# Comparison of Selected Parameters of a Planetary
## 1 Introduction  
The main contribution of this article is the analysis of the convex-concave teeth flanks used by a common mechanism broadly used in the automotive industry to show the potential of the small change of the tooth flank spline to the parameters influencing the service life of the gearbox (contact pressures, specific slide ratios) and the quality of the teeth contact (contact ratio). The research presents the results of the performed calculations for small external module and especially the internal gears, which had not yet been published. The application of the convex-concave gear teeth flanks in the reduced planetary gearbox design is not yet known. Smaller size gear arrangements of various plastic materials are becoming widespread due to their properties, such as wear resistance during dry running, low noise emission, good vibration damping, low inertia, low production costs, etc. Plastic gearboxes can be suitable for mass production in terms of production and manufacturing processes, where can be formed with other parts as one body, and they have outstanding functional features in terms of vibration reduction, low tar weight, and good corrosion resistance [1]. However, they display temperature-related problems, such as a rapidly decreasing load, thermal expansion, and the accuracy of formed gear parts. Therefore, the challenge to overcome is the production of gears with sufficient accuracy and durability such that they can be used in modern mechatronic applications in the automotive industry, medical equipment, electronics, and many other industries [2]. The selection of the right production structure is the keyelement in the design process of any production system because the structure used has long-term consequences for the efficiency, productivity, and operational costs of the designed system [3]. Planetary gears are widely used in aerospace applications, including space manipulators and satellite antenna propulsion mechanisms [4]. Rotating machine parts, such as shafts, bearings, and gears, are subject to a deterioration of performance, which if left unattended, may lead to failure or damage to the entire system [5]. Typical gear faults include chipped teeth, tooth breakages, root cracks, wear, pitting, and surface damage [6]. These forms of failure can lead to system imbalances and deterioration of the machining precision [7]. The presence of many faults in transmissions generates difficulties in their proper diagnosis. Diagnostics of these systems focus on digital signal processing (DSP) technologies, including the analysis of time (statistical) and frequency (spectral) domains [8]. Many researchers use methods such as Fourier and wavelet transforms [7; 9; 10], as well as Hilbert transforms (HTs) [11; 12] or neural networks [13], to detect defects and operational parameters in rotating systems. These methods give quick results, but they do not allow for easy retrieval of information hidden in noisy or non-stationary time series. The application of recurrence plots analysis seems to be adequate for obtaining additional information coming from measurements [14]. Therefore, the identification of faults in gears has become an important subject of extensive research over the past decade [7; 9; 10; 15]. In addition, the issues of wear mechanisms of mechanical systems of vehicles and combustion engines, as well as transmissions, are still an important issue. Many researchers show interest in damage to rotary units, such as turbochargers [16], kinematic pairs of charge exchange systems in combustion engines [17; 18; 19], injection systems [19; 20; 21; 22; 23], diesel engine [24; 25; 26; 27], and the reliability of various types of gears [6; 7; 13; 15; 28]. The main advantage of the convex-concave gears is the lowering of the contact pressure using teeth flank meshing and the lowering of the slide ratios compared to involute gears [29]. The research shows that the scoring resistance of tooth flanks can be significantly raised by using special convex-concave profiles in plain tooth gears [30].