Equal Angles Research Articles

A Digital Image Method for Calculating the Working Chamber Volume of a Combined Profile Scroll Compressor

Background: The efficient and accurate calculation of working chamber volume can greatly contribute to the optimized design efficiency of the combined profile scroll compressor, but current papers and patents lack research on the method of calculating the working chamber volume of a combined profile scroll compressor. Objective: A method of using digital image processing is proposed to efficiently calculate the working chamber volume of a combined scroll compressor. Methods: This method discretizes and reconstructs the scroll profile that forms the working chamber into a coordinate sequence with equal involute angle intervals. By calculating the relationship between the coordinate sequence and the rotation angle, a general coordinate sequence that forms the working chamber profile is obtained. The real-time changes in the projection image of the working chamber during all the suction, compression and discharge processes can be accurately depicted. The digital image is processed to obtain the actual projection area of the working chamber, and thus, the volume of the working chamber is accurately calculated. Results: The digital image method can accurately calculate the volume change of the working chamber of the combined profile scroll compressor by selecting the appropriate involute angle interval and digital image size, with a mean relative error of less than 1%. At the beginning of suction and the end of discharge, the calculated volume has been found to have poor accuracy, with a maximum relative error higher than 10%. Conclusion: The digital image method has been found to have high accuracy, greatly reduce the difficulty of the analysis of the working chamber volume, and promote the design optimization of the combined profile scroll compressor, thus broadening the idea for the calculation method of the working chamber volume of the scroll compressor.

Analyzing the Combined Effects of Axial Loads and Bending Moments on Unequal-Angle Steel Members

Angle steel is commonly used in inclined bracing components such as transmission towers. Due to its inherent section characteristics, unequal angle steel undergoes angular rotation when subjected to eccentric axial pressure, resulting in a change in the direction of action along the X and Y axes. In comparison to equal angle steel, the analysis of unequal angle steel is more complex. In design, particular attention should be given to whether the angle steel section is compact or noncompact, with a significant emphasis on the impact of the width-to-thickness ratio on strength. In study analyzed nine different angle steel sections, revealing that two of them exhibit a phenomenon known as control point transfer. This is especially prone to occur with shorter lengths of angle steel components, leading to Leg Local Buckling. In contrast, longer components are more susceptible to Lateral-Torsional Buckling. Summarizing the research findings, it is recommended to exercise caution when using non-compact section angle steel in design, and a preference for compact sections is advised to ensure the safety of the structure. Furthermore, it is advised to pay attention to the parameter βw in the AISC unequal angle steel calculation formula and adhere to relevant specifications to enhance the accuracy and reliability of structural design.

Compressive testing and modelling of additively manufactured stainless steel equal angle sections with stiffening wave patterns

Traditional structural steel manufacturing routes typically produce prismatic members comprising of flat plate elements. Under compressive actions, the capacity of these sections is often dominated by plate instability of the lowest buckling mode. The current study involves compressive testing of 6 different configurations of non-prismatic stub columns, comprising of pre-defined surface waves tested at 3 different slendernesses and 3 amplitudes including control prismatic sections. Absolute and normalised load-displacement curves are generated to compare against the control sections and assess the potential increase in strength and stiffness, and the samples’ weights are measured to evaluate the relationship between material use and strength when using this method of strengthening. Tensile coupon tests are also carried out on coupons printed from the same material to define material parameters, and an extensive parametric study is undertaken with numerical modelling software. The best case evaluated in this study indicated a strength gain of 89.9 % over a control section with an equal volume of used material. Eurocode-compatible buckling characterisation curves are then provided for two of the best performing sections. This study highlights the possibilities of this technology, paving the way towards unprecedented efficiency in future steel construction.

High-performance Mg–Zn alloy achieved by the ultrafine grain and nanoparticle design

Improving the comprehensive performance of low alloyed Mg is a significant challenge for biomedical applications. This paper developed a high-performance Mg–Zn alloy with uniform ultrafine grains and nano-precipitates through a straightforward, high-temperature reciprocating equal channel angle extrusion (ECAP) process and researched the microstructure, mechanical property, degradation behaviour, and biocompatibility of the developed alloy. Results showed that the lean Mg–2Zn alloy successfully refined grain to about 1 μm and produced plenty of nano-particles with uniform distribution, providing high comprehensive mechanical properties (YS: 235 MPa, UTS: 267 MPa, EL: 15.6 %). Additionally, Zn-riched nano-particles in the matrix could decrease the Zn aggregation at the corrosion layer-matrix interface and form a dense oxide film, achieving a low degradation rate (0.13 mm/year in vivo). Finally, this work realizes the low alloy content, low cost, and good properties of one biodegradable Mg alloy, which will benefit the promotion of future clinical applications.

Theoretical Analysis of the Plastic Property for Equal Angle Sections Subjected to Axial Force and Biaxial Bending

Theoretical Analysis of the Plastic Property for Equal Angle Sections Subjected to Axial Force and Biaxial Bending

Navigating the phase diagram of quantum many-body systems in phase space.

We demonstrate the unique capabilities of the Wigner function, particularly in its positive and negative parts, for exploring the phase diagram of the spin -(1/2-1/2) and spin-(1/2-1) Ising-Heisenberg chains. We highlight the advantages and limitations of the phase-space approach in comparison with the entanglement concurrence in detecting phase boundaries. We establish that the equal angle slice approximation in the phase space is an effective method for capturing the essential features of the phase diagram but falls short in accurately assessing the negativity of the Wigner function for the homogeneous spin-(1/2-1/2) Ising-Heisenberg chain. In contrast, we find for the inhomogeneous spin-(1/2-1) chain that an integral over the entire phase space is necessary to accurately capture the phase diagram of the system. This distinction underscores the sensitivity of phase-space methods to the homogeneity of the quantum system under consideration.

Experimental study of wire arc additively manufactured steel sections stiffened by sinusoidal waves

Numerical models and initial tests conducted on specimens produced using selective laser melting have indicated that structural sections may be stiffened by imposing sinusoidal waveforms on their geometries which delay buckling and improve the overall buckling resistance. Wire arc additive manufacturing (WAAM) stands out as the most promising additive manufacturing technique for fabricating sections of the scale required in the construction industry, however, there is currently a lack of understanding of how the undulating surface finish inherent to WAAM will affect the stiffening effect of the sinusoidal waveforms. Therefore, this paper details an experimental study involving ten WAAM equal angle sections stiffened with two different sinusoidal wave patterns identified as the optimal patterns in previous numerical analysis. The production, geometric measurement and testing of the sections are described and the material properties of the WAAM material are determined. All equal angle section specimens tested fall within Eurocode 3 Class 4 and the stiffening wave patterns are shown to benefit the slenderer sections more. Comparative analysis between the material consumption and relative strength is provided, highlighting the potential for sinusoidal WAAM sections to improve the material efficiency and facilitate economic design practices within the steel construction industry.

The elastic stiffness tensor of cellulosic viscose fibers measured with Brillouin spectroscopy

Brillouin light scattering spectroscopy is applied to study the micromechanics of cellulosic viscose fibers, one of the commercially most important, man-made biobased fibers. Using an equal angle scattering geometry, we provide a thorough description of the procedure to determine the complete transversely isotropic elastic stiffness tensor. From the stiffness tensor the engineering-relevant material parameters such as Young’s moduli, shear moduli, and Poisson’s ratios in radial and axial fiber direction are evaluated. The investigated fiber type shows that, at ideal conditions, the material exhibits optical waveguide properties resulting in spontaneous Brillouin backscattering which can be used to obtain additional information from the Brillouin spectra, enabling the measurement of two different scattering processes and directions with only one scattering geometry.

Study on ultimate capacity and design method of cold-formed steel equal lipped angle components under axial compression

This study focuses on evaluating the load-bearing capacity of cold-formed steel (CFS) equal lipped angle components. It delves into the structural behavior and design methods, taking into account various edge conditions and buckling modes. By considering the key parameters, which are component length, component thickness, total lip length, and lip bending angle, a total of 555 numerical models are developed for a systematic analysis on the components with two types of cross-sectional shapes. Since the coefficients within the direct strength method (DSM) inadequately capture the ultimate load-bearing capacity of lipped angle components, we introduce a design methodology rooted in the DSM framework to address global and global-local coupling buckling modes while imposing constraints to prevent local-distortion coupling buckling modes. The machine learning models (XGBoost, BPNN, and 1D-CNN) are adopted to predict the structural behavior of the two types of lipped angle components. These models can integrate the analysis of the components with two types of cross-section shapes in predictions of ultimate load capacity, axial deformation, and buckling modes. Meanwhile, the prediction accuracy of the machine learning models surpasses that of the analytical design methodology, offering more accurate prediction for ultimate load capacity, axial deformation and buckling modes.

Experimental and numerical failure mechanism evaluation of anisotropic rocks using extended finite element method

Rocks often show an anisotropic behavior due to microcracks, mineral-based structure, and unequal in-situ stresses. The crack tip's stress intensity factors (SIFs) that control rock failure heavily depend on anisotropy. Given the significance of extensive research to identify the effects of anisotropy on the mechanical behavior and strength of rocks, numerical modeling is considered an essential method in designing structures and analyzing their stability. This study experimentally and numerically evaluated the effects of the bedding angle, initial crack angle with the loading axis, crack length, and anisotropy ratio on the stress intensity factor of transversely isotropic rocks via the extended finite element method (XFEM). Cracked chevron-notched Brazilian disks (CCNBDs) were fabricated from phyllite under the International Society for Rock Mechanics (ISRM) standards and tested at different initial crack lengths and angles for validation. The XFEM approach was then used to predict toughness and crack propagation path in the tested and new specimens with varying ratios of anisotropy and bedding angles (ψ = 0, 30, 45, 60, and 90°). The results demonstrated that with the increase of the anisotropy ratio, in equal crack length and initial angle, the absolute value of the SIFs have larger values. In addition, with the increase of crack length, the first and second modes of SIF increased, which indicates the failure of the specimen at lower loads. Also, bedding angle is effective on the stress intensity factors and this effect becomes more intense as the crack length increases. Finally, the anisotropy properties not only affect the values of SIFs, but also can change the angle at which the specimen experiences pure mode I or mode II.

A fault diagnosis method for variable speed planetary gearbox based on ADGADF and Swin Transformer

The vibration signal of planetary gearboxes under variable speed conditions shows non-stationary characteristics, indicating that fault diagnosis has become more complex and challenging. In order to more accurately diagnose faults in planetary gearboxes under variable speed conditions, a new method is proposed based on the angular domain Gramian angular difference field (ADGADF) and Swin Transformer. This method initially employs the chirplet path pursuit (CPP) algorithm to fit the speed curve of the original time-domain signal and then combines the speed curve with computed order tracking (COT) to achieve equal angle resampling of the time-domain signal, obtaining a stationary signal in the angular domain. On the basis of the above, the angular domain signal is creatively encoded into the two-dimensional images using the Gramian angular field (GAF), which accurately represents the fault characteristics of the original signal. Finally, the Swin Transformer network, with efficient global feature extraction capability, is used to learn advanced features from the images, achieving accurate fault recognition and classification. The proposed method is verified by experiment on the planetary gearbox and its performance is compared with several common coding methods and intelligent diagnosis algorithms. The experimental results show that the proposed method reaches an accuracy of up to 99.8%. In addition, its performance in accuracy, precision, recall, F1-score and the confusion matrix is superior to traditional diagnostic methods. It also offers the advantage of strong robustness.

An efficient solver for the inverse kinematics of cable-driven manipulators with pure rolling joints using a geometric iterative approach

The inverse kinematics (IK) problem of cable-driven manipulators with pure rolling joints (CDM-PRJs) presents unique challenges due to the equal angle constraints and strict joint limits. These factors render existing IK solvers ineffective or result in substantial degradation of their performance. To address these challenges, we propose a three-phase geometric iterative method to efficiently solve the IK problem for CDM-PRJs, which is a variant of the forward and backward reaching inverse kinematics method. Our method begins by establishing a surrogate model for CDM-PRJs to handle the equal angle constraints. Subsequently, we introduce a geometric iterative approach comprising a forward reaching phase, a backward reaching phase, and a state update phase. Additionally, we devise two novel measures, the random disturbance measure and the branch change measure, to effectively address deadlock situations and asymmetric joint limits, respectively. Simulation results demonstrate that our method surpasses the inverse Jacobian method and the sequential quadratic programming method in terms of success rate and computational efficiency. Furthermore, our method exhibits generality across various CDM-PRJs.

Improved Synchronous Sampling and Its Application in High-Speed Railway Bearing Damage Detection

Synchronous analysis is one of the most effective and practical techniques in rotating machinery diagnostics, especially in cases with variable speed operations. A modern analog-to-digital convertor (ADC) usually digitizes an analog signal to an equal time interval data series. Synchronous resampling converts the data series from an equal time interval data series to an equal shaft rotation angle interval data series. This conversion is usually achieved in the digital domain with the aid of shaft speed information, through either direct measurement or identification from a measured vibration signal, which is a time-consuming process. In order to improve the computational efficiency as well as the data processing accuracy, in this paper, a fast synchronous time-point calculation method based on an inverse function interpolation procedure is proposed. By identifying the inverse function of the instantaneous phase with respect to time, the calculation process of synchronous time points is optimized, which results in improved calculation efficiency and accuracy. These advantages are demonstrated by numerical simulations as well as experimental verifications. The numerical simulation results show that the proposed method can improve calculation speed by about five times. The synchronous analysis based on the proposed method was applied to a bearing fault detection in a high-speed rail carriage, which demonstrated the advantages of the proposed algorithm in improving the signal-to-noise ratio (SNR) for bearing damage feature extraction.

Azimuth calibration based on equal angle balance correction algorithm for measurement-while-drilling system

The precision of azimuth calculation in measurement-while-drilling systems is heavily reliant on the triaxial magnetometer, necessitating proper calibration to minimize azimuth errors. To address the need for high-precision calibration of systematic errors such as sensor scale factors, bias, and non-orthogonality, a relationship between the error model and the correction matrix is derived and a novel equal angle balance correction method to calibrate azimuth is proposed. Experimental results demonstrate that the mean azimuth error generated by this algorithm is less than 0.00624°, which is at least 28 times lower than that of the ellipsoid fitting correction method. The algorithm effectively eliminates systematic errors and meets the practical engineering requirements for azimuth calibration in measurement-while-drilling systems.

A numerical exploration of structural efficiency of steel plates with 3D sinusoidal wave patterns

The current study proposes the use of innovative additive manufacturing to produce metallic plate elements with predefined wave patterns capable of postponing instability via the lowest buckling mode thus providing increased buckling resistances. Two plate boundary conditions - internal and outstand elements were considered and tested by employing square hollow section (SHS) and equal angle section (EAS) stub columns, respectively. An experimental testing programme comprising tensile coupon tests and stub column tests on flat-faced SHS and EAS has been carried out and used to validate numerical models. This was followed by a numerical parametric study exploring various combinations of pre-defined surface waves with different amplitudes in stainless steel plates of varying slenderness. Their relative stiffness, strength, and material consumption been assessed and the optimum wave patterns have been identified for each boundary conditions based on their structural efficiencies. The optimum geometric wave pattern has also been compared with and shown to outperform another two common stiffening methods based on the same material consumption. This innovative study highlights the significant potential of metallic additive manufacturing technologies in achieving unprecedented material efficiency and economic design in the future steel construction industry.

Crossing the linguistic causeway: Ethnonational differences on soundscape attributes in Bahasa Melayu

Despite being neighbouring countries and sharing the language of Bahasa Melayu (ISO 639-3: ▪), cultural and language education policy differences between Singapore and Malaysia led to differences in the translation of the “annoying” perceived affective quality (PAQ) attribute from English (ISO 639-3: ▪) to ▪. This study expands upon the translation of the PAQ attributes from ▪ to ▪ in Stage 1 of the Soundscapes Attributes Translation Project (SATP) initiative, and presents the findings of Stage 2 listening tests that investigated ethnonational differences in the translated ▪ PAQ attributes and explored their circumplexity. A cross-cultural listening test was conducted with 100 ▪ speakers from Malaysia and Singapore using the common SATP protocol. The analysis revealed that Malaysian participants from non-native ethnicities (▪) showed PAQ perceptions more similar to Singapore (▪) participants than native ethnic Malays (▪) in Malaysia. Differences between Singapore and Malaysian groups were primarily observed in stimuli related to water features, reflecting cultural and geographical variations. Besides variations in water source-dominant stimuli perception, disparities between ▪ and ▪ could be mainly attributed to ▪ scores. The findings also suggest that the adoption of region-specific translations, such as ▪ in Singapore and ▪ in Malaysia, adequately addressed differences in the ▪ attribute, since significant differences were observed in one or fewer stimuli across ethnonational groups. The circumplexity analysis indicated that the quasi-circumplex model better fit the data compared to the assumed equal angle quasi-circumplex model in ISO/TS 12913-3, although deviations were observed possibly due to respondents' unfamiliarity with the United Kingdom-centric context of the stimulus dataset. Furthermore, the alignment between Stage 2 listening tests and quantitative evaluation of attributes in Stage 1 revealed biases in the ▪–▪ dimension across ethnonational groups. This study provides insights into the perception of PAQ attributes in cross-cultural and cross-national contexts, facilitating the culturally appropriate adoption of translated PAQ attributes in soundscape evaluation.

Assessment of design procedures for the buckling resistance of hot-rolled steel equal leg angles under concentric and eccentric compression

This work presents an extensive advanced numerical study calibrated with recent experimental results available in the literature on the buckling behavior of hot-rolled steel angles under concentric and eccentric compression to support the ongoing revision in Europe of the design rules for angles concentrically and eccentrically loaded in compression. The numerical results were used for the assessment of existing design procedures commonly applied in practice (Eurocodes and AISC), as well as new recently proposed recommendations. In general, the current analytical rules do not present good agreement with the experimental and calibrated numerical results, even showing unsafe results for some slenderness ranges. In case of fixed members in eccentric compression, these design rules are extremely conservative, reaching ratios rN (numerical versus analytical resistances) in excess of 2. The new proposals resulting from the project ANGELHY present an improved agreement with the numerical results, showing that they may efficiently replace the current design rules in the Eurocodes. However, for concentric compression, a reliability assessment shows that the required partial factor is γM1* = 1.1.

Stab lesion of the L4/L5 intervertebral disc in the rat causes acute changes in disc bending mechanics

Low-back pain often coincides with altered neuromuscular control, possibly due to changes in spine stability resulting from injury or degeneration, or due to effects of nociception. The relative importance of these mechanisms, and their possible interaction, are unknown. In spine bending, the bulk of the load is borne by the IVD, yet the acute effects of intervertebral disc (IVD) injury on bending mechanics have not been investigated. In the present study, we aimed to quantify the acute effects of a stab lesion of the disc on its mechanical properties, because such changes can be expected to elicit compensatory changes in neuromuscular control. L4/L5 spinal segments were collected from 27 Wistar rats within two hours after sacrifice and stored at −20℃. Following thawing, bending tests were performed to assess the intersegmental angle-moment characteristics. Specimens were loaded in right bending, left bending and flexion, before and after a stab lesion of the IVD fully penetrating the nucleus pulposus. In the angle-moment curves, we found reduced moments at equal bending angles after IVD lesion in left bending, right bending and flexion. Peak stiffness, peak moment, and hysteresis were significantly decreased (by 7.8–27.7 %) after IVD lesion in all directions. In conclusion, L4/L5 IVD lesion in the rat caused small to moderate acute changes in IVD mechanical properties. Our next steps will be to evaluate the longer term effects of IVD lesion on spine mechanics and the neural control of trunk muscles.

Simulation of the Hydraulic Performance of Parallel Pivot Weirs with Different Angles

Pivot weirs are one of the most important structures for regulating the water level in rivers and canals. These weirs are constructed with one or more gates in a row in the waterways. Changing the angle of each gate is done individually with an independent system. Based on available information, the hydraulic performance of this type of weirs (especially in several gates and different angles) in different operational conditions has not been investigated. In present study, pivot weirs with two gates are simulated using Ansys CFX software with the angles of 27.8 to 90 degree and the discharges between 40 to 130 L/s. Further, the importance of the open space between the two adjacent weirs with different angles (lack of retail wall) and its hydraulic behavior have been studied. The model was calibrated based on valid laboratory data and using the K-ϵ turbulence model. Therefore, the weirs with equal angles were studied in the first step. In this case, the effective discharge angle coefficient was studied and its maximum value compared to the vertical angle was obtained 1.076 for the angle of 52°. Furthermore, relationships for discharge coefficient versus upstream water depth were developed. In the next step, the effective length of the crest was found to be increases by 30% under unequal angles operation and the discharge coefficient raised by 1.3 to 2.4 times. Also, it was recognized that, in case of two weirs with unequal angles, about 26% to 69% of the flow passes through the distance between the two weirs. Therefore, the performance of unequal angles operation seems to be more effective in controlling the water level and discharge in different conditions and especially in flood events.

Demodulation method of orbital angular momentum vortex wave by few fields sampled on an extremely small partial aperture in radiation region

In this paper, a demodulation method of electromagnetic wave carrying orbital angular momentum (OAM) has been developed by using few electric fields sampled on an extremely small portion of the whole circumference in the radiation region. Considering that the field of the OAM wave is naturally of the form of exp (ilφ) in the far-field region, the matrix pencil method is used to extract the magnitude terms and the exponential terms according to the real and imaginary parts of the fields sampled on a small portion of the whole circumference, and further, the mode purities corresponding to the desirable OAM modes can be easily solved. The proposed demodulation method only uses four sampling electric fields with the sampling angle ranges of 3.3° and 9° to well demodulate the mode purities of the OAM waves with the single mode and the mixed dual-mode, respectively. The prototype of a dual uniform circular array with the equal divergent angle for the OAM waves of the modes l = 1 and l = 2 is fabricated and measured. Good agreement between the simulation and the measurement is observed to verify the proposed demodulation method.