Critical Speeds of Geared Rotors by Including Mesh Stiffness and Using a Continuous System Model

1990 ◽  
Author(s):  
O. Sedat Sener ◽  
H. Nevzat Ozguven
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Natural Frequencies ◽  
Continuous System ◽  
Transmission Error ◽  
System Model ◽  
Graphical Form ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Dynamic Factors

Abstract Dynamic analysis of high speed gearing for the computation of critical speeds and dynamic factors is a must in a proper design, while some other dynamic characteristics of the system such as dynamic transmission error are to be determined for more critical designs. Numerous different models have been suggested for the dynamic analysis of geared systems. These models differ both in the effects included and in the basic assumptions made. A continuous system model is used in this analysis in order to determine the torsional natural frequencies of a gear shaft system composed of two gears, two shafts and two inertias representing the drive and the load. Gear mesh is modelled as a spring connected between two gears. The natural frequencies of the same system are also calculated by using a four degree of freedom classical discrete model in which shaft masses are ignored. The percentage differences in the natural frequencies calculated with the discrete and continuous system models are determined for several values of some nondimensional system parameters. The results are presented in graphical form in terms of the nondimensional parameters defined. Some conclusions which may be important for designers are drawn.

Dynamic Transmission Error Measurements From Spur Gear Pairs Having Tooth Indexing Errors

2017 ◽  
Author(s):  
Brian Anichowski ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
High Speed ◽  
Transient Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Transient Effects ◽  
Dynamic Factors ◽  
Frequency Domains ◽  
Error Dynamic ◽  
Dynamic Transmission Error

This paper complements recent investigations [Handschuh et al (2014), Talbot et al (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur test gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. Both measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors.

scholarly journals Dynamic Analysis of Telecommunication Tower for Optimum Modal Combination and Elemental Discretization

2019 ◽  
Vol 9 (1) ◽  
pp. 2229-2237
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Response Spectrum ◽  
Continuous System ◽  
Ground Level ◽  
Optimum Number ◽  
Lumped Mass ◽  
Mass System ◽  
Static And Dynamic Analysis ◽  
The Past

Over the past 35 years, the growing demand for wireless and broadcast communication has spurred a dramatic increase in steel telecommunication tower construction and maintenance. Failure of such structures due to severe earthquakes is a major concern. The Indian code suggests the detailed static and dynamic analysis provisions that are to be followed for lumped mass systems like buildings. In case of continuous structures the code only suggests the static analysis provisions in details. But, due to the lack of detailed Indian codal provisions for dynamic analysis of telecommunication tower, a comparative study using response spectrum method is being carried out with the help of suitable software for different ground level conditions in case of India. According to the theoretical approach of any structural dynamics problem, the structures without lumped mass system is considered as continuous system which is further idealized as a series of small elemental segments. Furthermore, the structural analysis of these elemental segments using the concept of Finite Element Method (FEM) is being carried out with the help of the mentioned software and the results of natural frequencies, time periods of the structure are compared to obtain the optimum number of elemental discretization along with the optimum method of modal combination.

Dynamic factor to live load regulation during structural calculation of bridges at high-speed networks

2017 ◽  
pp. 15-27 ◽  
Author(s):  
Leonid Dyachenko ◽  
Andrey Benyn ◽  
Vladimir Smyrnov
Keyword(s):  
Dynamic Analysis ◽  
High Speed ◽  
Strain State ◽  
Dynamic Factor ◽  
Live Load ◽  
Labor Costs ◽  
Stress Strain ◽  
Stress Strain State ◽  
Dynamic Factors ◽  
High Speed Trains

Objective: Improvement of dynamic analysis method of simple beam spans in the process of high-speed trains impact. Methods: Mathematical modeling with numerical and analytical methods of building mechanics was applied. Results: The parameters of high-speed trains influence on simple beam spans of bridges were analyzed. The method of dynamic factor to live load determination was introduced. The reliability of the method in question was corroborated by the results of numerical simulation of high-speed trains’ movement by beam spans with different speeds. The introduced algorithm of dynamic analysis was based on the connection between maximum acceleration of a beam span in resonance vibration mode and the basic factors of stress-strain state. The method in question makes it possible to determine both maximum and bottom values of main loading in a construction, which determines the possibility of endurance tests. It was noted that dynamic additions for the components of stress-strain state (bending moments, shear force, vertical deflections) were different. The fact in question determines the necessity of differential approach application to identify dynamic factors in the process of calculation testing on the first and the second groups of limit states. Practical importance: The method of dynamic factors’ determination presented in the study makes it possible to perform dynamic analysis and determine the main loading in simple beam spans without application of numerical modeling and direct analytical analysis, which considerably reduces labor costs on engineering.

Multilevel Optimization of the Geared Rotor-Bearing System for Multi-Objectives With Critical Speed Constraints

2004 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
W. B. Lu
Keyword(s):  
Critical Speed ◽  
Transmission Error ◽  
Mesh Stiffness ◽  
Error Response ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Unbalance Response ◽  
Multilevel Algorithm ◽  
Gear Mesh Stiffness ◽  
Bearing System

This paper presents the multi-objective optimization of a geared rotor-bearing system with the critical speeds constraints by using an efficient multilevel algorithm. The weight of each rotor shaft, the unbalance response, and the response due to the transmission error are minimized simultaneously under the critical speed constraints. The design variables are the inner radii of the shaft, the stiffness of bearings, and the gear mesh stiffness. The finite element method (FEM) is employed to analyze the dynamic characteristics and the method of feasible direction (MFD) is applied in the optimization of the single objective stage. Based on the sensitivity analysis that gear mesh stiffness has almost no influences on the critical speeds of the uncoupled modes of two shafts, an efficient multilevel algorithm composed of system and subsystem levels is developed. In the cycle of iteration, the minimization of the shaft weight is performed in the subsystem level with the critical speed constraints of only uncoupled modes of two shafts and the unbalance response and the transmission error response are reduced in the system level with the critical speed constraints of only coupled modes. It is indicated from the numerical results that the shaft weight, the unbalance response, and the transmission error response via the multilevel technique (ML) are all reduced much more than those via the weighting method (WM) and the goal programming method (GPM).

A Study of the Relationship Between the Dynamic Factors and the Dynamic Transmission Error of Spur Gear Pairs

2006 ◽  
Vol 129 (1) ◽  
pp. 75-84 ◽  
Author(s):  
V. K. Tamminana ◽  
A. Kahraman ◽  
S. Vijayakar
Keyword(s):  
Dynamic Models ◽  
Deformable Body ◽  
Nonlinear Behavior ◽  
Transmission Error ◽  
Spur Gear ◽  
Gear Mesh ◽  
Dynamic Factors ◽  
Wide Range ◽  
Dynamic Transmission Error ◽  
Torque Values

In this study, two different dynamic models, a finite-element-based deformable-body model and a simplified discrete model, are developed to predict dynamic behavior of spur gear pairs. Dynamic transmission error (DTE) and dynamic factors (DF) defined based on the gear mesh loads, tooth loads and bending stresses are computed for a number of unmodified and modified spur gears within a wide range of rotational speed for different involute contact ratios and torque values. Although similar models were proposed in the past, they were neither fully validated nor equipped to predict both DTE and different forms of DF. Accordingly, this study focuses on (i) validation of both models through an extensive set of experimental data obtained from a set of tests using spur gear having unmodified and modified tooth profiles, and (ii) establishment of a direct link between DTE and different forms of DF, especially the ones based on tooth forces and the root stresses. The predicted DF and DTE values are related to each other through simplified formulas. Impact of nonlinear behavior, such as tooth separations and jump discontinuities on DF, is also quantified.

Dynamic Analysis of a Geared Rotor-Bearing System With Viscoelastic Supports Under the Bow Effect

2007 ◽  
Author(s):  
T. N. Shiau ◽  
E. K. Lee ◽  
T. H. Young ◽  
W. C. Hsu
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Loss Factor ◽  
Critical Speed ◽  
Transmission Error ◽  
Steady State Response ◽  
Critical Speeds ◽  
State Response ◽  
Rotor Bearing ◽  
Bearing System

This paper investigates the dynamic behaviors of a geared rotor-bearing system mounted on viscoelastic supports under considerations of the gear eccentricity, excitation of the gear’s transmission error and the residual shaft bow. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The coupling effect of lateral and torsional motions is considered in the system dynamic analysis. The investigated dynamic characteristics include system natural frequencies and steady-state response. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. Larger loss factor and more rigid stiffness of the viscoelastic supports will suppress the systematic amplitude of resonance. Parameters, which include magnitude of the residual bow and phase angle, are also considered in the investigation of their effects on system critical speeds and steady-state response. Results show that they have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.

Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair

1993 ◽  
Vol 115 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Natural Frequencies ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Helical Gear Pair

In this paper, a linear dynamic model of a helical gear pair has been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational (rocking) motions due to the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of the helix angle in the analysis.

scholarly journals Rotor Dynamic Analysis of Driving Shaft of Dry Screw Vacuum Pump

2019 ◽  
pp. 436-439
Author(s):  
A. Purushotham ◽  
Shravan Kumar
Keyword(s):  
Dynamic Analysis ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vacuum Pump ◽  
Inertia Effects ◽  
Critical Speeds ◽  
Rotor Shaft ◽  
Gyroscopic Moment ◽  
Mass Moment ◽  
Rotor Dynamic

Rotor dynamics is the study of vibration behavior in axially symmetric rotating structures. Devices such as engines, motors, disk drives and turbines all develop characteristic inertia effects that can be analyzed to improve the design and decrease the possibility of failure. At higher rotational speeds, such as in a gas pumps, the inertia effects of the rotating parts must be consistently represented in order to accurately predict the rotor behavior. An important part of the inertia effects is the gyroscopic moment introduced by the precession motion of the vibrating rotor as it spins. As spin velocity increases, the gyroscopic moment acting on the rotor becomes critically significant. Not accounting for these effects at the design level can lead to bearing and/or support structure damage. The main objective of this project is to study the Rotor Dynamic behavior of the drive rotor shaft of the Dry screw vacuum pump. The design of the pump is considered from the one of the reputed pump manufacturing industry. The operational speed of the pump is 4500 rpm, whereas the maximum capable speed of the pump is 10,000 rpm. Rotating machinery produces vibrations depending on the unbalanced mass and gyroscopic effects. Thus an investigation is to be made on the rotor dynamic properties of the shaft to find the natural frequencies and critical speed. For this rotor dynamic analysis was carried out in ANSYS APDL and Workbench16 to find the natural frequencies and critical speeds in the range of 0 to 10000 rpm. Thus an effort is made to shift the mass moment of inertia of the shaft by varying the design of the shaft and to shift the critical frequency to the higher speeds of the shaft there by increasing the efficiency. The modal analysis is performed to find the natural frequencies and it is extended to harmonic analysis to plot the stresses and deflections at the critical speeds. The design of the rotor shaft is made in NX-CAD.

Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair

1991 ◽  
Author(s):  
Ahmet Kahraman
Keyword(s):  
Natural Frequencies ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Helical Gear Pair

Abstract In this paper, a linear dynamic model of a helical gear pair has. been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational motions because of the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of helix angle in the analysis.

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