Analytical determination of back-side contact gear mesh stiffness

• Analytical derivation of the back-side mesh stiffnesses for arbitrary gear pairs
• Quantitative determination of the impact from backlash and center distance changes
• Essential results for the static and dynamic analysis of gear systems

Back-side gear tooth contact happens when anti-backlash (or scissor) gears are used, tooth wedging or tight mesh occurs, or vibration amplitudes are high enough that teeth separate and pass the backlash zone. An accurate description of the back-side gear tooth mesh stiffness is needed to study gear mechanics in such cases. This work studies the time-varying back-side mesh stiffness and its correlation with backlash by analyzing the relationship between the drive-side and back-side mesh stiffnesses. Results of this work yield the general form of the back-side mesh stiffness in terms of the known drive-side mesh stiffness for an arbitrary gear pair. The analytical results are confirmed by simulation results from gear contact analysis software that precisely tracks drive- and back-side gear tooth contact.