KISSsys Application: Evaluation of Load Spectra for a CV … · 2020-03-05 · KISSsys Tractor CV-Transmission Model 3 from 17 QUALITY SWISS through a good hydrostatic power split

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KISSsys Application:

Evaluation of Load Spectra for a CV-Transmission using a parameterised Model

In collaboration with

MALI Special Vehicles Ltd Negele Engineers Office

Summary Based on a project for the design of a Tractor’s transmission, the typical difficulties that - ring the design and verification of machine elements – a design engineer must encounter will be illustrated and an approach to the solution using a modeling software for complete transmissions will be shown. Especially, the use of load spectra considerably increases the calculation effort for gear boxes because it is necessary to calculate beforehand local machine element-related collectives as a first additional step based on the globally defined load spectrum and the defined transmission shift positions within the individual load spectra step. Furthermore, the administration of the very many calculations that arise in a tractor transmission due to its complexity is laborious, unproductive and error-prone. The use of a calculation model, that simultaneously administrates all the calculations, brings many advantages for the manufacturing process, planning of tests and sales support. The manufacturer will have at his disposal a tool allowing him to quickly verify the transmission in case of changes in manufacturing parameters. Testing scheduling also profits from this because, with the help of the predetermined processes, it is possible to easily concentrate a load spectrum or to detect a critical load level. For sales support, there is now an Assistant Tool available allowing the analysis using customer supplied load spectra to dismiss any unrealistic demands with founded arguments. The basis for this, lays always in the parameterised model of the whole transmission, because the service life calculation by means of a globally defined load spectrum, is simultaneously applied for all machine elements and, as a result, not only reveals service life and security but also the individual damages.

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KISSsys Tractor CV-Transmission Model 2 from 17

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Problem Definition

Introduction In the design of a tractor, special attention is given to the transmission because it represents about a third of the tractor’s total cost.

Fig. 0-1 Tractor Transmission in KISSsys 3D Display

The main objective of transmission design is to get as close as possible to the ideal traction force hyperbola. The motor should operate within an optimal range of revolutions, since the various tasks of a tractor require different driving speeds between 3 and 50 km/h. The better this approach to a wide range of revolutions is achieved, the finer should the gradual work of the transmission be. This leads to a transmission design with a high number of speeds (up to 64 speeds for a tractor). The next step in designing consists in the use of continuous load transmission which, at present, are standard for tractors over 70 HP. At present, this transmission type is being introduced as direct gearbox in the personal car class industry (e.g. using double clutch designs). In both application areas, the central idea is that two or more couplings –electronically controlled and hydraulically driven- be simultaneously actuated upon while shifting gears. Whilst the continuous shifting is a question of comfort for a personal car, for a tractor is a must on account of the high traction forces required, for instance, by ploughing. At present, the CV-Transmission for vehicles represents the top step in transmission design and, once again, the agricultural technical field is leading (we mention here especially the manufacturer Fendt). Nowadays predominant are power split transmissions with a hydrostatic loading path as well as a planetary gear set. With it, the number of discrete speed transformations is again reduced, for instance to four. Figure. 3.1 -2 shows the two basic concepts for a hydrostatic CV-Transmission with power split or collection with a planetary gear set. This takes advantage of the Planetary Gear set kinematic properties (two of the three rev numbers can be predetermined, the third follows / a torque can also be predetermined, two follow in a determined ratio). In both types of design should be taken into consideration that,


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through a good hydrostatic power split control, it is possible to minimise the blind power [2], [3], [4].

Fig. 0 -2 Basic Concept for a hydrostatic CV-Transmission with external Power Split according to [1]. Input coupled Output coupled

The present work describes a transmission from MALI Special Vehicles Ltd, Eberhardzell, designed for a power of 230 kW. It is supposed to be used in tractors as well as in construction machinery. Figure 3.1 -1 shows a tractor prototype. Figure 3.1 -3 shows the transmission conceptual diagram. The transmission has two driving positions which concepts can be seen in Figure 3.1 -2. In position I (the slowest one) the concept on the left is active; in position II (the fastest one) the one on the right is active.

Fig 0 -3 Transmission conceptual Diagram. The hydrostatic Shafts, often mentioned in the Report, are signalled with Arrows.

Planet carrier

To the Take-off

All-wheel Coupling

To the front Shaft Hydrostatic Shafts

Power Split, fixed Revs ratio

Mechanical Power Split Mechanical Power Split

Concentration, fixed Revs ratio

Concentration, fixed Torque ratio

Continuous Transmission Hydrostatic Power Split

Continuous Transmission Hydrostatic Power Split

Power Split, fixed Torque ratio


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Objectives The objectives derive from the requirements of three areas, Manufacturing, Testing and Sales as follows:

Manufacturing - Give the manufacturer a tool allowing him to very quickly verify and optimise the

transmission in case of changing parameters (such as helix angle, bearing type, shaft diameter)

- Identify machine elements subject to excessive stress and carry out a documented operational fatigue proof

- Reduce the administration effort of calculating machine elements with the corresponding documentation.

Testing - Identify and eliminate load steps from the spectra that generally leads to negligible

damage to the components - Find a replacement Load Spectrum that, under a lower number of cycles (test

duration), leads to a comparable damage to all components concerned - Calculated identification of critical components (allows targeted observations during

the test).

Sales - Quick assessment of Customer-supplied load spectra, which load steps are relevant

and must, for instance, be defined with more precision or which load steps are estimated as too high or too low.

- Customer-specific stress analysis, documentation and confidence building through transparency in the statements about service life.

Problem

Kinematics Calculation When done by hand, kinematics calculation, including coupling powers, meshing powers and blind powers for planetary transmissions, is time-consuming and error-prone. The MKS or FEM Systems of units, for being based on body interactions, are here disadvantageous, that is because they are not parameterised. KISSsys allows quick and reliable calculation of number of revs, torque, coupling, meshing and blind power.

Handling many isolated Calculations The number of necessary separate calculations for the verification of machine elements of a tractor transmission lies, approximately, within the order of magnitude of:

- ±10 Shaft calculations - ±20 Bearing calculations - ±10 Gear pair calculations - ±10 Shaft-Hub connections.


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This means that the Engineer must dedicate a considerable part of his attentiveness to administrate the calculations in their various steps. This activity is very much error-prone, contains no creativity aspects and no Engineer likes it. Furthermore, the isolated calculations should not be considered as separate elements; for instance, a change of helix angle in a gear calculation has also repercussions in various shaft and bearing calculations. The work with isolated calculations will thus be very much slowed down.

Calculation with Load Spectra The calculation with load spectra for isolated machine elements does not constitute a problem in itself. Frequently, one has to use a service factor instead of a load spectrum or to work with one or more nominal loads. This procedure is very uncertain, especially in case of gear boxes where for the calculation with nominal loads that wrongly weigh the influence of the various load paths. Naturally, this statement is rather trivial because the calculated service life / safety using a load spectrum lies between two extreme load cases, it is however not any more intuitively understandable how strong the load assumption influences the various machine elements. Figure 3.3 -1 shows that the change in an assumed load (load spectrum, individual load ground work or slow speed transport case) in one machine element (here the bearing no. 3 on the no. 13 shaft) shows almost no influence upon the lifetime, but can, on the other hand, perceptibly change the values for other machine elements (for instance, bearing no. 2 on the no. 13 shaft).

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Shaft 4, bearing 1 Shaft 4, bearing 2 Shaft 13, bearing 2 Shaft 8, bearing 3 Shaft 13, bearing 3

Bearing

Life

time

[h]

Load spectraGround work

Slow speed transport

Fig. 0 -1 Different effects of Loading Assumptions in some Machine Elements

Testing The test to prove the lifetime of all transmission components will be carried out using a load spectrum specially conceived for the calculation. The transmission being designed for 10.000 h, it is not possible to test the complete spectrum. Instead, one normally starts with the last test step “accelerated testing”. However, the load increase in the test will influence component strain (for instance, tooth contact pattern or higher bearing deviation). Additionally, this procedure will be questionable in case of simultaneous testing of bearings, shafts and gears, since they have very different Wöhlerline


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p-gradients. A load spectrum concentration will also show errors in case where different machine elements (or flank and root, together) should be simultaneously examined.

Evaluation of Customer-supplied Load Spectra The illustrated transmission is supposed to be offered worldwide to different end-users in the areas of agriculture and construction. On account of this, the application conditions and the loads (for instance, due to the soil characteristics) considerably vary from customer to customer. This means that, for most customers, one must carry out an individual fatigue strength proof with customer-specific load spectra. The effort for these individual calculations should be minimal. Naturally, this specially applies for the required documentation effort. Furthermore, the manufacturer must be able to thoroughly analyse the given load spectra, to determine whether individual steps could lead to disproportionate high or low single damages. In this case, it is necessary to identify or subdivide steps with high damage share and those with low damage share that could be disregarded. The transmission manufacturer needs a tool enabling him to show his customers, vividly and quickly, that their load assumptions strongly influence the calculation results and, hence, require to be dealt with in a serious way. The customer is seldom conscious of the importance of imprecise load assumptions.

Approach to the Solution

System Formulation using KISSsys The objectives and the problem definition previously outlined, require an integrated calculation software that does not only work at machine element level but also at system level. KISSsoft AG offers such an engineering tool – KISSsys – an additional system to KISSsoft, the software for the calculation of machine elements. KISSsys (Figure 4.1 -1) allows the easy and rapid modeling of a complete driving step. The global parameters (for transmissions: torque, number of revs, external forces and other parameters such as temperature or lubrication) are defined in KISSsys. The individual system components are designed and optimized with the integrated KISSsoft calculations. KISSsys administrates all these data, calculates the local loads and number of revs from the global parameters and hands them over to KISSsoft for the calculation of the individual components. KISSsys has following properties: Kinematics Calculations:

• Power path / number of revs / with spur- conical- worm- and skew bevel gear steps • All kinds of planetary gear sets (planetary, Ravigneaux, Wolfrom, etc.) • Differential (with straight bevel- or spur gears) • The model covers shafts, bearings and shaft-hub unions • Chain- and belt- transmissions • Couplings may be activated / deactivated, slippage is taken into account • External loads applied to the system are taken into consideration • Bearing stiffness and efficiency • Calculation with load spectra for all machine elements in the Model • Several gear variants in the same Model


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• Calculation execution with display of critical elements • Automatic document production (stress analysis) fort he whole transmission • Integrated Macro-language for the implementation of special functions and new

elements

Fig. 0 -1 KISSsys Environment with Tree structure, Kinematics, 3D Display, Tables and Dialog

Transmission Modeling using KISSsys

Kinematics In order to simulate the various shift positions, KISSsys allows an easy and secure modeling of the kinematics of symmetric speed-transforming gears, in special, planetary sets with parallel shafts. In addition, it uses couplings (defined in open / closed position, as well as a value for slippage and maximal transferable torque). The hydrostatic power path modeling is accomplished by means of a power source (motor) and a power drop (pump). The modeling of the relationship between number of revs and torque of both hydrostatic elements is done in KISSsys by means of a kinematic boundary condition. The hydrostatic load paths’ efficiencies for the individual load steps must be placed in a table. The boundary conditions concerning the hydrostat H2 torque are defined as: # IF WSG.K2.config[0] THEN //Drive Position II RETURN -H1.torque*H1.speed/H2.speed/etages; ELSE; //Drive Position I, Retour RETURN -H1.torque*H1.speed/H2.speed*etages;

Is position II activated, then the torque is equal tot he pump power (hydrostat H1) reduced by the efficiency. Is position I or the reverse activated, then H2 operates as a pump and the power is multiplied by the efficiency. etages= Total efficiency of the hydrostatic power path


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ENDIF;

The transmission has three drive positions (slow, fast and reverse) as displayed in Figure 4.2 -1. KISsys displays the power path in Figure 4.2 -2.

Fig. 0 -1 CV-Transmission States. Gears which do not transmit Power are shown as transparent. Secondary Take-offs for the Lubrication Pump and Take-off Axle are not represented.

Top left: Conceptual Diagram

Bottom left: Drive Position I (v=0-17 km/h) (Input coupled)

Top right: Drive Position II (v=17-53 km/h) (Output coupled)

Bottom right: Reverse Gear

P: Hydrostat as Pump M: Hydrostat as Motor Arrows: Power Input (Motor), Power Output (Take-off) Red: Spur gears Blue: Planet gears Yellow: Internal gear Wheels Black: Coupling (open or closed)


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Fig. 0 -2 Kinematics Diagram in KISSsys, here for Drive Position I. Two different Power-off Variants are simultaneously modeled. Also modeled are the secondary Power outputs for the Lubrication Pump (above left) and the Power Take-off Shaft (bellow left).

Red Arrows: Power / motive power transmission Black Lines: Active connection without motive power transmission Gray Lines: Inactive Connection (e.g. open Coupling)

Efficiency Calculation Modern hydrostatic power split gearings have high efficiencies similar to those of manual ones. This is achieved, on the one hand, due to the relatively low hydrostatic power element and, on the other hand, through hydrostats with a high swivel angle. Here, to a great extent, two different operating ranges will be differentiated in both described transmissions in order that the advantages of the manual shifting (higher efficiency) be combined with those oft he CV-Transmission (continuous transmission ratio In KISSsys, the efficiency calculation takes into consideration the gear efficiency as well as the efficiencies of the hydrostatic components. In principle, the friction losses in bearings and seals and the churning losses that could be taken into consideration in the calculation but are ignored. In KISSsoft, the gear efficiencies can be estimated but, in this project they have to be input by hand (Figure 4.3 -2, 98.5 % per gear mesh).


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The hydrostatic load path efficiency is stored in a table of the Model; it will not be calculated but will be supplied by the hydrostat manufacturer. The volumetric and pressure efficiencies will be combined in a unique efficiency value.

Fig. 0 -3 Resulting Efficiency and Hydrostatic Power Share

Model Limitations Besides the already mentioned advantages and functions, the Model has also some limitations which are worth to mention:

- Dynamics: KISSsys does not allow dynamic analyses (no vibration analysis) - Transient Procedures: KISSsys only allows a quasi static system examination - Tooth Contact Graph Calculation: not foreseen in KISSsys - Bearing Calculation: the calculation is based upon the bearing load rating and not

upon the internal bearing geometry

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Calculation of the individual Components

Calculation Flowchart Figure 4.3 -1 displays the Stress Analysis work flowchart using KISSsys

Fig. 0 -1 KISSsys Calculation Flowchart

CALCULATION WITH LOAD

SPECTRA

READ SINGLE

LOAD-STEP FROM

COLLECTIVE

ENTER NOMINAL AND SHIFT SETTINGS

THROUGH USER INTERFACE

SET SHIFTS

CALC KINEMATICS

SAFETY FACTORS FOR SHAFTS AND GEARS, BEARING

LIFETIMES

SET SHIFT AND INPUT

CALC KINEMATICS FOR LOAD STEP n FROM

SPECTRA

n=n+1

CALC BEARING

CALC BEARING LIFETIME

DO UNTIL n=N

LOAD SPECTRA FOR GEAR

PAIR 1


PAIR 2

SAFETY FACTORS FOR GEAR

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SAFETY FACTORS FOR GEAR

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GEARBOX WITH k GEAR PAIRS / PLANETARY GEAR SETS

NOYES

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YES

LOAD SPECTRA WITH N STEPS AND INFORMATION ON -LOADS (SPEED,

POWER AND TORQUE) -STATUS OF COUPLINGS

READ STEP n

READ SINGLE LOAD STEP

FROM

SAFETY FACTORS FOR GEARS, SHAFTS AND

BEARING LIFETIMES FOR A NOMINAL LOAD

DISPLAY IN KISSsys EXPORT KISSsoft EXPORT TO OTHER FILES (.csv, .txt)


PAIR k

SAFETY FACTORS FOR GEARS AND BEARING LIFETIMES FOR THE

INDIVIDUAL GEAR PAIRS CALCULATED WITH A

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LIFETIMES FOR BEARINGS CALCULATED

FROM LOADSPECTRA


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The Calculation Model allows the calculation - with a nominal load - with a load spectrum - with a single load from the load spectrum.

Results will be displayed either directly in KISSsys in tabular form or exported as text, for instance, to Excel. Safeties, life times as well as individual damages will be identified. An important basic functionality is that, from the kinematics, KISSsys calculates all forces, torques and motive powers and passes these load data as input to KISSsoft. Afterwards, the individual KISSsoft calculations are carried out and the results are sent back to KISSsys for the purpose of creating a clear display. Globals -settings that are valid for all KISSsoft calculations- such as, for instance, Lubricant temperature (used for all gear and bearing calculations) can be extracted from a table, Figure 4.3 -2.

Fig. 0 -2 Calculation Parameter Input

Lifetime Calculation The user can select between the following calculation methods:

- Shafts: DIN 743 or FKM Norms. For shafts, no operational fatigue strength proof is produced but only a fatigue strength proof for each load step of the load spectrum.

- Bearings: with load ratings, with or without lubrication influence - Gears: DIN 3990, ISO 6336 or AGMA 2001 - Especially for the calculation of ring gears, a 60º Tangent can be used in the proposed

value in order to determine the proof point. The necessary settings for the calculations can mostly be extracted from the table in the Figure 4.3 -2. The Lifetime calculation should be carried out with the load spectrum shown in Figure 4.3-2.


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The Collective contains data for primary soil processing (high torques), secondary soil processing (low torques) and transport duties (high speeds). Both the Collective and KISSsys use the coupling status, codes K1 to K4, “1” meaning that the coupling is activated / closed and “0” open. Additionally, the Collective defines number of revs, torques and efficiencies for the hydrostats. With them, it is possible to control the transmission kinematic status (shift position) using the Collective.

Cl. Application Type

Action Type

Speed

km/h

Share of Time

(%)

Average Transmission

Load (%) max. P

Motor Number of Revs

Take-off Load

(%) max. P

Calculation Speed km/h

Max. Torque 3.)

1. Traction in Field 79 Primary soil work Furrow ploughing

1.1 Land ploughing 1.2 Disk harrow 1.3 Grubber

1.4 Subsoil Tiller

Secondary soil work

Seedbed combination

1.10 1.11 1.12

2. Power-off work 6 Secondary soil work

2.1 Rotary harrow 2.2 Dutzi System 3. Transport 10 Two-axle Trailer 50 3.1 Start Slide limit 3.2 3.3 3.4 One-axle Trailer 50 3.5 Start Slide limit 3.6 3.7 3.8 4. Reverse 2.) 6

Fig. 0 -3 Load Spectrum for the Design of the Tractor Transmission


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Fig. 0 -4 Collective’s Conversion in KISSsys

Lifetime calculation for gear toothing differentiates between damages on both flanks. However, for the roots, it will not be differentiated between traction- and compression strengths, this being a conservative assumption. The high strength amplitudes by torque reversal cannot be considered correctly in the calculation with the collective. This circumstance can be compensated with a reduced Kwb value.

Results

Operational Fatigue Proof: Influence on the Construction The calculated lifetimes for bearings (L10) are shown in a table (Figure 5.1 -1). It has been verified that some bearings do not reach the required 10,000 hour lifetime. For bearings showing an insignificant deviation from the required lifetime (reaching, at least, half of the lifetime) the solution could be the use of special bearings with a higher load rating (for instance, Explorer series). For the two most external bearings on the hydrostat shafts, in which the lifetimes present a difference factor of five and ten respectively, bearings with a bigger external diameter must be used leading to a modification of the cast case. Hydrostats


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Fig. 0 -1 Roller Bearing Lifetime (the Hydrostats are schematically displayed)

For the shafts, no operational fatigue proof is given; instead, a lifetime proof (infinite life) according to DIN 743 will be carried out for each load step in the collective. Figure 5.1 -2 shows the reserves against the required security with Sfreq=1.50 for one shaft (with five selected cross sections). The calculated reserves are altogether greater than zero.

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Load level from spectra [-]

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Section AASection BBSection CCSection DDSection EESection FF

Fig. 0 -2 Reserve R against the required Security Sfreq=1.5 (R=S/Sfreq-1) of a Hydrostat Shaft (above, right, with the Cross Sections concerned).

For the toothing, it showed that, the required lifetime (at the root) of Planet Z2 on the motor side, (Figure 3.1 -3) as well as for the sun Z1, at the root, connected to the motor was not achieved. There were two possible solutions under discussion (described here the one for Z1):

1) Solution I: Gear teeth with α=17.5˚, use of a higher resistant material and shot-peening of the root area

2) Solution II: Gear teeth with Pressure Angle α=22.5˚ and a chosen Addendum modification distribution in order to maximise the Root stress.

Preference was given to the first solution for having a contact ratio higher than the second and because, concerning noise level, it ran clearly better.


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Fig. 0-3 Sun Gear z1, left: Solution I, right: Solution II.

Component suppliers’ calculations (for instance, for bearings) can thus be quickly reconstructed and submitted to a plausibility check. In the case of the critical bearing of both hydrostatic shafts, a comparison of the suppliers’ calculation showed that, the error in the calculated Lifetime (KISSsoft calculation with bearing ratings) lies within a 20 % value. Compared to the high effort for calculating, this precision is absolutely sufficient. It is also planned to optimise the hydrostats neutral positions through an automatic parameter variation, in order to increase the lifetime of the bearing of the hydrostats shafts. The forces resulting from the swung-out hydrostats, when acting upon the hydrostats shafts overlap with the teeth forces. Depending upon the direction of the individual force vectors, this can lead to either a higher or a lower bearing load. The objective is to minimise the resulting forces by varying the hydrostats neutral positions. This parameter variation may be programmed with little effort in KISSsys with the integrated programming language. However, it should be noted that the packaging only permits little freedom on assembling the hydrostats.

Load Spectrum Concentration Another goal is to reduce by a factor of KLT the test duration, Ttest, as compared to the requested operational lifetime, Lrequest. The evaluation of the damage distribution (for instance, for the bearing of a hydrostat shaft, see Figure 5.2 -1) shows that many of the load spectrum levels (for instance, levels 8-12, 14-16) could be ignored because they only cause irrelevant single damages to the critical components. This leads to a –still unsatisfactory- reduction of about 12 % of the duration of the load spectrum. In order to further reduce the test duration, the test load level must be increased or a full load spectrum must be used instead. The load spectrum concentration tasks were not yet ready at the time of printing.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18FAG NU2208EFAG 32214ATimken JW7049-JW7010

0.00

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Fig. 0 -4 Isolated Damage Distribution for three Bearings in a Hydrostatic Shaft. There is a similar Graph for the critical Gear Toothing.

Sales Assistance The mention and the use of the calculation model in talks with suppliers and potential customers had, no doubt, resulted in a positive feedback. The examination of the basis of calculation and the calculation model made available to the end-user inspires confidence in the supplier. The sales force reaction time to technical inquiries can be drastically shortened using this calculation model, since a Lifetime calculation with some previous parameter adjustment (for instance, other bearings, changed toothing, other load spectrum, etc.) will take very little time –less than an hour-. With it, the sales force contact with technically versed customers will be enormously simplified.

Acknowledgments The authors thank the company MALI Special Vehicles Ltd. For the excellent and interesting cooperation in the described project as well as for the readiness to support the development of this publication.

Bibliography [1] K. Th. Renius, Hydrostatische Fahrantriebe für mobile Arbeitsmaschinen, VDI

Bericht 1793 [2] G. Gavioli, Agricultural tractor powertrains: trends and challenges, Proceedings of 3rd

AVL International Commercial Powertrain Conference, 2005 [3] H. Reiter, Latest tractor drivetrain technology – update and opportunities, Proceedings

of AVL International Commercial Powertrain Conference, 2003 [4] F. X. Moser, Three different industries sharing the same powertrain technology – an

opportunity for synergies? , Proceedings of 3rd AVL International Commercial Powertrain Conference, 2005

Bearing 1 Bearing 2 Bearing 3

Documents

KISSsys Application: Evaluation of Load Spectra for a CV … · 2020-03-05 · KISSsys Tractor CV-Transmission Model 3 from 17 QUALITY SWISS through a good hydrostatic power split