that the

value for profile shift and tooth

thickness allowance is constant over

the face width.

8. 3D models – Modifications for differential bevel gears


It is possible to add topological

modification as ‘grid data’, in order to

adopt the geometry of any bevel gear

into the KISSsoft 3D model.

The measurement data can be

provided to KISSsoft in the typical

format of GLEASON or

KLINGENBERG measuring machines.

8. 3D models - Topological modification


Using measuring data of an e.g.

existing bevel gear, the flank topology

of the KISSsoft bevel gear is modified

accordingly.

Finally, the modified KISSsoft model

contains the same flank geometry as

the existing bevel gear and can be

exported for milling.

8. 3D models - Topological modification


KISSsoft provides a software package,

which covers the differential bevel gear

calculation in a wide aspect

Within KISSsys, the design of

differential bevel gears within a system

is provided.

Within KISSsoft, the specific properties

of forged bevel gears due to the

specific manufacturing process are

considered.

For the gear pair, the design of macro

and micro geometry is possible, as well

as the analysis by contact analysis.

Finally a 3D model can be exported.

9. Conclusion


KISSsoft AG, A Gleason Company

Rosengartenstrasse 4, 8608 Bubikon, Switzerland

T. +41 55 254 20 50, [email protected], www.KISSsoft.com

Thank you for your attention!

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Calculation of differential bevel gears in KISSsoft · 2020. 12. 10. · KISSsoft Release 2020 provide both models as sample for the users. The kinematic (speed and torque) of the