Interesting Eigenvalue Behavior in High-Speed Planetary Gears With Gyroscopic Effects

2013 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Planetary Gear ◽  
Gyroscopic System ◽  
Critical Speeds ◽  
High Speeds ◽  
Lumped Parameter ◽  
Axially Moving ◽  
Gyroscopic Effects ◽  
Moving Media ◽  
Gyroscopic Systems

This study demonstrates interesting and unusual gyroscopic system eigenvalue behavior observed in a lumped-parameter planetary gear model. The focus of this work is on the eigenvalue phenomena that occur at especially high speeds rather than practical planetary gear behavior. The behaviors include calculation of exact trajectories across critical speeds, uncommon stability features near degenerate critical speeds, and unique stability transitions. These eigenvalue behaviors differ from those of other gyroscopic systems such as spinning disks, shafts, and rings, and axially-moving media.

Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Eigenvalue Problems ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
High Speeds ◽  
Wide Range ◽  
Modal Property ◽  
Gyroscopic Effects ◽  
Complex Valued

This study investigates the modal property structure of high-speed planetary gears with gyroscopic effects. The vibration modes of these systems are complex-valued and speed-dependent. Equally-spaced and diametrically-opposed planet spacing are considered. Three mode types exist, and these are classified as planet, rotational, and translational modes. The properties of each mode type and that these three types are the only possible types are mathematically proven. Reduced eigenvalue problems are determined for each mode type. The eigenvalues for an example high-speed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds.

Dynamic Modeling of Multi-Stage Planetary Gears Coupled with Bearings in Housing

2011 ◽  
Vol 86 ◽  
pp. 30-34
Author(s):  
Zheng Ming Xiao ◽  
Da Tong Qin
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Parameter Method ◽  
Rotational Degree ◽  
Planetary Gears ◽  
Multi Stage ◽  
Lumped Parameter ◽  
Shield Tunnelling ◽  
Gyroscopic Effects

This work develops an analytical model of multi-stages planetary gear transmission (PGT) coupled with bearings in housing based on analyzing the displacement relationships of gearing system. The model adopts three planar degree-of-freedom for each of the central components, and the rotational degree-of-freedom for the planets of each stage. Considering the gyroscopic effects, the modified transverse-torsional model is established in the rotating Cartesian coordinates by lumped-parameter method, which is more accurate and may match with the physical model better than the purely torsional model. According to the design parameters of the 3-stage planetary gears of main reducer of shield tunnelling machine, the natural frequencies and vibration modes are investigated by using this transverse-torsional model.

scholarly journals Planetary transmission for propeller propulsion in the new generation of flying models

Mechanik ◽  
2019 ◽  
Vol 92 (4) ◽  
pp. 282-284
Author(s):  
Jakub Sikorski ◽  
Witold Pawłowski ◽  
Łukasz Kaczmarek ◽  
Mariusz Stegliński ◽  
Sebastian Lipa ◽  
...  
Keyword(s):  
High Speed ◽  
High Performance ◽  
Planetary Gear ◽  
High Strength ◽  
Innovative Design ◽  
Gear Design ◽  
Low Weight ◽  
Planetary Transmission ◽  
Gyroscopic Effects ◽  
New Generation

The article presents a planetary gear design, which in combination with an electric motor will allow to obtain an increased torque enabling the propulsion of large, high-performance propellers of modern flying models. The proposed solution allows the use of standard high-speed DC or brushless motors. In addition, the innovative design of the transmission provides high stiffness of the mechanism necessary to counteract the gyroscopic effects generated by the large propeller. The use of high-strength aluminum alloy ensures low weight of the entire mechanism.

scholarly journals Investigation of Dynamic Load Sharing Behavior for Herringbone Planetary Gears considering Multicoupling Manufacturing Errors

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Fei Ren ◽  
Jinchen Ji ◽  
Guofu Luo ◽  
Shaofu Zhao ◽  
Liya Zhao ◽  
...  
Keyword(s):  
Planetary Gear ◽  
Load Sharing ◽  
Gear Train ◽  
Actual Structure ◽  
Lumped Parameter ◽  
Manufacturing Errors ◽  
Main Components ◽  
Gyroscopic Effects ◽  
Profile Errors ◽  
Sharing Behavior

In this study, based on the lumped-parameter theory and the Lagrange approach, a novel and generalized bending-torsional-axial coupled dynamic model for analyzing the load sharing behavior in the herringbone planetary gear train (HPGT) is presented by taking into account the actual structure of herringbone gears, manufacturing errors, time-dependent meshing stiffness, bearing deflections, and gyroscopic effects. The model can be applied to the analysis of the vibration of the HPGT with any number of planets and different types of manufacturing errors in different floating forms. The HPGT equivalent meshing error is analyzed and derived for the tooth profile errors and manufacturing eccentric errors of all components in the HPGT system. By employing the variable-step Runge–Kutta approach to calculate the system dynamic response, in conjunction with the presented calculation approach of the HPGT load sharing coefficient, the relationships among manufacturing errors, component floating, and load sharing are numerically obtained. The effects of the combined errors and single error on the load sharing are, respectively, discussed. Meanwhile, the effects of the support stiffness of the main components in the HPGT system on load sharing behavior are analyzed. The results indicate that manufacturing errors, floating components, and system support stiffness largely influence the load sharing behavior of the HPGT system. The research has a vital guiding significance for the design of the HPGT system.

Vibration Structure of Gyroscopic Planetary Gears

2011 ◽  
Author(s):  
Christopher G. Cooley ◽  
Robert G. Parker
Keyword(s):  
High Speed ◽  
Eigenvalue Problems ◽  
Planetary Gear ◽  
Vibration Modes ◽  
Planetary Gears ◽  
High Speeds ◽  
Wide Range ◽  
Mode Method ◽  
Complex Valued

This study investigates the vibration structure of high-speed, gyroscopic planetary gears. The vibration modes of these systems are complex-valued and speed dependent. Three mode types exist, and these are classified as planet, rotational, and translational modes. Each mode type is mathematically proven by the use of a candidate mode method. Reduced eigenvalue problems are determined for each mode type. The eigenvalues for an example high-speed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds.

Quasi-static and dynamic analyses of thin-webbed high-speed gears: Centrifugal effect influence

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7282-7291
Author(s):  
B Guilbert ◽  
P Velex ◽  
P Cutuli
Keyword(s):  
Finite Elements ◽  
High Speed ◽  
Operating Conditions ◽  
Centrifugal Effect ◽  
High Speeds ◽  
Load Distributions ◽  
Lumped Parameter ◽  
Dynamic Analyses ◽  
Gear Geometry

The objective of this paper is to analyse the effect of centrifugal effects on thin-rimmed/-webbed gears. To this end, an original hybrid gear model is used, which combines lumped parameter elements, finite elements and condensed sub-structures along with a mortar-based mesh interface aiming at coupling mismatched models. It is shown that due to gear body flexibility, centrifugal effects can strongly modify geometry and, consequently, tooth load distributions at high speeds. The possibility to counterbalance these effects by introducing profile and lead modification is investigated. It is finally shown that for the effective tooth design, both thin-rimmed gear geometry and operating conditions must be accounted for.

scholarly journals Theoretical and Experimental Analysis of Dynamic Characteristics for a Valve Train System

Sensors ◽  
2021 ◽  
Vol 21 (19) ◽  
pp. 6328
Author(s):  
Bo Hu ◽  
Yunzhe Li ◽  
Lairong Yin
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Industrial Applications ◽  
Valve Train ◽  
Dynamic Responses ◽  
Engine Vibration ◽  
High Speeds ◽  
Proposed Model ◽  
Gyroscopic Effects ◽  
Train System

The valve train is one of the main sources of engine vibration, and its dynamic performance is crucial for output power and fuel consumption. The flexibilities of slender bars and beams should be emphasised in the design of valve trains to develop high-power and high-speed engines with industrial applications. A flexible dynamic model of a valve train system is proposed. In the proposed model, the components, except the cam and gear bodies, are modelled as flexible bodies with multidirectional deformations. The gyroscopic effects of the camshaft, cams and gear discs are also considered to predict dynamic responses at high speeds accurately. Gear meshing, the friction of the cam–tappet pair, the centrifugal force of the cams and valve clearance are also considered. Experiments on housing vibration and pushrod stress are conducted to validate the proposed model. Results show that the proposed model can predict the dynamic stress of the flexible components well and predict the trend shown by the housing vibration. The proposed model shows that excessive cam rotation speed and valve clearance will cause intense bounce and jump phenomena. The proposed model can be an important reference for designing engine work speed, adjusting valve clearance and improving component durability.

A Statistical Study of Process Variables to Optimize a High Speed Curtain Coater: Part I

TAPPI Journal ◽  
2009 ◽  
Vol 8 (1) ◽  
pp. 20-26 ◽  
Author(s):  
PEEYUSH TRIPATHI ◽  
MARGARET JOYCE ◽  
PAUL D. FLEMING ◽  
MASAHIRO SUGIHARA
Keyword(s):  
Boundary Layer ◽  
Experimental Design ◽  
High Speed ◽  
Statistical Study ◽  
Process Variables ◽  
High Speeds ◽  
The Stability ◽  
Air Removal ◽  
Removal System

Using an experimental design approach, researchers altered process parameters and material prop-erties to stabilize the curtain of a pilot curtain coater at high speeds. Part I of this paper identifies the four significant variables that influence curtain stability. The boundary layer air removal system was critical to the stability of the curtain and base sheet roughness was found to be very important. A shear thinning coating rheology and higher curtain heights improved the curtain stability at high speeds. The sizing of the base sheet affected coverage and cur-tain stability because of its effect on base sheet wettability. The role of surfactant was inconclusive. Part II of this paper will report on further optimization of curtain stability with these four variables using a D-optimal partial-facto-rial design.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

RED CUT COBALT

Alloy Digest ◽  
1980 ◽  
Vol 29 (8) ◽  
Keyword(s):  
Fracture Toughness ◽  
Cast Iron ◽  
High Speed ◽  
Elevated Temperatures ◽  
High Speed Steel ◽  
Heat Treating ◽  
High Speeds ◽  
Red Hardness ◽  
Nonferrous Alloys ◽  
Cutting Point

Abstract RED CUT COBALT steel is made by adding 5% cobalt to the conventional 18% tungsten -4% chromium-1% vanadium high-speed steel. Cobalt increases hot or red hardness and thus enables the tool to maintain a higher hardness at elevated temperatures. This steel is best adapted for hogging cuts or where the temperature of the cutting point of the tool in increased greatly. It is well adapted for tools to be used for reaming cast-iron engine cylinders, turning alloy steel or cast iron and cutting nonferrous alloys at high speeds. This datasheet provides information on composition, physical properties, and hardness as well as fracture toughness. It also includes information on forming, heat treating, and machining. Filing Code: TS-367. Producer or source: Teledyne Vasco.

Sign in / Sign up

Export Citation Format

Share Document