Spiral bevel gear plays crucial role in the accessory drive system of an aeroengine. In special oil-depleted conditions such as a penetrated gearbox or a damaged lubrication system, the temperature at the meshing contact of spiral bevel gears rises rapidly, leading to gear failure. This research focuses on a certain type of spiral bevel gear in an aircraft’s accessory drive system to study the relationship between grinding wheel morphology, gear morphology, and tooth surface flash temperature.
1.1 Research Background and Significance
The accessory drive system is essential for an aeroengine, and spiral bevel gears are key components. In oil-depleted conditions, the local temperature increase due to dry friction can cause rapid gear failure.
Grinding is the final process in gear manufacturing and significantly affects the tooth surface quality. Understanding the relationship between gear morphology and flash temperature is vital for predicting the ultimate operating time of the aircraft in special conditions.
1.2 Research Objectives
To establish a three-dimensional solid model of spiral bevel gears considering surface morphology after grinding.
To analyze the relationship between grinding wheel morphology, gear morphology, and tooth surface flash temperature.
To optimize the grinding process parameters of spiral bevel gears.
2. Review of Related Research
2.1 Grinding Technology and Grinding Wheel Research of Spiral Bevel Gears
Spiral bevel gears are widely used in various fields. The development of grinding technology and grinding machines for spiral bevel gears has a long history.
Different countries have made progress in this area. For example, the Gleason Company in the US, and companies in Switzerland and Germany have their own technologies and machines. In China, research institutions and companies have also made certain achievements.
2.2 Research on Grinding Wheel Surface Morphology Simulation
Various methods have been used to simulate the grinding wheel surface morphology. Some researchers use simple shapes to represent grinding grains, while others use time series, wavelet and Fourier transform methods.
The fractal theory has also been applied, but there are still some limitations in simulating three-dimensional rough surfaces.
2.3 Research on Predicting Grinding Morphology
Many scholars have studied the prediction of gear grinding morphology to improve gear surface quality. Different models and methods have been proposed, but some do not consider the influence of wheel vibration on tooth surface morphology.
2.4 Research on Tooth Surface Flash Temperature
There are several methods for calculating tooth surface flash temperature, such as the flash temperature formula method, finite element simulation method, and a combination of both. However, existing research using finite element method in oil-depleted conditions has some deficiencies as it often uses a smooth gear model instead of considering the actual micro-convex contact on the tooth surface.
3. Modeling of Grinding Wheel Surface Morphology Based on Fractal Theory
3.1 Fractal Theory Overview
Fractal theory, proposed by Mandelbrot, can describe complex and random shapes. It has been widely used in various fields.
Some classic fractal curves and sets, such as Koch curve, Mandelbrot set, and Sierpinski triangle, have been studied.
3.2 Calculation and Analysis of Fractal Parameters of Grinding Wheel Surface Morphology
The structure function method is used to calculate the fractal dimension and fractal roughness parameters of the grinding wheel profile.
The grinding wheel used in this research is an SG grinding wheel. The surface morphology is measured using a Taylor Map CCI three-dimensional non-contact optical profilometer.
Grinding Wheel Model
Fractal Dimension
Fractal Roughness
SG46 M/#
1.2747
4.3842e – 5
SG60M/#
1.2909
3.9039e – 5
SG80 M/#
1.3068
3.4631e – 5
SG120 M/#
1.3272
2.9030e – 5
SG180 M/#
1.3503
2.4262e – 5
3.3 Construction of Three-Dimensional Rough Surface Morphology Model of Grinding Wheel Based on Fractal Theory
The Weierstras – Mandelbrot fractal function for the three – dimensional surface morphology of the grinding wheel is derived.
By comparing the simulated surface morphology with the measured one, the independent variable functions f(x,y)=(x^2+y^2)^1/2 and g(x,y)=arctan(x/y) are determined.
The simulated surface morphology of different grit sizes of grinding wheels is generated and analyzed.
4. Simulation of Spiral Bevel Gear Grinding Surface Morphology
4.1 Establishment of Tooth Surface Model Based on Grinding Trajectory
The grinding of spiral bevel gears follows the principle of “imaginary generating wheel”. The mathematical models of the tooth surfaces of the pinion and the gear are established considering the grinding process.
The machining coordinate systems for the pinion and the gear are defined, and the equations for the grinding surfaces and their normal vectors are derived.
Gear Type
Machining Coordinate System
Grinding Surface Equation
Normal Vector Equation
Pinion
Sm1(Om1,Xm1,Ym1,Zm1) etc.
rp1(Sp,θp)
np1
Gear
Sm2(Om2,Xm2,Ym2,Zm2) etc.
rp2(Sg,θg)
np2
4.2 Establishment of Solid Model of Spiral Bevel Gear Grinding Surface Morphology
The grinding process trajectory is calculated using discrete point interpolation and constraint solving methods. The tooth surface is discretized and projected onto an axial section.
Considering the vibration of the grinding wheel, the motion trajectory equation of a single grinding grain is derived.
The solid model of the spiral bevel gear grinding surface morphology is created by combining the grinding wheel surface morphology and the tooth surface data.
5. Experimental Analysis of Spiral Bevel Gear Grinding Surface Morphology
5.1 Grinding and Measuring Experiments of Spiral Bevel Gear Tooth Surface Morphology
The Gleason Phoenix 600G CNC gear grinding machine is used to grind spiral bevel gears. The grinding parameters and gear parameters are set.
Gear
Number of Teeth
Module
Tooth Width
Pressure Angle
Spiral Angle
Axis Angle
Pinion
/
2.54
18mm
20°
35°
90°
Gear
44
2.54
18mm
20°
35°
90°
5.2 Measurement and Comparison of Simulated and Real Tooth Surface Morphologies
A method for measuring the tooth surface morphology of a three – dimensional solid gear model is proposed. The coordinate system of the model is changed to be consistent with the measurement coordinate system of the non – contact profilometer.
The simulated and real tooth surface morphologies are measured and compared. The errors between the simulated and measured surface roughnesses are analyzed.
5.3 Analysis of Grinding Experiment and Optimization of Process Parameters
The orthogonal experiment method is used to analyze the influence of grinding parameters on the tooth surface quality. The main factors affecting the tooth surface roughness are grinding depth, wheel speed, wheel grit, and generating speed.
Level
Grinding Depth /mm
Wheel Speed /m/s
Wheel Grit /#
Generating Speed /m/min
1
0.02
16.5
46
2.7
2
0.05
26.5
60
3.6
3
0.08
35.5
80
4.4
4
0.11
52.5
120
7.2
The regression prediction equation of the grinding surface roughness is established using a power function model.
6. Calculation and Analysis of Tooth Surface Flash Temperature Considering Tooth Surface Morphology
6.1 Calculation of Tooth Surface Flash Temperature by Combining Theory and Simulation
The formula for calculating the meshing temperature considering tooth surface morphology is derived. The heat generated by friction is calculated based on the relative sliding speed, friction coefficient, and normal force.
The finite element software Abaqus is used to calculate the normal pressure of each micro – convex body on the tooth surface. The total normal force and the heat generated in the contact area are calculated.
The sliding speed of the contact points on the gear is calculated according to the kinematics of the gear. The non – uniform instantaneous heat density generated by friction in the contact area is calculated.
6.2 Finite Element Simulation Analysis of Tooth Surface Flash Temperature
The ANSYS Coupled Field Transient module is used to simulate the friction heat generation of the established rough gear model. The mesh of the gear model is processed to reduce the influence of meshing on the surface morphology.
The gear is divided into single teeth, and the meshes of the meshing tooth surfaces of some gears are encrypted.
6.3 Comparison and Analysis of Simulation Results and Theoretical Results
The simulation results and theoretical results of the tooth surface flash temperature are compared. The temperature distribution on the tooth surface and the maximum flash temperature in different regions are analyzed.
The results show that the temperature distribution trends calculated by the two methods are consistent, and the errors are small, which verifies the feasibility of the proposed calculation method and the accuracy of the established model.
7. Conclusions
The grinding wheel surface morphology is simulated based on fractal theory, and the three – dimensional surface morphology model is established. The influence of wheel vibration on the tooth surface morphology is considered, and the motion trajectory of grinding grains is derived.
The solid model of spiral bevel gears considering surface roughness after grinding is established. A method for measuring the tooth surface morphology of the model is proposed, and the feasibility of the method is verified.
The influence of grinding parameters on the tooth surface quality is analyzed, and the optimization configuration of the grinding process parameters is obtained. The regression prediction equation of the grinding surface roughness is established.
The calculation method of tooth surface flash temperature considering tooth surface morphology is proposed. The numerical calculation method and the finite element analysis method are combined to calculate the tooth surface temperature, and the simulation results verify the feasibility of the method.
