Chapter 7: Thermal Study of Transmission Gearbox 7.1 Introduction The main objective of this chapter is to investigate the performance of automobile transmission gearbox under the influence of load, rotational speed and lubrication on multi speed gearbox gear surface. Gear oil SAE 80W-90 was used as gearbox lubricant, for cooling of transmission gearbox for high performance. An assumption has been made at the air-gear oil mist within transmission is under steady state condition, in isothermal equilibrium with the transmission gear oil bath of lubricant. The lubrication in multi speed transmission is subjected to thermoelastohydrodynamic lubrication. The present chapter deals with the thermo-mechanical performance study of multi speed transmission (4 speed, excluding reverse gear) system which combines transient structure analysis of the gear train assembly. The engaged gear teeth pairs transmit torque subjected to thermo-elastohydrodynamic arrangements of lubrication. The study here analyzed transmission in second gear pair. In full torque loading condition the high temperature generated due to meshing action of gears and frictional conditions between the transmission gear train changes the thermo-physical property of gear oil. Transmission gear oil working temperature varies from (-18 to 100) o C. The overall vehicle transmission gearbox performance is governed by the gear oil properties and it also effects the fuel consumption. Transmission gear oil viscosity highly depends on temperature, it varies exponentially and the other properties vary linearly. This research study was performed at high loading 45 Nm, 1500 rpm rotational speed and (100-600) w/m k convection heat transfer variation. At each loading condition the thermal profile of transmission gearbox surface was evaluated using steady state thermal analysis in isothermal equilibrium. The analysis result shows that the gearbox oil thermal properties directly effect the performance and life span of automobile transmission gearbox. ANSYS 14.5 has been used as an analysis tool. The solid model of transmission gearbox assembly was designed using Solid Edge and Pro-E. The validation of Finite Element Analysis (FEA) simulation results was done using experimental results available in literature. In vehicle transmission gearbox assembly gear oil is used as lubricant for cooling of gear train assembly and release the heat to cooling fluid of radiator. Gear oil can perform the cooling function at (-18 to 100) 0 C temperature. Gear oil provides good sealing, friction durability, antifoam and non-corrosive to gear train parts and internal components of gearbox casing. 4- speed transmission gearbox excluding reverse gear was studied for transient structural and thermal characteristics. Researchers have performed various types of studies on transmission gearbox casing, gear train assembly, gear oil properties, role of gear oil for transmission efficiency and flow of lubricant in mini-micro channels heat exchangers. The inclusion of convective heat transfer coefficient is essential in the study of multi speed transmission when dealing with increasing the transmission thermo-mechanical performance. Under isothermal conditions the temperature around transmission gear train was assumed throughout same as bath gear oil. Steady state, isothermal condition reduces the complexity of simulation when considering average convective heat transfer coefficient. 103
7. Modelling of Gearbox Assembly Multi speed transmission (4 speed, excluding reverse gear) has been investigated here. The transmission gear train assembly comprises input shaft, output shaft and lay shaft. Noise, vibration and harness (NVH) with thermo-mechanical performance are the two important design parameters of compact multi speed transmission. Transmission gearbox consists of arrangement of gears and gearbox casing. The designing and assembly was done using solid Edge Solid Edge and Pro-E. All designing parameters were obtained from measurements and drawing sheets. The casing encloses the gear assembly, input, output and lay shaft. In this study only direct drive 4- speed gears were considered. Figure 7.1 shows the full assembly of transmission gearbox of vehicle. The isometric view of vehicle shows casing designed in three parts. The main part covers the gear assembly and other two parts used to enclose the transmission casing. Figure 7. shows 4-speed gear assembly and shafts for deformation analysis. The numerical simulation was performed for the transient structural, thermal analysis of gear train under the influence of load, rotational speed and convection heat transfer coefficient. Gear oil works as gearbox lubricant to cool the gears and transfer the heat through convective process. The overheating of gears reduces the efficiency and life span of gears. The transmission gearbox assembly replacement is costly, so this study focus the thermal prospectus of gearbox so that the life span of a transmission gear train can be increased. FEA simulation works on meshing of objects. The meshed model of gear assembly is shown in Figure 7.3. The gear assembly is meshed using 5, 75, 383 nodes and 3, 39,898 elements (Linear Tetrahedron Element, Tet 4). This research work presents a strong base for the thermal-mechanical analysis of gearbox to increase the performance by understanding the role of gear oil and loading parameters such as torque, rotational speed and average convection heat transfer coefficient. Transmission gearbox components were assigned materials (Qin-man [60]) for accurate analysis of temperature on gearbox surface. Figure 7.1 Heavy vehicle medium duty transmission gearbox assembly. 104
Figure 7. Gearbox assembly of 4-speed transmission gearbox. Figure 7.3 FEA meshed model of gearbox. 105
7.3 Material Properties and Boundary Conditions The teeth in contact causes thin film thickness lubrication, thus a thermo-elastohydrodynamic arrangement of lubrication is expected. The thin film thickness is due to heat generated between meshing teeth pairs, reduces the viscosity of lubricant. The simulation study of transmission model is reported here. The noted point is the isothermal temperature on gear train is assumed to be the temperature of bath of oil. FEA simulation mechanical strength was measured using structural analysis and steady state thermal analysis was performed by applying isothermal temperature of gear oil bath lubricant on gear train. By applying uniform isothermal temperature on gear train, the temperature variation on gears was measured under the effect of heat, friction and gear oil temperature. The dynamic response in terms of stress, strains and deformation was evaluated when vehicle was running on second gear at 1500 rpm and having 45 Nm torque. When vehicle was running on full loading and high rpm the heat generation due to engaged gear pair meshing is very high. High internal temperature around gear train changes the thermophysical properties of gear oil which effects the vehicle performance and service life. In this research work gear oil thermal properties (convective heat transfer coefficient (h) and gear oil temperature) effect was studied on gears surface. In first step 1500 rpm with 45 Nm torque load was applied on second gear assuming average convection heat transfer coefficient varies (100-600) w/m k and gear oil temperature varies in range of (70-80) 0 C. In second step for same loading conditions gear oil temperature was kept in higher range of (80-100) 0 C, by applying these conditions the effect was measured on gear surface in terms of temperature. 7.4 Dynamic Structural Analysis FEA based Ansys 14.5 evaluate the results of structural and steady state thermal analysis. Structural results evaluate the performance of transmission gear train on strength point. Inertia and damping effects was not considered for simulation. When vehicle was running at full loading and 1500 rpm and generates 45 Nm torque. Torque and rotational velocity were applied for full dynamic loading. At maximum torque condition the gear meshing causes heat generation in large value that was studied in this research work. Von-mises stress and strain were mentioned in Figure 7.4. Figure 7.4 (a) the simulation results shows that the equivalent (Von-Mises) stress distribution is within safe limit at its minimum value. The shear elastic strain due to dynamic load shows deformation. This deformation is safe (Figure 7.4 (b)). No high deformation regions were identified. Figure 7.4 structural results show that the gear train design is safe to sustain the applied dynamic load. Transient structural analysis was performed at 1500 rpm when vehicle was on high gearing (third gear selection) and producing 119.31 Nm torque. The time period of full loading was 9 seconds and dynamic behaviour of 4-speed transmission gear box was evaluated. Figure 7.4 (c and d) shows transient results. Figure 7.4 (c) explains the total deformation variation in gears. When gears are in meshing at full loading the red hues region shows stress concentration where deformation is maximum. The blue hues signify the minimum deformation level and light green hues shows the regions where deformation is average. Maximum value of total deformation (red hues) is 0.16 mm within limit. Figure 7.4 (d) shows maximum principal stress variation on 4-speed transmission gearbox. Maximum principal stress available on gears is 5.346e8 Pa. Blue hues show the principal stress variation, which is uniform in nature. A uniform stress signifies that failure chances are less. 106
(a) Equivalent (Von-Mises) stress distribution in gearbox surface. (b) Shear elastic strain distribution in XY plane. (c)total Deformation on gearbox (transient). (d) Maximum Principal Stress variation on gears (transient). Figure 7.4 Dynamic Structural Analysis of transmission gearbox. 107
7.5 Steady State Thermal Analysis The present research work concerns with the transmission assembly of medium duty trucks. In earlier study the authors have considered only gear tooth or simple geometry of transmission but here we have simulated the full assembly to highlight the effects of different operating conditions (load, rotational speed, lubrication). In steady state thermal analysis the effect of gear oil heating was considered. The gear oil temperature varies between (-18 to 100) 0 C. When vehicle is running at 1500 rpm and 45 Nm loading the gear oil temperature may vary (70-100) 0 C. Gear oil temperature variation is highly nonlinear problem totally depends on operating condition and loading. To simulate the gear oil heating a constant isothermal temperature was applied with varying (100-600) w/m k average convective heat transfer coefficient. When gear oil temperature is 80 0 C the performance of transmission fluid is high, and its life span increases. Gear oil cooling is an important medium for release of frictional heat from casing. The studies of gear oil play an important role to improve the efficiency in automotive industry. Gear oil thermo-physical properties depend on temperature and frictional environment inside the transmission. In this research work efforts have been made to measure the surface temperature variation of gearbox surface due to gear oil temperature, frictional condition and dynamic loading under the influence of SAE 80W-90 lubricating gear oil. The properties of SAE 80W-90 are- density 887 kg/m 3 (15.6 0 C), viscosity 139cSt (40 0 C), 15 cst (100 0 C), Viscosity Index 110, flash point 18 0 C, pour point (-7 0 C). A. Gear oil bath temperature (80 0 C) and Average convection heat transfer (h=100-600) w/m k (a) Temperature variation at h = 300 W/m k 108
(b) Temperature variation at h = 400 W/m k (c) Temperature variation at h = 500 W/m k (d) Temperature variation at h = 600 W/m k Figure 7.5 Gearbox surface temperature variation- Isothermal gear oil bath temperature (80 0 C). 109
Finite element analysis used for the structural and thermal simulation of transmission gearbox. The internal temperature of gearbox has an influence on thermal stresses and deformations leads to failure. Figure 7.5 shows the temperature variation at different point of gearbox surface for gear oil bath temperature of 80 0 C. Figure 7.5(a) highlights the temperature variation in gear train assembly at the value of h 100w/m k for convective heat transfer co-efficient (h). Temperature variation is shown in colour code. The minimum temperature is 34.94 k and maximum is 350.01 k. Maximum temperature effect is found on counter shaft right end in red hues, which was fixed in simulation. Red hues signify the maximum temperature change and thermal stress generation portion. In between minimum and maximum temperature 8 another temperatures are shown in figure. The temperature varies very gradually at different points, it can be seen from Figure 7.7. In Figure 7.7, h 100 (1) shows the gradual increment in temperature at different points of gear train. Around second gear pair the temperature and deformation is high. Figure 7.5(b) shows the temperature variation in gear train assembly at the value of h 00w/m k. As the value of h increases there is very small change in temperature profile of gear train. The minimum temperature decreases 0.09 k and increase in maximum temperature of 1.58 K. The temperature profile varies between (34.85-351.59) k. The high temperature region is at same place of fixed portion of right side end of counter shaft. Figure 7.5(c) shows the temperature increment on 3 rd gear. The temperature reached to 350.01 k. On nd gear the temperature is 349k under the influence of h 300w/m k. The temperature profile varies between (34.93-35.03) k. Figure 7.5(d) shows the gear train temperature profile varies (34.9-35.38) k. First gear is in loose meshing and its temperature is 347.1 k and nd, 3 rd gear shows temperature increment and have a value of (349.3-351.33) k. The lay/counter shaft also shows variation of temperature (346.07-35.38) k for h 400w/m k. The 3 rd gear profile shows temperature increment in red hues and this area is prone for thermal stresses more for (h 500w/m k, h 600w/m k ) convective heat transfer coefficient values. In Figure 7.7, h 400 and h 500 shows the gear train temperature profile variation. B. Gear oil bath temperature (100 0 C) and Average convection heat transfer (h=100-600) w/m k (a) Temperature variation at h = 00 W/m k 110
(b) Temperature variation at h = 300 W/m k (c) Temperature variation at h = 400 W/m k (d) Temperature variation at h = 500 W/m k Figure 7.6 Temperature profile variation on gearbox surface- Isothermal gear oil bath temperature (100 0 C). 111
Temperature Measurement (k) For second part of study the gear oil temperature is increased to 100 0 C. Figure 7.6 shows the temperature profile of gearbox surface at gear oil temperature of 100 0 C. Figure 7.6 (a) shows the temperature profile of gear train assembly at h 100w/m k convective heat transfer coefficient (h) value. The minimum temperature is 34.81 k and maximum is 364.0 k. Maximum temperature effect is found on same place as for h 100w/m k at 80 0 C on counter shaft right end in red hues. Red hues shows hot areas subjected to thermal stresses and deformation. Figure 7.8, h 100 shows the gradual increment in temperature profile of gear train at different points. Figure 7.6 (b) explains the temperature variation in transmission gear train at h 00 w/m k. As the value of h increases there is increase in temperature of gear train by 4.76 k, mention by red hues. The high hues temperature region is found at fixed portion of right side end of counter shaft. Figure 7.6 (c) shows dark yellow hues on 3 rd gear. The dark yellow hues designate increment in temperature. The maximum value of temperature reached to 370.09 k. The right side fixed counter shaft end temperature is maximum for h 300w/m k. The temperature profile varies between (34.8-370.09) k. In Figure 7.8, h 300 (3) shows the temperature linear temperature variation at different point on gear train. Figure 7.6 (d) shows gradual change in temperature. Gear profile of nd and 3 rd shows red hues of hot areas. In Figure 7.8, h 600 shows the gear train temperature profile variation. 7.6 FEA Results and Validation Multi speed transmission gearbox and gear oil analysis is highly nonlinear problem. From FEA analysis (Figure 7.5 and 6.7), when h is 100 w/m k and gear oil temperature is constant at 80 0 C, the gear train profile temperature varies very gradually and linearly. As we increase the value of convective heat transfer coefficient to 00 W/m k the difference in maximum temperature is only 1.58 k. Further as there is increment in value of h (300,400,500 & 600) the difference in gearbox surface temperature profile varies only (1.58-.7) k (Figure 7.7). 354 35 350 348 346 344 34 340 338 h=100 W/m k h=400 W/m k h=500 W/m k 1 3 4 5 6 7 8 9 10 Different temperature points on gear train assembly Figure 7.7 Temperature variations on gearbox surface at oil bath temperature 80 0 C with varying h. 11
Temperature measurement (k) Temperature Measurement (k) 375 370 365 360 355 350 345 340 335 330 35 h=100 W/m k h=300 W/m k h=600 W/m k 1 3 4 5 6 7 8 9 10 Different temperature points on gear train assembly Figure 7.8 Temperature variations on gearbox surface at oil bath temperature of 100 0 C with varying h. Same temperature profile as Figure 7.7 is generated when gear oil temperature is constant at 100 0 C and value of h increases from (100-600) W/m k, the difference in temperature is (1-8) k (Figure 7.8). From Figure 7.7 and Figure 7.8 it can be concluded that if gear oil temperature is constant (isothermal) the gear train thermal stresses at each convective heat transfer coefficient value is within permissible limits. The temperature profile of gear train shows that the lower temperature is approximate constant (Figure 7.5 & 6.6) and maximum temperature is varying by (1-5) k (Figure 7.7 & 6.8). Convective heat transfer co-efficient (h) refer to transfer of heat with fluid movement. In general for the increase value of h the rate of heat transfer increases. It signifies that the gearbox surface temperature should be reduced with increase in h value. The numerical simulation results show the same results as per thermal concept. In this research work for thermal analysis gear oil temperature was varied for 80 0 C and 100 0 C and h varied for (100-600) W/m k, for these loading conditions the temperature at 10 different gear assembly points was measured. 36 360 358 356 354 35 350 348 346 344 34 Low speed, low bath temperature-simulation result Low speed-experimental result 1 3 4 5 6 7 8 9 10 11 1 13 Different temperature points on gear surface Figure 7.9 FEA simulation result validation using experimental results, Long et al. [68] 113
FEA based numerical simulation result was validated with experimental results available in literature (Figure 7.9). Long et al. [68] have performed the experimental thermal analysis of single gear tooth of vehicle gearbox. The experimental study was performed at 000, 6000 and 10000 rpm with combined loading. At different rotational speed and loading conditions the gear surface temperature was evaluated. The gear temperature is mainly governed by loading condition, rotational speed has less effect. In this study when vehicle was running at low speed (1500-000) rpm at 45Nm load value, the gearbox surface temperature varies (349.56-353.8)k and the experimental results varies (348.14-360.4)k. FEA simulation temperature range lies within experimental gear surface temperature. The deviation in results for minimum temperature is less than 1% and for maximum temperature distribution deviation is less than %. It indicates that deviation in result is less than 5%, it shows satisfactory measurement of gearbox surface temperature. 7.7 Conclusions The analysis of multi speed transmission gearbox with gear oil has analytical and theoretical significance for thermo-mechanical performance improvement of gearbox. The FEA simulation results of medium duty transmission gearbox concludes that- I. Gradual increase in temperature around engaged gear pairs were reported due to effect of heat generation on surface of gears under the influence of gear meshing, frictional heat, average heat transfer and gear oil bath temperature. Increment in temperature is very low, in resultant thermal stress generation due to meshing action of gear will be very less. II. It was found that varying convective heat transfer (h) method reduces thermal stresses generation (Figure 7.5 & 6.6). All stresses like equivalent von-mises stresses and thermal strain are in permissible range for the transmission gearbox. III. The most important outcome of this analysis is that by varying convective heat transfer coefficient (h) phenomena overheating of gear oil is less, which refer cooling will be more and it increase the thermo-mechanical performance of multi speed transmission system. IV. Increase in thermo-mechanical performance of multi speed transmission system signifies higher fuel economy. 114