2010 Vol. 36, No. 8

Display Method:
Transient measurement of heat transfer coefficient
Ding Shuiting, Jiang Zugang, Xu Guoqiang, Luo Xiang
2010, 36(8): 883-886.
Abstract:
A new method called constant heat flux method was talked about the calculation of the heat transfer coefficient, h . The way of calculating h for the transient experiment was from step-change solution by giving a constant heat flux suddenly. If the time at which the changes colour of thermochromic liquid crystal(TLC) is known, then h can be found from the solution of so-called semi-infinite plate problem. Uncertainties of h calculated using the so-called two point method were discussed later. On the basis of this discussion it were found out how the accurate h could be got. The procedure of calculating h using constant heat flux method were listed and the free plant experiment are used to prove the method-s accuracy.
Fuzzy theory for uncertain structural analysis based on measurement data
Wang Xiaojun, Yang Haifeng, Qiu Zhiping, Song Weibo
2010, 36(8): 887-891.
Abstract:
Based on the measurement data,a fuzzy analysis method was proposed to deal with the problems of uncertain structural mechanics. A new membership function of the uncertain parameters was constructed by utilizing the difference coefficient, and then a finite number of scattered data points of the uncertain parameters were described as fuzzy parameters and quantified by this method. The true values and the probable intervals for them were estimated, which were applied into the fuzzy finite element analysis of structural mechanics to obtain the uncertain response of the structure.A 10-bar truss structure with parametric uncertainties was used to analyze the uncertain response by the presented method.Numerical results illustrate its feasibility and validity.
Scheme for vision-aided navigation in flight with reference of road intersections
Wu Liang, Hu Yun-an
2010, 36(8): 892-895.
Abstract:
To release the range limit caused by choosing the fixed landmark as reference, a vision-aided navigation scheme for aircraft with reference of road intersections was proposed. The road intersections were extracted based on the curvilinear structure extraction algorithm. The searching space was reduced by introducing intersection property restriction in matching image and map road intersections. The unreasonable match could be eliminated according to the azimuth and height output of the inertial navigation system (INS). Therefore, the computation cost was greatly reduced. The navigation parameters were computed by the projection matrix or homography matrix, which were estimated by golden standard algorithm. The simulation results verify the effectiveness of the scheme.
Assessment based on support vector machine for rolling bearing grade-life
Hong Jie, Han Lei, Miao Xuewen, Ma Yanhong
2010, 36(8): 896-899.
Abstract:
Grade-life was used to describe rolling bearing-s service life, and an assessment model was presented for bearing-s Grade-life. Signal feature extraction and pattern recognition algorithm were keys to construct the model. Vibration signals of the rolling bearing were analyzed, and the wavelet packet analysis theory was adopted to extract the grade-life characteristics. Through signal reconfiguration with wavelet package to extract energy feature of various frequency bands acting as the life feature vector was input into support vector machine (SVM) to realize the mapping between the grade-life vector and the grade-life of rolling bearing, and the model in establishing the identification by using bearing test stand run-to-failure data. The validity and creditability of model has been demonstrated by bearing test stand dates.
UDRE estimation approach based on satellite surveillance dilution of precision
Shao Bo, Liu Jiansheng, Huang Zhigang, Li Rui
2010, 36(8): 900-903.
Abstract:
Satellite based augmentation system (SBAS) provides user differential range error (UDRE) which guarantees satellite ephemeris and clock correction accuracies to the users to enhance their integrity. A method of calculating UDRE only used in the master station was introduced, then a concept of satellite surveillance dilution of precision (SSDOP) was proposed to reflect the effect of changing the reference stations- distribution on the satellite ephemeris and clock correction accuracies. A mathematical equation was deduced from the SSDOP and UDRE expressions, and from the view of the equation the UDRE was infected by SSDOP and restriction factor which could be replaced by, 0.7438, its statistic average value.The equation based upon SSDOP to estimate UDRE was established. The simulation results show that the estimation value of UDRE based on SSDOP can reflect the performance of the current UDRE and its accuracy is less than 0.8m. This approach can be used as an alternative method to calculate the UDRE when the user can-t receive the integrity information broadcasted by SBAS.
Numerical dissipation of Roe’s scheme with preconditioning for low-speed flows
Cao Ning, Wu Songping
2010, 36(8): 904-908.
Abstract:
Preconditioning is necessary for simulating of low-speed flows with Roe-s scheme. With most research on choosing preconditioning parameter, the solution may be wrong. Numerical experiments show the numerical dissipation of the scheme has a notable effect on low-speed flow numerical simulation with preconditioning method. A manner by using an adjustable parameter in preconditioning Roe-s scheme to control the numerical dissipation was proposed. The numerical dissipation of preconditioning Roe-s scheme with an adjustable parameter was more similar to the real dissipation of low-speed flows and reflected the real physical phenomena of low-speed flows. Numerical results show the efficiency of the new scheme and the low Reynold-number steady solutions of viscous flow past a circular cylinder and square cavity flow are satisfied. Also indicate that the applicability of the new scheme and different low Mach number with the same low Reynold-number steady solutions of viscous flow past a circular cylinder are also satisfied.
Real-time weak signal detection with the envelope mean filter algorithm
Ye Weidong, Li Xingshan
2010, 36(8): 909-912.
Abstract:
The weak signal detection in strong noise environment had been a big difficulty in signal processing domain. A new algorithm that was the envelope mean filter(EMF) was discussed. The waveform of the weak signals that deeply buried in uniformly distributed noise can be recovered by EMF algorithm in real time. By using the mean of upper border and lower border of the envelope as the estimated value of the weak signal, the output waveform was smoothed by a real-time sliding mode mean filter. The basic principles of EMF algorithm were described. The simulation on the envelope of the analysis algorithm, the optimal attenuation coefficient a, oversampling factor k, smooth sequence length M and different SNR of the weak signal to the accuracy of the impact of the recovered signal were studied. The simulation results show that EMF algorithm can improve SNR over 60dB. The EMF algorithm has been successfully used for IEEE 1588 clock synchronization clock precision servo algorithm.
Modeling, system identification and validation of small rotorcraft-based unmanned aerial vehicle
Yang Fan, Xiong Xiao, Chen Zongji, Zhang Ping
2010, 36(8): 913-917.
Abstract:
In order to realize the flight control system of small rotorcraft-based unmanned aerial vehicles (RUAV), a precise dynamics model is needed. A time-domain system identification framework was presented for AF25B RUAV. The modeling process considered the influence of fuselage, main rotor/stabilizer bar system and coupled dynamic derivatives. Then the on-board sensor and control system were designed and configured. Based on the real flight data which gathered under the radio controlled(RC) hovering fly tests, a liner time-invariant system model was obtained through the time-domain system identification method. The identification result was analyzed and proved that model can reflect the dynamic characteristics in hovering condition fully.
Numerical simulation of oxygen supply system's performance parameters characteristic at high altitude
Yu Zhongjun, Zhao Jingquan
2010, 36(8): 918-921.
Abstract:
The working process of aviation oxygen supply system(OSS)at high altitude was described, and the mathematic model for the performance parameters characteristics of OSS was built, combining with the principle of dynamics of gas flow. By the numerical simulation with Matlab/Simulink and the theoretical analysis, the performance parameters characteristics of OSS at high altitude were achieved. A detailed analysis was conducted for the characteristics of oxygen inflating time and ratio of pressure, and then the major parameters affecting the press in oxygen mask were found. The results are in good agreement with those measured in the experiments, which shows that the analytical model is correct and the simulation method is in accordance with the precision requirements. The study and its conclusions are useful for the design to the characteristics of OSS at high altitude and the system analyses.
Analysis of dynamic performance of crossflow heat exchangers for helicopters
Zhou Yi, Gao Hongxia, Yu Jianzu, Li Ming
2010, 36(8): 922-926.
Abstract:
Modeling and simulation of transient heat transfer in crossflow heat exchanger are necessary for developing the oil system in helicopters. The dynamic model of crossflow heat exchanger was established by using lumped thermal controlled methods, and its accuracy was proved by dynamic experimental results of crossflow heat exchanger. Through analysis of dynamic performance of the crossflow heat exchanger, especially considered the dynamic response of the outlet temperature in the hot side to the change of the inlet temperature in the same side or the cold side. Based on the analysis of dynamic transfer function, the most important influence coefficients are obtained, which are regenerative time constant of core and time constant of temperature changing in the hot side along with flow time. By reducing the values of two most important influence coefficients, the dynamic detention time could be reduced efficiently. The dynamic performance of heat exchanger and the whole system also could be improved efficiently.
Investigation of the design of wing hot-air anti-icing system
Bu Xueqin, Yu Jia, Lin Guiping, Song Xin
2010, 36(8): 927-930.
Abstract:
The thermal fluid system simulation tool Flowmaster and the computational fluid dynamic tool Fluent were combined for the simulation of the wing hot-air anti-icing system (WHAIS) design and thermal performance analysis. The design parameters contained the piccolo tube diameter, the jet hole diameter and the distance between holes. Mass flow of the hot air distribution per slat supplied by system was evaluated based on Flowmaster. Thermal efficiency of the WHAIS was predicted based on Fluent. The heat required for anti-icing was determined according to the results of external heat loads and the thermal efficiency of the system. Margin of the hot-air supply was introduced to analyze the WHAIS thermal performance. The method presented can be used in the engineering design and optimization of the WHAIS.
Modeling of wing flexure and filtering solution in transfer alignment
Xie Chunming, Zhao Yan, Wang Jinan
2010, 36(8): 931-935.
Abstract:
Focusing on the remarkable influence of wing flexure on transfer alignment(TA), a two-laser ranging method was presented to measure the wing flexure of missile-borne strapdown inertial navigation system(SINS) in different hook. An AR(n) model was put forward to simplify the ARMA(p,q) model to perform online modeling of wing flexure. In the modeling process, the recursive least squares algorithm was adopted to estimate the model parameters and F testing method using modeling estimation errors was applied to determine the rank of AR(n) model. Finally, the TA filter embracing multi-rank colored measurement noises was designed according to the online wing flexure model and rapid TA matching plan. Simulation experiments and results validate the feasibility and the validity of the online modeling method of wing flexure and the transfer alignment filter considering colored measurement noises, which provides an effective rapid and accurate TA method.
Fault diagnosis for independent power-supply system using multi-agent information fusion
Zhang Li, Yuan Haiwen, Lü Hong, Yuan Haibin
2010, 36(8): 936-939.
Abstract:
The fault diagnosis and prognosis research for Independent power-supply system(IPSS) was an important step to ensure the safety for the complex moving devices system. Current fault diagnosis system problems for IPSS were analyzed. The method of combining multi-sensor information fusion with multi-Agent was put forward to improve the diagnosis reliability and the system expansibility. A fault diagnosis system for IPSS using multi-Agent and information fusion was established based on Agent automation, distribution and collaboration. According to the fault symptom feature, Dempster-Shafer evidential theory was introduced into diagnosis result fusion. The multi-neural network local diagnosis Agent and the Dempster-Shafer evidential reasoning Agent implementation were disserted in detail. Finally, taking an aircraft electric power system as an example, the diagnostic process was simulated. The results indicate that the method can improve the diagnosis reliability.
Modeling and stability analysis for high altitude tethered balloon
Zhu Ming, Zuo Zongyu
2010, 36(8): 940-944.
Abstract:
Stratosphere high altitude tethered balloon (HATB) is a typical under-damping autonomous system, so it is required for the platform itself to be stable. However, it is hardly to investigate the platform stability theoretically through the classical Lyapunov first method, because there exist zero eigenvalues in the linearized model. The rigid translation and rotation equations with respect to any arbitrary point were presented, and then the general coordinate-based, second order, nonlinear dynamic model was proposed for HATB. In view of the limitation of the Lyapunov method, Lagrange theorem was applied to prove the platform stability problem from the perspective of energy. Numerical simulations demonstrate the coincidence with the theoretical analysis.
Modeling and simulation of soft ground arresting system for aircraft
Li Fengyu, Jiao Zongxia, Gui Yongquan
2010, 36(8): 945-948.
Abstract:
The arresting system stops the aircraft effectively when the aircraft passes beyond the end of the runway during an aborted takeoff or landing which minimizes the damage to the aircraft and the passengers. The arresting system is a kind of important safety facility for airports. Based on this, a new kind of soft ground arresting system was designed which has simple structure, high reliability, large maneuverability and outstanding generality. Combined with the aircraft 6-dof model and accurate resistance model, the soft ground arresting system mathematical model was built to analyze the process of arresting system. The system model was used to simulate the working process of the arresting system. Lots of important parameters, such as stopping distance and landing gear load were obtained. Compared with the experiments done in foreign countries, the simulation results were proved effective, which could be widely used in the construction and reconstruction of the airports.
Separation of variables solutions of stability problems of orthotropic rectangular thin plates
Wang Xingming, Liu Bo, Xing Yufeng
2010, 36(8): 949-952.
Abstract:
The stability problems of orthotropic rectangular thin plates were solved by using separation of variables, and the analytic solutions were obtained for three boundary conditions, which are the same with the results in literature. The present solution method is much simpler than traditional semi-inverse method.The effects of the force boundary conditions on the implementation of separation of variables were also investigated. The basic method without causing Poisson-s effect and rigid displacement has also been presented. The laminated plate was reckoned to be the orthotropic rectangular thin plate whose buckling problems were solved with present method for the plate subjected to in-plane unidirectional distributed compressive force, the results agree well with those of finite element method, which validate the correctness and practicability of present method.
FPGA-based power drive device for voice coil motor used in direct drive valve
Wang Dayu, Guo Hong, Yu Kaiping, Zhang Lijia
2010, 36(8): 953-956.
Abstract:
As the power drive device for voice coil motor requires a controller with higher computation speed, analog control is used in traditional method. There are inherent shortcomings, such as characteristics of drift, disabilities of interfacing with digital controller directly. A field programmable gate array (FPGA)-based power drive device for a voice coil motor used in direct drive valve is presented. The functions of generating pulse width modulation (PWM) signal, A/D sampling control, current sampling and digital filter, closed-loop current control, as well as communication with other digital controller were implemented by FPGA through modular design. Simulation and experimental results suggest the efficiency of FPGA-based power drive device to achieve high performances, and it can meet the requirements of direct drive valve system. The use of FPGA can greatly simplify the system hardware structure and improve the control system performances, and easily expand function and interface with other digital controllers.
Feature extraction of hyperspectral image based on locally linear embedding
Dong Chao, Zhao Huijie
2010, 36(8): 957-960.
Abstract:
Feature extraction can eliminate the redundant information hidden in the hyperspectral image. It is a necessary preprocessing step of the hyperspectral image analysis system, the classification for instance, to improve the precision and efficiency. Traditional feature extraction algorithms are based on linear transformation, which could not accurately describe the relationship between the original and reduced feature spaces. Therefore, locally linear embedding (LLE), the representative algorithm of nonlinear feature extraction, was adopted to reveal the intrinsic information of the hyperspectral image. For classification, the class labels of the training samples were utilized to adjust the distance matrix and the feature vectors of the test samples were calculated in the way that LLE mapped the unknown samples, realizing the supervised locally linear embedding (SLLE). In the experiment, the nonlinear feature extraction method was combined with three different classifiers and evaluated using the data collected by airborne visible/infrared imaging spectrometer. The experiments show that SLLE is superior to the linear feature extraction methods and can solve the small training set problem of classifying hyperspectral image.
Application of 3D control chart in performance monitoring and sorting of Li ion batteries
Wang Xiaohong, Li Tianye, Li Xiaogang
2010, 36(8): 961-964.
Abstract:
In order to sort Li ion batteries and monitor their performance status, the control chart method was applied, which used to utilize in quality control. Firstly some interrelated analyses were done about the failure mechanisms of Li ion battery to select the parameters that could reasonably describe the status of them. Then the optimization of the control chart especially for the batteries was carried out in detail. The 3D control chart which could monitor two parameters simultaneously was agreeable to our analysis. By Matlab and SPSS the chart was totally accomplished. And through the results, the judgments of the healthy situation, the prediction of the faults could be made using some specific and suitable principles. Some test results in the lab of reliability and environment of Beijing University of Aeronautics and Astronautics (Beihang University) were used as the source data and example. The test process is also concisely introduced.
Effect of stress amplitude on high-cycle fatigue life of 2A12-T4 aluminum alloy under proportional loading
Shi Xinhong, Zhang Jianyu, Bao Rui, Fei Binjun
2010, 36(8): 965-968.
Abstract:
Fatigue life experiments with funneled-shape specimens were conducted to investigate the effect of stress amplitude on multi-axial high-cycle fatigue failure of 2A12-T4 aluminum alloy under tension-torsion proportional loading. Based on the experiment results, three kinds of life-prediction criteria, which were widely used for multi-axial high-cycle fatigue analysis, were discussed. The results showe that under the same von-Mises equivalent stress, fatigue life raised gradually when the ratio of stress amplitude in tension and torsion increased. Fatigue life of uniaxial tension is the shortest and that of pure torsion is the longest. The forecast results of equivalent stress criteria are either too dangerous, or too conservative. Stress invariant criteria cannot predict the impact of stress-amplitude ratio on multi-axial high-cycle fatigue failure. Critical-plane criteria has better prediction capability than others.
Real perceive-based technology of time and space consistency in distributed virtual environment
Zhang Jiong, Lei Xiaoyong, Dai Shuling
2010, 36(8): 969-972.
Abstract:
Many existent methods emphasize on constructing absolute consistency models, but without analyze the movement rules of virtual environment (VE), their practical values were limited. Beginning from the rules of VE, a realistic-based consistency model was proposed. Based on the human perception, a mathematical model for temporal and spatial consistency were built, which can be used in distributed virtual environment (DVE), to determine and verify whether nodes in VE were temporal and spatial consistent. By using one way data transmission, it reduced the number of rollback nodes after time distortion, and increased the sense of immersive; a time delay neural network was used to predict node status which was greater than the maximum propagation delay. Therefore, the temporal and spatial consistency is guaranteed by these strategies. The experimental results demonstrated the effectiveness of this method and a conclusion had been drawn.
Kind of novel micro integrative transceiver module
Wei Xinguo, Chen Xiao, Song Jingming
2010, 36(8): 973-976.
Abstract:
Fiber optic gyroscope (FOG) can be affected greatly by temperature and vibration. The limitations of input channel depolarization scheme and full polarization maintaining scheme were analyzed. Then, a kind of micro integrative transceiver module was designed to integrate super luminescent diode (SLD) source, half transmission and half reflection glass slide, collimation lens, GRIN lens, PIN detector and field effect technology (FET) circuit. The system in package (SIP) technique was applied and the vacuum was created. The light propagation in vacuum didn-t produce birefraction. Thus, the system accuracy and liability effects caused by temperature and vibration were avoided and the whole performance of FOG was promoted. The Superlum Inc. SLD-57-HP type source model was created by beam scanner. According to Gaussian beam characteristic, the compact optical system was designed and the Fresnel reflection loss was analyzed. Then, the simulation was exerted by Zemax software. The results show the coupling efficiency is 38.98% which exceeds current 20% coupling efficiency.
High altitude simulation experiment system for low power hydrazine arcjet
Zhang Xinai, Tang Haibin, Shi Chenbo, Liu Yu
2010, 36(8): 977-980.
Abstract:
A high altitude simulation experiment system for low power hydrazine arcjet was presented. The elements in this system including vacuum facility, propellant feed system, power control unit, full elastic micro thrust measurement equipment, data acquisition system etc. were depicted in details. To meet the special demands in low power arcjet high altitude simulation experiment, the working process and principle of the propellant feed system, the full elastic steady weighting method micro flow measurement system and the full elastic micro thrust measurement equipment were emphasized. Tests to validate the system were conducted in this system. The results show that the high altitude simulation experiment is steady, reliable and competent for low power hydrazine arcjet high altitude simulation experiment.
Domain-oriented simulation designing and modeling tool
Wen Wei, Fang Wei, Huang Xiaodong, He You
2010, 36(8): 981-985.
Abstract:
The design and implementation of the domain-oriented designing and modeling tool, SIMDEMO, were discussed. A cooperative modeling methodology supporting multi-views modeling was built by decomposing system models which involve various modeling stages, users, aspects into multi-views based on principles of transparency, orthogonality and hiberarchy, and the guidelines for the modeling processes were also presented. In consideration of the different needs for the description, representation and operation of the models in different domains, a reflective architecture based on the meta-object model was built; The architecture has good adaptability, and can make the customization of the tool more flexible and concise. The system structure and functions were introduced briefly, and the software implementation was presented. At last, SIMDEMO was compared with the similar representative tools.
Unmanned helicopter autonomous board landing system and simulation experiment
Wulan Bagen, Hu Jizhong, Xu Yuanming
2010, 36(8): 986-990.
Abstract:
The unmanned helicopter autonomous landing system was composed of vision and recognition sytem, a target tracker, a deck-s state tracker and a fuzzy logic controller. The vision system performed to process the captured image and compute the image-s affine moment invariants. The label was recognized based on the fuzzy logic and those invariants. The label-s motion state was estimated based on the moment. A Kalman filter integrating into the control system was used to track the label and plan the route of unmanned helicopter. The board-s motion state, especially the pitch, roll and lift, is important for safe landing, so an improved Kalman forecast algorithm was designed to predict the board-s state of further one to five steps. The controller was customized based on behavior and fuzzy logic. Simulation results validate proposed algorithm. The unmanned helicopter can recognize the label accurately and track the label in any direction on ground. The improved Kalman filter can estimate the state future one to five periods, and there is less error than normal Kalman filters. The controller can generate the accurate commands and perform the autonomous landing on board safely.
Rudder flutter analysis method of missile with jet vane
Jing Zhiwei, Wu Zhigang, Yang Chao
2010, 36(8): 991-995.
Abstract:
Traditional flutter analysis and commercial software can not analyze rudder flutter of missile with jet vane. An approach for solving rudder flutter of missile with jet vane was presented. Dynamic sub-structure method was applied to establish dynamic formulation of rudder flutter in state space and analysis method of missile with jet vane. Structural mass matrix and stiffness matrix were partitioned according to the vectors of generalized coordinates. The aeroelastic influence of different stream and the influence of wing-body on the airstream were considered. The calculation model of unsteady aerodynamics in time-domain was based on the rational aerodynamic approximation method. Numerical results indicate that adverse stiffness coupling between jet vane shaft and rudder shaft can deteriorate the rudder flutter velocity. The analysis method and results above can supply reference for the missile design.
Decision-making of saturation attack for missile weapon-target assignment with multi-target
Yang Fei, Wang Qing, Dong Chaoyang
2010, 36(8): 996-999.
Abstract:
Saturation attack is an important tactical method in high-tech war against enemy-s important target and increase missile-s penetration probability. In accordance with saturation attack tactics- guiding ideology, the constraints and criterion of optimal allocation for multi-firepower-s coordinated attack were analyzed, then the weapon-target assignment optimization model was presented. Combining fire-distribution decision-making with route planning decision-making processes, a method to implement saturation attack under multi-firepower and multi-constraint condition was proposed. The simulation results indicate the model and the algorithm are correct and effective, it provides basis and reference for solving the problem of missile launch position disposition and fire-distribution.
Vision based navigation system of UAV and improvements of the corresponding filtering algorithm
Xu Chao, Fan Yaozu, Shen Xiaorong, Luo Yufeng
2010, 36(8): 1000-1004.
Abstract:
A vision/inertial integrated navigation system was built. The corresponding filtering model was established by treating the motion models of aerial vehicle and landmark as the system function and the vision information as the observation. Complex additive noise model was adopted to describe the system noise in the filtering process. The wavelet-unscented Kalman filter (UKF) algorithm was obtained by introducing the wavelet analysis into UKF, thus the influence of vision observation noise on the filtering was inhibited successfully. Maximum a posterior (MAP) adaptive method was utilized to estimate the observation noise covariance matrix, which was further fed back into UKF to overcome the difficulties in identifying the covariance of observation after the wavelet de-noising. The simulation proved that the improvements in the filtering process to be effective in increasing the filtering accuracy.
Principle and application of horizontal suspension isolator constituted by trilinear pendulum
Xu Dengfeng, Gao Zhenyu, Zhu Yu, Zhang Ming
2010, 36(8): 1005-1008.
Abstract:
For the suspension isolator constituted by trilinear pendulum, the Lagrangian equation with swing angle as generalized coordinate was established firstly at a particular direction. When the swing angle was a particular value, the three-dimensional graphic was projected onto a plane, other variables were converted to the functions of swinging angle by solving geometric relations, thus the horizontal natural frequency can be obtained. The impact to horizontal natural frequency from mechanism structure parameters were analyzed through adjusting the parameters in a certain range. A lot of simulation results were made by MATLAB. The results show that increasing supporting length can reduce the natural frequency, but increase mechanism height. It also shows that once mechanism stability is insured, increasing the ratio of fixed disk’s diameter to swing disk’s diameter and reducing the ratio of fixed disk and swing disk-s distance to supporting length can reduce the natural frequency, and not increase the height of the mechanism very much.