Modelling of Power Losses in Vehicle Transmission Systems

Transcription

1 Modelling of Power Losses in Vehicle Transmission Systems The Cooperation Project between IMS and Romax Technology Source: [Aufgerufen am ] Overall Ye Shen, M.Sc Research Associate Institute for Mechatronic Systems in Mechanical Engineering, Technische Universität Darmstadt, Germany Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering

2 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 2

3 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 3

4 Motivation o o o Research status No standard process to predict overall efficiency of a complete vehicle transmission Focused only on single transmission components (single gear pair or single shaft) Many parameters may hardly be measured directly What to do Developing a platform to Be possibly applied to different types of transmissions in a flexible way Compare several different products from different OEMs or suppliers in parallel Developing optimal systematic models for predicting the efficiency of a complete transmission based on the latest researches and Romax Using experiment data to Isolate each power loss phenomenon Identify transmission parameters Modify the developed models Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 4

5 Motivation Projects Project starts at Feb Cooperation between Romax Technology and IMS, TU Darmstadt Phase I Literature Reviewing about transmission power losses Collecting basic Romax modelling know-how Comparing and selecting power loss models Phase II modelling a complete gearbox system in Romax Building mathematical models from literature and Romax models Identifying the physical parameters from experimental data Phase III Optimizing the power loss model Applying the optimal model to other types of transmissions Verifying to set up the general efficiency modeling method Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 5

6 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 6

7 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission General Gear Mesh Drag Gear Blank Drag Bearings Power Loss Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 7

8 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission General Gear Mesh Drag Gear Blank Drag Bearings Power Loss Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 8

9 Phase I: Power Loss mechanisms inside the gearbox General - Separated power loss elements Oil shearing in gaps Source: Daimler Source: K. Michaelis, Influence factors on gearbox power loss Drag losses by lubrication Sliding/rolling friction Gear Mesh Drag Gear Blank Drag Source: Beaudaniels-illustration.com. Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 9 Source: Bloch, Heinz. "Lubrication Strategies for Electric Motor Bearings." Machinery Lubrication (2004): 72.

10 Phase I: Power Loss mechanisms inside the gearbox General - Models applied from literature Power Loss Elements Gear mesh drag Gear blank drag- Churning loss Bearings Power loss Literature ISO Gears Thermal capacity Part 2: Thermal load-carrying capacity Anderson s Simplified Model Anderson, Neil E., and Stuart H. Loewenthal. "Design of spur gears for improved efficiency." Journal of Mechanical Design (1982): Integration on the teeth face ANDERSON, Neil E.; LOEWENTHAL, Stuart H. Spur-Gear-System Efficiency at Part and Full Load. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CLEVELAND OHIO LEWIS RESEARCH CENTER, ISO Mauz Hydraulische Verluste von Stirnradgetrieben bei Umfangsgeschwindigkeiten bis 60 m/s. Institut für Maschinenkonstruktion und Getriebebau, Universität Stuttgart, Changenet Changenet, Christophe, and Philippe Velex. "A model for the prediction of churning losses in geared transmissions preliminary results." Journal of Mechanical Design (2007): ISO SKF 2004 Rolling Bearing Catalogue Applied in RxD? Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 10

11 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission General Gear Mesh Drag Gear Blank Drag Bearings Power Loss Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 11

12 Phase I: Power Loss mechanisms inside the gearbox Gear Mesh Drag - Models Model Integration on the Teeth Face Instantaneous power loss due to sliding/rolling friction on the tooth face P s x = V s x f x F n x V s -Sliding Speed, f-coefficient of friction, F n -Tooth normal force P R x = V R x F R x V r -Rolling Speed F r -Rolling friction force Model Anderson s In RxD applied Power loss due to sliding and rolling friction on the tooth face Evaluation point: 1/4 of the contact patch Average velocity at evaluation point for simplification Model ISO The model applied also in Rxd Power loss due to rolling friction on the tooth face is neglected Power loss due to sliding friction on the tooth face Friction is constant f m = f m (T, b, n, d, η oil, R a, X L ) A x P S x dx = x V s (x) f(x) F n (x) dx = H v f m P in Specific points on the Path of Contact B P C D Rolling Power Loss (W) Sliding Speed V s (m/s) l 4 V S Contack Contact Path(m) l Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 12

13 Phase I: Power Loss mechanisms inside the gearbox Gear Mesh Drag - Comparison ISO Anderson Integration on the Teeth Face ISO Anderson Integration on the Teeth Face Power Loss P(W) z1=16 z2=83 m=1.25 an=20 Tin=20Nm Tin=10Nm Power Loss P(W) z1=31 z2=96 m=1.6 an=17.5 Tin=20Nm Tin=10Nm 50 Tin=2,5Nm 50 Tin=2,5Nm Input Speed n(rpm) Similar input speed, low input torque x Input Speed n(rpm) For different gear pairs the tendency of results is different The simplification of the model and different friction models may be the reason Relative small portion of rolling friction power loss in gear meshing x 10 4 Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 13

14 Phase I: Power Loss mechanisms inside the gearbox Gear Mesh Drag - Summary The integration model Taking more calculation time Containing more factors of gear meshing like rolling frictional force Possible to employ different frictions models and compare them The ISO Model Applying same principle as above The Roughness plays a role in the calculation of friction Only based on the constant sliding friction coefficient The Anderson s simplified model Easily but too roughly Always bigger than the results of the integration model Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 14

15 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission General Gear Mesh Drag Gear Blank Drag Bearings Power Loss Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 15

16 Phase I: Power Loss mechanisms inside the gearbox Gear Blank Drag - Models Model ISO The model applied in RxD Simplified Model for gear set T Model Changenet = C Sp C 1 e C 2( V t V 0 ) Similar to the model applied in Romax Terekhov Model based on Boness.R(1989) T pl = 1 2 ρ 1,1047n 2 R p 3 S m C m C m dimensionless drag torque based on Dimensional analysis C m = f m n, b, h e, V oil, R e, F r Boness, R. J., 1989, Churning Losses of Discs and Gears Running Partially Submerged in Oil, Proc. ASME Int. Power Trans. Gearing Conf., Chicago,Vol.1, pp Model Mauz Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 16 The model not applied in RxD Empirical model T pl = 1, η oil 1,255 Ra η 0 R 0 C wz C wa C M C V η oil v t A B Calculation on each gear and combined effects Lots of factors taken account Turning direction, oil viscosity, housing effect, oil volume Additional oil squeezing torque is modeled Some factors hardly to be measured validity range is limited Normal module 3-6mm circumferential speed m/s Tip diameter mm

17 Phase I: Power Loss mechanisms inside the gearbox Gear Blank Drag - Comparison Power Loss P(W) ISO Mauz Changnet z1=24 z2=101 m=1.6 an=17.5 he1= he2= z1=31 z2=96 m=1.6 an=17.5 he1= he2= ISO Mauz Changnet Input Speed n(rpm) Higher h e /(z 2 m) tends to achieve larger difference between models results x Input Speed n(rpm) Model ISO apply fewest parameters but always overestimate the power loss of oil churning Results of Model from Mauz on the right shows 1/3 of the value of Model ISO x 10 4 Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 17

18 Phase I: Power Loss mechanisms inside the gearbox Gear Blank Drag - Summary Model ISO Simplifying the model so only several parameters are applied No effects of turning direction are considered The direction leads to totally different results The factor of housing in the model is hard to be estimated and not suitable for vehicle transmission Model of Mauz His experiments try to cover all the factors that influence the power losses due to churning oil Several factors are hard to be estimated and measured Those factors are important, for example those related to housing effects Model of Changenet A lot of research taking the same mathematical form Based on dimensional analysis to adjust the C m fomular The Influence from the housing of the gearbox shall also be added to the model Shall be modified to calculate the power loss when pinion and gear are meshing and immersed in lubrication Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 18

19 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission General Gear Mesh Drag Gear Blank Drag Bearings Power Loss Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 19

20 Phase I: Power Loss mechanisms inside the gearbox Bearings Power Loss - Models Model SKF 2004 The model applied in RxD Model based on SKF1994 T pl = T B0 + T B1 T B0 load independent bearing power losses T B1 load dependent bearing power losses Model SKF 2004 The model not applied in RxD Model based on SKF 2004 catalogue T pl = T rr + T sl + T drag + T seal T rr Rolling frictional torque T sl Sliding frictional torque T drag Drag losses for oil bath lubrication T seal power loss from sealing Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 20

21 Phase I: Power Loss mechanisms inside the gearbox Bearings Power Loss Comparison Power Loss P(W) ISO SKF 2004 Bearing on input shaft dm= 32 mm C0/P0=10,5 H=0mm Power Loss P(W) ISO SKF 2004 Bearing on output shaft dm= 38,5 mm C0/P0=9 H=14mm Input Speed n(rpm) Input Speed n(rpm) For different size of bearings the two models only have similar results at low input torque At high torque input the SKF 2004 model s results are far bigger than the ISO s Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 21

22 Phase I: Power Loss mechanisms inside the gearbox Bearings Power Loss - Summary Model ISO Some important factors rely on the table given out by the ISO Even for some factors have to be estimated Model SKF 2004 Relying on the table to find the value of factor lubrication conditions are involved in the model which could be interesting to be identified According to the simulation results the sliding friction domains the power loss from bearing Other models for sliding friction in bearing have to be compared Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 22

23 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 23

24 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Simulation on a 2-speed transmission in an electric vehicle Comparison with the measurement Parameter identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 24

25 Phase II: Simulation, Verification and Parameter Identification Simulation on a 2-speed transmission in an electric vehicle Model ISO Gear Mesh Drag : ISO Gear Blank Drag: ISO Bearings Power Loss: ISO Combined models Gear Mesh Drag : The integration model Gear Blank Drag: Model of Changenet Bearings Power Loss: Model SKF 2004 Overall Efficiency (%) Overall Efficiency (%) Comparison: Far less estimated power loss by the combined models at Low torque input area Estimated efficiency by the combined models all better than by ISO Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 25

26 Phase II: Simulation, Verification and Parameter Identification Simulation on a 2-speed transmission in an electric vehicle Model ISO Segment power losses(%) Input Torque 5 Nm Combined models Segment power losses(%) Input Torque 5 Nm Input Torque 15 Nm Input Torque 15 Nm Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 26

27 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Simulation on a 2-gear transmission in an electric vehicle Comparison with the measurement Parameter identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 27

28 Phase II: Simulation, Verification and Parameter Identification Comparison with the measurement The Deviation of Efficiency Between Experiment and Simulation(%) Model ISO Combined models Comparison: Lager difference by ISO ranging from (0.2375% %) Difference by combined models ranging from ( % ~ %) Better overall calculation by combined models Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 28

29 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Simulation on a 2-gear transmission in an electric vehicle Comparison with the measurement Parameter identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 29

30 Phase II: Simulation, Verification and Parameter Identification Parameter identification Selected input parameters Oil viscosity and oil level The temperature varied during the experiment The oil level may change R.M.S. of All the Deviation of Efficiency (%) Combined models Method Original 6.4mm 2 /s the R.M.S of all the efficiency deviation between measurement and simulation results Results Identifying the oil viscosity and relative oil level through minimized R.M.S Minimum 7.4mm 2 /s Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 30

31 Phase II: Simulation, Verification and Parameter Identification Parameter identification through different models R.M.S. of All the Deviation of Efficiency (%) Model ISO Combined models Minimum 10mm 2 /s Minimum 7.4mm 2 /s - the optimized parameter is on the boundary - Less relative to the viscosity - Low robust + Shorter calculation time Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 31 + the optimized parameter is within the measurement boundary + more relative to the viscosity + High robust - Langer calculation time

32 Phase II: Simulation, Verification and Parameter Identification Simulation with identified parameters The Deviation of Efficiency Between Experiment and Simulation(%) Model ISO Combined models Combined with identified models parameters Opitimizing the efficiency at low input toque area All deviations within [-4% +3%] Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 32

33 Number of the points Phase II: Simulation, Verification and Parameter Identification Simulation with identified parameters The Deviation of Efficiency Between Experiment and Simulation(%) Combined models with identified parameters Range of the deviation of the efficiencies The deviation points show close to normal distribution Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 33

34 Contents Motivation Phase I: Power Loss Mechanisms Inside the Transmission Phase II: Simulation, Verification and Parameter Identification Conclusion and Perspective Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 34

35 Conclusion Conclusion o Applying and comparing models of different power losses sources in transmission from literature o Applying the selected models on a gearbox of an electric vehicle o Comparison with the ISO models and validation with experiment results o Parameter identification of the bulk oil viscosity and oil immersion level o By the Combined models more approximate to the test data and more robust with the parameters, bulk oil viscosity and oil immersion level Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 35

36 Perspective Perspective Some models have to be updated (e.g. gear tooth sliding friction model) and to be added (e.g. synchronizer power loss model) More parameters have to be identified to obtain optimal overall efficiency map Modification of experiments for more accurate results with help of parameter identification Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 36

37 Thank you for your attention! Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 37

38 Back Up Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 38

39 Contents Modeling and calculating in RomaxDesigner Building Mathematical model in Simulink/Matlab Separated power loss elements Gear Meshing Oil Churning Bearing Test Bench Akabench and Tutorium Summary and Outlook Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 39

40 Building Mathematical model in Simulink/Matlab Gear Meshing-Integration on the Teeth Face Similar theory as the model applied in Romax Microgeometry based Instantaneous power loss due to sliding friction on the tooth face P s x = V s (x) f(x) F n (x) V s -Sliding Speed, f-coefficient of friction, F n -Tooth normal force Instantaneous power loss due to rolling friction on the tooth face P R x = V R (x) F R (x) V r -Rolling Speed F r -Rolling friction force Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 40

41 Building Mathematical model in Simulink/Matlab Gear Meshing-Integration on the Teeth Face-Sliding Friction Symbol Parameter Available in Romax? d a Tip diameter a Working Center Distance z Teeth number m n Normal module α n Normal pressure angle β Helix angle b Tooth width Specific points on the Path of Contact A B P C D Sliding Speed V t (m/s) V s x Contact Path(m) Rolling Speed V r (m/s) V r x Contact Path(m) Tooth Normal Force F n (N), F n (x) Contact Path(m) Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 41

42 Building Mathematical model in Simulink/Matlab Gear Meshing-Integration on the Teeth Face-Sliding Friction Symbol V s x, V r x, F n (x) Parameter Available in Romax? η oil Viscosity of oil Coefficient of friction f(x) Power Loss due to sliding friction P s x Length of Contact Path Sliding Power Loss (W) P s x Contact Path(m) 10 Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering Contact Path(m)

43 Building Mathematical model in Simulink/Matlab Gear Meshing-Integration on the Teeth Face-Rolling Friction Specific points on the Path of Contact D B P C Assumption: Only in the viscous-elastic lubrication regime 5.7 x A Rolling Force(N) F R x Flim Thikness(m) Contact Path(m) Contact Path(m) CROOK, A. W. The lubrication of rollers IV. Measurements of friction and effective viscosity. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1963, 255. Jg., Nr. 1056, S Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 43

44 Building Mathematical model in Simulink/Matlab Gear Meshing-Integration on the Teeth Face-Rolling Friction 34 Rolling Power Loss (W) P R x Power Loss due to Rolling friction P R x Lenght of Contact Path Contact Path(m) Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 44

45 Building Mathematical model in Simulink/Matlab Gear Meshing-Anderson s Simplified Model the model applied in Romax Anderson Power loss due to sliding and Rolling friction on the tooth face Evaluation point: 1/4 of the contact patch 34 Average velocity at evaluation point for simplification 33 Rolling Power Loss (W) Sliding Speed V s (m/s) l 4 V S l Contack Path(m) Contact Path(m) Rolling Power Loss (W) Rolling Speed V r (m/s) V R Contack Path(m) Contact Path(m) Apply the two velocity to the formulas to get average results Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 45

46 Building Mathematical model in Simulink/Matlab Gear Meshing-ISO The model applied also in Romax Power loss due to rolling friction on the tooth face is neglected Power loss due to sliding friction on the tooth face Friction is constant f m = f m (T, b, n, d, η oil, R a, X L ) x P S x dx = x V s (x) f(x) F n (x) dx = H v f m P in Symbol Parameter Available in Romax? d a Tip diameter a Working Center Distance Power loss coefficient H v z Teeth number m n Normal module Friction coefficient f m α n Normal pressure angle β Helix angle b Tooth width η oil Viscosity of oil X L Lubricant factor R a Average roughness Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 46

47 Building Mathematical model in Simulink/Matlab Gear Meshing-Model Results Comparison ISO Anderson Integration on the Teeth Face ISO Anderson Integration on the Teeth Face Power Loss P(W) z1=16 z2=83 m=1.25 an=20 Tin=20Nm Tin=10Nm Power Loss P(W) z1=31 z2=96 m=1.6 an=17.5 Tin=20Nm Tin=10Nm 50 Tin=2,5Nm 50 Tin=2,5Nm Input Speed n(rpm) Similar input speed, low input torque x Input Speed n(rpm) For different gear sets the tendency of results is different The simplification of the model and different friction models may be the reason Relative small portion of rolling friction power loss in gear meshing x 10 4 Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 47

48 Building Mathematical model in Simulink/Matlab Gear Meshing-Summery The integration model Taking more calculation time No roughness on the tooth face taken into accounts Containing more factors of gear meshing like rolling frictional force Possible to employ different frictions models and compare them The ISO Model Applying same principle as above The Roughness plays a role in the calculation of friction Only based on the constant sliding friction coefficience The Anderson s simplified model Easily but too roughly Always bigger than the results of the integration model Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 48

49 Contents Modeling and calculating in RomaxDesigner Building Mathematical model in Simulink/Matlab Separated power loss elements Gear Meshing Oil Churning Bearing Test Bench Akabench and Tutorium Summary and Outlook Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 49

50 Building Mathematical model in Simulink/Matlab Oil Churning - ISO The model applied also in Romax Simplified Model for gear set Original for industry gearbox (Simple layout) No account taken of the turning direction of gears No account taken of viscosity Symbol Parameter applied Available in Romax? H c H e2 H e1 H max z Teeth number m n Normal module β Helix angle H c Height of point of contact H e Tip circle immersion depth A g Cross-sectional area U m Circumference of the foundation b Tooth width n Input speed A g A g Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 50

51 Building Mathematical model in Simulink/Matlab Oil Churning - Mauz The model applied not in Romax Empirical model T pl = 1, η oil 1,255 Ra η 0 R 0 C wz C wa C M C V η oil v t A B Calculation on each gear and combined effects Lots of factors taken account Turning direction, oil viscosity, housing effect, oil volume Additional oil squeezing torque is modeled Some factors hardly to be measured validity range is limited Normal module 3-6mm circumferential speed m/s Tip diameter mm Symbol Parameter applied Available in Romax? z Teeth number m n Normal module β Helix angle H e Tip circle immersion depth b Tooth width η oil Viscosity of oil n Input speed w dir Turning direction Q v Target gearbox oil ratio s wz s wa distance from wall in the dir. oil outlet distance from wall in the dir. oil inlet Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 51

52 Building Mathematical model in Simulink/Matlab Oil Churning - Mauz Immersion depth are adjusted by added h Gear immersion area A B Module factor C M = m n /m 0 1/7 m 0 = 0,0045mm Factor of distance from wall C wz, C wa Judge by the distance s, and tip radius R a and circumferential speed v t s R a < 1.3 and v t > 10 m s Otherwise the value is 1 H c H e2 h H e1 H max Target gearbox oil ratio Q v = V oil V G V oil is the volume of oil V G is the volume of gearbox Quasi equaling to the ratio of area Oil Level A top A bot Q v = A bot A bot+atop oil volume factor C V Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 52

53 Building Mathematical model in Simulink/Matlab Oil Churning - Changenet Similar to the model applied in Romax Terekhov Model based on Boness T pl = 1 2 ρ 1,1047n 2 R p 3 S m C m S m surface area of contact between the gear and the lubricant Gear immersion area A B C m dimensionless drag torque based on Dimensional analysis C m = f m n, b, h e, V oil, R e, F r C m (-) Symbol Parameter applied Available in Romax? z Teeth number m n Normal module β Helix angle H e Tip circle immersion depth b Tooth width η oil Viscosity of oil n Input speed w dir Turning direction V oil Oil volume ρ Oil density Reynold number R e = 1,1047nR p b/η oil Input Speed n(rpm) x 10 4 decides the form of C m Boness, R. J., 1989, Churning Losses of Discs and Gears Running Partially Submerged in Oil, Proc. ASME Int. Power Trans. Gearing Conf., Chicago,Vol.1, pp Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 53

54 Building Mathematical model in Simulink/Matlab Oil Churning - Model Results Comparison Power Loss P(W) ISO Mauz Changnet z1=24 z2=101 m=1.6 an=17.5 he1= he2= z1=31 z2=96 m=1.6 an=17.5 he1= he2= ISO Mauz Changnet Input Speed n(rpm) Higher h e /(z 2 m) tends to achieve larger difference between models results x Input Speed n(rpm) Model ISO apply fewest parameters but always overestimate the power loss of oil churning Results of Model from Mauz on the right shows 1/3 of the value of Model ISO x 10 4 Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 54

55 Building Mathematical model in Simulink/Matlab Oil Churning - Summary Model ISO Simplifying the model so only several parameters are applied No effects of turning direction are considered The direction leads to totally different results The factor of housing in the model is hard to be got and not suitable for vehicle transmission Model of Mauz His experiments try to cover all the factors that influence the power losses due to churning oil Several factors are hard to got and measured Those factors are important for example those related to housing effects Model of Changenet A lot of research taking the same form Based on dimensional analysis to adjust the C m foumular The Influence from the house of gearbox shall also be added to the model Shall be modified to calculate the power loss when pinion and gear are meshing and immersed in lubrication Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 55

56 Contents Modeling and calculating in RomaxDesigner Building Mathematical model in Simulink/Matlab Separated power loss elements Gear Meshing Oil Churning Bearing Test Bench Akabench and Tutorium Summary and Outlook Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 56

57 Building Mathematical model in Simulink/Matlab Bearings - ISO The model applied also in Romax Symbol Parameter applied Available in Romax? Model based on SKF1994 T pl = T B0 + T B1 T B0 load independent bearing power losses T B0 = 10 7 f 0 η oil n 2/3 d m 3 η oil n f 0 d m 3 η oil n < 2000 f 0 depends on the lubrication type η oil Viscosity of oil n Input speed d m Mean bearing diameter f 0, f 1 Coefficients for bearing losses C 0 Static load rating P 0 Equivalent static bearing load F a Bearing thrust load F r Radial bearing load T B1 load dependent bearing power losses T B1 = f 1 P 1 a d m b a, b are 1 except the rolling bearings Bearing Property f 1 = f P 0, C 0 Romax P 1 = f(f a, F r ) Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 57

58 Building Mathematical model in Simulink/Matlab Bearings SKF 2004 The model applied not in Romax Model based on SKF 2004 catalogue T pl = T rr + T sl + T drag T rr Rolling frictional torque T rr = φ ish φ rs G rr η oil n 0,6 φ ish Inlet shear heating reduction factor φ ish = f(n, d m, η oil ) φ rs kinematic replenishment/starvation reduction factor φ rs = f(k rs, K Z, n, d m, η oil ) G rr Rolling friction Factor based on bearing type Symbol Parameter applied Available in Romax? η oil Viscosity of oil n Input speed d m Mean bearing diameter K rs K Z replenishment/starvation constant bearing type related geometric constant Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 58

59 Building Mathematical model in Simulink/Matlab Bearings SKF 2004 T sl Sliding frictional torque T pl = G sl μ sl G sl Sliding friction factor based on bearing type G sl = f(d m, F a, F r ) μ sl sliding friction coefficient considering the full-film and mixed lubrication conditions μ sl = φ bl μ bl + (1 φ bl )μ EHL - φ bl weighting factor for the sliding friction coefficient equation φ bl = f(n, d m, η oil ) - μ EHL i.e. 0,1 for lubrication with transmission fluids - μ bl generally 0,15 Symbol Parameter applied Available in Romax? η oil Viscosity of oil n Input speed d m Mean bearing diameter μ EHL μ bl sliding friction coefficient in full-film conditions coefficient depending on the additive package in the lubricant F a Bearing thrust load F r Radial bearing load Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 59

60 Building Mathematical model in Simulink/Matlab Bearings SKF 2004 T drag Drag losses for oil bath lubrication T drag = 0,4V m K ball d m 3 n 2 + 1, n 2 d m 3 nd m 3 f t η oil 1,379 R s V m depends on immersion height K ball The Rolling element related constants K ball = f(i rw, K Z, d m ) f t = sin 0,5t when t = f dm, H [0, n] Symbol Parameter applied Available in Romax? η oil Viscosity of oil n Input speed d m Mean bearing diameter V m Drag loss factor i rw Number of ball rows K Z Bearing type related geometric constant H Oil level R s = 0,36 d M 2 t sin t f A f A = f(d m, K Z ) Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 60

61 Building Mathematical model in Simulink/Matlab Bearings SKF Input Torque= Nm 250 Input Torque= Nm T rr T sl T drag Power Loss P(W) Power Loss P(W) Input Speed n(rpm) Input Speed n(rpm) Sliding frictional torque domains the power loss from bearing Drag torque s influence is only at high speed and low torque input Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 61

62 Building Mathematical model in Simulink/Matlab Bearings Model Results Comparison Power Loss P(W) ISO SKF 2004 Bearing on input shaft dm= 32 mm C0/P0=10,5 H=0mm Power Loss P(W) ISO SKF 2004 Bearing on output shaft dm= 38,5 mm C0/P0=9 H=14mm Input Speed n(rpm) Input Speed n(rpm) For different size of bearings the 2 model only have similar results at low input Torque At high torque input the SKF 2004 model s results far bigger than the ISO s Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 62

63 Building Mathematical model in Simulink/Matlab Bearing- Summary Model ISO Some important factors rely on the table given out Even for some factors estimation has to be made Model SKF 2004 Relying on the table to find the value of factor lubrication conditions are involved in the model which could be interesting to be identified According to the simulation results the sliding friction domains the power loss from bearing Other model for sliding friction in bearing to be found to compare and to identify some vital parameters Y. Shen Sep. 27, 2016 Institute for Mechatronic Systems in Mechanical Engineering 63