# Better temperature information in a gear pair using FE-simulations

**Abstract**

A 3D FE simulation is proposed to estimate the temperature distribution and at least the interfacial temperature of nylon 66/steel gear pair. The mean value of the simulation results obtained are comparable with those from the analytical solution in accordance to VDI 2736 [6]. In addition, the proposed FEM approach offers the opportunity to detect the critical areas throughout the gear pair.

** Keywords:** Polymeric gear; interfacial temperature, FE simulation.

## 1. Introduction

Frictional heat is generated as two surfaces are rubbed against each other, which can induce a temperature rise at the interface. This increase in the contact temperature can significantly impact the tribological performance of the gear pair, especially for components made of plastics. Hoskins et al. [1] studied the friction and wear properties of PEEK with a twin-PEEK-disc test approach under dry rolling-sliding conditions. They demonstrated that the interfacial temperature is above the glass transition temperature of PEEK under certain load conditions and the tribological performance changed dramatically, if the contact temperature is above this characteristic temperature. Studies [2, 3] have also found that the interfacial temperature reaches nearly the melting temperature of the studied polymeric materials by direct temperature measurement and indirect analysis of the molecular structure of the wear debris. Therefore, it is of great importance to study the thermal characteristics in the polymeric tribo-systems, in order to better tailor the tribological components for the purpose of reliable industrial applications under different load conditions. To estimate the interfacial temperature or flash temperature due to frictional heating of two gear parts, several analytical and numerical models have been developed in the past. Among these, the most commonly used method is the theory of moving heat sources [4-, 5]. A detailed procedure for determining the mean contact temperature in a gear pair based on these theories is described in the VDI guideline 2736 [6] and is well accepted in industry and acedemia.

In this communication, we utilize a novel and simple FE approach to determine the interfacial temperature and the temperature distribution in 3D direction of a nylon 66/steel gear pair. The main goal is to access the feasibility and accuracy for the determination of the contact temperature by using FE method, and finally to provide an effective and accurate solution to estimate the locally different interfacial temperature between rolling/rubbing gear pairs.

2. Methodology

### 2.1. Analytical solution

As mentioned above, there are several analytical approaches to determine the contact temperature between moving parts. In this study, we utilized Eq. (1), according to the standard [6], to calculate the interfacial flank temperature between polymeric gear made of nylon 66 and steel, which is described in the following form:

*T = T _{0} + P·µ·H_{v}·[k_{T}/(b·z·v_{t}·m_{n})^{0.75} + R_{λ,G}/A_{G}]·ED^{0.64}* (1)

For radial contact ratios between two gears, the term of degree of tooth loss can be determined by Eq. (2) as follows:

*H _{v} = [π·(*

*α*

*+1)/z·cosβ*

_{b}]·(1-*ε*

_{1}*-*

*ε*

_{2}*+*

*ε*

_{1}

^{2}*+*

*ε*

_{2}

^{2}*)*(2)

Table 1 presents the parameters applied for determining the flank temperature in the gear system.

*Table 1: Parameter for calculating the flank temperature*

### 2.2. FE simulation

By means of the analytical methods, only the mean flank temperature can be determined. However, for a reliable design of polymeric tribo-materials in service, it is crucial to know the temperature distribution at the interface or even the temperature distribution under the contact layer. Thus, we used commercially available simulation software ANSYS^{®} to simulate the 3D thermal characteristics in a polymeric gear system. The frictional heat is generated at the contact surface of the gears, and as a results, the temperature at the interface is increased. To precisely determine the temperature state between the two contacted gears by using FE simulation, the heat flux at the interface is required, which can be estimated by using the following equation:

*q* *= k·µ·p·v _{t }(3)*

Generally, the heat partition coefficient *k* can be iteratively determined by using experimental data of the temperature measurements outside of the contact area, if the contact pair are made of different materials. Based on the experimental data reported in [7], the *k*-values for the thermal simulation were calculated, which are **2.7**% and **2.4**% for a nominal output of 900 W and 1350 W, respectively. To simplify the model and to reduce the computer time for simulation, only the part of the polymeric gear was modelled. To determine the interfacial temperature using FE approach. First of all, a 3D model of the gear (cf. Fig. 1a) must be established and imported into ANSYS^{®}, and thereafter, it is meshed with different mesh density in different region, the mesh density in the contact area is high to achieve a better resolution of the temperature, outside the interface, the part is meshed roughly, to reduce the calculating time, as is shown in Fig. 1b.

*Fig. 1. Schematic introduction of (a) the 3D CAD model of a nylon gear and (b) the meshed part in 3D configuration (24758 elements in total). *

Several parameters are necessary as input data for the thermal simulation, which are the room temperature, thermal conductivity, heat transfer coefficient and the heat flux. The concrete data for the calculation are listed in table 2.

*Table 2: Input data for FE simulation. *

## 3. Results and discussion

The FE method allows to create a 3D thermal mapping of the teeth interface. Fig. 2a presents such a visualization of the thermal mapping calculated with a nominal output of 900 W. As we can see that, the maximum temperature is in the middle of the tooth flank and decreases to the edge of the tooth (cf. Fig. b). In the case of 900 W nominal output, the maximum flank temperature is approximate 107 °C. An increase in the nominal output results also in an elevation of the interfacial temperature, for example, if the nominal output is increased from 900 W to 1350 W, the maximum flank temperature rises by about 20 °C up to 136 °C.

*Fig. 2. The thermal map of the polymeric gear calculated with a normal output 900 W (a) and the corresponding temperature distribution along the tooth flank surface (b). The path is indicated by the white arrow. *

As described above, the mean flank interfacial temperature can be also determined by using simple analytical method, the temperatures calculated from the analytical approach and simulated using the FE method are compared with each other, the result is shown in Fig. 3. It can be clearly observed that the results from the analytical solution and FE simulation are quite similar, which means that the FE method is an effective way to estimate the interfacial temperature in particular the 3D temperature distribution in a tribological system.

*Fig. 3. Comparison of the maximum temperatures obtained from analytical solution and FE simulation. *

## 4. Conclusions

A finite element method was developed to determine the interfacial temperature in a polymeric/steel gear system, which exhibits a main advantage in comparison with conventional analytical solutions, i.e. three-dimensional modelling and simulation of the temperature within the tribological system. The results obtained were compared with those estimated by a well accepted analytical method. A good agreement of the mean surface temperature was achieved between these two methods. The key advantage of our FE-approach is the opportunity to simulate temperatures locally, and thus identify the critical loads/areas in a contact pairing.

**Acknowledgements **

The authors gratefully acknowledge German Research Foundation (DFG) for the financial support of this work according to the project SCHL 280/21-1. We also thank Marco Schott for the implementation of the model.

## Authors

Nicholas Ecke^{a}, Leyu Lin^{a,}*, and Alois K. Schlarb^{a,b,c}

^{a} Chair of Composite Engineering, Technische Universität Kaiserslautern (TUK), 67663 Kaiserslautern

^{b} State Research Center OPTIMAS, Technische Universität Kaiserslautern (TUK), 67663 Kaiserslautern

^{c} INM - Leibniz Institute for New Materials, 66123 Saarbruecken

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