27. März 2008 1 / 23

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.

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Table of contents

1 MODELLING TASK .......................................................................................................................2 2 BUILDING THE MODEL ...............................................................................................................2 2.1 Starting KISSsys ...........................................................................................................................3 2.2 Modelling the first stage ...............................................................................................................3

2.2.1 Machine elements, shaft analysis modules ...............................................................................3 2.2.2 Connections...............................................................................................................................4 2.2.3 Planetary gear calculation .........................................................................................................5

2.3 Modeling the second stage............................................................................................................6 2.4 Positioning the planetary shafts/bolts ...........................................................................................7 2.5 Power input, power output, connecting the two stages.................................................................8 2.6 Input of gear data ..........................................................................................................................9 2.7 Input of the shaft geometries.......................................................................................................11

2.7.1 Sun shafts ................................................................................................................................11 2.7.2 Planet carrier ...........................................................................................................................12 2.7.3 Shaft for ring gear / gearbox casing........................................................................................12 2.7.4 Planetary shaft / bolt ...............................................................................................................13

3 USER INTERFACE .......................................................................................................................15 3.1 Adding an user Interface .............................................................................................................15

3.1.1 Input and output power ...........................................................................................................15 3.1.2 Adding functions.....................................................................................................................16 3.1.3 Information on the strength analysis of the gears ...................................................................18

3.2 Additional functionality ..............................................................................................................20 3.2.1 Shaft-hub connection calculation............................................................................................20 3.2.2 Load spectra ............................................................................................................................21 3.2.3 Position of the ring gears ........................................................................................................21

4 SPECIALITIES...............................................................................................................................22 4.1 Speed of planetary bearings ........................................................................................................22 4.2 Number of planets.......................................................................................................................22 4.3 Tree structure ..............................................................................................................................23 4.4 Shaft analysis ..............................................................................................................................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)

Gear 1: Planet (zp) Gear 2: Ring (zr)

Figure 2.2-3 Adding the planetary connections

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 distance e.g. 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 called e.g. “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 may e.g. 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 use e.g. 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 2nd 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 on e.g. 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

„Input.power“ in „Expression“ 2. Output speed: as described above, variable name to be used „Output.speed“ 3. Output torque: as described above, variable name to be used „Output.torque“ 4. Output power: as described above, variable name to be used „Output.power“ 5. Ratio: use the following expression in „Expression“: abs(Input.speed/Output.speed), 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“ „Stage1.GP1.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 „Stage1.GP1.H“ in „Expression“ in variable „Stage2.GP1.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 “ins-301-LoadSpectrum-templates.pdf”

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(ss.zs,{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 not recommended...

- 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 if e.g. a strength analysis of the above machine element is required.

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