Natural frequency analysis and experiment for 3SPS+1PS parallel hip joint manipulator based on rigid-flexible coupling theory

Songtao Wang,Gang Cheng,Xihui Chen,Jianhua Yang 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.3

For analyzing natural frequency of a 3SPS+1PS parallel hip joint manipulator, a rigid-flexible coupling theory is proposed. 3SPS denotes that the PHJM has three legs and each leg type is SPS. 1PS denotes that the PHJM has one constrained leg and the constrained leg type is PS. The rigid finite element method and flexible finite element method are the base of the rigid-flexible coupling theory. Firstly, the basic element models of the PHJM are established based on the rigid-flexible coupling analysis. Secondly, the elastic dynamic models of the flexible legs are established based on the Lagrange equation and flexible finite method. Finally, the rigid-flexible coupling model of the PHJM is assembled by building the relationship between the rigid and flexible elements. Based on the rigid-flexible model, the natural frequency of the PHJM is analyzed. In addition, the effect parameters of the natural frequency are analyzed. The analysis results of the natural frequency show that the natural frequency is symmetric distribution in the working space, and the minimum value of the 1 st order natural frequency is 2.3 Hz. The operating frequency (1 Hz) is much lower than the 1 st order natural frequency, so the PHJM will not generate resonance and can operate stably. The analysis results of the parameter show that the PHJM has the minimal sensitivity with the effect parameter E and has the maximal sensitivity with the effect parameter H, so the length of the middle leg has the biggest impact on the natural frequency. Natural frequency analysis results have been checked by the hammer test, which verifies the feasibility of the rigid-flexible coupling theory. At the same time, the regression analysis is carried out based on the hammer test results. Using the rigid-flexible coupling theory to solve the natural frequency of the parallel manipulator, the physical meaning is explicit and the modeling process is clear, so the rigid-flexible coupling theory is a universal method.

Frequency error based identification of cracks in beam-like structures

Wenguang Liu,Mark E. Barkey 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.10

A crack identification method of a single edge cracked beam-like structure by the use of a frequency error function is presented in this paper. First, the dynamic theory of Euler-Bernoulli beams was employed to derive the equation of the natural frequency for a single edge cracked cantilever beam-like structure. Subsequently, the cracked section of the beam was simulated by a torsional spring. The flexibility model of the torsional spring due to the crack was estimated by fracture mechanics and energy theory. Thereafter, a function model was proposed for crack identification by using the error between the measured natural frequencies and the predicted natural frequencies. In this manner, the crack depth and crack position can be determined when the total error reaches a minimum value. Finally, the accuracy of the natural frequency equation and the viabilty of the crack identification method were verified in the case studies by the measured natural frequencies from the literature. Results indicate that the first two predicted natural frequencies are in good agreement with the measured ones. However, the third predicted natural frequency is smaller than the measured natural frequency. In the case of small measured frequency errors, the predicted crack parameters are in good agreement with the measured crack parameters. However, in the case of large measured frequency errors, the predicted crack parameters only give roughly estimated results.

Steering Wheel Core 진동해석을 통한 최적화 설계에 대한 고찰

채천우(Chunwoo Chae),박동진(Dongjin Park),홍찬호(Chanho Hong),남병찬(ByungChan Nam) 한국자동차공학회 2011 한국자동차공학회 학술대회 및 전시회 Vol.2011 No.11

With rapid change of automotive market, multi-function and complexity in limited shape, cost reduction and weight lightening become more and more popular topic in these days. So it is necessary to study on design optimization. Steering Wheel is one of the parts that drivers touch very often in a car and its main function is steering. Especially, steering wheel vibration and noise becomes one of important quality evaluation criterion. Steering Wheel needs to meet basic strength, resonance by low natural frequency, natural frequency that meets more than optimum level and avoids fatigue fracture. Though steering wheel weight will be increased and natural frequency will be decreased relatively, designers often add rib shape on weak part for strength reinforcement and optimum natural frequency. So those methods do not work effectively. This study focus on the method that improves both of strength and natural frequency by change of geometric moment of inertia through changing cross section shape of spoke (2~4 spoke) and keeping mass at same time.Model of steering wheel core for study was simplified and every model’s rim and base keep its own shape and changed only cross section shape of spoke. Natural frequency of steering wheel core was checked by Nastran FX that used as study solver (Mesh size: 2㎜, node qty: 390,000 ~ 430,000EA, element qty 240,000 ~ 250,000). The study was conducted at same condition of armature mass by every spoke quantity. It is possible to confirm the correlation between cross section size change and its natural frequency of steering wheel core through natural frequency study and it is also possible to apply cross section size change on stress concentrated point occurred for strength reinforcement. As result, it can be judged that cross section change in same mass works on strength reinforcement, high natural frequency and cost reduction.

Dynamic Analysis on the Effect of Pavement’s Natural Frequency to Pavement Performance Using Finite Element Modelling

Julius Marvin Flores,Carlo Elipse,Hyun Jong Lee,Kideok Kim 한국도로학회 2018 한국도로학회 학술대회 발표논문 초록집 Vol.2018 No.05

Pavement performance usually depends on the pavement’s material property, traffic and environmental conditions. Current pavement design programs such as the Mechanistic Empirical Pavement Design Guide use these factors in assessing the pavement life and performance in terms of different distresses like rutting and fatigue cracking. Theoretically, the cracking and rutting behaviour of pavements are based on accumulated strains experienced by the pavement which is brought by the weight and loading speed of vehicles. A steady state loading device was used in the field to evaluate pavement deflection’s behaviour in varying loading frequencies. It was observed that the pavement deflection increases as the loading frequency also increases until it approaches a certain frequency wherein the deflection decreases thereafter. In this study, a three-dimensional finite element pavement model was established using ABAQUS wherein the effect of the vehicle’s loading frequencies was analysed. The calculated static deflection and stress from the finite element (FE) model were found to have good correlation with the KENPAVE measured deflection and stress. The deflections of different pavement conditions were further studied and analysed by generating several pavement geometries and strength from the FE model using a frequency sweep response analysis. It was found that the geometric condition and the current modulus of the pavement can amplify the pavement deflection by a factor, β, depending on the loading frequency. The peak deflection was found to be occurring when the loading frequency approaches one of the pavement’s natural frequencies. Based on the finding from this study, the natural frequency is an important factor to be considered in designing pavements. Further study is recommended to understand more on how to minimize the effect of natural frequency to pavement life.

콘크리트 댐체의 고유진동수 측정과 변화거동

홍웅기(Woong-Gi Hong),이광재(Kwang-Jae Lee),진영문(Young-Moon Jin),송정언(Jeong-Un Song) 한국엔터테인먼트산업학회 2015 한국엔터테인먼트산업학회논문지 Vol.9 No.2

본 연구는 환경공해진동을 평가하기 위한 기초자료를 얻기 위하여 수행되었다. 콘크리트 댐체에서 고유진동수를 측정하여 다음과 같은 결론을 얻었다. 댐체의 양 끝단에서 저주파수 대역으로 측정되었고, 특히 E 측점과 J 측점 사이에서 주파수 대역의 편차가 크고 랜덤하게 나타났다. 이는 바람의 영향과 수압, 댐체 중앙 부근으로 갈수록 고유진동수가 다른 측점보다 더욱 크게 나타나는 특성 때문이라 판단된다. 변위가속도 또한 고유진동수와 유사한 경향을 보였다. 외부에서 전달되는 외력의 강제진동수는 댐체의 고유진동수 영역보다 항상 작은 값으로 산출되었으며, 주파수 대역은 대부분 충격성 저주파영역을 나타냈다. 이러한 전달 과정에서 매질자체가 갖는 고유특성이나 수진점의 고유진동수, 또는 실시간 주파수분석 등을 고려한 환경공해진동의 정량적인 진동영향평가 기법이 필요하며, 아울러 고유진동수를 고려한 예측모델을 구성하기 위하여 구조체의 기초물성 및 기여도를 분석하고, 계측 데이터의 오차분석, 표준편차 및 보정에 의한 모델의 타당성 평가와 검증 과정이 수행될 때 환경공해진동의 정량적인 평가가 확립될 수 있을 것으로 사료된다. The purpose of this study is to obtain basic data for assessment the vibration as one of the environmental pollution. Natural frequencies in free field were measured as follows: At both ends of the dam crest, the natural frequency was measured with a relatively low frequency. Particularly, the deviation of frequency domain at E and J M.Ps were large and determined randomly. Because toward the central part of the dam crest, the effects of wind, water pressure, and natural frequencies are more large compared to the other M.Ps. Additionally, acceleration values were also measured similar to the trend of natural frequency. Vibration impact assessment that considered the natural characteristics of the medium in the delivery process, natural frequency of vibration receptor and the real-time frequency analysis reached the point of need. This is intended to identify vibration amplification by the resonance of frequency and additional vibration energy. And in order to configure the prediction model which considering the characteristics of frequency, the basic physical properties and contributiveness to the general structure must be analyzed. Feasibility assessment and verification of the model using standard deviation, correction and error analysis of measurement data must be carried out. As a result, the quantitative assessment of the vibration as one of the environmental pollution can be expected to be established.

Effect of prestressing on the first flexural natural frequency of beams

Jaiswal, O.R. Techno-Press 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.5

In this paper the effect of prestressing force on the first flexural natural frequency of beams is studied. Finite element technique is used to model the beam-tendon system, and the prestressing force is applied in the form of initial tension in the tendon. It is shown that the effect of prestressing force on the first natural frequency depends on bonded and unbonded nature of the tendon, and also on the eccentricity of tendon. For the beams with bonded tendon, the prestressing force does not have any appreciable effect on the first flexural natural frequency. However, for the beams with unbonded tendon, the first natural frequency significantly changes with the prestressing force and eccentricity of the tendon. If the eccentricity of tendon is small, then the first natural frequency decreases with the prestressing force and if the eccentricity is large, then the first flexural natural frequency increases with the prestressing force. Results of the present study clearly indicate that the first natural frequency can not be used as an easy indicator for detecting the loss of prestressing force, as has been attempted in some of the past studies.

Effect of prestressing on the first flexural natural frequency of beams

O. R. Jaiswal 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.5

In this paper the effect of prestressing force on the first flexural natural frequency of beams is studied. Finite element technique is used to model the beam-tendon system, and the prestressing force is applied in the form of initial tension in the tendon. It is shown that the effect of prestressing force on the first natural frequency depends on bonded and unbonded nature of the tendon, and also on the eccentricity of tendon. For the beams with bonded tendon, the prestressing force does not have any appreciable effect on the first flexural natural frequency. However, for the beams with unbonded tendon, the first natural frequency significantly changes with the prestressing force and eccentricity of the tendon. If the eccentricity of tendon is small, then the first natural frequency decreases with the prestressing force and if the eccentricity is large, then the first flexural natural frequency increases with the prestressing force. Results of the present study clearly indicate that the first natural frequency can not be used as an easy indicator for detecting the loss of prestressing force, as has been attempted in some of the past studies.

교반기용 임펠러가 달린 축의 베어링 지지점에 따른 진동특성

홍도관(Do-Kwan Hong),안찬우(Chan-Woo Ahn),백황순(Hwang-Soon Baek),최석창(Seok-Chang Choi),박일수(Il-Soo Park) 한국기계가공학회 2009 한국기계가공학회지 Vol.8 No.3

This paper deals with the dynamic characteristics of the impeller shaft model which is the most important part in developing the resin mixing machine. The can is rotating by air motor in mixing machine. Then the end of shaft is fixed. The bearing support is to increase the fundamental natural frequency. The natural frequency analysis using finite element analysis software are performed on the imported commercial impeller shaft model. This paper presents calculated bearing stiffness of Soda, Harris and modified Harris formula considering contact angle according to bearing supported position. The most important fundamental natural frequency of the impeller shaft except bearing support is around 13.932 ㎐. This paper presents one bearing and two bearings support position to maximize the 1st natural frequency. The maximized fundamental natural frequency is around 48.843 ㎐ in one bearing support and 55.52 ㎐ in two bearings support.

철도교량 시험체의 가진방법에 따른 고유진동수 측정치 변동에 대한 비교 분석

김성일(Kim Sung-Il),이정휘(Lee Jungwhee),이필구(Lee Pil-Goo),김충언(Kim Choong-Eon) 대한토목학회 2010 대한토목학회논문집 A Vol.30 No.6A

철도교량과 같이 주기적 가진에 의해 공진발생의 가능성이 높은 구조물에 있어서, 정확한 구조물의 동적특성치 파악은 설계단계 및 공용중 안정적인 응답을 확보하기 위해 필수적이다. 이 논문에서는 실축척 구조물을 대상으로 하는 강제 진동실험에서 일반적으로 사용할 수 있는 가진방법인 가진기 및 충격해머를 사용한 가진실험의 결과를 상호 비교하여 가진방법에 따른 고유진동수 추출결과의 차이 및 차이의 발생원인을 분석하고, 보다 정확한 구조물의 고유진동수를 산출하기 위한 보정 방법을 제안하였다. 또한, 철도교량의 시공단계에 따라 궤도부절 전, 후에 진동실험을 수행하였으며, 궤도부설에 의한 고유진동수 변화를 관찰하였다. 가진방법에 따른 측정 고유진동수의 차이는 가진기의 경우 부가질량의 효과, 충격해머의 경우 동적 응답 레벨에 따라 변화하는 지점강성효과에 기인하는 것으로 파악되었으며, 이에 대한 보정을 통해 보다 신뢰성 높은 고유 진동수로 환산하는 것이 기능하였다. 궤도부설의 효과는 일반적으로 부가질량으로만 고려하여 궤도부설 전에 비해 고유진동수가 감소하는 것으로 예상되어 왔지만, 이 연구에서 수행한 실험의 결과로 질량추가의 효과에 상당하는 강성기여 효과도 있는 것으로 나타났으며, 강성증가율은 발생변위의 수준에 비례하여 증가하는 것으로 나타났다. 따라서, 설계단계에서 완성계의 고유진동수 예측시 궤도의 발생변위수준을 고려하여 적절히 강성기여 효과를 고려하는 것이 필요할 것으로 판단된다. Precise estimation of a structure's dynamic characteristics is indispensable for ensuring stable dynamic responses during lifetime especially for the structures which can experience resonance such as railway bridges. In this paper, the results of forced vibration tests of different excitation methods (vibration exciter and impact hammer) are compared to examine the differences and the cause of differences of extracted natural frequencies. Consequently a natural frequency modification method is suggested to eliminate effects of non-structural disturbance factors. Also, sequential forced vibration tests are performed before and after track construction according to the construction stage of a railway bridge, and the variation of natural frequencies are examined. Effect of added mass of vibration exciter and variation of support condition due to the level of excitation force are concluded as the major cause of natural frequency differences. Thus eliminating these effects can enhance the reliability of the extracted natural frequencies. Construction of track affects not only the mass of structure but also the stiffness of the structure. Also, the amount of increase in stiffness varies according to the level of structural deflection. Therefore, reasonable estimation of the level of structural response during operation is important for precise natural frequency calculation at design phase.

A natural frequency sensitivity based stabilization in spectral stochastic finite element method for frequency response analysis

Gil-Yong Lee,진승섭,박용화 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.75 No.3

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.