# The Impact of Pitch Error on the Dynamics and Transmission Error of Gear Drives
## 1 Introduction  
Gear whine remains one of the most persistent comfort issues in modern power-trains, especially in battery electric vehicles where the masking effect of an internal combustion engine is absent. A long research tradition attributes the tonal component of this noise to transmission error (TE), the deviation between the theoretical and actual angular position of the driven gear [1, 2]. TE captures both the quasi-static displacement caused by mesh stiffness variation and the dynamic response arising from system inertia, making it a powerful, load-independent indicator of gear quality [3]. Recent loaded tooth contact analyses that integrate measured profile maps can predict static TE with sub-micron fidelity and show excellent agreement with bench tests [4]. Among the many sources of TE, manufacturing deviations in tooth spacing--commonly referred to as pitch or indexing errors--have been shown to enlarge peak-to-peak TE and excite low-frequency shaft order tones [5]. Monte Carlo robustness studies further reveal that even micrometer-scale macrogeometry deviations (tip diameter, center distance) can raise peak-to-peak static TE by more than 30% across the operating torque range [6]. At the tooth level, optimized microgeometry modifications--such as lead crowning and tip relief--remain the most effective countermeasure; hybrid spur experiments have demonstrated up to 40% TE attenuation without mass penalties [7]. Nevertheless, design trade-offs persist, because a correction that flattens TE at one load can amplify it at another [7]. To evaluate these competing effects, researchers combine analytical thin-slice formulations with high-fidelity finite-element or semi-analytical contact solvers [3], while NASA-derived dynamic codes still serve as benchmarks for studying pitch error superposition and profile relief effectiveness [8]. On the system level, multibody dynamics (MBD) platforms such as **MSC ADAMS** translate quasi-static TE inputs into housing vibration and acoustic response, enabling the virtual prototyping of gearbox faults [9; 10]. Despite these advances, the isolated impact of measured pitch error--decoupled from intentional microgeometry--remains underexplored for helical gears operating in the low-frequency shaft order regime relevant to e-powertrains. The present study therefore quantifies how realistic pitch error reshapes quasi-static TE and the accompanying dynamic mesh forces in a single-stage helical reducer. By combining a loaded tooth contact analysis calibrated with shop-floor pitch charts and an MBD model of the entire drivetrain, we provide new insight into the sensitivity of TE to indexing faults and establish design guidelines for pitch quality targets in next-generation quiet gearboxes. Recent studies have highlighted the pronounced effects of gear pitch errors on drivetrain NVH characteristics. [PERSON] et al. (2017) [11], for example, showed that even small pitch errors in helical gears increase mesh stiffness variation and elevate both the loaded transmission error (TE) and vibration levels (as measured by the RMS of mesh acceleration), while also shifting the gear's resonant frequencies. Manufacturing-induced pitch errors degrade the smoothness of meshing and tend to amplify gear noise and vibration [11]. [PERSON] and [PERSON] (2018) integrated actual measured pitch errors into a dynamic helical gear model and found a marked deterioration in contact stability and an increase in dynamic TE, which corresponded with higher vibration amplitudes and the onset of complex nonlinear responses [12]. In a similar vein, [PERSON] et al. (2021) reported that introducing a periodic pitch error in a nonlinear helical gear pair model had the most significant influence on the system's torsional vibration, substantially amplifying oscillation magnitudes and triggering rich bifurcation and chaotic behavior as the error magnitude grew [13]. Even for spur gears, recent analyses confirm that pitch imperfections can dramatically worsen dynamics. [PERSON] et al.