Abstract
This paper focuses on the issues of uneven load distribution caused by crossed axes and the lack of an effective flash temperature calculation method in the anti-scuffing design of herringbone gear. Based on the influence coefficient method, the paper proposes a non-Hertz contact analysis method for herringbone gear under crossed axes, considering the influence of geometric transmission errors and crossed axes errors on the initial contact gap. A dynamic calculation model for the flash temperature of herringbone gear tooth surfaces under non-Hertz contact is established by improving the Blok flash temperature formula. The accuracy of the proposed method is verified through comparison.
1. Introduction
Herringbone gear is widely used in high-speed and heavy-load applications due to their stable transmission and high load-carrying capacity. However, issues such as uneven load distribution and a lack of effective flash temperature calculation methods arise due to crossed axes, affecting gear performance and reliability. Therefore, it is crucial to study the non-Hertz contact flash temperature calculation method for herringbone gear under crossed axes.
2. Non-Hertz Contact Analysis Method for Herringbone Gear Tooth Surfaces under Crossed Axes
2.1 Calculation of Initial Contact Gap of Tooth Surfaces under Crossed Axes
Due to manufacturing and installation errors, the actual axes of the bearing seats do not completely coincide with the theoretical axes, and there are assembly gaps between the bearings and the bearing seats. This results in a slight crossed axes angle between the two gear axes in space, causing changes in the initial contact gap between the tooth surfaces of the two meshing gears.
The initial contact gap of the tooth surface is composed of the unloaded tooth gap and the normal gap of the tooth surface, which determine the load distribution of each tooth when bearing a load and the load distribution on the tooth surface at the instant of meshing.
Table 1. Influential Factors of Initial Contact Gap
| Factor | Description |
|---|---|
| Geometric transmission error | Influences the relative tooth gap when unloaded |
| Crossed axes error | Causes changes in the initial contact gap of the tooth surface |
2.2 Non-Hertz Contact Analysis of Herringbone Gear Tooth Surfaces
Since the teeth on both sides of the herringbone gear mesh simultaneously, the displacement and deformation of one side’s teeth cannot be considered in isolation from the load shared by the other side’s teeth and their meshing process.
This paper establishes a non-Hertz contact analysis model for herringbone gear under crossed axes by referring to Tsai’s deformation coordination equation. This method regards the total deformation at each point on the tooth surface as the result of the superposition of individual loads acting on the contact area and simultaneously considers the influence of tooth surface contact deformation and tooth bending deformation, avoiding the issue of limited contact width in Hertz theory.
3. Dynamic Calculation Model of Flash Temperature for Herringbone Gear Tooth Surfaces Based on Non-Hertz Contact
3.1 Calculation of Relative Sliding Speed at Discrete Points in the Tooth Surface Contact Area
The position vectors and normal vectors of points on the contact area can be obtained from the coordinate system of the contact point, allowing the calculation of the relative sliding speed at discrete points.
3.2 Calculation of Friction Coefficient at Discrete Points in the Tooth Surface Contact Area
The flash temperature of the tooth surface causes changes in the viscosity of the lubricating oil within this range, which in turn affects the change in the friction coefficient of the tooth surface. This, in turn, will affect the change in the flash temperature of the tooth surface.
The friction coefficient at discrete points can be calculated using the following formula:
Where Vt1,j,i and Vt2,j,i are the tangential velocities of the driving and driven gear at discrete point i; R1,j,i and R2,j,i are the curvature radii of the driving and driven gears at discrete point i; Ra1 and Ra2 are the roughnesses of the driving and driven gear; and LX is the correction coefficient of the lubricating oil.
3.3 Dynamic Calculation of Flash Temperature for Herringbone Tooth Surfaces Based on Non-Hertz Contact
This paper discretizes the tooth contact line into two dimensions, calculates the contact stress at discrete points on the contact line using the non-Hertz contact analysis method, and considers the contact half-width varying along the tooth width. A dynamic calculation model for the flash temperature of herringbone gear tooth surfaces based on non-Hertz contact is established, as shown in the following formula:
Where Pj,i is the load at discrete point i on the j-th meshing tooth surface; Bj,i is the corresponding contact half-width at point i; Vj,i and Vr,j,i are the sliding speed and rolling speed, respectively; c is the specific heat capacity; ρ is the density; and fj,i is the friction coefficient.
4. Results and Analysis
4.1 Verification of the Non-Hertz Contact Model for Herringbone Gear Tooth Surfaces
Under high-speed and heavy-load conditions, the contact stress distribution of the herringbone gear tooth surfaces calculated using the non-Hertz contact method, Romax industrial simulation software, and the traditional LTCA method are compared.
Table 2. Comparison of Contact Stress Distribution Calculation Methods
| Method | Contact Stress Distribution | Accuracy |
|---|---|---|
| Non-Hertz Contact Method | Accurate distribution, varying contact half-width | High |
| Romax Simulation | Consistent with non-Hertz method, but limited to specific software | Medium |
| Traditional LTCA Method | Idealized contact area, constant contact half-width | Low |
4.2 Analysis of Flash Temperature Results
The flash temperature results based on the dynamic calculation model for non-Hertz contact herringbone tooth surfaces. The flash temperature is highest in the long axis direction within the contact area.
When there is a crossed axes error in the herringbone gear, the uneven load distribution on the left and right tooth surfaces leads to differences in flash temperature between the two sides.
5. Conclusion
This study improves the method for determining the contact half-width in the Blok flash temperature formula, expanding its application from Hertz contact to non-Hertz contact and enabling continuous.