1. Introduction
The involute spline connection can meet the connection requirements of large torque and high speed. It is widely used for shaft-to-shaft connections in aerospace driveline systems because it is assembled in a way that ensures shaft guidance and alignment. In the aviation transmission system, there are usually two ways to connect the shaft to the involute spline coupling; one is fixed, and the other is floating. When the spline pair of a floating connection transmits torque, due to the existence of the tooth side clearance, there is a slight relative movement between the inner and outer splines. On the other hand, the axial floating of the spline is caused by the existence of an axial force or the change of external load. Under the combined action of these two relative displacements, the aeronautical gradual floating open-line spline coupling has extremely serious wear and failure. X Z Xue et al. [
1,
2] used the finite element method to analyze the aviation floating gradual opening. The wear conditions of the linear spline coupling are studied under different tooth surface wear factors, loads, and operating cycles, and a plane spline coupling structure that can simulate the floating involute spline coupling is designed to verify the theoretical research. Since the axial floating distance is one of the key factors affecting the wear of floating involute spline pairs; therefore, exploring the wear conditions of aeronautical floating involute spline pairs under different floating distances has important guiding significance for the design of high-precision, high-strength, and high-reliability involute spline pairs required by advanced aeroengines.
At present, many scholars have studied the wear mechanism of spline coupling. Z L Song et al. [
3,
4,
5] used the Archard wear calculation formula to obtain the wear depth of the spline coupling within the simulation time. Zheng et al. [
6] used the MATLAB–Abaqus joint development method to study the depth of wear of the spline coupling tooth surface. Chen et al. [
7,
8] studied the wear behavior of spline couplings under various misalignment conditions through experiments and studied the wear of spline couplings with different materials and different heat treatment methods for the tooth surface. Hu et al. [
9,
10] studied the depth distribution of the wear of the tooth surface under the condition of compound misalignment of the spline coupling. Zhao et al. [
11,
12,
13] studied the wear of aviation involute spline couplings under vibration based on the traditional Archard wear calculation formula. Ratsimba et al. [
14] proposed a method to predict the fretting wear of spline couplings based on the Archard model. McColl et al. [
15] proposed a finite element method to calculate fretting wear based on the modified Archard equation; it simulates the wear process of the pin–disk structure. In addition, the Archard wear formula is often used to calculate the wear of the tooth surface of involute spline couplings, and the model in the research content is also simplified. Therefore, the existing Archard wear formula is unsuitable for gradual floating in aviation and the calculation of the wear depth of the spline coupling.
At the same time, as the basis for calculating the wear of spline couplings, many studies have focused on the contact characteristics of spline couplings. Hong et al. [
16] studied the changes in the stress distribution on the tooth surface of the spline coupling under different helical gear helical angles to obtain the optimal helical gear helical angle. Tjernberg et al. [
17] established an analysis model to study axial load distribution and torque transmission and concluded that modifying the spline teeth in the axial direction can make the axial load of the spline coupling evenly distributed. Barrot and Paredes et al. [
18] also studied the axial torque transmission of the spline coupling and concluded that the main factor affecting the wear of the spline coupling is the distribution of the axial torque. Ding et al. [
19] analyzed the slip distance and contact pressure under different conditions. This study laid a good foundation for the research on the wear of aviation spline couplings. Medina et al. [
20] studied the elastic contact model of spline couplings based on the boundary finite element method. Cuffaro et al. [
21] used numerical analysis models and experimental methods to study the stress distribution of spline couplings and verified it with finite element simulation. Leen et al. [
22] analyzed the effects of tooth profile modification on the spline tooth’s surface contact stress, slip distance, and friction factor. The research objects of the above studies are all fixed spline couplings, and the influence of floating distance is not considered. Xiao Li et al. [
23,
24] investigated the wear fatigue damage model of the floating spline considering the wear effect; the cumulative damage distribution law of fretting fatigue of the axial misalignment and the angular eccentric lower surface of the tooth was analyzed, and the life of the floating spline was predicted.
There is almost no research on the wear of axial floating distance aviation spline couplings. In view of the aviation floating involute, the wear failure of the spline coupling has caused great damage to the aviation transmission system and caused a serious threat to the safety of the whole machine. Therefore, based on the traditional Archard model, this work proposes a wear calculation model for aviation axial floating involute spline coupling with axial floating distance. The contact stress and relative slip rate between the teeth were investigated with axial floating distances of 0 mm, 3 mm, and 0.6 mm. Then, the distribution law of the wear depth along the axial and radial directions was studied. Finally, the theoretical results were verified by the experimental results of the wear depth of the tooth surface of the floating spline coupling. This work provides a theoretical basis for designing and maintaining the involute spline coupling in aviation.
2. Research on the Wear Mechanism of Aviation Floating Involute Spline Coupling
Through the observation and analysis of a large number of scrapped aviation involute spline couplings, the surface topography of some typical abrasion and failure spline couplings is shown in
Figure 1. There are many small pits formed by wear in
Figure 1a, the analysis here shows that the wear form of the spline coupling tooth surface is mainly fretting wear. In
Figure 1b, we can see the corrugated relief, indicating that the wear form here is mainly oxidative wear. In
Figure 1c,d, it can be seen that the tooth surface has oxidized wear and adhesive wear. Particles adhere to the tooth surface, forming scratches during the working process of the spline coupling. In addition, it can be observed in
Figure 1e that cracks have formed on the tooth surface of the spline coupling, indicating that the main form is fatigue wear. In
Figure 1f, the existence of large pits can be seen; these are the pits formed by the large material of the spline coupling being worn away under the action of adhesive wear. This will seriously affect the roughness of the spline coupling’s tooth surface. This further intensifies the wear of the spline coupling.
Combined with the above analysis results of the wear of the tooth surface of the scrapped aero involute spline, as well as the three operating conditions of takeoff, cruise, and landing experienced by the helicopter involute spline, the wear mechanism of the helicopter floating aero involute spline can be derived as follows:
When the helicopter is in the takeoff phase, the aircraft’s power system has maximum afterburner in the state, the vibration frequency of the spline coupling increases, and the input torque of the spline coupling is alternating. The alternating external load constitutes the external excitation of spline secondary vibration. The time-varying nature of the comprehensive meshing stiffness introduced by the change in the number of meshing teeth and the geometric errors caused by manufacturing and installation constitute the internal excitation of the spline vibration. This kind of nonlinear vibration of the spline coupling, which exists in extreme working conditions, is caused by the combined action of internal and external excitation, which makes the relatively static contact surface of the two splines of the original design produce obvious slight motion, and the repeated action of micromotion. On the one hand, the contact surface produces fretting wear. The temperature during its operation increases and the lubricating oil in the contact area is forcibly squeezed out, resulting in poor lubrication conditions. The deformation of the tail shaft makes the inner and outer splines designed to move axially produce a relatively large sliding distance of the spline, leading to serious abrasive wear between the contact surfaces of the spline. Sliding caused by deformation of the tail shaft is more intense. This will wear off the surface of the key tooth after fretting wear, and the spline coupling temperature change in the movement process causes the adhesion effect, and the adhesion node formed by this effect will shear and fracture with the relative slippage of the friction pair surface, which makes the surface and subsurface of the movement spline coupling produce a lot of adhesive wear; metal migration occurs, and separation of metal particles occurs. These separated metal particles act as abrasive particles, which promotes and accelerates the appearance of more furrows on the contact surface of the spline coupling at this stage, so the abrasive wear phenomenon is aggravated. Therefore, spline wear is mainly in the form of abrasive wear, adhesive wear, and fretting wear at this stage.
- (2)
Cruise state
When the aircraft is cruising, the spline coupling is in a steady-state working environment, and the phenomenon of abrasive wear is reduced. However, spline coupling is still dominated by adhesive wear and abrasive wear due to its complex working conditions and manufacturing and processing errors. The micromovements inside and outside the spline are inevitable; there is still micromovement wear at this stage. However, as a result of the effect of lubricating oil and the above three forms of wear, there is also oxidative wear. This is due to the wear of the key teeth during the takeoff phase, which makes the contact area of the key teeth larger, resulting in close contact of the key teeth involved in the contact, making it difficult for the oxide wear debris generated by oxidative wear to be discharged. Under the relative displacement caused by the cyclic alternating load, these oxidation products act as abrasive particles together with the wear debris generated by the adhesive wear and the foreign abrasives (dust, impurity particles contained in the lubricating oil, etc.) that fall into the connecting parts. During the rotation and sliding process of the auxiliary part, it moves on the surface of the key teeth of the inner and outer spline couplings to participate in frictional contact, causing the surface material of the spline coupling to fall off, thereby forming three-body abrasive wear.
- (3)
Landing state
When the aircraft is landing, it is subjected to irregular frequency impact loads; abrasive wear is very serious and is accompanied by slight adhesive wear, fretting wear, and oxidation wear, which continue to accelerate the wear of spline teeth. This is the wear mechanism of the aircraft in one take-off and landing cycle.
As a result of the accumulation of early wear, the involute spline without a centering surface will be worn out earlier than the fixed load cycle under a certain number of load cycles. The clearance of the tooth side of the spline on the heart surface is increased, the vibration effect is strengthened, and the deformation of the tail shaft causes the spline to slide relative to the tail surface, and its wear becomes more and more severe and eventually fails. However, the spline with a centering surface improves the spline misalignment to a certain extent, and when the spline without a centering surface wears to a certain degree in the early stage, the spline with a centering surface wears well. The center surface is important, but after accumulation of wear in the later period, the centering surface is worn out, the positioning gap increases, and the increase in the positioning gap makes the working condition of the spline with the centering surface worse than that of the spline without the centering surface. The misalignment condition is more serious, so after a certain number of wear cycles, the spline with a centering surface will wear out quickly under the coupling effect of misalignment, tail shaft deformation, and external input alternating load.
The material of the aviation floating involute spline couplings is alloy steel 40CrNiMoA, and its chemical composition (wt%) is shown in
Table 1.
3. Floating Spline Coupling Wear Prediction Model
In recent years, the Archard adhesive wear calculation formula has generally been used for calculating the tooth surface wear of the spline coupling. Due to the traditional Archard calculation model being mainly based on the macroscopic wear situation, to make the Archard wear calculation formula more suitable for the actual wear of the involute spline coupling, scholars have conducted a lot of research. Ding et al. organized and analyzed the abrasive wear calculation formula and the Archard adhesive wear calculation model and introduced an Archard calculation model suitable for fretting wear, as shown in Equation (1):
where
is the wear coefficient;
is the relative sliding distance of the spline coupling, in mm; and
is the contact pressure on the tooth surface of the spline coupling, in MPa.
Aiming at the special working environment of the aviation floating involute spline coupling, in order to make the above Equation (1) more suitable for calculating the tooth surface wear of the aviation floating involute spline coupling, this article focuses on the aviation involute spline; the specific force situation of the auxiliary tooth surface is analyzed. Taking the midpoint of the contact width of the single tooth surface of the spline coupling, the normal force of the tooth surface is simplified to the normal force
at the midpoint of the concentration, and
is decomposed at this midpoint. The tooth surface normal force
is decomposed into a circumferential component force
and a radial component force
. At the end of the driven shaft in the external spline, the relative sliding speed of this node is the same as the circumferential component force of the normal force. The force distribution of a node on the tooth surface is shown in
Figure 2 below.
For the aviation floating involute spline coupling in the working process, there is the relative slip distance in the axial direction and the relative slip distance in the radial direction, respectively. The plane coordinate system is established on the tooth surface of the node
. During the simulation of the open-line spline coupling, every time a cycle is performed, the relative slip distance of this node in the two directions is expressed as
and
, respectively, so after a cycle, the relative slip distance at this node is Equation (2). Because the existence of the axial floating distance will affect the axial relative slip distance at the spline coupling tooth surface node, the relative slip distance is expressed as
at this time, and the calculation formula is Equation (3).
Aiming at the change of the involute slip distance of the above formula, the classic Archard formula of Equation (1) is optimized, and the calculation equation of the wear depth of the spline coupling in one cycle is shown in the following Equation (4);
corresponds to the node in each where the wear depth under the cycle can realize a more accurate prediction of the wear depth of the tooth surface of the floating spline coupling.
As the spline coupling is in the working process, the tooth surface contact pressure of the spline tooth surface is constantly changing, and the relative sliding speed between the spline and the external spline is also constantly changing within a certain period of time. During the operation of the spline coupling, there are relative slip speeds in two directions at a certain node on the tooth surface of the spline coupling, as shown in
Figure 3. Calculating the time derivative at both ends of the above Equations (2) and (3) to obtain the relative slip rate at the node, there is the relative slip velocity
in the axial direction and the relative slip
in the radial direction, respectively. The figure is a schematic diagram of two relative slip speed directions at a certain node, and the direction indicated by the arrow is the positive direction, as shown in the following formula. After the relative slip speed is compounded, the relative slip speed of a certain point on the surface of the key tooth is as shown in Equations (5) and (6).
During the operation of the spline coupling, with fretting wear, temperature rise, and other factors, the relative slip rate at the node will continue to change with time, and then the above equation is used to derive the event and integrate it on both sides, as shown in the following Equations (7) and (8); as shown, the optimized Archard wear calculation formula is obtained.
In the formula, and are the curves calculated by simulation, j is a point on the curve, the unit of is m/s, and the unit of is pa.
The optimized Archard wear calculation model is combined with the finite element simulation calculation, and the modeling calculation of the aeronautical floating involute spline coupling under actual working conditions is carried out in the Abaqus software in order to obtain the tooth surface contact stress of the spline coupling and the relative slip rate simulation results. The contact stress and the relative slip rate at the tooth surface nodes of the spline coupling obtained by simulation change with time increments, and they are brought into the optimized Archard formula. The trapezoidal formula is defined by a definite integral to calculate the spline coupling’s certain node depth of wear. The definite integral trapezoidal formula is applied to the optimized Archard calculation model, and the wear calculation model suitable for aviation floating involute spline couplings is finally determined, as shown in the following Equations (9)–(11):
where
is the wear base area, mm
2;
is a dimensionless unit;
h is the wear depth, mm;
is the length of the microsegment, and the subscript is the
ith microsegment;
is the speed of point
j on the curve at time
t of the
ith segment; and
is the stress at this point at time
t.
6. Conclusions
This study observed the tooth surface of the existing aviation involute spline coupling and analyzed the wear mechanism of the tooth surface. Through the analysis of the force on the tooth surface of the aviation floating involute spline coupling, the traditional Archard wear theory model was optimized, and finite element software was used to simulate the aviation floating involute spline coupling under different floating distances. Finally, through the wear parts of aviation floating involute spline coupling, the wear depth of the tooth surface was measured with a digital microscope to realize the combination of the wear calculation model proposed and the finite element method to calculate the aviation floating involute spline coupling. The results of the study are as follows:
(1) The mechanism of wear of the tooth surface of the failed parts was analyzed and obtained. The main form of aeronautical floating involute spline wear was obtained; it is mainly abrasive wear, and the abrasive wear is very serious, accompanied by slight adhesive wear and fretting. Oxidative wear continues to accelerate the wear of spline teeth.
(2) In view of the axial movement of the aviation floating involute spline coupling, the axial movement speed is coupled with the relative slip rate caused by contact between the teeth to obtain a suitable model for calculating the wear of involute spline couplings.
(3) The actual working conditions of the aviation floating involute spline coupling are simulated. When the floating distance is 0.3 mm, the wear depth of the tooth surface changes significantly, and the wear depth increases along the floating end, which intensifies the damage to the spline coupling. When the wear depth reaches a certain value, the spline coupling is severely deformed and cannot meet the usage requirements.