Application of symbolic manipulation to inverse dynamics and kinematics of elastic robots

An inverse dynamics and kinematics of a flexible manipulator is derived in symbolic form based on the recursive Lagrangian assumed mode method. A PC-based program has implemented the algorithm to automatically generate the inverse dynamics and kinematics for an elastic robot in a symbolic form. A case study is given to illustrate how to use this program for inverse dynamic and kinematic generation. Simulation results for a case study by considering different mode shape are compared with the rigid case.Nomenclature A _i joint transformation relates systemi to systemi-1 - E _i link transformation relates the deflection of systemi to systemi - F _i joint torque acting on jointi - g gravity vector expressed at the base coordinates - J inertia = - K kinetic energy of the system - l _i length of linki - M _i a mass concentrated at the joint i - m _i number of modes used to describe the deflection of link i - n number of links - q _h joint variable of thehth joint - q _hk time-varying amplitude of mode k of link h - R vector of remaining dynamics and external forcing terms = - r _i vector locating the centre of mass of linki - R _j dynamics from the joint equation j, excluding second derivatives of the generalized coordinates - R _if dynamics from the deflection equation jf, excluding second derivatives of the generalized coordinates - V potential energy - W _i transformation from the base to theith link - transformation from the base to the systemî - z the vector of generalised coordinates = - link density     

Relation between the Residual Magnetization and Change in Magnetization on Steel and Alloy Return Curves

The relation between the residual magnetization M _r and change in magnetization on the return curves as a function of the coercive force is studied experimentally for heat-treated steels of different chemical compositions and a number of polycrystalline iron–nickel–cobalt alloys. It is shown that in the quenched condition the ratios M _s /M _r and M _r / are almost constant and close to 2 and 4, respectively, for all investigated steels regardless of their chemical composition. For highly tempered steels and annealed alloys these ratios represent structurally sensitive quantities depending on the critical fields in the material and characterize the relation between reversible and irreversible remagnetization processes. A model interpretation of the results obtained is given.     

The run sum t control chart for monitoring process mean changes in manufacturing

The $ \overline{X} $ type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL₁) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the $ \overline{X} $ type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL₁ and lower minimum cost. The run sum t chart surpasses the $ \overline{X} $ type charts by having lower ARL₁ when the charts are optimally designed for large shifts but the run sum $ \overline{X} $ and EWMA $ \overline{X} $ prevail for small shifts. In terms of minimum cost, the $ \overline{X} $ type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations.     

An intelligent sensor system approach for reliable tool flank wear recognition

An intelligent sensor system approach for reliable flank wear monitoring in turning is described. Based on acoustic emission and force sensing, an intelligent sensor system integrates multiple sensing, advanced feature extraction and information fusion methodology. Spectral, statistical and dynamic analysis have been used to determine primary features from the sensor signals. A secondary feature refinement is further applied to the primary features in order to obtain a more correlated feature vector for the tool flank wear process. An unsupervised ART2 neural network is used for the fusion of AE and force information and decision-making of the tool flank wear state. The experimental results confirm that the developed intelligent sensor system can be reliably used to recognise the tool flank wear state over a range of cutting conditions.Notation mean - ² variance - k _n end condition factor of the cantilever beam - E Young's modulus of tool holder - I moment of inertia of tool holder at cross section - m mass of tool holder per unit length - L length of tool overhang - l the size of the moving window - fm, pm, sm, km the mean values of the four primary features (the tangential force component, the frequency band power, the skew, and the kurtosis) - fs, ps, ss, ks the standard deviation values of the four primary features - F= resultant feature vector ART2 neural network parameters I _i element of input vector - Y _i output node - W _i ,X _i ,U _i ,V _i ,P _i ,Q _i parameters inF ₁ layer - R _i orienting parameter - vigilance parameter - b _ij ,t _ji bottom-to-top and top-to-bottom weights - a, b, c network parameters - f() thresholding function     

Accuracy and strength of a joint loaded by suddenly applied torque

The influence of the required quality (fit and degree of accuracy) of prismatic joints to achieve guaranteed clearance was a speciality of experienced designers. The problem becomes quite complicated owing to stresses arising in the joint elements during torque transmission under dynamic loading.In this paper a widely used prismatic joint with a hexagonal cross-section is considered. A dynamic loading, generated by a spring mechanism is applied. D'Alambert's principle was employed in solving the kinesthetic problem.The paper presents equations for the dynamic coefficient, the angle of clearance, _i and the maximum tangential stress. It is pointed out that torque-loaded elements cannot be produced from rolled stock, obtained from drawings.The presented graphs permit selection of the steel grade in accordance with the fit and the degree of accuracy of the joint and with the permissible torsional stress.The proposed procedures may be used for computer-aided design of torque-transmitting prismatic splines, key joints and torsion mechanisms.Nomenclature d ₁ diameter of hole (see Fig. 1) - d _max D _n + es maximum limit of shaft size - d _min D _n + is minimum limit of shaft size - D _max D _n + ES maximum limit of hole size - D _min D _n + EI minimum limit of hole size - D _n nominal size of the hole and of shaft - ES, es upper deviation of hole and shaft - EI, ei lower deviation of hole and shaft - F area of hexagon - G modulus of transverse elasticity - (see Fig. 1) - I _p polar moment of intertia - polar moment of inertia of hexagon - polar moment of inertia of circle - K dynamic coefficient - l length of shaft - m number of polygon sides - M _d torque under dynamic loading - M _s torque under static loading - S _i clearance - S _max = ES-ei maximum clearance of joint - S _min = EI-es minimum clearance of joint - T tolerance - W section modulus of torsion - W _c circle section modulus of torsion - W _h hexagon section modulus of torsion - (see Fig. 1) - maximum tangential stress under dynamic loading - maximum tangential stress under static loading - _d twist angle under dynamic loading - _i angular displacement - _s twist angle under static loading     

The use of generalized magnetic parameters for magnetic structural analysis and nondestructive testing

The results of studies regarding the dependence of the product of the coercive force and the initial magnetic susceptibility of a nickel single crystal with an intermediate orientation on the shear stress are analyzed. It is concluded that an increase in the aforementioned product for a nickel single crystal upon cold plastic deformation is due to refining of magnetic domains that is caused by formation of cells and subgrains within the single crystal. The tentative size of magnetic domains was determined based on the value of generalized magnetic parameter . The variations in the product and in the calculated dimensions of magnetic domains in polycrystalline nickel are analyzed using data reported by Kersten-Gottschalt. It was also shown that, the density of dislocations being constant, the generalized magnetic parameter is sensitive to changes in the sizes of nonferromagnetic inclusions, whereas in the case of small nonferromagnetic inclusions, an increase in the generalized parameter is due to an increase in the density of dislocations.Translated from Defektoskopiya, Vol. 40, No. 7, 2004, pp. 62–76.Original Russian Text Copyright © 2004 by Bida.     

Improving the Accuracy in Determining the Insulator Capacitance in Metal–Insulator–Semiconductor Structures

The results of the voltage–capacitance spectroscopy of interface states in metal–insulator–semiconductor (MIS) structures are critical functions of the accuracy in determining the insulator capacitance C _i, which is typically no higher than a few fractions of a percent. This substantially limits the energy range of the observed spectrum of the interface states (E 0.5 eV for Si-based MIS structures) and the sensitivity to the density of the interface states at the spectrum edges (N _ss 1 × 10¹⁰ cm^–2 eV^–1). We propose a method for minimizing these errors that is based on a sequential variation of the initial estimate C _i C _{i 0} C _ij, j = 0, 1, 2, ... and the identification of singular points in the dependences and on C _ij, where are the mean arithmetic values of the voltage difference between the experimental and ideal voltage–capacitance characteristic and are the rms deviations of the voltage values taken in the high-accumulation (ac) and inversion (in) regions from values. The highest (10^–4%) accuracy in determining C _i is achieved in the regions of the equidistant experimental and ideal voltage–capacitance characteristic. This method, combined with the technique of _s / _s diagrams, ensures an extension of E to 0.9 eV at N _ss 1 × 10¹⁰ cm^–2 eV^–1 and the possibility of determining the sign and density of the fixed charge in the gate insulator.     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed     

Atmospheric effects of friction,friction noise and wear with silicon and diamond. Part III. SEM tribometry of polycrystalline diamond in vacuum and hydrogen

In this part III of a multi-part paper series, the results of additional SEM tribometric experiments are described, performed with polished, mostly C(100)-oriented polycrystalline CVD diamond film [PCD_C(100) vs. PCD_C(100)] counterfaces sliding in Torr and in 0.1–0.3 Torr partial pressures of pure hydrogen gas. These tests were completed under a 28 g (0.27 N) normal load, under standard and slow thermal ramping conditions at temperatures ranging from room temperature to 1000^°C. The friction data were examined per the computer logging and analysis techniques described in part I. The treatment of the data is similar to that of Si in part II: the maximum and the average coefficients of friction (MAX.COF and COF) and their ratios (the friction noise FN) are employed to measure possible lubricative interaction of the diamond surfaces with rarefied hydrogen. The results indicate that excited species of molecular hydrogen enter into tribothermally catalyzed reactions not only with Si but with PCD_C(100) surfaces as well. Similar to the behavior of Si, the most beneficial friction-reducing regime occurs in a temperature range just before the thermal desorption of adsorbates. The general magnitudes of MAX.COF, COF and the FN are significantly lower than those of the Si crystallinities, in both vacuum and . The wear rate of the PCD_C(100) film characteristic of the standard thermal ramping test procedure performed mostly in is around , in good agreement with the wear rate previously measured in vacuum for unpolished, fine-cauliflowered diamond films. The data indicate that smooth polycrystalline diamond is a significantly better bearing material for miniaturized moving mechanical assembly applications than Si. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of structure and defect on fatigue limit in high strength ductile irons

In this paper, the influence of several factors such as hardness, internal defect and non-propagating crack on fatigue limits was investigated with three kinds of ductile iron specimens. From the experimental results the fatigue limits were examined in relation with hardness and tensile strength in case of high strength specimens under austempering treatment; in consequence the marked improvement of fatigue limits were not showed. The maximum defect size was an important factor to predict and to evaluate the fatigue limits of ductile irons. And, the quantitative relationship between the fatigue limits (σ _w ) and the maximum defect sizes ( $\sqrt {area} _{\max } $ ) was expressed as $\sigma _w ^n \cdot \sqrt {area} _{\max } = C_2 $ . Also, it was possible to explain the difference for the fatigue limits in three ductile irons by introduction of the non-propagating crack rates.     

An economic design for variable sampling interval MA control charts

Most of the studies done on the economic design of control charts focus on a fixed-sampling interval (FSI); however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI moving average (MA) control chart is proposed. The results of a numerical example adopted from an actual case indicate that the loss cost of VSI MA control charts is consistently lower than that of the FSI scheme.Design variables n Sampling size for each moving plot - h_a Subsequent sampling interval when preceding sample mean is located at sub-control region I_a, a=1,2,..., - Number of different sampling-interval lengths, 2 - k_a Threshold limit expressed in units of - k₁ Control limit expressed in units of Parameters related to assignable cause µ₀ Target mean - True-process standard deviation - Magnitude of an assignable cause expressed in units of - Occurrence rate of an assignable cause per unit timeCost and technical parameters D Average time taken to find and repair an assignable cause after detection - e Time for a sample to be taken, transmitted to laboratory, and results phoned back to process control room - M Income reduction when =₀+ - T Average cost of looking for an assignable cause when a false alarm occurs - W Average cost of looking for and repairing an assignable cause when one does exist - F_c Fixed cost per subgroup of sampling, inspecting, evaluating and plotting - V_c Variable cost per subgroup of sampling, inspecting, evaluating and plotting     

Temperature measurement in orthogonal metal cutting

Orthogonal cutting experiments were carried out on steel at different feedrates and cutting speeds. During these experiments the chip temperatures were measured using an infrared camera. The applied technique allows us to determine the chip temperature distribution at the free side of the chip. From this distribution the shear plane temperature at the top of the chip as well as the uniform chip temperature can be found. A finite-difference model was developed to compute the interfacial temperature between chip and tool, using the temperature distribution measured at the top of the chip.Nomenclature contact length with sticking friction behaviour [m] - c specific heat [J kg^–1 K^–1] - contact length with sliding friction behaviour [m] - F _P feed force [N] - F _V main cutting force [N] - h undeformed chip thickness [m] - h _c deformed chip thickness [m] - i,j denote nodal position - k thermal conductivity [W m^–2 K^–1] - L chip-tool contact length [m] - p defines time—space grid, Eq. (11) [s m^–2] - Q _C heat rate entering chip per unit width due to friction at the rake face [W m^–1] - Q _T total heat rate due to friction at the rake face [W m^–1] - Q _% percentage of the friction energy that enters the chip - q ₀ peak value ofq(x) [W m^–2] - q _e heat rate by radiation [W] - q(x) heat flux entering chip [W m^–2] - t time [s] - T temperature [K] - T _C uniform chip temperature [°C] - T _max maximum chip—tool temperature [°C] - T _mean mean chip—tool temperature [°C] - T _S measured shear plane temperature [°C] - x,y Cartesian coordinates [m] - V cutting speed [m s^–1] - V _C chip speed [m/s] - rake angle - ,, control volume lumped thermal diffusivity [m² s^–1] - emmittance for radiation - exponent, Eq. (3) - density [kg m^–3] - Stefan-Boltzmann constant [W m^–2 K⁴] - (x) shear stress distribution [N m^–2] - shear angle     

Analysis of the diamond sawing process

There are three methods in use for separating diamonds, i.e. by cleaving, by laser beam and by sawing. Sawing is one of the main methods used for this purpose. This operation is carried out on special sawing machines equipped with a sawing disk blade, 0.04–0.14 mm thick and 76 mm initial diameter. The rotational velocity (n) of the disk is between 6000 and 12 000 r.p.m. Diamond powder is embedded in the periphery of the disk. The outcome surface of a diamond after the sawing operation must be flat and smooth, Whenever such a surface is actually obtained, the polishing time and the loss in size and weight of the diamonds are reduced.In the present work, the positioning of the diamond to be sawed, with respect to an embedded particle in the disk, to create a favourable cutting angle is discussed. This would make it possible to reduce the rake angle () to near-zero, and thereby the cutting forces. Furthermore, a method to control the morphology and grain size of the diamond powder to be used in the cutting was developed.In the diamond industry, two modes of sawing operations are in practice. One uses the periphery of the disk for the sawing while the other employs a circular hole in the centre of the disk. Analysis of the two modes showed that the hole mode is more promising, as the design in that case requires tensioning of the disk and makes for better lateral stability during the sawing process. In addition the tangential and the radial stresses, developed in both sawing methods, were calculated. To support the above, data was obtained from existing literature and analysed.Nomenclature n rotational velocity of the disk, r.p.m. - rake angle, degrees - back clearance angle, degrees - cutting angle, degrees - m relative frequency - f feed - b disk radius, mm - a disk hole radius, mm - r current disk radiusb>r>a, mm - density of disk material, kg m^–3 - angular velocity - Poisson ratio of disk material - g acceleration of gravity, m s^–2 - _r radial stress, kg cm^–2 - _{r max} highest radial stress, kg cm^–2 - _t tangential stress, kg cm^–2 - tangential stress at outside circumference, kg cm^–2 - tangential stress at inside circumference, kg cm^–2     

Using target costing concept in loss function and process capability indices to set up goal control limits

This paper depicts the relationship among the loss function, process capability indices and control charts to establish goal control limits by extending the target costing concept. The specification limits derived from the reflected normal loss function is linked through the C _pm value, computed either directly from the raw data or given by management or engineers, to conventional control charts to obtain goal control limits. The target value can be taken into consideration directly. The advantages of applying the target costing philosophy are also discussed. This paper explains, from a quantitative approach, that reducing process variation is not enough to solve quality problems. In fact, reducing process variation should be used along with bringing the process mean to the target value.A list of symbols K: The maximum-loss parameter in the reflected normal loss function - : The shape parameter in the reflected normal loss function, /4 - T: The target value - : The distance from the target value to the point where K first occurs (tolerance or specification limit) - E(L(y)): The expected loss associated with the reflected normal loss function - : The average value (mean) of a population - : The standard deviation of a population - _T : The standard deviation from the target value of a population - : The estimated standard deviation of - : The new process standard deviation when 2 are applied - n: The sample size of the subgroup - d ₂: The parameter used to estimate , determined by n - D ₄, D ₃, and A ₂: The parameters in and R control charts, determined by n - c ₄: the parameter used to estimate , determined by n - B ₄, B ₃, and A ₃: The parameters in and S control charts, determined by n - L(y): The general loss function - L ₁(y): The general loss function when the quality improvement is implemented - h: The parameter used to determine L ₁(y), where L ₁(y)=hK - f(y): The probability density function     

SURFACE FINISH AND TOOL WEAR CHARACTERIZATION IN HARD TURNING USING A MATHEMATICAL CUTTING TOOL REPRESENTATION

The development of a general 3D model for a corner-radiused, chamfered, edge-honed cutting worn tool is elaborated. The surface of the cutting tool was constructed using one angular scalar specifying location on the corner radius and leading/trailing edges and another non-dimensional scalar for specifying location on the relief, edge-hone, chamfer and tool-top. Then, for given geometric parameters and cutting conditions, the angular extremities of contact on the corner radius and leading/trailing edges was obtained and validated. The kinematic surface finish on the workpiece surface including the Brammertz and sideflow effects was then simulated in typical hard turning. The model was expanded to allow wiper edges and flank wear. A simplified crater wear model was adopted for continuous hard turning to allow virtual cross-sectioning. Accurate estimation of flank and crater wear volume was also enabled. The model results for the fresh tool agreed with well-known trends from 2D modeling. Preliminary results indicate that there exists a geometric basis for higher R_a and R_t for a worn tool. The Brammertz effect simulation, though not in agreement with the data of Knuefermann (2003 Knuefermann , M.M.W. ( 2003 ) Machining surfaces of optical quality by hard turning, School of Applied Sciences, Cranfield University, Cranfield, Bedfordshire, UK . [Google Scholar]) corroborated the modification proposed therein.     

Prediction of tool failure rate in turning hardened steels

This paper presents a stochastic model for predicting the tool failure rate in turning hardened steel with ceramic tools. This model is based on the assumption that gradual wear, chemical wear, and premature failure (i.e. chipping and breakage) are the main causes of ending the tool life. A statistical distribution is assumed for each cause of tool failure. General equations for representing tool-life distribution, reliability function, and failure rate are then derived. The assumed distributions are then verified experimentally. From the experimental results, the coefficients of these equations are determined. Further, the rate of failure is used as a characteristic signature for qualitative performance evaluation. The results obtained show that the predicted rate of ceramic tool failure is 20% (in the first few seconds of machining) and it increases with an increase in cutting speeds. These results indicate that there will always be a risk that the tool will fail at a very early stage of cutting. Such a possibility should not be overlooked when developing proper tool replacement strategies. Finally, the results also give the tool manufacturers information which can be used to modify the quality control procedures in order to broaden the use of ceramic tools.Nomenclature c constant - ch chamfer width of the tool, mm - d depth of cut, mm - h _i hardness value at theith location on the workpiece during machining - h mean ofh ₁,h ₂,h ₃, ...,h _nn - n hardness mean location - m Meyer exponent determined experimentally to define the nonlinear relation between the cutting force and the ratioh _i/h - f feedrate, mm rev^–1 - f(t) probability density function of tool failure - f ₁(t) probability density function of tool failure due to breakage caused by tool quality - f ₂(t) probability density function of tool failure due to breakage caused by workpiece condition - f ₃(t) probability density function of tool failure due to tool chipping caused by chemical wear - f ₄(t) probability density function of tool failure due to flank wear - f ₅(t) probability density function of tool failure due to crater wear - O() error - t cutting time, min - x ₁,x ₂,...,x _n independent variables - A _i instantaneous area of contact between the tool and the workpiece - C ₁ chip load, which can be determined as a function of the cutting conditions and tool geometry - K _I crater wear index - K _T maximum depth of crater wear on tool face, mm - K _M crater centre distance, mm - N number of failures - P(t) probability function of tool failure - P _j(t) corresponding probability of failure, such that 1j5 - R tool nose radius, mm - R(t) reliability function - R _j(t) corresponding reliability function, such that 1j5 - T _V estimate of tool life for a set value of average flank wear (V _B ^* ) - T _K estimate of tool life for a set value of maximum depth of crater wear (K _T ^* ) - V cutting speed, m/min - V _B average tool wear, mm - Z(t) instantaneous failure rate or hazard function - ₃ shape parameter in the Weibull probability density function - rake angle - ₃ scale parameter in the Weibull probability density function, min - failure rate of the cutting tool - mean of a logarithmic normal distribution function - standard deviation of a logarithmic normal distribution function - tool wear function - time corresponding to the occurrence of tool failure - (.) standard logarithmic normal distribution function     

A faster, more reliable solver of regular-grid TSPs: single value threshold accepting

The main point of this paper is to provide a simple and efficient threshold value for the threshold accepting (TA) algorithm to attempt an optimal solution for the regular grid travelling salesman problems (TSPs) in a reliable way. This new algorithm is named the single value threshold accepting algorithm (SVTA). The number of the threshold value is one and its value is: where g is the grid size and is the smallest integer not less than a real number x. For the regular-grid TSPs, g can be set as where n is the problem size. It is shown empirically, with 100 independent simulations performed with 441 cities, in 16 different cases, that the SVTA is far superior to (at least five times faster on average than) the previous double threshold accepting (DTA) with respect to the speed of finding a global optimal reliably. Particularly in the case of the 441 cities, the proposed algorithm is at least 21 times faster and rises up to 96 times on average and optimistically 284 times faster than the previous one. Important insight is provided that reveals how the formula works and why it works successfully.Notation ={} State space of the tours in TSP - L() The length of a tour - L_opt The optimal tour length - TH Threshold - g Grid size in a square regular-grid TSP - n Number of points in TSP - L Lid value of a "pocket" around a good suboptimal solution x_min - N(L) Volume (= number of tours) of the "pocket" around a good suboptimal solution x_min with lid value L - M(L) Number of local minimum in the pocket with lid value L - K(n) Number of experienced local minima in a simulation by the SVTA     

Theoretical Investigation of the Viscous Damping Coefficient of Hydraulic Actuators

The viscous damping coefficient(VDC) of hydraulic actuators is crucial for system modeling,control and dynamic characteristic analysis.Currently,the researches on hydraulic actuators focus on behavior assessment,promotion of control performance and efficiency.However,the estimation of the VDC is difficult due to a lack of study.Firstly,using two types of hydraulic cylinders,behaviors of the VDC are experimentally examined with velocities and pressure variations.For the tested plunger type hydraulic cylinder,the exponential model B=αυ~(-β),(α0,β0)or B=α_1e~(-β_1υ)+α_2e~(-β_2υ)(α_1,α_20,β_1,β_20),fits the relation between the VDC and velocities for a given pressure of chamber with high precision.The magnitude of the VDC decreases almost linearly under certain velocities when increasing the chamber pressure from 0.6 MPa to 6.0 MPa.Furthermore,the effects of the chamber pressures on the VDC of piston and plunge type hydraulic cylinders are different due to different sealing types.In order to investigate the VDC of a plunger type hydraulic actuator drastically,a steady-state numerical model has been developed to describe the mechanism incorporating tandem seal lubrication,back-up ring related friction behaviors and shear stress of fluid.It is shown that the simulated results of VDC agree with the measured results with a good accuracy.The proposed method provides an instruction to predict the VDC in system modeling and analysis.     

Making decision to evaluate process capability index C p with fuzzy numbers

The process capability index C _p has wide applications in the manufacturing industry. This paper extends those applications to a fuzzy environment, with a methodology for testing the index C _p of fuzzy numbers. A pair of nonlinear functions is formulated to find the α-cut of index . From various values of α, the membership function of index is constructed, and the probability of rejecting the null hypothesis is calculated based on this membership function. Different from classical tests, the statistical decision proposed in this paper shows a grade of acceptability of the null hypothesis and the alternative hypothesis, respectively. With crisp values, the developed approach not only can boil down to the classical formula for calculating Ĉ _p , but also lead to a binary decision: to reject or to accept the null hypothesis. An example is used to illustrate the performance of the proposed approach.     

Competitive parameter optimization of multi-quality CNC turning

Surface roughness, tool wear, and material removal rate (MRR) are major intentions in the modern computer numerical controlled (CNC) machining industry. In this paper, the ${\text{L}}_9 \left( {3^4 } \right)$ orthogonal array of a Taguchi experiment is selected for four parameters (cutting depth, feed rate, speed, and tool nose runoff) with three levels (low, medium, and high) in optimizing the finish turning parameters on an ECOCA-3807 CNC lathe. The surface roughness (R_a) and tool wear ratio (mm^?2) are primarily observed as independent objectives for developing two combinations of optimum single-objective cutting parameters. Additionally, the levels of competitive orthogonal array are then proposed between the two parameter sets. Therefore, the optimum competitive multi-quality cutting parameters can then be achieved. Through the machining results of the CNC lathe, it is shown that both tool wear ratio and MRR from our optimum competitive parameters are greatly advanced with a minor decrease in the surface roughness in comparison to those of benchmark parameters. This paper not only proposes a competitive optimization approach using orthogonal array, but also contributes a satisfactory technique for multiple CNC turning objectives with profound insight.