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In this study, an analytical approach is presented to find stability limits in terms of radial immersion for a given axial depth of cut, and vice versa. Under the assumption of axis-symmetric structure and using the zero order force model, the direction coefficient matrix is decoupled to reduce the 2D milling system to a 1D stability problem. The effect of the radial immersion and radial cutting coefficient on the system stability are explicitly represented through the eigenvalue function of the directional coefficient matrix. The resulting characteristic equation allows the limiting radial immersion be solved for a given axial immersion. A procedure is presented in obtaining the radial stability diagram, in which additional unstable island and secondary lobes are shown to exist besides the traditional lobes. Stability diagrams in both axial and radial immersion are presented to demonstrate the physical insights offered by the presented method. The model is validated by comparing with results from the existing analytical and numerical models.

Soil arsenic (As) levels are particularly high in parts of China, where wheat and rape are widely grown. Understanding the effects of As concentration on the growth of these two major crops is of significance for food production and security in China. A pot experiment was carried out to study the uptake of As and phosphorus (P), and the soil As bioavailability at different growth stages of wheat and rape. The results indicated that winter wheat was much more sensitive to As stress than rape. Wheat yields were elevated at low rates of As addition (< 60 mg/kg) but reduced at high rates of As concentrations (80–100 mg/kg); while the growth of rape hadn’t showed significant re sponses to As addition. Phosphorus concentrations in wheat at jointing and ear sprouting stages increased with increasing soil As concentrations, and these increases were assumed to contribute a lot to enhanced growth of wheat at low As treatments. Arsenic did not significantly affect P concentrations in rape either. The highest As concentra tions in wheat shoot and rape leaf were 8.31 and 3.63 mg/kg, respectively. Arsenic concentrations in wheat and rape grains did not exceed the maximum permissible limit for food stuffs of 1.0 mg/kg. When soil As concentration was less than 60 mg/kg, both wheat and rape could grow satisfactorily without adverse effects; when soil As concentra tion was 80–100 mg/kg, rape was more suitable to be planted than wheat.

This paper presents a method for the identification of cutter offset through milling force without requiring the specific cutting coefficients to be known as priori. The total milling force in the presence of cutter offset is first obtained on the basis of dual cutting mechanisms, where the local force is comprised of a constant plowing force and a linear shearing force proportional to the chip load under the cutter offset. The total milling force is synthesized through convolution and is shown to be the sum of three force components: the nominal chip shearing force component, the plowing force components and the offset related shearing force component. Fourier analysis of these force components reveals the effects of offset geometry and yields formulas for the identification of offset geometry. The identification process requires only two cutting tests and the evaluation of two algebraic expressions; the shearing constants are found from the average forces of cutting tests and the offset geometry is identified from the force component at the spindle frequency. Through numerical simulation and experimental results, the efficacy of the identification method is demonstrated; the effects of feed per tooth and cutting depths on the accuracy of the model are investigated and criteria for the appropriate selection of these parameters are suggested.

Online methods for the identification of shearing and plowing cutting constants from forces in a single milling operation are presented. By virtue of the analytical nature of the milling force model in the frequency domain, the shearing and plowing constants are expressed, in a linear closed-form equation, in terms of cutter geometry, cutting depths and the Fourier coefficients of the milling forces. Two methods are presented to identify these cutting constants. The first method uses only the first harmonic components of the milling forces, and the second method utilizes the average forces as well as the ratio of the first harmonic forces. Limitations on the cutting conditions for each identification method are discussed. The accuracy and consistency of these two methods in extracting the shearing and plowing constants from a single set of force measurements are verified through simulation and milling experiments.

Two methods are presented for the estimation of tangential, radial and axial cutting coefficients for the shearing and ploughing mechanisms from a single set of cutting forces in ball-end milling. These estimation methods are based upon the invertibility of the analytical milling force model, which considers both the shearing and the ploughing mechanisms by incorporating their respective cutting constants in the local force model. The periodic milling forces are established as the convolution integral of the differential local cutting forces and their Fourier coefficients are derived and expressed in a matrix expression as a linear function of the unknown cutting constants in terms of cutting conditions and cutter geometry. This linear expression thus leads to a systematic formulation of the estimation methods allowing the six unknown cutting constants to be determined from the measured milling forces. The first method uses the first harmonic forces as the source signal while the second method extracts the six cutting constants from the average force as well as the first harmonics. Limitations of both estimation methods are discussed. The consistency and accuracy of the estimated cutting constants are confirmed by the experimental results.

An analytical force model with both shearing and ploughing mechanisms is established for the end milling processes. The elemental forces are defined as the linear combination of shearing and ploughing forces in six cutting constants. The analytical model for the total milling forces in the angular and frequency domain are derived by convolution approach and Fourier transform respectively and are expressed as the superposition of the shearing force component and ploughing force component. This dual-mechanism model is analyzed and discussed in the frequency domain and compared with the lumped shear model. An expression is derived for identifying the cutting constants of the dual-mechanism model from the average milling forces. Explicit inclusion of ploughing force in the model is shown to result in better predictive accuracy and yields a linear force model with constant cutting coefficients. Experiments verify the accuracy and the frequency analysis of the dual-mechanism model and show that cutting constants for the dual-mechanism model are fairly independent of chip thickness.

This paper presents an analytical model for the direct identification of global shearing and ploughing cutting constants from measured average cutting forces in ball-end milling. This model is based on the linear decomposition of elemental local cutting forces into a shearing component and a ploughing component. Then, a convolution integral approach is used to obtain the average cutting forces leading to a concise and explicit expression for the global shearing and ploughing cutting constants in terms of axial depth of cut, cutter radius and average milling forces. The model is verified by comparisons with an existing force model of variable cutting coefficients. Cutting constants are identified through milling experiments and the prediction of cutting forces from identified cutting constants coincides with the experimental measurements. A model for identifying the lumped shearing constants is obtained as a subset of the presented dual mechanism model. Experimental results indicate that a model with dual-mechanism cutting constants predicts the ball-end milling forces with better accuracy than the lumped force model.

The polymorphism, similarities and relationships among Nicotiana tabacum L. cultivars were assessed with RAPD analyses. One hundred and forty-nine bands were detected, of which 94 were polymorphic (63.1 %). A primer distinguishing all of the tested cultivars was found. High similarity between cultivars was revealed, and cultivar relationships were estimated through cluster analysis (UPGMA) based on RAPD data.

In a systematic manner, this paper investigates the effects of harmonic force components on the regenerative stability of an end milling process. By representing the milling force pulsation in a Fourier series expansion form, the dynamic force components and the average forces due to bi-directional dynamic feed rates are both included in the generalized system dynamics formulation. In the resulting expression for the stability criterion, the spectral features of the milling forces are integrated with the dynamics of the structure, showing the significance or insignificance of the dynamic components of the milling forces in affecting the stability of the milling process. Key system parameters discussed include the magnitude of the average and harmonic forces, the cutter helix angle and the spindle speed. It is shown that a low helix angle and a smaller number of cutting flutes increase the effect of dynamic forces on the system stability. The significance of the harmonic forces is exemplified by the special cutting conditions where the average force becomes zero and the stability limits would be infinite as predicted by models using the average force alone. Improvements in the accuracy of stability lobes resulting from the inclusion of the dynamic forces and the validity of the presented model in general will be illustrated by numerical simulation and verified by experiments as well as by comparison with published results.Copyright © 2003 by ASME

For a generalized helical end mill, this paper presents a frequency domain force model considering the ploughing as well as the shearing mechanisms. The differential chip load and the corresponding cutting forces are first formulated through differential geometry for a general helical cutting edge. The differential cutting force is assumed to be a linear function of the chip load with a proportional shearing force and a constant ploughing force. The total milling force in the angle domain is subsequently composed through convolution integration and analyzed by Fourier analysis. The frequency domain model has the parameters of a general milling process all integrated in a single framework with their roles clearly defined so that Fourier coefficients of the milling force can be obtained for any analytically definable helical cutter. Applications are illustrated for three common helical cutters: the cylindrical, taper, and ball end mills. Furthermore, as an inverse application, a linear algebraic equation is formulated for the identification of six cutting constants from the average forces of two slot milling tests. Demonstration and verification of the milling force model as well as the identification of cutting constants are carried out through experiments with three types of milling cutters.Copyright © 2002 by ASME

Activities of 325 single cochlear nerve fibers in response to pure tones at various frequencies including ultrasonic sounds were observed in rats. The stimulus sounds were measured with a probe tube inserted into an ear canal and a microphone and expressed in dB SPL. The best frequency (BF, characteristic frequency) and the threshold at BF were determined in every fiber. The measured BF ranged from 0.58 kHz to 62.6 kHz. BF and the threshold at BF of a fiber with the lowest BF-threshold were 27.49kHz and 6dB SPL respectively. The highest sensitivity was found in fibers with BF from 20 to 50 kHz. The tuning curve rose from BF and its slope was steeper for the high side than the low one as observed in other animals. The sharpness of the tuning curve was expressed by QN values, where QN is the ratio of BF to the band width at N dB above the BF threshold. Mean and the variance of Q10dB, Q20dB, Q30dB, Q40dB, Q50dB, all increased as the BF did. Almost all fibers had spontaneous discharge. The discharge rate increased with the increase in sound intensity and saturated at about 30 dB above the threshold. The auditory threshold curve obtained from distribution of the lowest BF-threshold of 325 fibers was consistent with the audiograms determined behaviorally.