Geometric Axis Research Articles

A Gauss kernel non-local stress-driven plate theory

This study presents a novel stress-driven formulation, incorporating Kirchhoff’s plate assumptions and accounting for the non-local size-dependent feature in both plate geometric axes, which is practical, especially near the origin of the axis in the polar coordinates. The presented formulation does not impose any additional constraints on the elastic radial curvatures, which are known as constitutive boundary conditions. Therefore, taking into account the non-local behavior in both radial and circumferential directions does not lead to an overconstrained problem. The study focuses on the analysis of a circular plate with an outer radius (R), thickness (h), and the length scale parameter (L). The governing differential equations are derived in Cartesian coordinates and then transformed to the polar coordinates to analyze circular plates. When R tends to infinity, the governing equation is solved analytically. Using the Galerkin technique, a finite element solution is presented for the analysis of a bounded circular plate with a clamped boundary condition at the outer radius R. The study discusses the size effects and the gradient properties of functionally graded plates in stress-driven non-local theory. It reveals that while increasing the non-local parameter results in a reduction of transverse displacement, the moments remain unaffected.

Experimental study on concrete-filled L-shaped steel tubular columns and beam-columns

Concrete-filled L-shaped steel tube (CFLST) is an efficient structural form for corner columns in high-rise buildings, which avoids column protrusion. This paper presents an experimental and theoretical study on the structural behavior of CFLST columns and beam-columns. A total of nine full-scale specimens (i.e., three stub columns, two slender columns, and four slender beam-columns) was tested under compressive loads and the specimen ends were free to rotate about a geometric axis. Plastic local buckling was observed for the stub columns and the confinement effect was not obvious. Flexural buckling occurred for the slender columns and beam-columns. With the increase in the applied load, the neutral axis shifted to the compressive side of the beam-column. Performance of current design codes, which apply for rectangular CFSTs, on predicting the ultimate capacities of CFLSTs was assessed. The prediction for section capacity was conservative and it was likely caused by the reduction in the design strength of concrete. The buckling curve in design codes for rectangular CFSTs was applicable for CFLST columns whereas the interaction relationship specified in design codes underestimates the ultimate capacities of CFLST beam-columns. Based on fiber element analysis, out-of-plane bending moment was found in the tested CFLST slender members and the values were quantified. A new interaction relationship was proposed for CFLST beam-columns, which exhibited good agreement with experimental and numerical results. Finally, design methods were recommended for CFLST columns and beam-columns.

A new method for assessing tibial torsion using computerized tomography in a pediatric population.

Tibial torsion disorders may lead to abnormal gait, frequently leading to a consultation with a pediatric orthopedic surgeon. The present study evaluated an alternative method for assessing tibial torsion on computerized tomography (CT) images that considers the tibial distal axis to be equivalent to the geometric axis of the tibiotalar joint. One hundred CT scans were reviewed retrospectively, and four measurements were taken: proximal transtibial angle (PTTA), posterior margin tibial plateau angle (PMTPA), intermalleolar angle (IMA), and talar angle (TA). The tibial torsion angle was then calculated using these different angles. The patient cohort comprised 38 girls and 62 boys, with a mean age of 12 ± 4.4 years. Median PTTA and PMTPA were -8.4° ± 14.7° and -8.8° ± 14.2°, respectively, with no statistically significant difference. Mean IMA and TA were 23° ± 16.2° and 17.2° ± 16.9°, respectively, with a statistically significant difference. Mean total measurement time per patient was 6'44", with means of 2'24" for PTTA, 36" for PMTPA, 2'14" for IMA, and 1'12" for TA. Tibial torsion values may differ significantly depending on the axis chosen to define tibial orientation. At the level of the proximal tibia, the choice of PTTA or PMTPA had little influence on the calculation of the tibial torsion angle. There was a significant difference of 5.8° when measuring the distal tibia. Measuring the PMTPA and TA is probably more suited for use in clinical practice because their tracing is simple and faster.

Safety assessment of masonry undamaged and damaged arches subjected to gravitational loads and horizontal forces. A numeric procedure to identify the optimal thrust line

In 2019 the authors formulated a numerical procedure for assessing the safety of masonry arches based on their geometry and the shape of the thrust line. The thrust line is calculated to be nearest to the geometric axis of the arch, because it is that corresponding to the optimal inner stress state. The original procedure, which focused on the safety analysis of undamaged fixed arches subject to gravitational loads, is reformulated here to also consider arches on pinned supports as well as damaged arches, i.e. one- and two-hinged arches. The procedure is further extended to also assess safety against horizontal actions, such as those resulting from an earthquake. Finally, safety is evaluated by identifying the domain of admissible thrust lines within the thickness of the arch and by computing the degree of safety in terms of the capacity of the thrust line to be moved vertically within the domain. The reformulation and extension of the procedure exploits the technique of partitioned matrices to enable automation and easy implementation in structural calculation software.

Paleostress Analysis Using Fracture Data, a Case Study of Kewa Charmula Anticline, Kurdistan Region, Northeastern Iraq

Fracture analysis was carried out through three adjacent traverses. The study area is considered a part of the Arabian Plate and geologically falls within the boundary between the Low Folded Zone and the High Folded Zone of the Western Zagros Fold-Thrust Belt in the Iraqi Kurdistan Region. Five formations are cropped out in this anticline, extending from the Late Oligocene up to the Late Miocene – Pliocene. Those formations are (Anah, Jeribe, Fatha, Injana, and Mukdadiya). In addition, identify an Oligocene unit the Kirkuk Group, represented by the (Anah Fn.) that no other studies have previously referred to, in addition, to observing the Jeribe Formation along Tilyan Gorge. About 350 fracture planes were measured for the study and classified into sets and systems concerning their relations to the three mutually perpendicular geometrical axes (tectonic axes). Tension sets are (ac), which are formed by extension along the fold axis accompanying direct compression perpendicular to the fold trend, whereas the (bc) set is supposed to be the product of relaxation that motivated the primary compressional stress. The shear systems are each of hk0, h0l, and 0kl developed successively during direct compression and subsequent relaxation episodes of each tectonic stress. The results of the paleostress analyses showed that there is a general coincidence in the direction of the major stress axis (σ1) and the minor stress axis (σ3), which were derived from the joints (fracture planes). Joints are presented as sets and systems. The analysis of joint attitudes revealed that the joints might be due to the influence of the main horizontal compression paleostress in the direction NE – SW that is responsible for folding, or they might be caused by the stretching of the outer arc for the folded layers. According to field observations and paleostress studies, the region experienced four stress stages. The first is a main compressive tectonic phase in the NE – SW direction. The second phase is the second compressive tectonic stress in the direction NW – SE. The third was a NE – SW extension tectonic phase that originated during the final uplift stage of folding and it is representative of the major fold trend. The fourth is the NW – SE extension face considered as the extension stress connected to the principal NE – SW compressive stress.

Effects of horizontal self-rotation on flow and heat transfer of supercritical n-decane in regenerative circular/rectangular cooling channels

Concerning the rotation flight of a hypersonic vehicle centered on its geometric axis, the rotational flow and heat transfer characteristics of supercritical n-decane in horizontal circular and rectangular tubes were comprehensively analyzed based on numerical simulation. The computational domain was established and the corresponding governing equations of mass conservation, momentum conservation, and energy conservation were mathematically formulated as well were the thermophysical properties and boundary conditions. A procedure for setting up the numerical simulation was finally implemented. A mesh independence study in the case of a rotating speed of 300 rpm and a turbulence model study based on a stationary/swinging tube were comprehensively conducted and the RANS model was well validated. For the circular tube, the wall temperature distribution trend along the flow direction is similar but the magnitude is not uniform. Also, the fluid temperature near the upper wall is larger than that in the vicinity of the lower wall, i.e., the relaminarization plays an essential role in this phenomenon. The velocity difference near the wall can be weakened by the centrifugal force. For the rectangular tube, the velocity magnitude and temperature distribution are found to be greatly affected by the rotation (i.e., centrifugal force). The relative temperature magnitude near the upper and lower walls will be reversed at a rotation speed of n = 100–500 rpm. Subsequently, a symmetrical temperature distribution can be observed once the speed increases to a certain value (e.g., n = 700–900 rpm). In summary, the centrifugal force plays a more important role in a rectangular tube than in a circular tube.

An efficient method for measuring and identifying geometric and dynamic errors in dual five-axis machine tools

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS.

Dynamic instability of an eccentrically rotating ring-shaped structure

Ring-shaped structures are widely used in engineering. However, their rotation axes are typically not coincident with the geometric axes, thus resulting in a rotational centrifugal force and significant vibration. This study focuses on the dynamic instability caused by constant and time-varying eccentricities. An analytical model is established using Hamilton’s principle and the Galerkin method, in which the rotational centrifugal forces resulting from constant and time-varying eccentricities are incorporated. Based on this model, the effects of rotation, revolution, eccentricity ratio, and damping on instability behaviors are examined. The instabilities caused by constant eccentricity are predicted using eigensolutions, whereas those caused by time-varying eccentricity with single- and multifrequency components are estimated by applying the Floquét theory. The results show that the instability domains from the multifrequency eccentricity are not a simple superposition of those from the single-frequency eccentricity but contain more instability domains originating from their combinations. The instability suppressions imposed by damping and gyroscopic effects are compared. Finally, the instability domains from constant and time-varying eccentricities are verified via numerical calculations.

Axis convergence in C. elegans embryos

Embryos develop in a surrounding that guides key aspects of their development. For example, the anteroposterior (AP) body axis is always aligned with the geometric long axis of the surrounding eggshell in fruit flies and worms. The mechanisms that ensure convergence of the AP axis with the long axis of the eggshell remain unresolved. We investigate axis convergence in early C.elegans development, where the nascent AP axis, when misaligned, actively re-aligns to converge with the long axis of the egg. We identify two physical mechanisms that underlie axis convergence. First, bulk cytoplasmic flows, driven by actomyosin cortical flows, can directly reposition the AP axis. Second, active forces generated within the pseudocleavage furrow, a transient actomyosin structure similar to a contractile ring, can drive a mechanical re-orientation such that it becomes positioned perpendicular to the long axis of the egg. This in turn ensures AP axis convergence. Numerical simulations, together with experiments that either abolish the pseudocleavage furrow or change the shape of the egg, demonstrate that the pseudocleavage-furrow-dependent mechanism is a major driver of axis convergence. We conclude that active force generation within the actomyosin cortical layer drives axis convergence in the early nematode.

Assessing automatic data processing algorithms for RGB-D cameras to predict fruit size and weight in apples

Data acquired using an RGB-D Azure Kinect DK camera were used to assess different automatic algorithms to estimate the size, and predict the weight of non-occluded and occluded apples. The programming of the algorithms included: (i) the extraction of images of regions of interest (ROI) using manual delimitation of bounding boxes or binary masks; (ii) estimating the lengths of the major and minor geometric axes for the purpose of apple sizing; and (iii) predicting the final weight by allometric modelling. In addition to the use of bounding boxes, the algorithms also allowed other post-mask settings (circles, ellipses and rotated rectangles) to be implemented, and different depth options (distance between the RGB-D camera and the fruits detected) for subsequent sizing through the application of the thin lens theory. Both linear and nonlinear allometric models demonstrated the ability to predict apple weight with a high degree of accuracy (R2 greater than 0.942 and RMSE < 16 g). With respect to non-occluded apples, the best weight predictions were achieved using a linear allometric model including both the major and minor axes of the apples as predictors. The mean absolute percentage error (MAPE) ranged from 5.1% to 5.7% with respective RMSE of 11.09 g and 13.02 g, depending to whether circles, ellipses, or bounding boxes were used to adjust fruit shape. The results were therefore promising and open up the possibility of implementing reliable in-field apple measurements in real time. Importantly, final weight prediction error and intermediate size estimation errors (from sizing algorithms) interact but in a way that is not easily quantifiable when weight allometric models with implicit prediction error are used. In addition, allometric models should be reviewed when applied to other apple cultivars, fruit development stages or even for different fruit growth conditions depending on canopy management.

Tibial Tuberosity Rotation in Patients With Patellar Instability Versus Age- and Sex-Matched Controls.

Several methods have been described to measure external rotation of the tibial tuberosity; all use femoral landmarks. To develop reproducible tibial-based methods to measure external rotation of the tibial tuberosity in patients with patellar instability. Cross-sectional study; Level of evidence, 3. Included were magnetic resonance images of 61 patients with patellar instability and 61 age- and sex-matched healthy controls. Three novel methods using tibial landmarks to measure the rotation of the tibial tuberosity (plateau axis-tuberosity axis [PA-TA] angle, tibial geometric center-tuberosity axis [GC-TA] angle, and plateau axis-midtuberosity point [PA-MT] angle) as well as a femoral-based rotational measurement (surgical transepicondylar axis-tuberosity axis [sTEA-TA] angle) and the tibial tuberosity-trochlear groove (TT-TG) distance were measured and compared in instability patients and controls using unpaired t tests, and the cutoff values for predicting instability were calculated using receiver operating characteristic curves. The correlations between the angle measurements and the TT-TG distance were analyzed. Instability patients had significantly higher external rotation of the tibial tuberosity compared with controls with regard to the PA-TA angle (18.2° ± 9.6° versus 13.1° ± 6.8°; P = .001), GC-TA angle (8.4° ± 4.5° versus 11.5° ± 3.9°; P = .0001) and sTEA-TA angle (122° ± 8.5° versus 113.6° ± 6.3°; P = .0001). The mean TT-TG distance was also significantly higher in the instability group (18.2 ± 5.4 versus 11.5 ± 2.7 mm; P = .001). The cutoff values were 17.5° (area under the receiver operating characteristic curve [AUC] = 0.66) for PA-TA angle, 8.5° (AUC = 0.705) for GC-TA angle, 118.8° (AUC = 0.79) for sTEA-TA angle, and 15.2 mm for TT-TG distance (AUC = 0.863). PA-TA angle was significantly correlated with all other measurements (r = 0.35-0.71; P ≤ .006 for all), whereas sTEA-TA angle had the strongest correlation with TT-TG distance (r = 0.78; P = .001). The tibial tuberosity was externally rotated in patellar instability patients compared with age- and sex-matched controls, and this intrinsic malalignment of the proximal tibia was demonstrated in the tibial-based measurements.

Geometric error calibration and analysis of rotary axes on a five-axis dispensing machine

Geometric rotary axis errors are one of the main factors affecting the dispensing positioning accuracy of five-axis vision dispensing machines. Hence, the accurate detection and compensation of these error terms is an important and challenging problem. In this study, a decoupling identification method for both position-dependent geometric errors and position-independent geometric errors of a rotary dispensing table is proposed based on vision measurement technology. According to this strategy, the screw theory and exponential product formula are used to establish a kinematic model of the end-effector, followed by the definition of the mapping relationship between position-independent geometric errors and axis posture. Then, to separate the coupling error terms of the rotating axes, a step-by-step identification strategy is proposed based on the least squares method. Furthermore, a coordinate search-based error compensation algorithm is developed, which avoids the inverse singular value problem and is insensitive to the error model. Finally, the effectiveness of the proposed identification algorithm and compensation algorithm is experimentally validated.

Mathematical Modeling of the Correction of the Shape of the Rotor of the Hydraulic Unit in a Three-Dimensional Setting

The presented work is devoted to the wedging of the rotor rim of the hydraulic unit to restore its geometry. To assess the technical condition of the rotor, measurements of its shape are performed beforehand. The shape of the rotor is decomposed into a Fourier series, and the location of its geometric axis and ellipticity are determined. Based on this, a decision is made about the need for work on the centering of the hydraulic unit. Then, the vibrations of the critical components of the hydraulic unit are measured at idle without excitation and with excitation, under load in generator and pump modes to assess the possibility of its further operation. At this stage, the reasons for the unsatisfactory vibration condition of the hydraulic unit are determined. At the last stage, the boundary conditions are determined and the problem statement is performed for performing a mechanical calculation in a three-dimensional setting to take into account expansions that compensate for mechanical deformations. The calculation itself is carried out and a decision is made to wedge the rotor rim of the hydraulic unit.

Thermal Analysis of a Micro-Satellite in a Low Earth Orbit

The thermal design of a micro-satellite is presented in the paper. The theoretical studies are carried out to describe briefly the relationship among various design orbital parameters and are depicted graphically. Solar heating on a micro-satellite is considered as a thin walled circular cylinder rotating with uniform speed about its geometric axis is analyzed for a situation in which heat transfer by convection and heat exchange within the cylinder is negligible. The nonlinear ordinary differential equations for the thin walled cylinder are solved using fourth order Runge-Kutta method to compute temperature distribution. The results of the analysis are presented at various revolution per minute RPM of the micro-satellite. Radiation heat transfer inside the package is analyzed with networking method.

Case study on the shaft line alignment for a 180 000 tdw bulk carrier vessel

Alignment means the determination of displacements and breaks between two shafts and their elimination so that the geometric axes of the shafts become approximately collinear, and the deviations are within the permissible limits. This paper presents the methodological steps of the shaft line alignment (as a case study for a bulk carrier vessel of 180 000 tdw) through two classic approaches: with the help of a ruler and feeler gauge (templet) respectively with the help of dial gauge. Comparative analysis of the performances of the two methods, can provide essential information to an engineer in choosing the optimal option for alignment of the shaft lines both in the case of vessels in service and, mainly, in the case of new building’s. The originality of the work consists in carrying out the detailed calculations for displacements and breaks, with the graphical highlighting of the calculated values in the limit allowed intervals. Also, for each method are presented and commented the advantages and disadvantages.

A frame orientation optimisation method for consistent interpretation of kinematic signals

In clinical movement biomechanics, kinematic data are often depicted as waveforms (i.e. signals), characterising the motion of articulating joints. Clinically meaningful interpretations of the underlying joint kinematics, however, require an objective understanding of whether two different kinematic signals actually represent two different underlying physical movement patterns of the joint or not. Previously, the accuracy of IMU-based knee joint angles was assessed using a six-degrees-of-freedom joint simulator guided by fluoroscopy-based signals. Despite implementation of sensor-to-segment corrections, observed errors were clearly indicative of cross-talk, and thus inconsistent reference frame orientations. Here, we address these limitations by exploring how minimisation of dedicated cost functions can harmonise differences in frame orientations, ultimately facilitating consistent interpretation of articulating joint kinematic signals. In this study, we present and investigate a frame orientation optimisation method (FOOM) that aligns reference frames and corrects for cross-talk errors, hence yielding a consistent interpretation of the underlying movement patterns. By executing optimised rotational sequences, thus producing angular corrections around each axis, we enable a reproducible frame definition and hence an approach for reliable comparison of kinematic data. Using this approach, root-mean-square errors between the previously collected (1) IMU-based data using functional joint axes, and (2) simulated fluoroscopy-based data relying on geometrical axes were almost entirely eliminated from an initial range of 0.7°–5.1° to a mere 0.1°–0.8°. Our results confirm that different local segment frames can yield different kinematic patterns, despite following the same rotation convention, and that appropriate alignment of reference frame orientation can successfully enable consistent kinematic interpretation.

Investigation of Characteristic Motion Patterns of the Knee Joint During a Weightbearing Flexion.

This study aimed to develop and validate a novel flexion axis concept by calculating the points on femoral condyles that could maintain constant heights during knee flexion. Twenty-two knees of 22 healthy subjects were investigated when performing a weightbearing single leg lunge. The knee positions were captured using a validated dual fluoroscopic image system. The points on sagittal planes of the femoral condyles that had minimal changes in heights from the tibial plane along the flexion path were calculated. It was found that the points do formulate a medial-lateral flexion axis that was defined as the iso-height axis (IHA). The six degrees of freedom (6DOF) kinematics data calculated using the IHA were compared with those calculated using the conventional transepicondylar axis and geometrical center axis. The IHA measured minimal changes in proximal-distal translations and varus-valgus rotations along the flexion path, indicating that the IHA may have interesting clinical implications. Therefore, identifying the IHA could provide an alternative physiological reference for improvement of contemporary knee surgeries, such as ligament reconstruction and knee replacement surgeries that are aimed to reproduce normal knee kinematics and medial/lateral soft tissue tensions during knee flexion.

EXPERIMENTAL RESEARCH OF MIXING NATURAL GAS IMPINGING JETS AND AIR DURING COMBUSTION AT A VERTICAL REFRACTORY SURFACE

In the work determined the conditions for the start of chemical reactions of natural gas and air mixture at combustion on a refractory surface, when a single submerged turbulent impinging jet is fed from a natural gas collector at the angle α to the vertical refractory surface, at the relative distance L/d0 along the geometric axis of the jet. It is determined that combustion starts under the condition when the excess air coefficient in the mixture reaches about λ = 0.93, at which the laminar flame propagation velocity S°L, m/s, for a premixed mixture of methane and air is maximum. The dependence of the height of the flame Lf, m, on the relative dimensionless step of the location of the nozzles s/d0 in the row was obtained during studying the groups of gas nozzles with the supply of natural gas for combustion through them range diameters 1–3.5 mm (which are used at precent time in the construction of slot bottom burners). It was determined that the flame height of slot bottom burner during its operation on natural gas (tested for the pressure of natural gas in the collector from 2 kPa to 18 kPa, respectively, natural gas outflow velocity, WNG from about 60 m/s to 185 m/s) depends slightly on gas pressure, the relative distance L/d0 that the aerated jet of natural gas travels to the refractory surface in the range of 15 ≤ L/d0 ≤ 30 and the Reynolds number, and strongly depends from on the dimensionless step of the nozzles in the row — s/d0. It has been experimentally proven that by adjusting the dimensionless step of the nozzles (holes) s/d0 in the row of the slot bottom burner, it is possible to adjust the height of the flame and thus obtain the flame of the appropriate height for different heights of fireboxes and boilers powers. Bibl. 29, Fig. 3, Tab. 3.

Three-dimensional carpal alignment: computer-aided CT analysis of carpal axes and normal ranges.

Assessment of carpal alignment traditionally uses carpal bone axes measured on lateral radiographs. In this study, three-dimensional axes were defined for carpal bones using segmentation and numerical modelling of CT data of 121 neutrally positioned, asymptomatic wrists. The geometric axis was used for radius, scaphoid and capitate, whereas the axis based on a line perpendicular to the articular surface was used for the other carpal bones. Normal values of radiocarpal angles in the radial coordinate and the reliability of the computer-aided analysis are reported. The mean sagittal radiocarpal angles (positive in palmar direction) were as follows: scaphoid 58° (SD 10°), lunate 0° (SD 11°), triquetrum 12° (SD 8°), trapezium 17° (SD 8°), trapezoid -10° (SD 7°), capitate -17° (SD 9°) and hamate 2° (SD 7°). The mean coronal radiocarpal angles (positive in ulnar direction) were -42° (SD 9°), -20° (SD 4°), -49° (SD 4°), -32° (SD 6°), -16° (SD 5°), 2° (SD 7°) and 8° (SD 6°), respectively. The intra-observer reliability of the measurements was excellent (mean intraclass correlations coefficient 0.98). This study provides guidelines on how to measure and quantify carpal alignment three-dimensionally, and a database for the normal values. Together, these may be useful when analysing various wrist pathologies and kinematics of the wrist.

Study on the Effect of Two Angle and Two Flow Oxygen Lance Jet on Molten Pool in Converter

To achieve the smelting effect of low splash in large and medium-sized converters, the jet flow field simulated by compressed air at room temperature is studied by the oxygen lance (OL) jet detection experimental system in this paper. This paper mainly analyzes the variation law of jet velocity at the geometric axis of the OL nozzle and scalar distribution and attenuation of jet isovelocity line at different cross sections. The results show that the oxygen jet cross-section of all OL nozzles gradually expands with the rise of OL position. When the large hole flow ratio is between 55% and 65%, the large hole angle is between 12° and 14° and the small hole angle is between 16° and 18°, therefore the angle of hole plays a significant role in the impact radius. The larger the angle is, the larger the impact radius is. The area of action between jet and molten pool could be enlarged by staggered double-structure six-hole OL.