Test Rig Research Articles

Experimental study on operating characteristics of rotor-bearing system lubricated by gallium-based liquid metal

PurposeThe purpose of this paper is to explore the operating characteristics of gallium-based liquid metals (GLMs) by directly adding them as lubricants in real mechanical equipment.Design/methodology/approachThis paper conducts an analysis of the rotor-bearing system under GLM lubrication using a constructed test rig, focusing on vibration signals, surface characteristics of the friction pair, contact resistance and temperature rise features.FindingsThe study reveals that GLM can effectively improve the lubrication condition of the tribo-pair, leading to a more stable vibration signal in the system. Surface analysis demonstrates that GLM can protect the sample surface from wear, and phase separation occurs during the experimental process. Test results of contact resistance indicate that, in addition to enhancing the interfacial conductivity, GLM also generates a fluid dynamic pressure effect. The high thermal conductivity and anti-wear effects of GLM can reduce the temperature rise of the tribo-pair, but precautions should be taken to prevent oxidation and the loss of its fluidity.Originality/valueThe overall operating characteristics of the rotor-bearing system under GLM lubrication were investigated to provide new ideas for the lubrication of the rotor-bearing system.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0067/

ECT in a large scale industrial pneumatic conveying system

The application of electrical capacitance tomography (ECT) for monitoring of industrial processes has been studied and proposed by many researchers. Examples can be found in monitoring of multiphase flows or mixing processes in reactors. Demonstrations of the functionality based on lab and test rig measurements have proven the potential of the proposed principles. This paper discusses the application of an ECT system in a heavy industries application. The harsh operating conditions in the industrial environment pose several challenges for the application of sophisticated measurement technology. This work addresses key aspects for the application of an ECT measurement system in such an environment. Specifically the electrical system design and the influence of the temperature are addressed. Relevant parameters and possible solutions are discussed. Furthermore the application of ECT as instrument for mass flow metering in pneumatic conveying processes is addressed. Supportive measurement studies from test rig experiments and comparative simulation studies are presented. Therefore, the paper provides a concise discussion on the application of ECT under harsh operating conditions, as well as the use of ECT as a measurement device for process measurement. The work concludes with a presentation of a measurement system in an industrial plant in which the proposed concepts were succesfully implemented.

Theoretical and Experimental Study on the Performance of Hermetic Diaphragm Squeeze Film Dampers for Gas-Lubricated Bearings

Low damping characteristics have always been a key sticking points in the development of gas bearings. The application of squeeze film dampers can significantly improve the damping performance of gas lubricated bearings. This paper proposed a novel hermetic diaphragm squeeze film damper (HDSFD) for oil-free turbomachinery supported by gas lubricated bearings. Several types of HDSFDs with symmetrical structure were proposed for good damping performance. By considering the compressibility of the damper fluid, based on hydraulic fluid mechanics theory, a dynamic model of HDSFDs under medium is proposed, which successfully reflects the frequency dependence of force coefficients. Based on the dynamic model, the effects of damper fluid viscosity, bulk modulus of damper fluid, thickness of damper fluid film and plunger thickness on the dynamic stiffness and damping of HDSFDs were analyzed. An experimental test rig was assembled and series of experimental studies on HDSFDs were conducted. The damper fluid transverse flow is added to the existing HDSFD concept, which aims to make the dynamic force coefficients independent of frequency. Although the force coefficient is still frequency dependent, the damping coefficient at high frequency excitation with damper fluid supply twice as that without damper fluid supply. The results serve as a benchmark for the calibration of analytical tools under development.

ANALYSIS OF LUBRICANT OIL DEGRADATION AND SOUND PRESSURE LEVEL FOR CI ENGINE USING BLEND FUELS

Long-term engine running has been the subject of extensive research on the deterioration of engine oil. In contrast, it is not fully clear what effect synthetic and biofuels will have. Modern engines, traditional fuels and lubricants should be used to provide a research basis for characterizing novel fuel-related phenomena in engines. This study makes an effort to characterize how lubricating engine oil behaves over the course of its service life using data on friction and wear. Every 20 hours, oil samples from the engine were obtained to evaluate its chemical makeup. On a reciprocating test rig, friction and wear measurements were taken. Kinematic viscosity, density, and wear metals such as cadmium (Cd), cobalt (Co), and lead (Pb) were measured for the lubricant oil analysis. In general, n-pentanol aids in the reduction of engine wear debris, contamination, and lubricating oil oxidation. According to the findings of this study, a D60WCO20Pe15 ternary combination can be used in a diesel engine without any alteration. The sound pressure level (SPL) increased by 7.8 dB at engine speed of 1300 RPM in the case of the DF95WCO5. However, when compared to base line, the average SPL of D60WCO20Pe15 ternary blend was 4.3 dB lower.

Friction-induced nonlinear dynamics in a spline-rotor system: Numerical and experimental studies

Excessive vibrations induced by intrinsic internal friction in spline joints critically impact the reliability and safety of high-speed rotating machinery. To address this concern, this paper presents experimental and numerical research on a flexible rotor system subjected to frictional contact within the spline joint. Experiments are conducted on a scaled rotor test rig designed to emulate the tail rotor drive shaft of helicopters, aiming to explore vibration behaviors under various operating conditions. A reduced-order mathematical model based on the test rig, considering the multi-interface friction of the spline joint and deformation coordination with a flexible coupling, is formulated. The numerical study, which incorporates both stability analysis and transient nonlinear dynamics, is then presented to quantitatively evaluate the occurrence conditions and excitation mechanisms leading to friction-induced instabilities. A parameter study is further conducted to elucidate the roles of various parameters in shaping self-excited vibration behaviors. The results reveal that the cross-coupling of frictional forces within the spline joint acts as the driving force of instabilities at supercritical speeds, with the resulting self-excited responses dominated by the frequency of the first critical speed. The study also highlights the necessity of integrating experimental and numerical analysis to better predict and understand the self-excited vibration phenomena in the spline-shaft systems.

An innovative dry-lab test rig for mechanical-hydraulic power take-off of wave energy conversion system

A dry-lab test rig is a powerful means to reduce costs in the design process of a wave energy conversion system (WECs). A dry-lab test rig technique allows the use of real components inside a simulation of a mathematical model. This paper presents the development of an innovative dry-lab test rig for the mechanicalhydraulic power take-off (MHPTO) unit of WECs. The development of a drylab test rig of MHPTO involves several processes, such as three-dimension (3D) modelling, component purchasing, structure fabrication, component installation, and operational testing. The developed dry-lab test rig consists of two main parts, such as the simulated wave emulator plant and the real MHPTO unit plant. The simulated wave emulator plant was developed in this test rig to replicate the interaction motion between the ocean wave motion and the wave absorber device. The developed dry-lab test rig was tested using five different irregular wave input conditions to ensure it could perform under the five different wave input conditions. The overall results demonstrate that the developed dry-lab test rig was successfully performed in all sea states. From the results, the profile of electrical power produced by the real MHPTO unit can be clearly obtained in each sea state.

Experimental Study of Partial Open Side Effect on Natural Convection in a Porous Cavity

This research provides information on the heat transfer in the cavity by natural convection which has a partially open side with a ratio (A = 1, 0.75, 0.5, 0.25) to the surroundings for cooling. It is filled with porous media (glass beads) and saturated with air. The bottom wall was heated with a constant heat flux (q = 1500, 3000, 4500, 6000) W/m2 while the top and other walls of the cavity were well insulated. The porous media had small porosity (0.418), a range of Rayleigh number Ra (57.6-1470). The distribution of temperatures, the local Nusselt number, and the average Nusselt number were all extracted from the testing rig's temperature data. It is clear that the fluid flow and heat transfer are affected by heat flux and the ratio of partially open side. Observed that, the greatest temperature values at maximum heat flux (q) and minimum open ratio (A). Thus, the temperature rising at all values of the constant heat flux and the enhancement of the local Nusselt number at (q = 6000) W/m2 about (5.47%, 3.85%, 1.76%) for (A = 1, 0.75, 0.5) respectively, when compared with (A = 0.25). The enhancement of the average Nusselt number at (q = 6000) W/m2 is about (7.28%, 4.55%, 2.27%) for (A = 1, 0.75, 0.5) respectively, compared with (A = 0.25).

Effects of activated fuel and staged secondary air distributions on purification, combustion and NOx emission characteristics of pulverized coal with purification-combustion technology

Under the strategic objectives of carbon peaking and carbon neutrality, clean and efficient coal combustion was important in China. As a novel combustion technology, purification-combustion technology had good research prospects, and high-temperature reduction unit (HTRU) played a crucial role in fuel activation, subsequent combustion and NOx emissions based on the design of this technology. Despite previous research had proved the pivotal role of fuel and combustion air distributions in combustor in influencing the entire thermochemical process, there was the lack of research on their effects in HTRU employing purification-combustion technology. To realize deep NOx emission reduction, this study focused on influences of activated fuel and staged secondary air distributions in HTRU on purification, combustion and NOx emission characteristics in a 30 kW purification-combustion test rig. With the exception of carbon microcrystalline structure, the majority of reductive char properties exhibited superior performance when activated fuel was introduced tangentially, as opposed to axially. Nevertheless, the relationship of carbon microcrystalline structure was regulated by staged secondary air ratio (c12). Properly increasing c12 improved reductive char properties. Additionally, axial introduction of activated fuel more consistently yielded ultra-low levels of NOx emissions; however, this often occurred at the expense of combustion efficiency (η). Properly increasing c12 reduced NOx emissions while increasing η; nevertheless, the benefits derived from c12 were limited. By adjusting introduction direction and c12 (axial, 0.33), minimum NOx emissions decreased to 39.10 mg/m3 (@6 % O2) while maintaining high η of 99.39 %.

Plasma sprayed duplex ytterbium disilicate/monosilicate EBCs and the transformation from ytterbia to ytterbium monosilicate during burner rig testing

Environmental Barrier Coating systems (EBCs) were thermally cycled in a burner rig test facility. Yb2Si2O7 (YbDS) layer was deposited by air plasma spraying while two suspension plasma sprayed Yb2SiO5 (YbMS) microstructures were evaluated in duplex (YbDS/YbMS) systems: columnar and segmentation cracked. EBCs underwent 2000 cycles at a surface temperature of 1300 °C without signs of delamination failure. A porous YbMS layer formed at the base of intercolumnar gaps and segmentation cracks in the duplex systems, presumably due to reactions with entrapped water vapor. Furthermore, Yb2O3 depletion zones were evident at both the surface and YbDS/YbMS interface of the duplex EBCs.

Vibration characteristics of blade-casing rubbing fault considering rotor–stator coupling

Blade-casing rubbing is a typical fault of aero-engine, but due to the complex structure of the equipment, it is still challenging to diagnose. This paper studies the characteristics of rubbing faults under rotor stator coupling. Firstly, a numerical model, which includes the rotor, bearings, and casing with blades, is constructed. Secondly, simulate the rubbing fault by setting the non-uniform initial gap between the blades and the casing, and the vibration response of the rotor and casing is obtained. Thirdly, combined with the test rig, the vibration characteristics under rubbing fault are verified. Finally, additional theoretical research is conducted on the vibration characteristics of the rotor, casing and blades under different degrees of rubbing fault. Theoretical and experimental results indicate that rubbing faults have different effects on the vibration of the rotor and stator: the rotational frequency amplitude of the rotor decreases while the frequency amplitude of the stator increases. As the fault degree increases, these phenomena become more significant. When rubbing faults occur, the harmonics near the system’s natural frequencies are more affected than the others. Moreover, rubbing faults can also cause the vibration of the rotor to be affected by the blade mode. The conclusions obtained in this paper can provide a reference for diagnosing rubbing faults in aero-engine.

Repeatability in Measurements and Control Settings of a Small Francis Turbine Test Rig

Repeatability in Measurements and Control Settings of a Small Francis Turbine Test Rig

A new multiple mixed augmentation-based transfer learning method for machinery fault diagnosis

With the continuous development of various industries, the diagnosis of industrial equipment faults has been receiving increasing attention in recent years. Considering the complex and variable working conditions, and the limited amount of fault data, transfer learning has become an effective solution for fault diagnosis. Data augmentation techniques, particularly generative adversarial networks, have achieved tremendous development within the field of transfer learning fault diagnosis. However, traditional data augmentation methods experience difficulty in extracting features conducive to fault diagnosis from fault data under complex operating conditions, particularly in the case of raw vibration data from bearings. Therefore, this study proposes a new multiple mixed augmentation-based transfer learning (MMATL) method for machinery fault diagnosis. First, an augmentation chain that dynamically adjusts data augmentation strategies in accordance with the model’s performance is constructed based on AutoAugment. Then, a multiple mixed augmentation strategy that integrates fault data into the augmented data from the augmentation chain to obtain enhanced data suitable for training is proposed. This strategy consists of multiple augmentations, augmentation mixing, and data mixing. Finally, experiments confirm the effectiveness of MMATL on the bearing datasets from the gearbox of the Chinese CRH380A high-speed train, the test rig at the University of Paderborn in Germany and the self-made bearing failure test platform. Results indicate that the method can adaptively extract features from fault data that are conducive to fault diagnosis under complex operating conditions.

Deep learning based fault detection of automobile dry clutch system using spectrogram plots

Dry friction clutches are extremely important in the context of power transmission systems. Continuous exposure to extreme heat and loading makes clutch extremely susceptible to various faults. The timely detection and diagnosis of such faults are of utmost importance to prevent any damage to internal components and also helps in avoiding transmission system failures. In this research study, a novel approach that leverages the power of transfer learning (a famous deep learning technique) is proposed to diagnose multiple types of clutch faults including, worn release fingers, fractured pressure plates, deteriorated pressure plates, loss of friction material and distorted tangential strips using spectrogram plots. To train and validate the diagnostic system, vibration readings were taken from a specially designed test rig with the help of piezoelectric accelerometer while the clutch system was operated under different load conditions of 0 (no load), 5 and 10 kg This procedure of data collection was then repeated to acquire the vibration data for all of the fault conditions by replacing the good with fault components individually. These vibration signals were further processed and transformed into spectrogram plots that serves as the input data for the deep learning models considered. Fine-tuning techniques were applied on pretrained networks to maximise the prediction accuracy of the models to effectively determine and diagnose faults in the clutch system. For this study 12 pre-trained networks were chosen namely, Xception, InceptionResNet, DenseNet, AlexNet, VGG16, GoogLeNet, VGG19, ResNet101, ResNet50, InceptionV3, MobileNetV2 and ShuffleNet. To optimize the performance of deep learning models, a systematic adjustment of hyperparameters such as the train-test split ratio, learning rate, optimizer and batch size for each network model was carried out. Through careful experimentation and analysis, significant improvements in fault classification accuracy were achieved thereby enhancing the reliability and effectiveness of the diagnostic system. From the results it was noted that 100% classification accuracy was displayed by AlexNet (for the no load condition and the 10 kg load condition) and GoogLeNet (for 5 kg load condition) with extremely low computation times.

Scaling procedure for on-ground testing of a robust attitude and vibration control architecture for a large flexible satellite

The agility of satellites equipped with large and flexible structures, such as solar panels or antennas, poses a significant challenge due to the influence of elastic dynamics on attitude motion. This results in reduced pointing accuracy and dimensional stability of the payload. To address this issue, an Active Collocated Attitude Control (ACAC) system has been developed, utilizing actuators for both the elastic dynamics (distributed piezoelectric devices) and attitude control (ON-OFF thrusters). In the initial phase of the project, the algorithm underwent extensive verification using a high-fidelity numerical model of a spacecraft with two very-low frequency flexible solar panels and a payload consisting of two long booms and a transversal antenna's reflector. The paper focuses on the second phase of the project, which revolves around the experimental verification of the control architecture concept. To achieve this, a scaling procedure employing the dynamic analogy approach was implemented to determine the design parameters of a free-floating platform equipped with elastic appendages. This ensured that the resulting elastic multibody system displayed similar dynamic behavior to the full-scale satellite. Based on the scaling parameters, a test rig was manufactured, and actuators and sensors were optimally positioned. The performance of the ACAC system was then compared to that of traditional benchmark controllers. The results show that the ACAC system demonstrates superior capabilities in performing fast slew maneuvers without developing unstable interactions with the elastic dynamics.

Stiffness increase in main spindles by using tapered roller bearings for aluminum cutting tests

AbstractDue to increasing demands regarding higher manufacturing accuracy and the machining of high-strength materials, the stiffness and load-carrying capacity of main spindles must be enhanced. One approach is to replace the conventionally used angular contact ball bearings, so called spindle bearings, with tapered roller bearings of the same size, which have a higher stiffness and load carrying capacity due to their larger rolling contact. In case the speed requirement is below a speed parameter $$n\cdot d_{m}=0.9\times 10^{6}$$ n · d m = 0.9 × 10 6 mm/min, the poorer speed parameter of tapered roller bearings can be compensated by a sufficiently high lubrication quantity. However, the stiffness increase by using this bearing type in main spindles has not yet been quantified in field tests. Therefore, the aim of this paper is to demonstrate the stiffness advantage of a spindle with an elastically arranged tapered roller bearing compared to a conventional spindle with angular contact ball bearings by machining tests. First, the radial load displacement characteristic of the newly developed tapered roller bearing spindle is tested in advance on an isolated test rig. In machine cutting tests, full slots are milled in an aluminum block. During the tests, the axial and radial displacements of the spindle shaft relative to the housing are measured and evaluated in radial and axial direction. These tests are repeated and compared with the conventional spindle. By varying the process parameters such as cutting depth, feed rate or rotational speed, the increased stiffness of the tapered roller bearing spindle compared to the conventional spindle is illustrated based on the measured displacements. Moreover, frequency response measurements at different speeds underpin the improved damping of the tapered roller bearing spindle. Assuming that the speed requirements are not too high and the tapered roller bearing is sufficiently lubricated, the use of this type of bearing can significantly increase the stiffness and thus the manufacturing precision in the long term for main spindles.

Biomechanics‐based study of muscle activation under different driving conditions for Chinese percentiles

AbstractIn this paper, we determined the adjustment levels of the human–machine layout under the preferred driving posture for individuals with different body sizes. We also comparatively analyzed the maximum activation levels of various muscles under straight‐line driving and steering conditions. To increase the accuracy of the results, AnyBody biomechanics software was used to establish a human skeletal muscle mechanics model, which we analyzed for consistency with rig test results. The results showed that people with larger body sizes preferred a driving position with the seat reclined back. Steered driving was associated with a significant (p < .05) increase in the maximum activation of the wrist extensors, serratus anterior, deltoid, and triceps brachii, which are the main force‐generating muscle groups for steered driving, compared with straight driving. Moreover, the measured and simulated results of maximum muscle activation were relatively consistent, with the error between them within a 15% margin. In summary, this study explored the relationship between different driving conditions and preferred driving postures from a biomechanical perspective. A combined experimental and simulation approach was adopted to ensure the reliability of the findings. The insights from this study can inform ergonomic considerations for the comfort and health of Chinese drivers with varying physical characteristics.

Practical Evaluation of Ionic Liquids for Application as Lubricants in Cleanrooms and under Vacuum Conditions

As part of a publicly funded cooperation project, novel high-performance lubricants (oils, greases, assembly pastes) based on ionic liquids and with the addition of specific micro- or nanoparticles are to be developed, which are adapted in their formulation for use in applications where their negligible vapor pressure plays an important role. These lubricants are urgently needed for applications in cleanrooms and high vacuum (e.g., pharmaceuticals, aerospace, chip manufacturing), especially when the frequently used perfluoropolyethers (PFPE) are no longer available due to a potential restriction of per- and polyfluoroalkyl substances (PFAS) due to European chemical legislation. Until now, there has been a lack of suitable laboratory testing technology to develop such innovative lubricants for extreme niche applications economically. There is a large gap in the tribological test chain between model testing, for example in the so-called spiral orbit tribometer (SOT) or ball-on-disk test in a high-frequency, linear-oscillation test machine (SRV-Tribometer from German “Schwing-Reib-Verschleiß-Tribometer”), and overall component testing at major space agencies (ESA—European Space Agency, NASA—National Aeronautics and Space Administration) or their service providers like the European Space Tribology Laboratory (ESTL) in Manchester. A further aim of the project was therefore to develop an application-orientated and economical testing methodology and testing technology for the scientifically precise evaluation and verifiability of the effect of ionic liquids on tribological systems in cleanrooms and under high vacuum conditions. The newly developed test rig is the focus of this publication. It forms the basis for all further investigations.

Resolving nonuniform flow in gas turbines: challenges, progress, and moving forward

Abstract The flow in gas turbines exhibits a highly unsteady, complex and nonuniform manner, which presents two main challenges. Firstly, it introduces instrumentation errors, contributing to uncertainties when calculating one-dimensional performance metrics during rig or engine tests using fixed-location rakes. Secondly, it raises mechanical concerns, including high-cycle fatigue due to blade row interactions in turbomachines and thermal fatigue caused by hot-streaks at the combustor exit. Experimental characterisation of the flow nonuniformity in gas turbines is highly challenging due to the confined space and harsh environment for instrumentation. This paper presents recent efforts to address this issue by resolving the nonuniform flow in gas turbines using spatially under-sampled measurements. The proposed approach utilises discrete probe data and leverages a ‘Fourier-based approximation’ method developed by the author. The technique has undergone preliminary experimental validation involving reconstruction of the total pressure distribution in a multi-stage axial compressor and the total temperature field at the exit of the combustor and high-pressure turbine. Results show that, in the multi-stage axial compressor environment, reconstruction of inter-stage total pressure is achieved using a reduced dataset covering less than 20% of the annulus with reasonably good accuracy. The reconstructed total pressure yields almost identical mean total pressure values at all spanwise locations, with a maximum deviation of less than 0.02%. Additionally, reconstruction of the total temperature distribution at an engine-representative full annulus combustor is achieved using measurements at ten carefully selected circumferential locations. Results show that the reconstructed temperature field successfully captures the primary features associated with combustor exit temperature flow. The reconstructed temperature field yields excellent agreement in the magnitude of radial temperature distribution factor (RTDF) and overall temperature distribution factor (OTDF) predictions to the experiment, with a deviation of less than 0.5% for RTDF and less than 2.5% for OTDF. Lastly, reconstruction of the total temperature distribution at the exit of the GE E3 high-pressure turbine (HPT) is achieved using measurements at eight carefully selected circumferential locations. Results demonstrate remarkable robustness in resolving the temperature profile at the HPT exit with high fidelity, irrespective of the HPT inlet conditions. The initial validation results are promising, demonstrating that the new probe layout scheme and the Fourier-based approximation method enable effective characterisation of flow nonuniformity in gas turbines, thereby providing valuable insights into the complex flow of gas turbine engines.

Studies on the Evolution of Fatigue Strength of Aluminium Wires for Overhead Line Conductors.

Traditional ACSR overhead wires, which consist of a high-strength steel core and several layers of aluminium wires, are currently the most popular overhead line conductor (OHL) design globally. Operating conditions, particularly operating under varying stresses from Karman vortices, lead to the fatigue cracking of wires of the outer layer, followed by wires of the inner layers. Karman vortices are formed by the detachment of a laminar wind stream flowing around the conductor, which causes vibrations in the conductor called wind or aeolian oscillations. Aluminium wires are manufactured using standard batch material drawing technology. Although the fatigue strength of such wires is not standardised, there are various criteria for evaluating this characteristic, as well as established limits on the number of cycles needed to break the first wires of the outer layer. Fatigue strength also strongly depends on the geometric structure of the wire and its operating conditions. The article analyses the influence of the mechanical condition of aluminium wires used in ACSR cables on their fatigue strength. We then present results from aluminium wire fatigue tests conducted on a specially constructed test rig. In addition, fatigue cracks were interpreted using scanning microscopy.

Laboratory Tests of Large-Scale Block Models on the Load Transfer and Failure Mechanisms of Rock Masses Subjected to Anchor Loading

AbstractThis paper presents a laboratory testing rig designed to investigate the failure mechanisms and load transfer of rock masses under rock anchor loading. The study revealed that joint patterns significantly affect the strength and capacity of the rock mass, with existing design approaches based on apex angles of 90$$^{\circ }$$ ∘ or 60$$^{\circ }$$ ∘ found to be potentially overly conservative. Joint orientation and spacing should be included in the anchor design to obtain a more precise design criterion. In all the studied patterns, increasing the horizontal and vertical stress increased the block models’ capacity, and load arching did not occur in the model with an unfavourable joint orientation. This study also revealed that the failure surface followed the joints in all tests and that the block model capacity was significantly higher than estimated with the design principle based on the weight of the overlying rock. The findings of this work have important implications for designing rock anchoring systems in mining and civil engineering demonstrate that joint orientation and block size significantly affect the rock mass capacity. This study confirms the need to consider the influence of in situ stresses on rock mass capacity when designing of rock anchors. Overall, this work guides the development of more precise design criteria for rock anchors, contributing to more efficient and effective rock engineering practices.