## 1 Introduction  
Due to high power density, high reliability, as well as high transmission efficiency, gear transmission devices are widely applied to wind turbine, marine, automotive, and other industrial fields. Owing to manufacturing and heat treatment processes, which cause tooth displacement relative to its ideal position, manufacturing errors with various distribution forms and different magnitudes can be found in actual gears. During the past several decades, a great deal of researchers have investigated the dynamic behaviors of spur/helical gear systems (in consideration of manufacturing errors) in published works. Gear errors consist of short and long period components. The short period gear errors were usually assumed as simple harmonic functions related to mesh frequency, the long period ones were regarded as a sine wave related to shaft frequency, and the time-varying mesh stiffness was regarded as a stiffness excitation which was independent with gear errors [1; 2; 3; 4; 5]. Moreover, when gear errors are introduced, the three-dimensional contact state of the tooth surface will differ under different load conditions. The phenomenon of partial contact loss may occur and lead to the changes of mesh stiffness and transmission error [6; 7; 8; 9]. Hence, there is a nonlinear coupling relationship between mesh stiffness and gear errors because the contact patterns are dependent with load conditions. The short period gear errors mainly include profile deviation, helix deviation, and gear modification. Mesh misalignment [10], which is caused by mounting errors and system deflection, is also regarded as a special short period gear error. Some scholars established the calculation models of load distribution [11; 12; 13; 14], mesh stiffness, and transmission error [15; 16; 17; 18] in consideration of short period gear errors, and further numerically and experimentally investigated the dynamic behaviors of gear system [19; 20; 21]. Cumulative pitch deviation is a very important and inevitable long period gear error. When introducing the long period gear error, the gear engagement processes will differ during different mesh cycles, and the system will be subjected to hybrid mesh excitations related to the mesh frequency and shaft frequency. In published works, considering cumulative pitch deviations, the determination of long period mesh excitations using three-dimensional contact analysis and dynamic behaviors analysis of gear system are rather rare. In recent years, few relevant research was conducted, and most of the research focused on the spur gear pair. [PERSON] [22] developed an enhanced model to study the influence of cumulative pitch deviation on load sharing ratio, as well as static transmission error (STE) and dynamic mesh forces of a spur gear pair. The results showed that index errors not only influence the vibration and noise, but also lead to high overloads. [PERSON] [23] and [PERSON] [24] employed a special test setup with transmission ratio of 1:1 to study the effect of tightly controlled intentional cumulative pitch deviations on the baseline vibration responses and vibration frequency spectrum of spur gear pairs. Moreover, [PERSON] [25] preliminarily investigated the influences of sinusoidal cumulative pitch deviations on mesh excitations and frequency spectrum of a helical gear pair. In engineering practices, the pitch deviation values distributed over gear teeth usually has random characteristic because of manufacturing tolerance. For helical gear pairs, the number of teeth engaged at the same time is more than spur gear pairs. In addition, gear tooth flank is usually modified in order to reduce vibration. At this time, gear modification and cumulative pitch deviation have a comprehensive influence on tooth engagement process of helical gear pairs. Thus, the effects of cumulative pitch deviations on long period mesh excitations and vibration responses of the helical geared rotor system (HGRS) are much more complex. The relevant researches have not been reported in published works.