Test and Theory for a Refined Structural Model of a Hirth Coupling

2021 ◽  
Author(s):  
Baik Jin Kim ◽  
Joseph Oh ◽  
Alan Palazzolo
Keyword(s):  
Surface Finish ◽  
Structural Model ◽  
Natural Frequencies ◽  
Contact Stiffness ◽  
Mating Surface ◽  
Industry Practice ◽  
Computation Algorithm ◽  
Surface Profiles ◽  
Solid Finite Elements ◽  
3D Solid

Abstract Hirth coupling transmits high torques in the rotating assemblies of compressors and turbines. Their mating surface contacts cause local changes in lateral shaft stiffness. This is affected by the teeth geometry, contact surface area, coupling preload, and surface finish at the contact faces. Industry practice ignores localized lateral flexibility from the Hirth coupling, or is guided by limited experience-based rules of thumb. The authors provide a novel modeling approach utilizing 3D solid finite elements which accounts for contact deformations, intricate interface teeth geometries, stress concentration, and surface finish. This provides an increased accuracy localized stiffness model for the Hirth coupling, to improve rotordynamic response predictions. Free-free natural frequencies of a test rotor including a Hirth coupling are experimentally measured. The rotor is instrumented with strain gauges for preload force measurements, and the Hirth coupling contacting surface profiles are measured with a stylus type surface profiler. A GW contact model is obtained from the measured surface profiles. An iterative computation algorithm is utilized to calculate Hirth coupling contact stiffness and contact pressure at the complex-shaped contact surfaces. Predicted and measured natural frequencies are compared vs. preload.

Test and Theory for a Refined Structural Model of a Hirth Coupling

2021 ◽  
Author(s):  
Baik Jin Kim ◽  
Joseph Oh ◽  
Alan Palazzolo
Keyword(s):  
Surface Finish ◽  
Structural Model ◽  
Natural Frequencies ◽  
Contact Stiffness ◽  
Mating Surface ◽  
Industry Practice ◽  
Computation Algorithm ◽  
Surface Profiles ◽  
Solid Finite Elements ◽  
3D Solid

Abstract Hirth coupling transmits high torques in the rotating assemblies of compressors and turbines. Their mating surface contacts cause local changes in lateral shaft stiffness. This is affected by the teeth geometry, contact surface area, coupling preload, and surface finish at the contact faces. Industry practice ignores localized lateral flexibility from the Hirth coupling, or is guided by limited experience-based rules of thumb. The authors provide a novel modeling approach utilizing 3D solid finite elements which accounts for contact deformations, intricate interface teeth geometries, stress concentration, and surface finish. This provides an increased accuracy localized stiffness model for the Hirth coupling, to improve rotordynamic response predictions. Free-free natural frequencies of a test rotor including a Hirth coupling are experimentally measured. The rotor is instrumented with strain gauges for preload force measurements, and the Hirth coupling contacting surface profiles are measured with a stylus type surface profiler. A GW contact model is obtained from the measured surface profiles. An iterative computation algorithm is utilized to calculate Hirth coupling contact stiffness and contact pressure at the complex-shaped contact surfaces. Predicted and measured natural frequencies are compared vs. preload.

Leakage characteristics of flanged pipe joints

1977 ◽  
Vol 12 (1) ◽  
pp. 29-36 ◽  
Author(s):  
H Fessler ◽  
D A Perry
Keyword(s):  
Surface Finish ◽  
Joint Surface ◽  
Clamping Force ◽  
Face Surface ◽  
Joint Efficiency ◽  
Wide Range ◽  
Pipe Joints ◽  
Surface Profiles ◽  
Leakage Characteristics ◽  
Gasket Material

Standard flanges for five widely differing pressure ratings, having a wide range of different joint surface profiles, were sealed by flat rubber or asbestos gaskets. Different initial bolt tensions were applied and the variation of clamping force with internal pressure was measured up to leakage of the joint. The joint efficiency, defined as: (end thrust due to leakage pressure on bore area of pipe)/(total initial bolting force), is not affected by variations in joint-face surface finish if machining grooves across the joint surface are avoided. Minimum values of joint efficiency are given. The effects of gasket material, width and thickness and number of bolts on joint efficiency are considered.

Analysis of Mistuned Blade Vibrations Based on Normally Distributed Blade Individual Natural Frequencies

2015 ◽  
Author(s):  
Felix Figaschewsky ◽  
Arnold Kühhorn
Keyword(s):  
Probability Distribution ◽  
Development Process ◽  
Structural Model ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Lumped Mass ◽  
Mass Model ◽  
Influence Coefficients ◽  
Random Mistuning ◽  
Rotor Assembly

With increasing demands for reliability of modern turbomachinery blades the quantification of uncertainty and its impact on the designed product has become an important part of the development process. This paper aims to contribute to an improved approximation of expected vibration amplitudes of a mistuned rotor assembly under certain assumptions on the probability distribution of the blade’s natural frequencies. A previously widely used lumped mass model is employed to represent the vibrational behavior of a cyclic symmetric structure. Aerodynamic coupling of the blades is considered based on the concept of influence coefficients leading to individual damping of the traveling wave modes. The natural frequencies of individual rotor blades are assumed to be normal distributed and the required variance could be estimated due to experiences with the applied manufacturing process. Under these conditions it is possible to derive the probability distribution of the off-diagonal terms in the mistuned equations of motions, that are responsible for the coupling of different circumferential modes. Knowing these distributions recent limits on the maximum attainable mistuned vibration amplitude are improved. The improvement is achieved due to the fact, that the maximum amplification depends on the mistuning strength. This improved limit can be used in the development process, as it could partly replace probabilistic studies with surrogate models of reduced order. The obtained results are verified with numerical simulations of the underlying structural model with random mistuning patterns based on a normal distribution of individual blade frequencies.

A Sensitivity-Enhancing Control Approach for Structural Model Updating

2007 ◽  
Author(s):  
L. J. Jiang ◽  
K. W. Wang ◽  
J. Tang
Keyword(s):  
Closed Loop ◽  
Structural Model ◽  
Natural Frequencies ◽  
Model Updating ◽  
Measurement Data ◽  
Frequency Measurement ◽  
Physical Parameters ◽  
Fe Model ◽  
Initial Model ◽  
Closed Loop Systems

Model updating plays an important role in structural design and dynamic analysis. The process of model updating aims to produce an improved mathematical model by correlating the initial model with the experimentally measured data. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper focuses on the model updating methods using the measured natural frequencies of the structure. The practice of model updating using only the natural frequencies encounters two well-known limitations: deficiency of frequency measurement data, and low sensitivity of measured natural frequencies with respect to the physical parameters that need to be updated. To overcome these limitations, a novel model updating method is presented in this paper. First, closed-loop control is applied to the structure to enhance the sensitivity of natural frequencies to the updating parameters. Second, by including the natural frequencies based on a series of sensitivity-enhanced closed-loop systems, we can significantly enrich the frequency measurement data available for model updating. Using the natural frequencies of these sensitivity-enhanced closed-loop systems, an iterative process is utilized to update the physical parameters in the initial model. To demonstrate and verify the proposed method, case studies are carried out using a cantilevered beam structure. The natural frequencies of a series of sensitivity-enhanced closed-loop systems are utilized to update the mass and stiffness parameters in the initial FE model. Results show that the modeling errors in the mass and stiffness parameters can be accurately identified by using the proposed model updating method.

Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Aaron M. Rimpel ◽  
Matthew Leopard
Keyword(s):  
Natural Frequencies ◽  
Contact Stiffness ◽  
Butt Joint ◽  
Design Stage ◽  
Design Calculation ◽  
Butt Joints ◽  
Modeling Approach ◽  
Stiffness Model ◽  
Joint Location ◽  
Simple Contact

Abstract Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors—including butt joints, Hirth couplings, and Curvic couplings—exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

Simple Contact Stiffness Model Validation for Tie Bolt Rotor Design With Butt Joints and Pilot Fits

2019 ◽  
Author(s):  
Aaron M. Rimpel ◽  
Matthew Leopard
Keyword(s):  
Natural Frequencies ◽  
Contact Stiffness ◽  
Butt Joint ◽  
Design Stage ◽  
Design Calculation ◽  
Butt Joints ◽  
Modeling Approach ◽  
Stiffness Model ◽  
Joint Location ◽  
Simple Contact

Abstract Tie bolt rotors for centrifugal compressors comprise multiple shaft components that are held together by a single tie bolt. The axial connections of these rotors — including butt joints, Hirth couplings, and Curvic couplings — exhibit a contact stiffness effect, which tends to lower the shaft bending frequencies compared to geometrically identical monolithic shafts. If not accounted for in the design stage, shaft bending critical speed margins can be compromised after a rotor is built. A previous paper had investigated the effect of tie bolt force on the bending stiffness of stacked rotor assemblies with butt joint interfaces, both with and without pilot fits. This previous work derived an empirical contact stiffness model and developed a practical finite element modeling approach for simulating the axial contact surfaces, which was validated by predicting natural frequencies for several test rotor configurations. The present work built on these previous results by implementing the same contact stiffness modeling approach on a real tie bolt rotor system designed for a high pressure centrifugal compressor application. Each joint location included two axial contact faces, with contact pressures up to five times higher than previously modeled, and a locating pilot fit. The free-free natural frequencies for different amounts of tie bolt preload force were measured, and the frequencies exhibited the expected stiffening behavior with increasing preload. However, a discontinuity in the data trend indicated a step-change increase in the contact stiffness. It was shown that this was likely due to one or more of the contact faces becoming fully engaged only after sufficient tie bolt force was applied. Finally, a design calculation was presented that can be used to estimate whether contact stiffness effects may be ignored, which could simplify rotor analyses if adequate contact pressure is used.

scholarly journals Limitations of a dynamic shear-frame model based in a small-scale experimental steel structure

2018 ◽  
Vol 211 ◽  
pp. 14005
Author(s):  
Augusto de S. Pippi ◽  
Pedro L. Bernardes Júnior ◽  
Suzana M. Avila ◽  
Marcus V. G. de Morais ◽  
Graciela Doz
Keyword(s):  
Dynamic Behavior ◽  
Geometric Modeling ◽  
Structural Model ◽  
Natural Frequencies ◽  
Numerical Models ◽  
Steel Structure ◽  
Small Scale ◽  
The Real ◽  
Frame Model ◽  
Shear Frame

Many engineering problems require geometric modeling and mechanical simulation of structures. Through the structural models, engineers try to simulate the real behavior of these structures. It is important that a model contain all the necessary parameters that describe the structure and its behavior during its useful life. In the field of dynamics, one of the most used models is the shear-frame, in which the stiffness of the structure is given by the stiffness of the columns and the whole mass is concentrated in the floor levels, which are considered with infinite stiffness. In some cases, this simplification offers more conservative results, which can lead to considerable errors, especially in the case of natural frequencies. Knowing that the quality of a structural model depends on the simplifications considered, an experimental 3D steel frame, constructed to typify the dynamic behavior of a tall building, was tested with a data acquisition system and accelerometers, in order to obtain its natural frequencies. In addition, a numerical model was developed in order to ascertain the results. These values of natural frequencies are compared with an idealized shear-frame model obtained from the experimental model. This comparison allows a critical analysis of the numerical models that can be employed to represent the real dynamic behavior of structures. The aim of the investigation is to show the results of the modal analysis for each model, comparing them with the experimental results and commenting their advantages and the limitations.

scholarly journals Dynamic Analysis of a Rod Vibro-Impact System with Intermediate Supports

2018 ◽  
Vol 12 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Volodymyr Gursky ◽  
Igor Kuzio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain State ◽  
Natural Frequencies ◽  
Contact Stiffness ◽  
Free Oscillations ◽  
The Finite Element Method ◽  
Rod System ◽  
Design Diagram

Abstract The two-mass resonant vibro-impact module is presented as the rod system with cylindrical intermediate supports. The corresponding design diagram is constructed. Based on the finite element method, the frequency of free oscillations is defined for the corresponding location of the intermediate supports. A stress-strain state of the elastic element is considered. The stiffness of the intermediate supports is defined by solving the contact problem between the cylindrical rod supports and the flat spring. The dynamics of the vibro-impact rod system with multiple natural frequencies is analyzed taking into account the contact stiffness of the intermediate supports. The determination of contact and equivalent stresses occurring during the operation of the vibro-impact rod system is performed.

Effect of Tool Condition on Cutting Mechanism in Micromilling

2019 ◽  
Author(s):  
Alwin Varghese ◽  
Vinay Kulkarni ◽  
Suhas S. Joshi
Keyword(s):  
Surface Finish ◽  
Micro Milling ◽  
Machining Parameters ◽  
Cutting Mechanism ◽  
Workpiece Material ◽  
Tool Condition ◽  
Force Signal ◽  
Surface Profiles ◽  
Cutting Mechanisms ◽  
Rapid Tool

Abstract Cutting mechanism in micromilling is governed by the tool condition along with the machining parameters and workpiece material properties. A rapid tool wear in micromilling often deteriorates the surface quality, which could be due to the occurrence of plowing. The effects of tool condition on the transition in cutting mechanisms from shearing to plowing have not been adequately addressed in micro milling. In this work, we attempt to correlate cutting mechanism with tool conditions, so that their influence on force and surface profiles are investigated. Micro milling experiments are performed to investigate these correlations. A fluctuation parameter has been defined to quantify the fluctuation in force signal. It is evident that as the feed varies from 0.2 μm/teeth to 5 μm/teeth, the fluctuation reduces and similar fluctuations are reflected on the generated surface also. The surfaces corresponding to lower force fluctuations has an Ra value less than 350 nm. As cutting edge radius increases, surface finish decreases. However, with chipping, new sharper cutting edges are formed which may improve the surface finish locally but contribute to the overall variation in the surface profiles.

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