An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response

1999 ◽  
Vol 122 (4) ◽  
pp. 508-514 ◽  
Author(s):  
Anette Andersson
Keyword(s):  
Dynamic Response ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Contact Ratio ◽  
Constant Stiffness ◽  
Gear Mesh ◽  
Critical Rotational Speed ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

Further Evaluation of Spur Gear Tooth Profile Designs Used in Heavily Loaded Transmissions

2011 ◽  
Author(s):  
Nihat Yıldırım ◽  
Hakan I˙s¸c¸i ◽  
Abdullah Akpolat
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Design Parameters ◽  
Preference Order ◽  
Spur Gears ◽  
Tooth Root ◽  
Contact Ratio ◽  
Practical Applications

Aerospace applications require special procedures for component design and manufacturing. Spur gears of different designs, because of their simpler geometries, are used in vital units-transmissions of helicopters and alike aerospace vehicles. In this study, performances of various profile designs of previously researched low and high contact ratio spur gears with some realistic design parameters are studied. Effects of the realistic parameters of variable tooth pair stiffness, relief shape, and adjacent pitch error on Transmission Error (TE), tooth loads and root stresses are presented; composition of these parameters determines the efficiency of the gearbox assembly. Detail of minimization of tooth root stress through optimized/proper design of relief is described. More comprehensive comparison of the gear tooth profile design cases is done to be able to guide aerospace transmission designers for practical applications with realistic parameters for each of the design cases. A preference order is done among the design cases, depending on effect of some design parameters on the results such as tooth loads, tooth root stresses, TE curves and peak-to-peak TE values.

A parameterized numerical model for the evaluation of gear mesh stiffness variation of a helical gear pair

2008 ◽  
Vol 222 (7) ◽  
pp. 1321-1327 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Numerical Model ◽  
Transmission Error ◽  
Helical Gear ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Fe Method ◽  
Gear Design ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

One of the most common challenges in gear drive design is to determine the best combination of gear geometry parameters. These parameters should be capable of being varied effectively and related to gear mesh stiffness variation in advanced excitation and vibration analysis. Accurate prediction of gear mesh stiffness and transmission error requires an efficient numerical method. The parameterized numerical model was developed for the evaluation of excitation induced by mesh stiffness variation for helical gear design purposes. The model uses linear finite-element (FE) method to calculate tooth deflections, including tooth foundation flexibility. The model combines Hertzian contact analysis with structural analysis to avoid large FE meshes. Thus, mesh stiffness variation was obtained in the time and frequency domains, which gives flexibility if comparison is made with measured spectrums. Calculations showed that a fairly low number of elements suffice for the estimation of mesh stiffness variation. A reasonable compromise was achieved between design trends and calculation time.

Effect of Involute Contact Ratio on Spur Gear Dynamics

1999 ◽  
Vol 121 (1) ◽  
pp. 112-118 ◽  
Author(s):  
A. Kahraman ◽  
G. W. Blankenship
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Design Guidelines ◽  
Forced Response ◽  
Contact Ratio ◽  
Test Rig ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Selection Of

The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

Evaluation of spur gear mesh compliance using the finite element method

1999 ◽  
Vol 213 (6) ◽  
pp. 569-579 ◽  
Author(s):  
M H Arafa ◽  
M M Megahed
Keyword(s):  
Finite Element ◽  
Experimental Methods ◽  
Spur Gear ◽  
Spur Gears ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Fe Modelling ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Gear Mesh Stiffness

This paper presents a finite element (FE) modelling technique to evaluate the mesh compliance of spur gears. Contact between the engaging teeth is simulated through the use of gap elements. Analysis is performed on several gear combinations and the variation in tooth compliance along the contact location is presented in a non-dimensional form. Results are compared with earlier predictions based on analytical, numerical and experimental methods. Load sharing among the mating gear teeth is discussed, and the overall gear mesh stiffness together with its cyclic variation along the path of contact is evaluated.

scholarly journals Selection of Pressure Angle based on Dynamic Effects in Asymmetric Spur Gear with Fixed Normal Contact Ratio

2019 ◽  
Vol 69 (3) ◽  
pp. 303-310
Author(s):  
Benny Thomas ◽  
K. Sankaranarayansamy ◽  
S. Ramachandra ◽  
Suresh Kumar S.P.
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Dynamic Factor ◽  
Spur Gears ◽  
Contact Ratio ◽  
Normal Contact ◽  
Pressure Angle ◽  
Side Pressure ◽  
Static Transmission Error

Asymmetric spur gears are finding application in many fields including aerospace propulsion and automobile which demand unidirectional or relatively higher load on one side of the gear flank. Design intend to maximise the load carrying capacity of the drive side of asymmetric gear by increasing the pressure angle is achieved at the expense of coast side capacity. Multiple solution for coast to drive side pressure angle exist for a given contact ratio and each of these have relative merits and demerits. In the present work asymmetric spur gears of theoretically equal contact ratio as that of corresponding symmetric gears are selected to investigate the change in gear tooth static transmission error and dynamic behaviour with coast and drive side pressure angle. Study shows that dynamic factor of normal contact ratio asymmetric spur gears below resonance speed are relatively lower than corresponding symmetric gears of same module, contact ratio, number of teeth, coast side pressure angle and fillet radii. Results also show that, coast and drive side pressure angle can be suitably selected for a given contact ratio to reduce the single tooth and double tooth contact static transmission error and dynamic factor of asymmetric spur gears.

Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears

1986 ◽  
Vol 108 (1) ◽  
pp. 86-94 ◽  
Author(s):  
M. S. Tavakoli ◽  
D. R. Houser
Keyword(s):  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Errors ◽  
Gear Mesh ◽  
Starting Point ◽  
Frequency Components ◽  
Design Loads ◽  
Static Transmission Error ◽  
Optimum Profile

A procedure for computing static transmission errors and tooth load sharing was developed for low and high contact ratio internal and external spur gears. A suitable optimization algorithm was used to minimize any combination of the harmonics of gear mesh frequency components of the static transmission error. Different combinations of tip and root relief may be used to achieve optimization. These include varying the starting point of relief and varying the magnitude of relief, and selecting the gear and/or the pinion teeth to be tip and/or root-relieved. Also, there exists an option for using either linear or parabolic relief. In addition to the presentation of optimal profile modifications, the effects of off-design loads, nonoptimum modifications, and random spacing errors are presented.

Modelling of spur gear mesh stiffness and static transmission error

1998 ◽  
Vol 212 (4) ◽  
pp. 287-297 ◽  
Author(s):  
S Du ◽  
R B Randall ◽  
D W Kelly
Keyword(s):  
High Precision ◽  
Transmission Error ◽  
Spur Gear ◽  
Mesh Stiffness ◽  
Transmission Errors ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Simulation Results ◽  
Gear Mesh Stiffness ◽  
Error Computation

A modified transmission error (TE) model is introduced for analysing the effects on the transmission error of variation of tooth body stiffness with load application point, and a simulation program for transmission error computation with varying stiffness has been developed. In order to obtain the case where the tooth deflection component is the dominant source of the TE, nylon gears were used in this study. All the simulation results have been compared with the measured transmission errors from a single-stage gearbox. Even though carried out on low precision gears, the validity of the model for the more flexible nylon gears indicates that the model can be used for analysing the transmission error of high-precision gear sets.

Design of High Speed Gears, Low Load Gears for Minimizing Gear Whine Noise

2013 ◽  
Author(s):  
Rodney Glover
Keyword(s):  
High Speed ◽  
Sliding Friction ◽  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Contact Ratio ◽  
Low Load ◽  
Gear Manufacturing ◽  
The Cost

The main purpose of the supercharger timing gears is to keep the rotors from contacting each other. They are often lightly loaded and designed for low noise. As timing gears, they have by definition a ratio of 1.0. Furthermore, the timing gears are presently spur gears due to the cost of assembling helical gears onto the rotor shafts without allowing timing errors between the rotors. The original timing gear designs were spur gears with contact ratios slightly above 2.0. A major NVH issue has been gear whine noise, because most applications are in luxury vehicles and are evaluated with the hood open and the engine at idle. In this operating condition, the background noise is very low and any tonal gear whine noise is audible. The first effort was to push the gear manufacturing quality to the limits of modern grinding capability. In order to further reduce gear whine noise, the designs have evolved to finer pitch gearing with a contact ratio over 3.0 to reduce transmission error. Micro-geometries were optimized for low transmission error (TE) at low load. OSU Gear Lab’s RMC and LDP became primary tools in optimizing the gear designs for minimum TE. An important factor when increasing the contact ratio is to not increase the sliding friction significantly to keep the fixed oil sump temperature from increasing too much and cause wear issues in operation. Typically, the new high contact ratio spur gear designs in production have reduced the gear whine levels by more than 6 dB and have had very few noise complaints.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

Low excitation spur gears with variable tip diameter

2021 ◽  
Vol 263 (5) ◽  
pp. 1275-1285
Author(s):  
Joshua Götz ◽  
Sebastian Sepp ◽  
Michael Otto ◽  
Karsten Stahl
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Low Noise ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Axial Forces ◽  
Tooth Width ◽  
Drive Trains ◽  
Static Transmission Error

One important source of noise in drive trains are transmissions. In numerous applications, it is necessary to use helical instead of spur gear stages due to increased noise requirements. Besides a superior excitation behaviour, helical gears also show additional disadvantageous effects (e.g. axial forces and tilting moments), which have to be taken into account in the design process. Thus, a low noise spur gear stage could simplify design and meet the requirements of modern mechanical drive trains. The authors explore the possibility of combining the low noise properties of helical gears with the advantageous mechanical properties of spur gears by using spur gears with variable tip diameter along the tooth width. This allows the adjustment of the total length of active lines of action at the beginning and end of contact and acts as a mesh stiffness modification. For this reason, several spur gear designs are experimentally investigated and compared with regard to their excitation behaviour. The experiments are performed on a back-to-back test rig and include quasi-static transmission error measurements under load as well as dynamic torsional vibration measurements. The results show a significant improvement of the excitation behaviour for spur gears with variable tip diameter.

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