Optimization of Gear Tooth Surfaces

SAE International Journal of Passenger Cars - Mechanical Systems, 2013

The static transmission error is a well-recognized source, and thus tooth modifications are often undertaken to minimize the excitation at specific loads to reduce gear whine noise [1]. Yet, at high torque loads, noise levels are still relatively high [2]. This suggests that tooth surface waviness and sliding friction could manifest itself as an alternate noise source. For instance, Mark [3] found that the surface waviness is related to the machining process kinematics. Furthermore, the experiments conducted by Mitchell [4] and Amini et al. [5] on gears and by Othman et al. [6] on rotating disks show an increase in the sound level with an increase in the surface waviness amplitude. The role of tooth surface waviness on gear noise is not well understood, especially for structure-borne noise source(s) or path(s), due to the complexity in modeling micro-surface characteristics. This article employs a six degree of freedom (6DOF) linear timevarying (LTV) model of a spur gear pair to quantify the structure-borne noise source and to illustrate a relationship between waviness amplitude and wave number to gear dynamics source and resulting sound radiation. The overall procedure for predicting the sound pressure level (L) is previewed in Fig. 1, where θ is the angular displacement of the pinion or gear, while x and y are the translational motions along the line-of-action (LOA) and the off-line-of-action (OLOA) directions, respectively. Subscripts p and g represent pinion and gear, respectively. (Also, refer to the list of symbols for the identification of variable and parameters.) LINEAR TIME-VARYING SPUR GEAR MODEL The proposed 6DOF LTV model is schematically shown in Fig. 2. The gear and pinion are considered rigid discs of polar moments of inertia J p and J g with external torques T p and T g. Here, h p (t) and h g (t) represent tooth surface waviness with respect to perfect involute profiles. The governing equations are described by torsional and translational motions. The effective shaft-bearing stiffness elements are given by k pSx and k gSx in the X direction (LOA) and k pSy and k gSy in the Y direction (OLOA). The time-varying mesh stiffness (k(t)) is calculated for a range of torques by using a well-known gear contact mechanics code (Load Distribution Program or LDP) [7]. The parameters of the unity gear pair example used in this study are as follows: Number of teeth = 28, outside diameter = 94.95 mm; root diameter = 79.73 mm; diametral pitch = 0.315 m −1 ; center distance = 88.9 mm; pressure angle = 20°; face width = 6.35mm; tooth thickness = 4.851 mm; and elastic modulus = 206.9 kN/mm 2. Further, it is assumed that the bearings of the gear and pinion are frictionless, and the waviness amplitude is independent of the load.

Strojniški vestnik – Journal of Mechanical Engineering, 2012

The basic hypothesis of the paper is that machine part surfaces are membranes that divide inner and outer space, receive disturbance power from inner space and emit it to the surroundings. Additionally, machine systems operation causes numerous disturbances such as collisions, sliding, rolling, etc. Gear drives are a very interesting case for analysis of teeth impacts, which cause restorable free vibrations and spreading of disturbance power through elastic structure. The gear unit housing has a dominant role in the transformation of disturbance power and modulation of the sound emitted to the surroundings. This is an important detail for monitoring and diagnostics by emitted noise measurements. By combination of theoretical, numerical and experimental analyses, using a classical gear drive unit (reducer), this article explains the process of spreading disturbance power through the elastic structure, especially the role of the gear unit housing. Its role in the noise frequency spectrum modulation is determined by modal sensitivity to disturbances and noise isolation ability of the housing. The analysis of modal behavior of the housing and its modal shape excitation presents the main content of the paper.

IOP Conference Series: Materials Science and Engineering, 2019

The purpose to optimize gears requires a very good understanding of their dynamic behaviour. Very important is the influence of vibrations on the operation of the gears. As a result of environmental constraints such as acoustics, gears are increasingly subject to stringent requirements in terms of load capacity, efficiency, noise and vibrations. The deformations of the gears involve deformations, in particular, located near the contacts that require great finesse. Gearboxes are equally sources of current vibrations as they are commonly used in industry. They are the subject of numerous studies to characterize their kinematic and dynamic behaviour. At present, research activities focus on the development of multidisciplinary experimental, theoretical and numerical skills that are put into play when designing structures, machine elements or, in general, mechanical systems. In this paper, we have proposed to find the dynamic response of the gearbox to the action of external disturbing factors. To this end, we have called for the use of integral transformations which, algebraizing the problem, greatly simplifies calculations.

American Journal of Engineering and Applied Sciences

The paper presents an original method for the determination of the yield of the gearbox, gears forces, gearbox and power. It analyzes the influence of certain parameters which affects the efficiency of the gearbox. Also an original method for the determination of the yield of the drive shafts oriented on the basis of the ratio of contact is presented the brief. The relations submitted, can be dynamic synthesis of the drive shafts oriented, in order to enhance the effectiveness of the mechanisms of mesh.

MATEC Web of Conferences

Search for an improved gear tooth flank shape arose from heavy industry problems rolling mills. Original involute gears suffered severe flank damages. So, better gear teeth flanks should improve contact circumstances, decrease the flank pressure, and enhance a lubrication film. This was achieved by a curved, pole symmetric path of contact by purely graphical methods. And the developed gears, proven in heavy industry applications, showed highly improved properties. Specimens of both gear geometries, which were made of tempered and nitrided alloy steel, were tested on an FZG testing machine, and results confirmed the theoretical foundations of S-gears. Then it was necessary to replace the graphical method by a numerical one and to define the tool. So, the rack profile was defined by a pole symmetric parabolic-type function, which in turn defined the path of contact and finally gears with an arbitrary number of teeth. Many applications were developed with S-gear shape, e.g., helical, c...