Analytical Model for the Heat Transfer in Impingement Cooled Spur Gears

2020 ◽  
Author(s):  
Christian Kromer ◽  
Felix C. von Plehwe ◽  
Marc C. Keller ◽  
Corina Schwitzke ◽  
Hans-Jörg Bauer
Keyword(s):  
Heat Transfer ◽  
Analytical Model ◽  
Gear Tooth ◽  
Gear Train ◽  
Spur Gears ◽  
Impingement Cooling ◽  
Oil Film ◽  
Low Pressure Turbine ◽  
Tooth Flank ◽  
Oil Jet

Abstract The geared turbofan is a promising concept for civil aircraft jet engines. With the introduction of a gearbox between the low-pressure turbine and the fan, both components can rotate at their respective optimum speed. The geared turbofan enables a lower specific fuel consumption as well as jet engine noise reductions. A planetary gear train is usually chosen for the transmission with the sun gear connected to the low-pressure turbine. This high-speed reduction gear train needs to transmit high loads with a high efficiency in limited installation space. To ensure a safe operation of the gear train, the thermal behavior of the gears needs to be understood. The heat generated by the meshing processes is dissipated by oil impingement cooling. While the field of Elastohydrodynamic lubrication yields good results for the heat generation, no validated model for the impingement cooling process is available in literature. In this study, an analytical model is developed and validated against experimental data. First, the surface area of the oil film on the gear tooth flank formed by the impinging oil jet is calculated. Second, the heat transfer from the gear tooth flank to the oil film is determined. The fluid motion is modeled as an oil film that is flung off the gear tooth flank by centrifugal forces. In addition to the film flow, the presented model takes into account the temperature dependence of the viscosity of the oil and the initial oil film height. The effect of a lubrication oil film on the gear tooth flank before the oil jet impinges is included and its effect on the heat transfer is assessed. The analytical model agrees well with experimental results over the entire range of investigated operating conditions. Finally, a discussion on the effect of several assumptions in the derivation of the analytical model is presented. The validated analytical model can be used as an efficient tool for the design of gear trains with impingement cooled spur gears.

Analytical Solution to the Heat Transfer in Fling-Off Cooling of Spur Gears

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Christian Kromer ◽  
Laura Cordes ◽  
Marc C. Keller ◽  
Corina Schwitzke ◽  
Hans-Jörg Bauer
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Numerical Solution ◽  
Analytical Model ◽  
Gear Tooth ◽  
Heat Transfer Process ◽  
Spur Gears ◽  
Tooth Flank

In this research paper, the cooling process of an impingement cooled spur gear is examined by means of an analytical model. The process is modeled as a coolant film, which is flung off a rotating gear tooth flank by centrifugal forces. During the process, heat is transferred from the isothermal gear tooth flank to the coolant film. With a numerical solution to the analytical model, a formulation for the transient local Nusselt number is derived. The evaluation of the numerical solution revealed that the heat transfer is dominated by heat conduction in the coolant film. The heat transfer process ends when the thermal capacity of the coolant film is reached. The transient Nusselt number is used to derive a time-averaged and a global heat transfer coefficient. Furthermore, the influence of the initial coolant film height is examined by using a modified version of the analytical model. The global heat transfer coefficient decreases toward smaller initial cooling film heights. The analytical model is then extended to include the temperature dependency of the viscosity of the coolant. A viscosity that decreases with increasing temperature yields a moderate decrease in heat transfer. A discussion is presented regarding the applicability of the analytical model toward impingement cooled spur gears. The effect of the simplifications made in the derivation of the analytical model is outlined and assessed with regard to the heat transfer mechanism.

Into Mesh Lubrication of Spur Gears With Arbitrary Offset Oil Jet. Part 1: For Jet Velocity Less Than or Equal to Gear Velocity

1983 ◽  
Vol 105 (4) ◽  
pp. 713-718 ◽  
Author(s):  
L. S. Akin ◽  
D. P. Townsend
Keyword(s):  
Inclination Angle ◽  
Gear Tooth ◽  
Optimum Operating ◽  
Spur Gears ◽  
Optimum Operating Condition ◽  
Operating Condition ◽  
The Common ◽  
Jet Velocity ◽  
Oil Jet

An analysis was conducted for into mesh oil jet lubrication with an arbitrary offset and inclination angle from the pitch point for the case where the oil jet velocity is equal to or less than pitch line velocity. The analysis includes the case for the oil jet offset from the pitch point in the direction of the pinion and where the oil jet is inclined to intersect the common pitch point. Equations were developed for the minimum oil jet velocity required to impinge on the pinion or gear and the optimum oil jet velocity to obtain the maximum impingement depth. The optimum operating condition for best lubrication and cooling is provided when the oil jet velocity is equal to the gear pitch line velocity with both sides of the gear tooth cooled. When the jet velocity is reduced from pitch line velocity the drive side of the pinion and the unloaded side of the gear is cooled. When the jet velocity is much lower than the pitch line velocity the impingement depth is very small and may completely miss the pinion.

scholarly journals Study of Lubricant Jet Flow Phenomena in Spur Gears

1975 ◽  
Vol 97 (2) ◽  
pp. 283-288 ◽  
Author(s):  
L. S. Akin ◽  
J. J. Mross ◽  
D. P. Townsend
Keyword(s):  
Motion Picture ◽  
High Speed ◽  
Drop Size ◽  
Gear Tooth ◽  
Jet Flow ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Flow Phenomena ◽  
Oil Jet

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 using a 8.89-cm- (3.5-in.) pitch dia 8 pitch spur gear at oil pressures from 7 × 104 to 41 × 104 N/m2 (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet so that the impingement depth could be determined. An analytical model was developed for the vectorial impingement depth and for the impingement depth with tooth space windage effects included. The windage effects on the oil jet were small for oil drop size greater than 0.0076 cm (0.003 in.). The analytical impingement depth compared favorably with experimental results above an oil jet pressure of 7 × 104 N/m2 (10 psi). Some of this oil jet penetrates further into the tooth space after impingement. Much of this post impingement oil is thrown out of the tooth space without further contacting the gear teeth.

Measurement of Oil Film Thickness Between W-N Helical Gear Tooth Profiles Using Laser Transmission Method

1990 ◽  
Vol 112 (4) ◽  
pp. 708-711 ◽  
Author(s):  
Yang Ji-Bin ◽  
Qi Yu-Lin ◽  
Chen Chen-Wen
Keyword(s):  
Film Thickness ◽  
Gear Tooth ◽  
Helical Gear ◽  
Spur Gears ◽  
Measuring Apparatus ◽  
Transmission Method ◽  
Helical Gears ◽  
Oil Film ◽  
Measurement Results ◽  
First Time

In this experiment, it was the first time that the center oil film thickness between W-N helical gear tooth profiles has been measured indirectly through measuring the change of gaps of a pair of unloaded involute spur gears mounted on the extended shafts of W-N gear box by means of laser transmission method. During the measurement of every time, it was calibrated separately, so that all errors could be eliminated completely except ones of measuring apparatus. The accuracy of this method has reached 0.1 μm (dynamic) and 0.01 μm (static), respectively. Measurement results were identical with theoretical ones. This method is also suitable for the measurement of center oil film thickness between tooth profiles and deformation of any cylindrical spur and helical gears.

Experimental Investigation of the Minimum Oil-Film Thickness in Spur Gears

1963 ◽  
Vol 85 (3) ◽  
pp. 451-455 ◽  
Author(s):  
D. W. Dareing ◽  
E. I. Radzimovsky
Keyword(s):  
Film Thickness ◽  
Voltage Drop ◽  
Planetary Gear ◽  
Gear Train ◽  
Spur Gears ◽  
Minimum Thickness ◽  
Testing Technique ◽  
Oil Film ◽  
Gear Teeth ◽  
Gear Drive

As a pair of gears is loaded, the minimum oil-film thickness between the gear teeth decreases and can approach a magnitude equal to the magnitude of the surface roughness. Metal-to-metal contact then occurs between the microscopic peaks on both mating teeth surfaces. Therefore, the minimum thickness of the film separating the mating teeth surfaces may be considered as one of the criteria of capacity for a gear drive. A testing technique that was developed for measuring oil-film thickness between loaded gear teeth while running is presented in this paper. The voltage drop across a thin oil film that is required to cause an electrical discharge was used to determine the oil-film thickness. A specially designed machine containing a planetary gear train was used in these experiments. The relationships between the minimum oil-film thickness and the load transmitted by the gearing under certain conditions were determined using this method.

Convection heat transfer and temperature analysis of oil jet lubricated spur gears

2016 ◽  
Vol 68 (6) ◽  
pp. 624-631 ◽  
Author(s):  
Yanzhong Wang ◽  
Wentao Niu ◽  
Yanyan Chen ◽  
Guanhua Song ◽  
Wen Tang
Keyword(s):  
Heat Transfer ◽  
Convection Heat Transfer ◽  
Distribution Coefficients ◽  
Frictional Heat ◽  
Spur Gears ◽  
Convection Heat ◽  
Transfer Coefficients ◽  
Content Type ◽  
Heat Transfer Coefficients ◽  
Oil Jet

Purpose This paper aims to provide an analytic technique for determining the convection heat transfer and temperature of oil jet lubricated spur gears. Design/methodology/approach A multiphase flow model is developed to calculate the convection heat transfer coefficients on different gear faces during different contact conditions. The frictional heat is calculated and a method to distribute between the two gears is developed. A finite element model is established to calculate the temperatures in both meshing and cooling processes. Findings The convection heat transfer coefficients on different surfaces are obtained successfully. Area-related formulae are developed to calculate the heat distribution coefficients. The gear temperature reaches a maximum at the beginning of meshing, then reduces and gets minimum at pitch point, after that it increases again. The gear temperature descends rapidly to steady temperature during the short time of jet cooling process. The tendency of computational results coincides well with the experimental results. Originality/value The research presented here could be used in the design phase of the jet lubricated spur gears. The precise temperature is obtained to assess the thermal capacity of gears, from which the gear parameters and oil supply conditions could be adjusted and designed.

scholarly journals Influence of the movement of involute profile gears along the off-line of action on the gear tooth position along the line of action direction

2021 ◽  
Vol 23 (4) ◽  
pp. 736-744
Author(s):  
Łukasz Jedliński
Keyword(s):  
Analytical Model ◽  
Frictional Force ◽  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Tooth Position ◽  
Pressure Angle ◽  
Number Of Teeth ◽  
The Impact

When gears change their distance along the off-line of action (OLOA) direction, this affects the distance between the working surfaces of the meshing teeth along the line of action (LOA). This effect is usually neglected in studies. To include this effect precise equations are derived for spur gears. The analysis is carried out for the general case of spur gears with shifted profiles frequently used in the industry. The influence of OLOA gear displacement on LOA direction is also a function of gears parameters. An analysis is conducted, and the impact of parameters such as module, pressure angle, gear ratio, and the number of teeth is determined. As an example, a simulation of a 12 DOF analytical model is presented. The movement of gears along OLOA is caused by a frictional force that can be high during tooth degradation e.g. scuffing. Results show that when the movement of gears along the OLOA direction is significant, its influence on the distance between the mating teeth should not be neglected.

A Novel Method for Calculation Gear Tooth Stiffness for Dynamic Analysis of Spur Gears With Asymmetric Teeth

2014 ◽  
Author(s):  
F. Karpat ◽  
O. Dogan ◽  
S. Ekwaro-Osire ◽  
C. Yuce
Keyword(s):  
Gear Tooth ◽  
Load Capacity ◽  
Operating Conditions ◽  
Spur Gears ◽  
Finite Elements Analysis ◽  
Gear Teeth ◽  
Research Activities ◽  
Tooth Surfaces ◽  
Tooth Stiffness ◽  
Tooth Flank

Recently, there have been a number of research activities on spur gears with asymmetric teeth. The benefits of asymmetric gears are: higher load capacity, reduced bending and contact stress, lower weight, lower dynamic loads, reduced wear depths on tooth flank, higher reliability, and higher efficiency. Each of the benefits can be obtained through asymmetric teeth designed correctly. Gears operate in several conditions, such as inappropriate lubrication, excessive loads and installation problems. In working conditions, damage can occur in tooth surfaces due to excessive loads and unsuitable operating conditions. One of the important parameters of the tooth is stiffness, which is found to be reduced proportionally to the severity of the defect by asymmetric tooth design as described in this paper. The estimation of gear stiffness is an important parameter for determining loads between the gear teeth when two sets of teeth are in contact. In this paper, a 2-D tooth model is developed for finite elements analysis. A novel formula is derived from finite element results in order to estimate tooth stiffness depending on the tooth number and pressure angle on the drive side. Tooth stiffness for spur gears with asymmetric teeth is calculated and the results were compared with well known equations in literature.

Computer Aided Design of Internal Involute Spur Gears

1988 ◽  
Author(s):  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Aided Design ◽  
Gear Tooth ◽  
Gear Train ◽  
Modern Theory ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Computer Aided ◽  
Tooth Surfaces ◽  
Aided Design

Abstract The modern theory of gearing provides principles of generation for conjugate gear tooth surfaces while computer aided design is a very powerful tool in designing a gear train with conjugate shaped tooth surfaces. It is possible to set up a mathematical model for internal involute spur gears if the theory of gearing and the concept of differential geometry together with computer aided design technique have been applied. The derived mathematical model of internal involute spur gears can be used for computer simulation of conditions of meshing, tooth contact analysis, stress analysis, dynamic analysis, lubricating analysis, and wearing analysis of the gear train. This paper covered the solutions to the following problems : (a) method of generation for internal spur gears with conjugate tooth surfaces; (b) derivation of equations for gear tooth surfaces and their surface unit normals; and (c) computer graphics of generated internal involute spur gears.

Sign in / Sign up

Export Citation Format

Share Document