CH - 8634 Hombrechtikon Telefon: +41 55 264 20 30 · PDF fileKISSsoft Gear Pump Analysis 1 of...

KISSsoft Gear Pump Analysis 1 of 33

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KISSsoft AG Frauwis 1 CH - 8634 Hombrechtikon

Telefon: +41 55 264 20 30 Calculation Software for Machine Design Fax: +41 55 264 20 33 www.KISSsoft.ch [email protected]

KISSsoft Gear Pump Analysis

_________________________________________________________________________________________ For release: 10-2004 File: G:\KISSDOKU\Beschreibungen\Weitere\Anleitungen\kisssoft-anl-035-E-GearPump Instructions.doc Created / modified: 7.1.05 Mike Fish, Ulrich Kissling __________________________________________________________________________________________

1 Introduction (English) KISSsoft offers a very complex option for the calculation of the significant properties of gear pumps (both internally and externally geared).

1.1 Basic option (Z26) The basic option Z26 carries out the calculation of the transported volume (without consideration of any feed-back volume). If this option is activated (under „Settings“ -> „Module-Specific“ -> „Calculations“), then the transported volume is calculated through the exact numeric integration of the tooth space, and subsequently given as output in the report documentation. In addition, the transportable volume for each design variant generated by the optimisation function (Z4) will also be given. Because of this, the largest possible transport volume can be quickly established.

1.2 Expert option (Z26a) The additional option Z26a allows a very detailed analysis of the gear pump. The changes in important parameters of a pump during contact are calculated and graphically displayed. The detailed analysis includes properties such as the enclosed volume (that which is trapped between two engaging tooth pair contacts, i.e. 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), and 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. If the enclosed volume is reduced then the pressure of this volume will rise sharply. This causes high pulsating forces in the bearing which produces noise.

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With the addition of a pressure relieving groove, this pressure rise can be avoided. The calculation and illustration of the course of the pressure change in the enclosed volume during the meshing cycle is therefore very useful. The calculation facilitates the analysis of arbitrary cylindrical gear designs with both involute and non-involute tooth forms. The only important restriction at this point exists in the limitation to spur gears.

1.3 Optimizing strategy for gear pumps Important and critical problems for gear pumps are:

- Noise - Efficiency - Construction size - Wear

Only some notes on the criteria for the evaluation of a gear pump can be given here. Noise:

- The variation of the flow in the pump produces noise. The flow (Q) should therefore be as continuous as possible.

- The enclosed volume (V1) should not be reduced during the mesh so much as to cause a massive increase in the pressure of V1 fluid producing large dynamic forces on the bearings and shafts. Through accurate dimensioning of the relief groove, this effect can be significantly reduced.

- Supply speed of the oil through the narrowest point between teeth kept as low as possible.

Efficiency:

- Keep the fed-back volume as small as possible. Construction size:

- The KISSsoft – Precision sizing capability offers a very efficient development method in order to achieve the highest possible transported volume for a given size.

Wear:

- Pay attention to the changing course of the wear characteristic number (sliding speed and Herzian stress between the flanks)


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2 Einführung (Deutsch) KISSsoft bietet eine sehr komplexe Option zur Berechnung der wesentlichen Eigenschaften von Zahnradpumpen (Aussen- und Innenzahnpumpen).

2.1 Basis Option (Z26) Die einfache Basis-Option Z26 führt die Berechnung des Transportvolumens (ohne Berücksichtigung des Rückführvolumens) durch. Wenn diese Option aktiviert wird (unter „Einstellungen“ -> „Modul-Spezifisch“ -> „Berechnungen“) wird durch exakte numerische Integration der Zahnlücken das Transportvolumen berechnet und im Protokoll ausgegeben. Ausserdem wird bei der Feinauslegung (Z4) bei jeder Variante zusätzlich das Transportvolumen berechnet und ausgegeben. Damit kann sehr schnell die Variante mit beispielsweise grösstem Fördervolumen gefunden werden.

2.2 Experten Option (Z26a) Die Zusatz-Option Z26a erlaubt eine sehr detaillierte Zahnradpumpen-Analyse. Die Veränderung der wichtigen Parameter einer Pumpe während des Zahneingriffs werden berechnet und dargestellt. Dazu gehören geometrische Parameter wie das eingeklemmte Volumen (zwischen zwei Zahnpaaren im Eingriff, Rückführvolumen), das Volumen mit kritischer Zuflussfläche (Ölzustrom sollte möglichst kontinuierlich sein), engste Stelle (kleinster Abstand zwischen dem ersten Zahnpaar ohne Berührung), Zuflussgeschwindigkeit, Ölzufluss beim Eingang (mit Fourieranalyse zur Beurteilung der Geräuschentwicklung), Volumen unter Eingangsdruck. Weitere wichtige Ausgaben sind der Verlauf des Drehmomentes an beiden Zahnrädern, der Verlauf der Hertzschen Pressung sigH, der Gleitgeschwindigkeit vg und der Verschleisskenngrösse sigH*vg. Bei der Berechnung der Kräfte kann die Hertzsche Abplattung im Zahnkontakt mitberücksichtigt werden, da dieser Effekt hat einen beträchtlichen Einfluss hat. Das eingeklemmte Volumen ist abhängig von der Pumpenkonstruktion unter Eingangs- oder Ausgangsdruck, dies wird durch eine entsprechende Eingabe bestimmt und hat einen bedeutenden Einfluss auf den Drehmomentverlauf. Wenn sich das eingeklemmte Volumen verkleinert, steigt der Druck momentan in diesem Volumen sehr stark an. Dies bewirkt hohe pulsierende Kräfte auf die Lagerung und erzeugt damit Lärm. Durch das Anbringen einer Druckentlastungsnut kann der Druckanstieg vermieden werden. Die Berechnung und Darstellung des Druckverlaufs im eingeklemmten Volumen ist deshalb sehr nützlich. Die Berechnung erlaubt die Analyse von beliebigen Stirnrädern mit evolventischen und nicht-evolventischen Zahnformen. Die einzige wesentliche Restriktion besteht zur Zeit noch in der Beschränkung auf Geradverzahnungen.


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2.3 Optimierungs-Strategien für Zahnradpumpen (Deutsch) Wichtige und kritische Probleme bei Zahnradpumpen sind:

- Lärm - Wirkungsgrad - Baugrösse - Verschleiss

Hier nur einige Hinweise nach welchen Kriterien Pumpen beurteilt werden können. Lärm:

- Die Variation des Durchflusses in der Pumpe erzeugt Lärm in den Leitungen. Der Durchfluss (Q) sollte deshalb möglichst kontinuierlich sein.

- Das eingeschlossene Volumen (V1) sollte beim Abwälzen nicht verkleinert werden, da dadurch der Druck in V1 massiv ansteigt und dynamische Kräfte auf Lager und Wellen erzeugt. Durch präzise Auslegung von Entlastungsnuten kann dieser Effekt verringert werden.

- Zufluss-Geschwindigkeit des Öls durch die engste Stelle möglichst niedrig halten

Wirkungsgrad: - Rückführvolumen möglichst klein halten -

Baugrösse: - Die KISSsoft-Feinauslegung bietet eine sehr effiziente Methode um ein möglichst

hohes Fördervolumen bei gegebener Baugrösse zu erreichen.

Verschleiss: - Verlauf der Verschleiss-Kenngrösse beachten (Gleitgeschwindigkeit und Herztsche

Pressung zwischen den Zahnflanken)


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3 DESCRIPTION OF THE CALCULATION AND THE RESULTS

3.1 Data Input.

The data for the gear pair to be used should be entered first. A spur gear design should be selected from the main user interface as shown in Figure 1.

Fig 1 : Choosing the option to design a spur gear pair from the main KISSsoft menu system.


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The data for a gear pair to be used should be entered using the interface as seen in Figure 2.

Fig 2 : The interface for the design of spur and helical gear sets. The 2D and 3D view buttons

are seen in the bottom right of the interface.

2b : Design data for an internal gear pair.

2a : Design data for an external gear pair.


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The interface can be used to design either internal or external gear systems which can be viewed using the 2D viewer button. An example of both gear systems displayed in the 2D viewer is shown in Figure 3.

Fig 3 : 2D-Display of the gears for an internal pump in KISSsoft with the datum axis marked as a dashed line.

For details of how to enter and modify gear design, please consult the appropriate KISSsoft documentation.

3a : 2D KISSsoft diagram of gears for an external gear pair.

3b : 2D KISSsoft diagram of gears for an internal gear pair.


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3.2 Selecting Geared Pump Analysis Function Choose the gear pump item (“Z26 ”) from the calculations menu of the gear design module to activate the analysis module. When activated an interface for the calculations appears as in Figure 4.

Fig 4a : External Gear Pumps Fig 4b: Internal Gear Pumps

Fig 4c: Internal/External Gear Pumps – when defining a relief groove


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Fig 4a-c : The interface requires entry pressure, exit pressure, and the limit angle for sealing the input chamber. The “Consider Herzian Flattening” box should be checked if the torque calculations are to consider Hertzian compression effects.

Fig 4d: Defining a relief groove

The values of entry pressure and exit pressure should be entered in mega-Pascals (MPa). Without these values no evaluation of the torque can be made. The check box on this interface can also be used to include a calculation considering Hertzian compression effects. Section 3 (Torque) gives more details on the torque and Figure 11 compression calculations. To demonstrate, Figure 4 is an example of how the interface should look after entering entry pressure of 1MPa, and exit pressure of 21MPa, and an offset of 13.0mm (for an external gear pump), and entry pressure of 1MPa, and exit pressure of 20MPa, and an entry chamber angle of 70° (for an internal gear pump). The enclosed oil volume (that which is trapped between two tooth pair contacts) can either be under entry or exit pressure depending upon the construction of the pump. Input or output pressure can be applied during the calculation using the drop down menu in the interface to specify the enclosed volume under pressure to either pIn or pOut respectively. This option has a significant influence on torque. The seal for the entry chamber should also be defined at this point to establish volume. For external gear pumps this is a distance from the datum axis, hs, as shown in Figure 5a. A minimum value is the intersection of the outside diameters. For internal gear pumps this is the angle formed by the seal of the entry chamber (see α indicated in Figure 5b) given in


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degrees. If no seal angle is given, the intersection of the outer diameters of the gears is used as a default. This is rounded up to the nearest degree.

Fig 5a : Externally geared pump system with a seal on the entry chamber at an offset, hs, from the datum axis. The sense of rotation, n, is also indicated, as is the current position of

the operating pitch point in the datum position (OP) of the gear, φ.

Fig 5b : Internally geared pump systems with a seal on the entry chamber forming an angle α, called ‘Seal angle’, with the reference axis of rotation. The sense of rotation, n, is also indicated, as is the current position of the operating pitch point in the datum position

(OP) of the gear, φ.

ENTRY CHAMBER

SEAL

GEAR 2 PROFILE

GEAR 1 PROFILE

hs

ENTRY CHAMBER SEAL

GEAR 2 PROFILE

GEAR 1 PROFILE

OPERATING PITCH DIAMETER, dw

OPERATING PITCH DIAMETER, dw


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The displacement (or roll) of the gear, φ, from a datum position where the tooth form of the driving flank of the driving gear crosses the datum axis of definition (φ=0) at the pitch circle is also shown in Figure 5. The constant angle, θ, between the operating pitch point (OP) and the middle of the tooth tip is used to define this datum, and is shown in the report. The sense of φ is defined by the rotation of the driving wheel. There is a check-box on this interface which indicates the requirement for calculations which consider Hertzian compression effects at the contact point. There are also cells in the interface which can not be edited. These are mean values of torque experienced during the mesh considering the sum of torque in the system and the drive system only respectively, and are only returned after a calculation cycle has been carried out. When the required specifications have been entered, press the calculate button (“Calculate”) to carry out the analysis. The volumes through the meshing cycle are calculated, and the data is stored to the current working directory. The buttons to illustrate characteristics of the pump through the mesh cycle over the line of engagement will automatically activate once the calculations are completed. The interface will look as it does in Figure 6.

Fig 6a : External Gear Pumps Fig 6b: Internal Gear Pumps

Fig 6 : The interface after the calculation button has been pressed and the analysis completed. If any values in the cells are changed, the buttons will once again deactivate automatically and the interface will revert to that shown in Figure 4. The “Calculate” button must once again be pressed in order to view characteristics for the new specification. The buttons can be used to show gear pump characteristics of torque (on gear 1) , oil volume enclosed by engaging tooth pair during mesh (“V1”), critical in-flow area (“V2”), the volume induced into pump (“V3”) , the volume of the entry chamber (“V4”), and gap between tooth profiles at the boundary of critical area (“Gap”) will automatically activate the once the calculations are completed. A more detailed description of each of these is given in the next section of this document.


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3.3 Calculated And Graphed Properties. Values for several characteristics are generated during the mesh over the path of engagement. The graphed properties can be plotted relative to roll angle of the driving gear. A dashed blue line has been included to indicate an interval of one tooth pitch of the driving gear. The graphs can be printed or saved to various file formats in the usual manner according to standard KISSsoft documentation. This section describes in more detail the calculations and graphical output developed for each property in the analysis. The properties determined by both the external and internal gear pump analysis will be the same. Results from the sample design for the internal pump described earlier in the document (Figure 2 and Figure 4) have been used to illustrate the output of the analysis. • Torque (Mt) The torque value is calculated as the sum of the moments experience by both gear wheels. The equations which have been used to determine the torque at the point of contact on the pinion (p) and gear (g) are : M_p = b.( r2a_p – µ2 ). ∆P / 2 M_g = b. (λ2 – r2a_g ). ∆P / 2 Where : b = gear face width r a = tip radius µ,λ = contact radius on wheel ∆P = Pressure difference in the pump (P_out – P_in) Modifications to the calculations due to Figure 11 compression effects can also be determined at this point by an iterative loop if required. Values calculated at several positions during the mesh cycle generate the full torque curve such as is shown in Figure 7.

Fig 7 : The graph of torque in Newton-metres (Nm) at positions over the range of tooth mesh.

Tj Tj


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In this diagram it is clear to see the point at which the following tooth pair engages. This is also highlighted by the dashed blue line which indicates the tooth pitch interval. The graph in Figure 8 shows a similar analysis carried out when Hertzian compression effects are taken into account. Tj EOSC

Fig 8 : The graph of torque in Newton-metres (Nm) at positions over the range of tooth mesh taking into account Figure 11 compression at the contact.

With the height of Hertzian ellipse 2*a the equation for the torque is changed as follows: M_p = b.( r2a_p – (µ+a)2 ). ∆P / 2 M_g = b. ((λ-a)2 – r2a_g ). ∆P / 2 Explanation of the ‘jumps’ in the torque curve: In the position marked „Tj” (tooth jump) the torque calculation is changed from being based on the leading tooth pair contact (PII) to being based on that of the following tooth pair (PI). The contact position on the tooth profile also changes as a result. When Hertzian pressure is considered in the calculation of torque, a second jump in the torque plot will also be evident as indicated at the position „EOSC“ (end of single contact) in Figure 8. At the transition where the contact changes from one tooth pair to being shared by two adjacent pairs (or vice versa), the Hertzian pressure also changes due to a consequent change in the size of contact area. Detailed data :


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More data documenting the calculation of the Hertzian ellipse can be found in the file named Z26-H2.TMP of the working directory after the calculation cycle has been carried out. This file contains a set of intermediate results for the calculation.


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• Enclosed Volume (Eingeklemmtes Volumen, V1) Two contact points on consecutive tooth pairs form an enclosed volume along the contact line. These points are labelled as PI and PII in Figure 9.

GB GN Fig 9 : This diagram shows points PI and PII compared to the sense of rotation, n, on the path

of contact marking the beginning and end of the volume V1 respectively which is enclosed by the tooth profiles.

GN: Nearest gap between previous tooth pair GB: “ “ “ reverse driving flank The enclosed volume is calculated over the period of rotation in which the volume is isolated from the entry and exit volumes. At some points during along the path of contact the point PII may not exist, at which point the volume is no longer enclosed and the V1 value will be zero. When calculated at various values of φ through the meshing cycle the graph will look similar to that seen in Figure 10a.

PI

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Fig 10a : This shows the change in enclosed volume at positions over the range of tooth mesh

. The point at which the volume is no longer enclosed can be seen clearly.

Fig 10b : This shows the change of ressure in enclosed volume at positions over the range of

tooth mesh. Without pressure relief groove, there is a high pressure peek when volume V1 is reducing.

There will be at some point during the mesh, a position in which the tooth forms no longer create an enclosure for the oil. Here the volume V1 forms the critical in-flow volume (see V2), and the value for V1 no longer exists for the tooth pair. The V1 value is then given as zero. Such an effect can be clearly seen in Figure 10.


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• Critical In-Flow Area (V2) The volume from the end of the enclosed volume (PII) to the minimum gap of entry into the entry chamber is termed as the critical in-flow volume. At some point in mesh cycle the enclosed volume (V1) is released and is then classed as the critical volume of in-flow (V2). This means the V2 value immediately jumps to approximately the V1 at the end of the enclosure cycle. This sudden change in critical in-flow region volume can be seen in Figure 11. The V1 and V2 values around the jump position should be comparable.

Fig 11 : This graph shows the change in volume which leads to the entry chamber at positions over the range of tooth mesh. The point at which this area is transferred to the preceding tooth pair boundary is clearly indicated by the sudden drop in area.


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• Oil Volume At Inlet (V3) and Oil Inlet flow The volume (V3) value represents the total oil which has passed through the entry port to this point. A special index is included in the calculations to store information about how much oil has been removed from the entry chamber by the sealing action of the both gear tooth space forms (V5I and V5II) as they rotate (see Figure 12).

Fig 12 : A diagram to show the 5I and 5II sealed volumes formed by the tooth spaces of gear 1 and gear 2 respectively which transport oil out of the entry chamber as they pass the

seal. An example of a plot showing the increase in oil which must flow into the pump system is illustrated in Figure 13.

5I

5II

ENTRY CHAMBER

SEAL


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Fig 13 : This graph shows the total oil flow through the chamber at positions over the range of tooth mesh, representing the oil which must be drawn in at the entry port.

The plot in Figure 13 shows distinctly the points at which a sudden increase in V3 is registered due to the re-introduction of oil from the mesh at the end of the V1 contact range. Through differentiation the actual oil flow (“Delta V3”) is calculated; the deviation of the oil flow from a mean rate of flow during the meshing cycle is presented. An example of this can be seen in Figure 14. The mean flow rate value calculated for the pump is indicated by the horizontal dashed line.

Fig 14 : This graph shows the deviation of oil flow relative to a constant flow rate through

the entry chamber at positions over the range of tooth mesh. Through the Energy Conservation Equation it is possible to calculate directly the oil-flow: Q = b*π*[(r2a_p – µ2)*n1 + (r2a_g – λ2)*n2] Where : b = gear face width r a = tip radius µ,λ = contact radius on wheel n1,n2 = Rotation of wheels This equation does suppose that the oil is an incompressible fluid, which is not 100% true. However the calculation of the oil flow with 2 completely different methods is a good check for the calculation of the different volumes. If the curves are very different there must be a problem in the calculation of the Volume V3 through the meshing cycle.


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Fig 14a: This graph shows the deviation of oil flow relative to a constant flow rate through

calculation by Energy Conservation Law. Here, the instantaneous rate of new oil flow into the entry chamber is calculated at each step through the mesh cycle. During the calculations, the sudden increase due to the influence of the volume returned from the mesh (at the end of V1 contact range) is not considered as it is not newly induced oil. Changes can occur in certain circumstances due to tooth form or contact conditions. From values such as these, critical properties of a pump such as noise level and tendency to build up a partial vacuum (resulting in cavitation) can be assessed. A Fourier spectrum analysis as shown in Figure 15 is also produced for the oil flow deviation curve.

Fig 15 : A Fourier spectrum analysis of the oil flow curve in Figure 14.


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• Volume under Input Pressure (V4) The instantaneous volume of the entry chamber is also calculated during the mesh cycle. An example is shown in Figure 16.

Fig 16 : The volume of the entry chamber containing oil at entry pressure at positions over

the range of tooth mesh . Three sudden changes in the volume can be seen over any tooth pitch. Two sudden decreases represent points at which the tooth space seals after the entry chamber and can no longer be counted in the sum of the volume. A sudden increase occurs at the point at which the V1 value becomes the V2 value as this is included in the sum of entry chamber volume. A change in pump design in changing the seal can change volume and the phase of the V4 curve relative to an initial enclosed volume position. The diagram in Figure 17 shows this effect due to an increase of α (Seal Angle) in the default design described earlier from 70° to 75°.


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Fig 17 : Comparison to the graph in Figure 12 showing changes in the total volume and phase of the curve of the entry chamber containing oil at entry pressure due to an increase in seal angle.

• Transport Volumes (V5) The transportable volume V5 is derived from the tooth space on the drive gear (V5I), the tooth space on the driven gear (V5II), and the enclosed volume at the first point of contact (V1a). For a drive gear with ‘z_1’ teeth, this value is calculated as : V5 = V5I . z_1 + V5II . z_1 - V1a. z_1 The value is written to the report (see Section 4 Documented Report of Analysis later in this document) as part of the description of the pump characteristics. If a rotation speed for the system is also defined, the transported volume per minute can be calculated. The rotation speeds of both gears and the resulting transported volume are also written in the report. • Gap to Entry Pressure Chamber (GN) This value is the bound GN of the critical volume (V2) as at enters the entry pressure chamber. A graph is shown in Figure 18.

Fig 18 : This shows the change in entry gap GN from the critical surface region to the entry chamber at positions over the range of tooth mesh .

The graph will show a sudden jump at the point at which the enclosed volume V1 opens to form V2, and the contact point is transferred back to the preceding tooth pair. The gap is suddenly reduced as this pair in the majority of cases (other than the case of special tooth forms) will have a smaller spacing between the flanks. In a continuous curve the value should reach zero precisely at the point of contact transfer. Though it always be close, this may not


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always be fully achieved due to the discrete nature of the analysis over a finite number of points. If this value is negative, it implies that the gear set design creates interference at the tip of the drive gear. It is possible to calculate the area over the gap GN forming the boundary between V2 and V4 by multiplying this value by the face width of the gears. Then the velocity of oil through this gap can be determined for an incremental change in V2. A graph such as this is shown in Figure 19 for this example.

Fig 19 : A graph showing the velocity of oil flow through the window created at the gap GN

forming the boundary between V2 and V4. Here changes in the velocity reflect the changes in the gap GN value where an increased gap (resulting in increased area) requires that the oil need move with lower velocity to achieve the required change in volume. The velocity at the point of transition is set to zero. In pumps with reduced backlash, the gap between the reverse flank of the tooth in contact can be smaller then the gap GN. The gap on the reverse (or ‘back’) driving flank GB is therefore also calculated.


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Fig 19a : This shows the change in gap on back flank GB at positions over the range of tooth

mesh . • Stress, Sliding Velocity, and Wear.

Fig 20 : A graph of Hertzian Pressure due to load over the contact cycle.


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Fig 21 : The sliding velocity at the tooth contact point.

Fig 22 : The wear number determined by velocity and pressure at the contact. Because the transmitted torque in the tooth contact changes during a tooth mesh, the performance of the Hertzian Pressure over the tooth flank is completely different from the performance of a normal gear reduction. This is why the display of the Hertzian Pressure is so important. Gear pumps are mostly damaged due to wear. The product of the pressure multiplied by the sliding velocity is a good criterion to indicate the most critical points.


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3.4 Documented Report of Analysis. A report containing a description of the pump characteristics can be generated in a similar manner to that employed in all KISSsoft modules. On pressing the results button in the interface, a report is generated containing the input and output characteristics of the pump as shown in Figure 23.

Fig 23 : An example of the report generated for the gear-pump analysis.

The data used to generate the graphs is stored in file \tmp\Z26-H4.TMP of the working directory. The file is tabular, which is easily viewed using a text editor. The columns represent the different parameters calculated at each point along the path of contact (defined by a roll angle position, phi, in the first column).


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4 Validation. The calculations have been confirmed using 2D images exported using DXF format files into a Solid Edge CAD system. These files have been stored in T:\mf\Zahnradpumpe for future reference. A test was made to assess the influence on number of points used in the profile generation. The areas determined by the CAD using 30 and 60 points were compared. The enclosed volumes were then compared at the first point of enclosure (V1a) and at the end of the enclosure range (where V1 becomes V2). The table in Figure 24 below shows the comparison of calculated area and that determined by the CAD (see accompanying print outs). TEST METHOD POINTS AREA (mm2) DIFFERENCE Number of Points CAD 30 67.6 0.3 % CAD 60 67.8 Start of Enclosure CAD 30 67.6 0.6 % Calculation 30 67.2 End of Enclosure CAD 30 71.0 1.4 % Calculation 30 72.0 Fig 24 : A table to compare calculated values from program with those derived from DXF files

imported in to Solid Edge CAD program. From the table it can be seen that the increase in number of points had a negligible effect on area definition. Also, the calculations of area compare well to within 2%. Some difference can be attributed to the tolerance of roll positions when creating the DXF file in the 2D diagram function, which could lead to a slight mismatch of the comparison.


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(This side is in german only: Concerns only validation procedure) Vergleich mit der Flächenberechnung für Zahnradpumpen in Version KISSsoft 10-2003 Die Berechnung des Transportvolumens von Zahnradpumpen in der KISSsoft-Feinauslegung wurde vor 2 Jahren komplett unabhängig und mit anderem Algorithmus programmiert. Ein Vergleich der beiden Resultate ist deshalb aufschlussreich. In KISSsoft-Feinauslegung wird nur das Transportvolumen (ohne Rückführvolumen) berechnet. Im beiliegenden Beispiel wurde die Variante 5 der Feinauslegung übernommen. Das Transportvolumen wird mit 5.639 l/min angegeben. Die Zahnradpumpen-Berechnung ergibt V5 = 0.00564 l/rev = 5.64 l/min (bei 1000 rpm). KISSsoft/Hirnware Rel. 10-2003 Katum: 10.12.2003/15:22:38 Anwender: example B ANALYSE DER RESULTATE (Bewertung von wichtigen Eigenschaften) Kommentar: No. = Nummer der Variante V = Fördervolumen als Zahnradpumpe (l/min) (simplified calculation) Summary = Gesamtbewertung (gewichtet) (50.00%:Noise 20.00%:diff_i 10.00%:kg 75.00%:Slide 0.00%:v.Slide 0.00%:AC/AE 10.00%:1-eta 100.00%:Safety) (Generell gilt in dieser Tabelle: Je kleiner die Zahl, desto besser!) No. Noise diff_i kg Slide v.Slide AC/AE s_Rig 1-eta Safety Summary V 1 0.427 -0.452 0.252 1.360 0.280 1.602 0.738 0.598 0.478 5.181 2 0.379 -0.452 0.256 0.880 0.260 1.555 0.635 0.361 0.370 5.169 3 0.509 0.962 0.259 1.498 0.255 1.198 0.507 0.725 0.551 5.316 4 0.465 0.962 0.263 0.849 0.231 1.147 0.418 0.385 0.398 5.324 5 0.532 -0.452 0.276 1.756 0.266 1.260 0.523 0.818 0.598 5.639 6 0.483 -0.452 0.280 0.926 0.241 1.214 0.431 0.389 0.404 5.645 7 0.571 0.962 0.283 1.631 0.232 0.948 0.338 0.263 0.374 5.781 8 0.601 -0.452 0.301 2.140 0.243 1.000 0.351 0.251 0.381 6.121 ANALYSE DER RESULTATE (mit Angabe der Varianten-Nummer in abnehmender Reihenfolge) Beste Varianten bezüglich Uebersetzung: 1 2 5 6 8 3 4 7 Beste Varianten bezüglich Geräusch: 2 1 4 6 3 5 7 8 Beste Varianten bezüglich kleinstes Gewicht: 1 2 3 4 5 6 7 8 Beste Varianten bezüglich Reibverhalten (AC/AE): 7 8 4 3 6 5 2 1 Beste Varianten bezüglich Variation der Steifigkeit: Beste Varianten bezüglich Festigkeit: 8 7 2 4 6 1 3 5 Beste Varianten insgesamt (Summary) : 2 7 8 4 6 1 3 5 Ende Report Zeilen : 53

KISSsoft/Hirnware Rel. 10-2003 Datum: 10.12.2003/15:23:48 Anwender: example ZAHNRAD-PUMPE Öldruck am Eintritt (MPa) [pIn] 1.000 Öldruck am Austritt (MPa) [pOut] 200.000 Beginn Einlegekeil ab Mittellinie (°) [alfa] 70.474 Drehzahl (rpm) [n] 1000.000 772.727 Mittleres Antriebes-Drehmoment (Nm) [T1] 145.977 Mittleres Drehmoment im Zahnkontakt (Nm) [Tc] 105.600 Volumen Zahnlücke (l) [V5_1/2] 0.000175 0.000157 Mittleres eingeklemmtes Volumen (l) [V1] 0.000065 Eingeklemmtes Volumen im ersten Moment des Kontaktes (l) [V1a] 0.000072 Transportvolumen (l/rev) [V5] 0.00564 Rückführvolumen (l/rev) [V1a*z1] 0.00122 Fördervolumen als Zahnradpumpe (l/min) [dV] 4.424 Ende Report Zeilen : 24


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5 APPENDIX I Example using arbitrary profiles in the pump analysis.

Tooth form is not an involute, but is defined in a CAD and then imported in KISSsoft as DXF-description :

Figure I.1 : The calculated paths of contact for an arbitrary tooth.

BEFORE CALCULATION AFTER CALCULATION


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Figure I.2 : Input parameters used in the sample analysis. Buttons allowing graphed analysis of characteristics are activated after the calculations. The average torque at

the contact mesh and the torque experienced on the drive system are returned to the interface.

Without Hertzian Compression With Hertzian Compression

Figure I.3 : Torque calculated with and without the consideration of Hertzian compression effects taken into consideration.

Figure I.4 : This graph shows the enclosed volume over the range of contact (tooth pitch is indicated by a blue dashed line at positions along the x-axis where contact has taken place).


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Figure I.5 : The volume between the tooth mesh at the beginning of the oil entry chamber.

Figure I.6 : The rate of new oil (does not include V1 contribution) inducted by the action of the pump (“Delta V3”) from the constant rate in litres per minute as stated in the report.


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Figure I.7 : The volume enclosed by a seal point in the gear tooth contact mesh and the seal at the end of the entry chamber.

Figure I.8 : The minimum distance between the tooth flanks (gap GN) allowing oil from the mesh to enter the entry chamber.


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Figure I.9 : The printable report of results showing pump characteristics.

CH - 8634 Hombrechtikon Telefon: +41 55 264 20 30 · PDF fileKISSsoft Gear Pump Analysis 1 of...

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