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2024年3月14日发(作者：抗绮玉)

KISSsys Tutorial:

Two Stage Planetary Gearbox

Using this tutorial

This tutorial illustrates how a two stage planetary gearbox can be modelled in KISSsys. Some modelling

techniques where special attention and knowledge are required are described in detail.

It is recommended that the user completes the first tutorial, KISSsys-Tutorial-001 (modelling of a two stage

helical gearbox), before this tutorial is used.

The model described here can be further refined. For this, a series of instructions exists, however, their

application requires some experience with KISSsys.

If questions arise when working through this tutorial, contact the KISSsoft support using the address given

above.

27. März 2008

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Table of contents

1 2

2 BUILDING 2

2.1 3

2.2 Modelling the 3

2.2.1 Machine elements, shaft .3

2.2.4

2.2.3 Planetary 5

2.3 Modeling the 6

2.4 Positioning the planetary 7

2.5 Power input, power output, connecting the .8

2.6 Input of 9

2.7 Input of the 11

2.7.1 .11

2.7.2 12

2.7.3 Shaft for ring gear / 12

2.7.4 Planetary shaft / 13

3 15

3.1 Adding an 15

3.1.1 Input and .15

3.1.2 16

3.1.3 Information on the strength analysis of 18

3.2 20

3.2.1 Shaft-hub 20

3.2.2 21

3.2.3 Position of the 21

4.1 Speed of 22

4.2 Number 22

4.3 23

4.4 23

1 Modelling task

A KISSsys model for the analysis of a two stage planetary gearbox with integrated gear, shaft and bearing

calculation should be built. The model can then be used for design, optimisation and rating of such a system.

Note:

- The two ring gears shall have zero speed

- The planetary gear of the first stage shall be supported by two bearings arranged symmetrically on the

planetary bolt

- The planetary gear of the second stage shall be supported by a single bearing on the planetary bolt

(sitting in the centre of the planetary gear)

2 Building the model

The new system is modelled from elements such as gears, shafts, bearings and so on and includes the

corresponding KISSsoft analysis. The elements and analysis modules are taken from a library, the so called

„Templates“. For the descriptions given below, it is assumed that the user has already completed and understood

the first KISSsys tutorial on modelling a two stage helical gearbox.

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2.1 Starting KISSsys

First, a project folder has to be created. Then, KISSsys is started using Windows-Start/Programs/KISSsoft

03/2008 /KISSsys and the intended folder is choose as project folder.

Using menu “Extras”, activate the administrator modus. Then, the templates should be opened using “File/Open

templates…”.

2.2 Modelling the first stage

2.2.1 Machine elements, shaft analysis modules

From the templates, the elements shown below are copied and arranged (note that the shaft element representing

the planetary bolt should be placed underneath the planet carrier shaft). Add a special component from

templates “kSysPlanetCarrierCoupling” under “sc” shaft called “cc”. This component will define in the program

the carrier component and the number of planet shafts.

Figure 2.2-1 Building the model, first step, first stage

Note that when adding the KISSsoft shaft analysis for each shaft element, a dialog appears where the shaft to be

analysed has to be chosen. Also, choose „Save file in KISSsys“ in the same dialog.

Furthermore, under coupling element “cc” is a variable „NofPlanets“ of type „Real“ where user can change

number of planet shafts in system. Access to the variable from tree – cc – Properties – NofPlanets.

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Figure 2.2-2 Creating the variable „NofPlanets“ for defining the number of planets in the stage. Here, three planets

are present

2.2.2 Connections

Now, the connections are added. Copy the element “kSysPlanetaryGearPairConstraint“ from the templates) and

insert it two times into the group “Stage1”. One time for the connection between sun and planet named “zszp”,

one time for the connection between planet and ring named “zpzr”:

Gear 1: Sun (zs)

Gear 2: Planet (zp)

Figure 2.2-3 Adding the planetary connections

Gear 1: Planet (zp)

Gear 2: Ring (zr)

The KISSsys model should now look as follows:

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Figure 2.2-4 KISSsys model with connections added

2.2.3 Planetary gear calculation

From the templates, the planetary gear calculation “PlanetGearSet” from “kSoftCalculations/withSystem” is

imported and added underneath the group “Stage1” and called “GP1”. In the dialog, the two connections and the

saving mode for the KISSsoft data have to be defined:

Figure 2.2-5 Adding the planetary gear set calculation

The KISSsys model should now look as follows:

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Figure 2.2-6 KISSsys model with planetary gear set calculation added

2.3 Modeling the second stage

The first stage which has been created above is now copied and pasted in the same level of the tree structure

using the name „Stage2”:

Figure

2.3-1 Copy the first stage and paste it as second stage

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The KISSsys model should now look as follows:

Figure 2.3-2 KISSsys model with two stages

The second stage now has to be positioned in space with respect to the first stage. Using “Dialog” in the group

“Stage2” (right mouse click on “Stage2”), the second stage can be positioned (e.g. using 200mm distance in

axial direction):

Figure 2.3-3 Positioning the second stage with respect to the first stage

2.4 Positioning the planetary shafts/bolts

The planetary shafts of the two stages now have to be positioned in space. For this, use “Dialog” (right mouse

click on the planetary shaft elements) to position them parallel to the respective sun shaft in a distance equal to

the centre distance of the gear pair sun-planet and axial so that gears will be always in the same

place:

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Figure 2.4-1 Positioning the two planetary shafts with respect to the corresponding sun shaft

2.5 Power input, power output, connecting the two stages

The planet carrier of the first stage (power output of the first stage) has to be connected with the sun shaft of the

second stage (power input of the second stage). For this, use a coupling constraint from the templates

(kSysCouplingConstraint), adding as shown below:

Figure 2.5-1 Configuration of the connection of the two stages

This connection can be “StageConnection”.

Using „kSysSpeedOrForce“ elements (copied from the templates), power is put into the system / taken from the

system (the power input shall be the coupling on the sun shaft of stage 1, power output shall be the coupling on

the planet carrier of the second stage). The two ring gears are constrained again using

„kSysSpeedOrForce“elements.

In this example, speed and torque are defined for

the power input (sun shaft of first stage).

Therefore, for the power output (planet carrier of

second stage), no additional kinematic constraint

may be defined.

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The speed of the ring gear of stage 1 is set to zero

The speed of the ring gear of stage 2 is set to zero

Figure 2.5-2 Adding „kSysSpeedOrForce“ elements to define the kinematic boundary conditions

Now, the kinematic calculation can be tested by calling the function „Calculate Kinematics“ in menu (a mouse

click). At the lower end of the screen, a message „Kinematic calculated“ should appear. Now, press „Refresh

All“ (symbol number eight from the left side in the menu bar, see mark below).

The KISSsys model should now look as follows:

Figure 2.5-3 KISSsys model, modeling of the structure completed

2.6 Input of gear data

Now, the gear data can be defined in the respective KISSsoft planetary gear calculation can be defined. For this,

double click on „GP1“ for stages 1 and 2 to get to the respective KISSsoft interface. Here, the gear data can

either be defined or a suitable gear set can be sized using the sizing functions in the usual manner. It is also

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possible to use an existing gear set by using File/Open. Please ignore the follow warning, because it’s just

information for the gear calculation.

Figure 2.6-1 Input of gear date in KISSsoft

The number of planets used however is not defined using the KISSsoft interface but is defined through KISSsys

(using the value given in the variable „NofPlanets“). The number defined previously is now shown in KISSsoft:

In order to get a 3D representation of the system modelled, the element“kSys3DView“ has to be copied from the

templates and pasted underneath „System“. Using „Show“ (right mouse click), the 3D windows shows:

Figure 2.6-2 3D view

The ring gears are not visible yet. For this, go to the two ring gears and add a value to the variables “di” (use

negative values since this is an inner gear). You use formula df-10*mn, instead of fixed value

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Figure 2.6-3 Definition of the outer diameter (index „i“ since it is in fact the inner diameter) for the ring gear

The 3D graphics should now look as follows:

Figure 2.6-4 3D view with ring gears

2.7 Input of the shaft geometries

2.7.1 Sun shafts

Support sun shaft “ss” on Stage1 rigidly on left end. To do this add new component “kSysBearing” on the shaft

“ss” in Stage1 and call it “b1”. Use “UpdateShaftElements” function from tree under“SS” calculation to add

bearing on the shaft. On double click on „SS“, get to the KISSsoft interface for the shaft analysis. Using the

graphical shaft editor, the sun shaft can be defined , e.g. using the simple geometry shown below:

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Figure 2.7-1 Defining the sun shaft

Note that the sun is present several times on the sun shaft (as many times as planets are present) to simulate the

multiple contacts between the sun gear and the several planets (such that the radial forces on the sun shaft are

equal to zero). You may now model the second sun shaft similarly, but two normal bearing to support

the shaft (kSysRollerBearing).

Figure 2.7-2 Defining the sun shaft

2.7.2 Planet carrier

Modelling the planet carrier is not necessary for the analysis of the gearbox and is hence not described here.

Note! If you don’t want to define data for the carries, please remove calculation modules “SC” from the tree to

avoid error messages. When geometry is created, please remember to add also sufficient supports.

2.7.3 Shaft for ring gear / gearbox casing

The shaft for the ring gear is the same as the casing of the gearbox. It is not necessary to model it.

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2.7.4 Planetary shaft / bolt

In this example, the planet of the first stage is supported by two bearings (arranged symmetrically). The planet

of the second stage is supported by a single bearing. The modelling of the two shafts / bolts is therefore

different.

First, the bearings („b1“, „b2“) and the respective bearing calculations („Bearing2“, „Bearing1“) have to be

added to the tree structure. Note that for the first planetary stage a bearing calculation element for two bearings

should be used (“Bearing2” in templates, from “kSoftCalculations/withSystem”), whereas for stage 2, a bearing

calculation element for one bearing should be used („Bearing1“ in templates, from

“kSoftCalculations/withSystem”). For the 2

stage planet pin add also “kSysBearing” to create rigid support on

left side.

Figure 2.7-3 Tree structure with bearings and bearing calculations added

Since new elements have been added to the shafts, use „UpdateShaftElements“ (right mouse click on „SP“) in

order to have these newly added elements (the bearings) present in the graphical shaft editor in KISSsoft. Now,

KISSsoft can be used (double click on „SP“ on both stages) to model the planetary shafts. It is recommended

that the second bearing (on the planetary shaft of stage 1) is positioned first 5mm so it can be

distinguished from the first bearing (initially, they both have the same position, y=0 mm and they can hence not

be distinguished in the graphical shaft editor).

In this example, the two bearings of the second stage shall be positioned symmetrically with respect to the

centre of the planetary gear. In which distance to the centre of the gear the bearings are placed does not matter

since the radial force of the planet is distributed equally on the two bearings (as long as the planetary gear has

not helix angle, if the planetary gear has a helix angle, the bearings have to be positioned at the correct distance

from the centre of the gear since a moment from the radial force and the helix angle results). After the definition

of the planetary shaft / bolt use “Calculate F5”.

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Figure 2.7-4 Support of the planet of the first stage. The objective is to have an even distribution of the force acting

on the planetary gear on the two bearings. As long as there are only radial forces acting, the distance from the

centre of the gear to the bearing does not change the result as long as the bearings are positioned symmetrically.

The bearing of the second planet is to be placed in the centre of the gear. Since only one bearing is present, the

system is not statically defined yet. Therefore, a second boundary condition is necessary for the shaft. Use

support element to fix shaft from the left shaft end.

Figure 2.7-5 Arrangement for second planetary shaft

Figure 2.7-6 Shaft end on the left side

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In the 3D view, the bearings are at first not visible. For this, go to the KISSsoft bearing calculations and press

„Calculate F5“ in order to update the bearing data. Using “Refresh “, the bearings should then become visible.

Figure 2.7-7 3D view of the gearbox

3 User Interface

3.1 Adding an user Interface

In order to simplify the management of the KISSsoft calculations, a user interface is used allowing for input and

output of values. For this, copy a table „UserInterface“ from the templates into the tree structure (beneath

„System“). Using right mouse click and „Show“, the table is shown. Using „Dialog“ the number of rows and

columns can be modified.

3.1.1 Input and output power

In this example, the torque and the speed are defined for the input (sun / sun-shaft of stage 1). Add a descriptive

text in the user interface (just type it in a field), e.g. „Input speed“ and „Input torque“. To add the values, use

right mouse click on the next field and select „Insert Real“. Now, press “Reference” and define the variable

which shall be addressed:

Figure 3.1-1 Defining the input speed

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Figure 3.1-2 Defining the input torque

Additional values (output) can be added

1. Input power: press right mouse click in a field, select „Insert Real“ and use the variable name

„“ in „Expression“

2. Output speed: as described above, variable name to be used „“

3. Output torque: as described above, variable name to be used „“

4. Output power: as described above, variable name to be used „“

5. Ratio: use the following expression in „Expression“: abs(/), Where “abs”

returns the absolute value of the expression in brackets.

The user interface then looks as follows:

Figure 3.1-3 User interface with information and input regarding the kinematics of the gear box

3.1.2 Adding functions

In the user interface, three different functions shall be available: Calculation of the kinematics, execution of the

KISSsoft calculations and generation of the KISSsoft calculation reports. For this, three functions „Kinematic“,

„Strength“ and „Write Reports“ are added to the User Interface (right mouse click on the field of choice, choose

„Insert Function“ and define the following)

Note! User is also able to use these functions from menu, using shortcut buttons.

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Figure 3.1-4 Calculation of kinematic followed by „Refresh All“

Figure 3.1-5 Before the KISSsoft calculations are executed, the kinematics are calculated

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Figure 3.1-6 Writing the KISSsoft reports (saved into the KISSys project directory)

3.1.3 Information on the strength analysis of the gears

Furthermore, in the user interface, the required lifetime of the gears and the resulting safety factors (minimum

value for sun, planet, ring, for root and flank) shall be shown. The required lifetime is stored in the variable „H“

of the KISSsoft calculation for the planetary gear set. To add it to the user interface, use right mouse click on the

field of choice, select „Insert Real“, „Reference“ and „Reference to“ „1.H“. With this the value given

in the user interface will be forwarded to the variable “H”. For the second stage, the same lifetime is required (in

this example). In order to have the second stage calculated with the same lifetime as the first, add

„1.H“ in „Expression“ in variable „1.H“. This will set the required lifetime of the second

stage equal to the required lifetime of the first stage:

Figure 3.1-7 Connecting the required lifetime of the second stage to the required lifetime of the first stage

In the User Interface the resulting minimal safety factors are added. The safety factors for the gear pairs (sun-

planet, planet-ring) are stored in the variables SF1, SF2, SF3 (root) and SH1, SH2, SH3 (flank). For the User

Interface the minimum of these values is used:

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Figure 3.1-8 Output of the minimal safety factor, stage 1 root

Figure 3.1-9 Output of the minimal safety factor, stage 1 flank

Note: In the variable „SFmin“ and „SHmin“, the required, not the minimal, lifetime is given. The index used is

somewhat misleading!

The user interface should then look – once the KISSsoft calculations have been executed through double click

on “Strength” to generate results as follows:

Figure 3.1-10 User interface with required lifetime and some basic results (minimal safety factors)

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3.2 Additional functionality

3.2.1 Shaft-hub connection calculation

The power input of the gearbox, the coupling on the first sun shaft, should be modelled using a key/keyway.

The corresponding calculation is to be added to the tree structure. For this, copy the KISSsoft calculation

„FeatherKey“ from the templates and add it to „Stage1“. In the dialog, choose the coupling where the key is

used and choose „Save file in KISSsys“.

Figure 3.2-1 Copy the key analysis from the templates and paste it into the tree structure

Figure 3.2-2 Choose the respective coupling and saving mode in the dialog

Some parameters of the key analysis are now taken from the KISSsys system. These are the torque (for nominal

torque) and the shaft diameter (see markings in Figure 3.2-3). Using double click on the KISSsoft calculation,

the key calculation is shown. Here, the key calculation can be defined completely.

Note that the length of the key is equal to the length of the coupling used. The length of the coupling can be

defined using the variable “b” of the coupling element “cIn” on the sun shaft.

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Figure 3.2-3 KISSsoft key analysis. Some values are defined from KISSsys directly

3.2.2 Load spectra

A load spectrum can be used for analysis. See “”

3.2.3 Position of the ring gears

Position of the ring gear can be set according to the sun in axial direction using function l_p(reference,point on

parent element). Because shaft for the rings are not defined ring gears can be set correctly for graphical

presentation. Open ring gear properties “zr” from tree there a variable “position” is available. Set expression for

this as follows “l_p(,{0,0,0})*{0,1,0}”. This will automatically set position of the ring to be same as for the

sun in the coordinate system.

Figure 3.2-1 Set position definition for the ring gear according to the sun gear

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4 Specialities

4.1 Speed of planetary bearings

The speeds calculated for the planetary bearings are absolute speeds (revolutions in space) with reference to a

co-ordinates system which is fixed in space. However, the bearings / planetary shafts rotate with the speed of

rotation of the planet carrier in space. For the calculation of the lifetime of the planetary bearings, the relative

speed with respect to the planetary shaft (relative speed of outer ring of bearing to inner ring of bearing) is

relevant. The planet shaft, in turn rotates with the speed of the planet carrier. The speed of the planetary bearings

therefore has to be corrected as follows:

Relative speed planet compared to planet-shaft (Outer ring of bearing compared to inner ring)=Absolute speed

of planet (speed of outer ring of bearing) – absolute speed of planet carrier / planet-shaft (speed of inner ring of

bearing):

Figure 4.1-1 Initial bearing speed (shown for first stage)

Figure 4.1-2 Corrected speed, shown for first stage, corresponding expression for second stage

Note: set the flag “KISSsys->KISSsoft” and de-activate the flag “KISSsoft->KISSsys” since the value of the

bearing speed shall be calculated in KISSsys only and not be defined in KISSsoft directly.

4.2 Number of planets

In the coupling element of the planet carrier („cc“), the number of planets for each stage can be modified using

the variable „NofPlanets“. After changing this value, use “UpdateShaftElements” for all sun and ring shaft

calculations in order to update the number of gear contacts.

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4.3 Tree structure

It is strongly recommended to use the tree structure as shown above. Especially the planetary shafts should be

arranged underneath the planet carrier shafts such that the rotation of the planetary shafts in space is calculated

correctly.

4.4 Shaft analysis

If a shaft analysis (KISSsoft calculation) is added underneath a shaft element (KISSsys element) in the tree

structure, a shaft geometry has to be defined in the graphical shaft editor. If no shaft geometry has been defined

(as in this example for the carrier shafts and the ring shafts), a message will show when the KISSsoft

calculations are executed (e.g. by double click on “Strength” in the user interface)

This is not an error message and the kinematic calculation and all other KISSsoft calculations (e.g. the gear

calculations) are still executed correctly and will give correct results.

There are three ways to avoid this message:

- The most dangerous way is to simply suppress the messages. For this, go to “Extras” in the KISSsys

menu bar and choose „Suppress Messages“. Note that now all messages, even error messages are now

suppressed. Using KISSys is still possible but

- All shaft geometry are defined, including the geometry of the planet carrier and the ring gear shaft /

casing. This has the advantage that the 3D view looks very realistic.

- Those shaft calculations which are not necessary are removed from the tree structure. A shaft

calculation is necessary only if the shaft itself is to be calculated (e.g. in terms of fatigue strength) or if a

bearing calculation is to be performed. In the latter case, the shaft analysis is necessary since it is in the

shaft analysis where the bearing forces are calculated. These bearing forces are then used in the bearing

calculation module for the lifetime calculation of the bearings. In this example, only the sun and planet

shafts needed to be modelled in fact. In the most extreme case, if only the gear analysis is of interest and

no bearings or shafts should be calculated.

Again: there is a difference between the KISSsys shaft element „kSysShaft“ and the corresponding KISSsoft

shaft calculation „Shaft“. The first is necessary for calculation of the kinematics and is used when building a

model. It represents a machine element. The calculation is only necessary a strength analysis of the above

machine element is required.

Figure 4.4-1 Left: KISSsys shaft element, right: KISSsoft shaft analysis

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