Wheel polygonal wear is a common and severe defect,which seriously threatens the running safety and reliability of a railway vehicle especially a locomotive.Due to non-stationary running conditions(e.g.,traction and b...Wheel polygonal wear is a common and severe defect,which seriously threatens the running safety and reliability of a railway vehicle especially a locomotive.Due to non-stationary running conditions(e.g.,traction and braking)of the locomotive,the passing frequencies of a polygonal wheel will exhibit time-varying behaviors,which makes it too difficult to effectively detect the wheel defect.Moreover,most existing methods only achieve qualitative fault diagnosis and they cannot accurately identify defect levels.To address these issues,this paper reports a novel quantitative method for fault detection of wheel polygonization under non-stationary conditions based on a recently proposed adaptive chirp mode decomposition(ACMD)approach.Firstly,a coarse-to-fine method based on the time–frequency ridge detection and ACMD is developed to accurately estimate a time-varying gear meshing frequency and thus obtain a wheel rotating frequency from a vibration acceleration signal of a motor.After the rotating frequency is obtained,signal resampling and order analysis techniques are applied to an acceleration signal of an axle box to identify harmonic orders related to polygonal wear.Finally,the ACMD is combined with an inertial algorithm to estimate polygonal wear amplitudes.Not only a dynamics simulation but a field test was carried out to show that the proposed method can effectively detect both harmonic orders and their amplitudes of the wheel polygonization under non-stationary conditions.展开更多
An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible numbe...An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.展开更多
Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrat...Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrating differences(different characters)in map-view 3D seismic data covering an area of 334km^(2) of the Changchang(CC)sag,are used to document the mapview and cross-sectional characteristics of PFs.These data also help investigate the irregularly polygonal geometries of PFs due to the presence of influence factors,such as transtensional faults,submarine fans,channels,diapirs/gas chimneys,and the basal slope within the lower-middle Miocene strata.Results show that various irregularly polygonal geometries of PFs can be classified into enechelon and arcuate PFs,channel-segmenting and-bounding PFs,radial PFs,and rectangular PFs in map-view.En-echelon and arcuate PFs are induced by transtensional faults and exhibit a unique‘flower’structure in NE-and SE-trending cross-sections in the NW area of the study area.This finding is documented for the first time.Channel-segmenting PFs occur in the(northwest)low-amplitude muddy channel and are inhibited in the(southeast)high-amplitude sandy channel in the SW area.Radial PFs are radially aligned around a gas chimney/diapir containing some high-amplitude anomalies(HAAs)in the middle area.The presence of intrusive sandstones with HAAs along the periphery of the diapirs restricts the occurrence of PFs.Two high-amplitude submarine fans act as a mechanical barrier to the propagation of PFs.Meanwhile,the(moderate)slope in the NE area induces rectangular PFs.Additionally,the geneses of the PFs in the current study are comprehensively discussed.This study adds to our understanding of the differences between PFs with irregularly polygonal geometries.展开更多
Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present diffe...Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present differences when they encounter deep-water(coarse-grained vs.fine-grained)channels with different lithology,which has not been further studied to date.Three-dimensional(3D)seismic data and a drilling well from Beijiao sag of Qiongdongnanbasin,South China Sea were utilized to document the plan view and cross-sectional properties of the PFs and their differences and genetic mechanism were investigated.Results show that,first,PFs can be divided morphologically into channel-segmenting PFs and channel-bounding PFs in plan view.The former virtually cuts or segments the axes of channels in highand low-amplitudes,and the latter nearly parallels the boundaries of the channels.Both are approximately perpendicular to each other.Secondly,channel-bounding PFs that related to low-amplitude channels are much longer than those of high-amplitude ones;channel-segmenting PFs related to low-amplitude channels are slightly longer than the counterparts related to high-amplitude channels.Lastly,the magnitudes(e.g.,heights)of the PFs are proportional to the scales(e.g.,widths and heights)of low-amplitude channels,whereas the magnitudes of the PFs are inversely proportional to the scales of high amplitude channels.Coarse-grained(high amplitude)channels act as a mechanical barrier to the propagation of PFs,whereas fine-grained(low-amplitude)channels are beneficial to the propagation and nucleation of PFs.Additionally,the genetic mechanism of PFs is discussed and reckoned as combined geneses of gravitational spreading and overpressure hydrofracture.The differences of the PFs can be used to reasonably differentiate coarse-grained channels from fine-grained channels.This study provides new insights into understanding the different geometries of the PFs related to coarse-grained and fine-grained channels and their genetic mechanism.展开更多
Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on ...Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.展开更多
After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organiz...After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.展开更多
The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promisi...The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promising, informative and operational geophysical methods. The results of long-term geomagnetic studies on the problem of forecasting strong earthquakes in Uzbekistan are presented. Geomagnetic studies were carried out on the territories of the Tashkent, Ferghana, and Kyzylkum geodynamic polygons in the epicentral zones of strong earthquakes that occurred. Long-term, medium- and short-term precursors of earthquakes have been identified. Anomalous changes in the geomagnetic field associated with the decline in aftershock activity were also revealed. The dependence between the duration of the manifestation of long-term magnetic precursors and the magnitude of earthquakes is determined. Absolute proton magnetometers MMP-1, MV-01 (Russia), and G-856 (USA) were used to measure the geomagnetic field.展开更多
The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlu...The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlusion. Its ability to redistribute blood flow depends on its morphology, the presence and size of the vessels that constitute it and their variants, knowledge of which is essential. The morphology of the carotid system is not constant and a number of variants are well recognized with greater hemodynamic importance. In this context, we undertook this work which aims to seek the anatomical variants of the anterior part of the PW;to determine the diameters of the vessels of the latter and to correlate these results with epidemiological data. We carried out a retrospective, descriptive and analytical study over a period of 4 months at Fann University Hospital, targeting patients who had undergone brain MRI with a 3D TOF sequence whatever the indication. Patients with lesions of cerebrovascular pathologies such as ischemia, hemorrhage, aneurysm, arteriovenous malformations or presenting a limited analysis examination due to the presence of kinetic or other artifact, were not included. Demographic data and anatomical variants were studied as well as the measurements of any continuous arterial segment greater than 0.8 mm in diameter. Those less than 0.8 mm in diameter were considered hypoplastic. The C3 segment of the internal carotid arteries, the A1 segment of the anterior cerebral arteries, the anterior communicating artery, constituted our main measurement sites. The sex ratio was 1.06, the mean age of the patients was 43 years ± 17.9 with extremes of 11 and 85 years. The anterior configuration of the polygon was complete in 57.5% representing 50% of men and 65.5% of women, in 56% of subjects under 40 years old and 58% in subjects over 40 years old. We noted a predominance of type a in 47% of patients followed by type g found in 35% of patients. The morphology of the anterior system of the Willis polygon is a function of its variants, some of which have greater hemodynamic importance than others. Its knowledge is essential for the management of cerebrovascular diseases.展开更多
In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between t...In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.展开更多
Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model,the criterion of regular polygonal box stamped parts without wrinkle was deduced and u...Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model,the criterion of regular polygonal box stamped parts without wrinkle was deduced and used to predict and control the wrinkle limit.According to the fracture model,the criterion of regular polygonal box stamped parts without fracture was deduced and used to predict and control the fracture limit.Combining the criterion for stamping without wrinkle with that without fracture,the stamping criterion of regular polygonal box stamped parts was obtained to predict and control the stamping limit.Taken the stainless steel0Cr18Ni9(SUS304)sheet and the square box stamped part as examples,the limit diagram was given to predict and control the wrinkle,fracture and stamping limits.It is suitable for the deep drawing without flange,the deep drawing and stretching combined forming with flange and the rigid punch stretching of plane blank.The limit deep-drawing coefficient and the minimum deep-drawing coefficient can be determined,and the appropriate BHF(blank holder force)and the deep-drawing force can be chosen.These provide a reference for the technology planning,the die and mold design and the equipment determination,and a new criterion evaluating sheet stamping formability,which predicts and controls the stamping process,can be applied to the deep drawing under constant or variable BHF conditions.展开更多
Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model, the criterion of regular polygonal box stamped parts without wrinkle was deduced and ...Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model, the criterion of regular polygonal box stamped parts without wrinkle was deduced and used to predict and control the wrinkle limit. According to the fracture model, the criterion of regular polygonal box stamped parts without fracture was deduced and used to predict and control the fracture limit. Combining the criterion for stamping without wrinkle with that without fracture, the stamping criterion of regular polygonal box stamped parts was obtained to predict and control the stamping limit. Taken the stainless steel 0Cr18Ni9 (SUS304) sheet and the square box stamped part as examples, the limit diagram was given to predict and control the wrinkle, fracture and stamping limits. It is suitable for the deep drawing without flange, the deep drawing and stretching combined forming with flange and the rigid punch stretching of plane blank. The limit deep-drawing coefficient and the minimum deep-drawing coefficient can be determined, and the appropriate BHF (blank holder force) and the deep-drawing force can be chosen. These provide a reference for the technology planning, the die and mold design and the equipment determination, and a new criterion evaluating sheet stamping formability, which predicts and controls the stamping process, can be applied to the deep drawing under constant or variable BHF conditions.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grant Nos.52005416,51735012,and 51825504)the Sichuan Science and Technology Program(Grant No.2020YJ0213)+1 种基金the Fundamental Research Funds for the Central Universities,SWJTU(Grant No.2682021CX091)the State Key Laboratory of Traction Power(Grant No.2020TPL-T 11).
文摘Wheel polygonal wear is a common and severe defect,which seriously threatens the running safety and reliability of a railway vehicle especially a locomotive.Due to non-stationary running conditions(e.g.,traction and braking)of the locomotive,the passing frequencies of a polygonal wheel will exhibit time-varying behaviors,which makes it too difficult to effectively detect the wheel defect.Moreover,most existing methods only achieve qualitative fault diagnosis and they cannot accurately identify defect levels.To address these issues,this paper reports a novel quantitative method for fault detection of wheel polygonization under non-stationary conditions based on a recently proposed adaptive chirp mode decomposition(ACMD)approach.Firstly,a coarse-to-fine method based on the time–frequency ridge detection and ACMD is developed to accurately estimate a time-varying gear meshing frequency and thus obtain a wheel rotating frequency from a vibration acceleration signal of a motor.After the rotating frequency is obtained,signal resampling and order analysis techniques are applied to an acceleration signal of an axle box to identify harmonic orders related to polygonal wear.Finally,the ACMD is combined with an inertial algorithm to estimate polygonal wear amplitudes.Not only a dynamics simulation but a field test was carried out to show that the proposed method can effectively detect both harmonic orders and their amplitudes of the wheel polygonization under non-stationary conditions.
基金Supported by National Natural Science Foundation of China(Grant No.12271139)。
文摘An F-polygon is a simple polygon whose vertices are F-points, which are points of the set of vertices of a tiling of R~2 by regular triangles and regular hexagons of unit edge. Let f(v) denote the least possible number of F-points in the interior of a convex F-polygon K with v vertices. In this paper we prove that f(10) = 10, f(11) = 12,f(12) = 12.
基金supported by the Key Laboratory of Marine Mineral Resources,Ministry of Land and Resources of China(No.KLMMR-2018-B-07)the National Basic Research Program of China(No.2011ZX05025-006-02)the National Natural Science Foundation of China(No.41672206)。
文摘Polygonal faults(PFs)generally have a classic polygonal geometry in map view.However,under the influence of tectonic faults,diapirs,channels,and slopes,the classic polygonal geometry of PFs is not preserved,demonstrating differences(different characters)in map-view 3D seismic data covering an area of 334km^(2) of the Changchang(CC)sag,are used to document the mapview and cross-sectional characteristics of PFs.These data also help investigate the irregularly polygonal geometries of PFs due to the presence of influence factors,such as transtensional faults,submarine fans,channels,diapirs/gas chimneys,and the basal slope within the lower-middle Miocene strata.Results show that various irregularly polygonal geometries of PFs can be classified into enechelon and arcuate PFs,channel-segmenting and-bounding PFs,radial PFs,and rectangular PFs in map-view.En-echelon and arcuate PFs are induced by transtensional faults and exhibit a unique‘flower’structure in NE-and SE-trending cross-sections in the NW area of the study area.This finding is documented for the first time.Channel-segmenting PFs occur in the(northwest)low-amplitude muddy channel and are inhibited in the(southeast)high-amplitude sandy channel in the SW area.Radial PFs are radially aligned around a gas chimney/diapir containing some high-amplitude anomalies(HAAs)in the middle area.The presence of intrusive sandstones with HAAs along the periphery of the diapirs restricts the occurrence of PFs.Two high-amplitude submarine fans act as a mechanical barrier to the propagation of PFs.Meanwhile,the(moderate)slope in the NE area induces rectangular PFs.Additionally,the geneses of the PFs in the current study are comprehensively discussed.This study adds to our understanding of the differences between PFs with irregularly polygonal geometries.
基金Supported by the Key Laboratory of Marine Mineral ResourcesMinistry of Land and Resources of China(No.KLMMR-2018-B-07)+1 种基金the National Basic Research Program of China(No.2011ZX05025-006-02)the National Natural Science Foundation of China(No.41672206)。
文摘Deep-water coarse-grained channels are embedded within a polygonal fault tier,and the polygonal faults(PFs)present non-polygonal geometries rather than classic polygonal geometry in plan view.However,PFs present differences when they encounter deep-water(coarse-grained vs.fine-grained)channels with different lithology,which has not been further studied to date.Three-dimensional(3D)seismic data and a drilling well from Beijiao sag of Qiongdongnanbasin,South China Sea were utilized to document the plan view and cross-sectional properties of the PFs and their differences and genetic mechanism were investigated.Results show that,first,PFs can be divided morphologically into channel-segmenting PFs and channel-bounding PFs in plan view.The former virtually cuts or segments the axes of channels in highand low-amplitudes,and the latter nearly parallels the boundaries of the channels.Both are approximately perpendicular to each other.Secondly,channel-bounding PFs that related to low-amplitude channels are much longer than those of high-amplitude ones;channel-segmenting PFs related to low-amplitude channels are slightly longer than the counterparts related to high-amplitude channels.Lastly,the magnitudes(e.g.,heights)of the PFs are proportional to the scales(e.g.,widths and heights)of low-amplitude channels,whereas the magnitudes of the PFs are inversely proportional to the scales of high amplitude channels.Coarse-grained(high amplitude)channels act as a mechanical barrier to the propagation of PFs,whereas fine-grained(low-amplitude)channels are beneficial to the propagation and nucleation of PFs.Additionally,the genetic mechanism of PFs is discussed and reckoned as combined geneses of gravitational spreading and overpressure hydrofracture.The differences of the PFs can be used to reasonably differentiate coarse-grained channels from fine-grained channels.This study provides new insights into understanding the different geometries of the PFs related to coarse-grained and fine-grained channels and their genetic mechanism.
文摘Waterside creatures or aquatic organisms use a fin or web to generate a thrust force. These fins or webs have a non-convex section, referred to as a non-convex shape. We investigate the drag force acting on a non-convex plate during unsteady motion. We perform the experiment in a water tank during free fall. We fabricate the non-convex plate by cutting isosceles triangles from the side of a convex hexagonal plate. The base angle of the triangle is between 0° to 45°. The base angle is 0 indicates the convex hexagonal thin plate. We estimate the drag coefficient with the force balance acting on the model based on the image analysis technique. The results indicate that increasing the base angle by more than 30° increased the drag coefficient. The drag coefficient during unsteady motion changed with the growth of the vortex behind the model. The vortex has small vortices in the shear layer, which is related to the Kelvin-Helmholtz instabilities.
文摘After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.
文摘The article is devoted to the problem of forecasting strong earthquakes by the geomagnetic method. The geomagnetic method is widely used on this problem in seismically active regions of the world as one of the promising, informative and operational geophysical methods. The results of long-term geomagnetic studies on the problem of forecasting strong earthquakes in Uzbekistan are presented. Geomagnetic studies were carried out on the territories of the Tashkent, Ferghana, and Kyzylkum geodynamic polygons in the epicentral zones of strong earthquakes that occurred. Long-term, medium- and short-term precursors of earthquakes have been identified. Anomalous changes in the geomagnetic field associated with the decline in aftershock activity were also revealed. The dependence between the duration of the manifestation of long-term magnetic precursors and the magnitude of earthquakes is determined. Absolute proton magnetometers MMP-1, MV-01 (Russia), and G-856 (USA) were used to measure the geomagnetic field.
文摘The anterior system of the polygon of Willis plays an anastomotic role between the carotid territories and communicates with the posterior system. It ensures adequate cerebral blood flow in the event of internal occlusion. Its ability to redistribute blood flow depends on its morphology, the presence and size of the vessels that constitute it and their variants, knowledge of which is essential. The morphology of the carotid system is not constant and a number of variants are well recognized with greater hemodynamic importance. In this context, we undertook this work which aims to seek the anatomical variants of the anterior part of the PW;to determine the diameters of the vessels of the latter and to correlate these results with epidemiological data. We carried out a retrospective, descriptive and analytical study over a period of 4 months at Fann University Hospital, targeting patients who had undergone brain MRI with a 3D TOF sequence whatever the indication. Patients with lesions of cerebrovascular pathologies such as ischemia, hemorrhage, aneurysm, arteriovenous malformations or presenting a limited analysis examination due to the presence of kinetic or other artifact, were not included. Demographic data and anatomical variants were studied as well as the measurements of any continuous arterial segment greater than 0.8 mm in diameter. Those less than 0.8 mm in diameter were considered hypoplastic. The C3 segment of the internal carotid arteries, the A1 segment of the anterior cerebral arteries, the anterior communicating artery, constituted our main measurement sites. The sex ratio was 1.06, the mean age of the patients was 43 years ± 17.9 with extremes of 11 and 85 years. The anterior configuration of the polygon was complete in 57.5% representing 50% of men and 65.5% of women, in 56% of subjects under 40 years old and 58% in subjects over 40 years old. We noted a predominance of type a in 47% of patients followed by type g found in 35% of patients. The morphology of the anterior system of the Willis polygon is a function of its variants, some of which have greater hemodynamic importance than others. Its knowledge is essential for the management of cerebrovascular diseases.
文摘In this article, authors study the growth of Laplace-Stieltjes transform with zero order convergent in the right half-plane, define the exponential order and the exponential low order, and find the relations between them. Some results similar to Dirichlet series are obtained.
文摘Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model,the criterion of regular polygonal box stamped parts without wrinkle was deduced and used to predict and control the wrinkle limit.According to the fracture model,the criterion of regular polygonal box stamped parts without fracture was deduced and used to predict and control the fracture limit.Combining the criterion for stamping without wrinkle with that without fracture,the stamping criterion of regular polygonal box stamped parts was obtained to predict and control the stamping limit.Taken the stainless steel0Cr18Ni9(SUS304)sheet and the square box stamped part as examples,the limit diagram was given to predict and control the wrinkle,fracture and stamping limits.It is suitable for the deep drawing without flange,the deep drawing and stretching combined forming with flange and the rigid punch stretching of plane blank.The limit deep-drawing coefficient and the minimum deep-drawing coefficient can be determined,and the appropriate BHF(blank holder force)and the deep-drawing force can be chosen.These provide a reference for the technology planning,the die and mold design and the equipment determination,and a new criterion evaluating sheet stamping formability,which predicts and controls the stamping process,can be applied to the deep drawing under constant or variable BHF conditions.
文摘Based on the deformation characteristic of regular polygonal box stamped parts and the superfluous triangle material wrinkle model, the criterion of regular polygonal box stamped parts without wrinkle was deduced and used to predict and control the wrinkle limit. According to the fracture model, the criterion of regular polygonal box stamped parts without fracture was deduced and used to predict and control the fracture limit. Combining the criterion for stamping without wrinkle with that without fracture, the stamping criterion of regular polygonal box stamped parts was obtained to predict and control the stamping limit. Taken the stainless steel 0Cr18Ni9 (SUS304) sheet and the square box stamped part as examples, the limit diagram was given to predict and control the wrinkle, fracture and stamping limits. It is suitable for the deep drawing without flange, the deep drawing and stretching combined forming with flange and the rigid punch stretching of plane blank. The limit deep-drawing coefficient and the minimum deep-drawing coefficient can be determined, and the appropriate BHF (blank holder force) and the deep-drawing force can be chosen. These provide a reference for the technology planning, the die and mold design and the equipment determination, and a new criterion evaluating sheet stamping formability, which predicts and controls the stamping process, can be applied to the deep drawing under constant or variable BHF conditions.