Stiffness Components Research Articles

Complaint constant force mechanism using variable stiffness leaf-spring-like beam: Design and experiment

<p style='text-indent:20px;'>This research provides a design for a complaint constant-force mechanism employing a leaf-spring-like beam with variable stiffness to address the negative stiffness stroke underutilization issue of the bistable beam. By designing the compression of the leaf-spring-like beam at each given displacement and the compression ramp slope, this technique allows the constant force mechanism to potentially take full utilization of the bistable beam's negative stiffness component. Innovative design of a complaint constant force mechanism based on positive and negative stiffness is shown in this study. In addition, we conduct simulation analysis and experimental verification. The experimental results illustrate the feasibility and effectiveness of the proposed method.</p>

Programmable and resilient metamaterials with anisotropic and non-linear mechanical responses composed exclusively of stiff constituents.

Recently, significant progress has been made in the field of flexible bulk metamaterials composed of soft and elastic materials, unlocking the potential for achieving programmable non-linear mechanical responses, such as shape morphing, energy absorption, and information processing. However, the majority of these metamaterials utilize expensive hyperelastic materials and require complex fabrication processes. Additionally, constructing eco-friendly stiff constituents for these metamaterials remains challenging due to their limited elastic limit strains (<0.1). Here, we propose a systematic design strategy by combining curved beams with chiral metastructures to generate a family of three-dimensional programmable resilient mechanical metamaterials without relying on flexible or hyperelastic constituents. These tiled metamaterials demonstrate robust, anisotropic and non-linear resilience under large elastic compression strains (>0.75), while exhibiting a programmable effective modulus reduction of nearly 6 orders of magnitude compared to the native stiff components. Furthermore, leveraging their stable resilience under high-frequency stimuli, we successfully developed a meter-scale soft robot capable of traversing complex narrow scenarios on demand without the need for flexible materials or sophisticated pipelines. We anticipate that these mechanical metamaterials could serve as a universal platform for programmable active dampers, modular flexible robots, and medical rehabilitation equipment at various scales.

Numerical and Experimental Analysis of Stress-Strain Characteristics in DP 600 and TRIP 400/700 Steel Sheets.

The body constitutes the largest proportion of the total vehicle weight. Recently, increasing efforts have been made towards reducing its weight and improving its crashworthiness. By reducing its weight, fuel consumption will be reduced, and this will also translate into lower CO2 emissions. In terms of safety, vehicle body components use high strength steel which can absorb a substantial amount of impact energy. The present study pays attention to DP 600 and TRIP 400/700 stress-strain characteristics at quasi-static strain rates. The stress-strain characteristics of absorption capacity, stiffness, and deformation resistance force were investigated experimentally by tensile tests, three-point bending tests, and numerical simulations. The results indicate the potential for increasing the absorption capacity, stiffness, and deformation resistance force of the vehicle body's deformable steel components. The present study verified the possibility of replacing physical testing with numerical simulation. A reasonably satisfactory agreement between the experimentally determined stress-strain characteristics and the numerical simulation was achieved, which can reduce the development time of deformable vehicle body components, reduce costs and optimize the selection of materials. The results extend the state of knowledge on the deformation characteristics of high-strength materials and contribute to the optimization of body components in terms of passive safety and weight.

Damage inference and residual capacity assessment for an E-Defense 2018 ten-story RC test structure

This paper presents an enhanced vision-based, post-earthquake performance assessment framework for RC building structures. This framework incorporates a damage inference method that can estimate the stiffness and strength reduction factors of components in stories without damage inspection based on the inter-story drift. The framework was validated by the application to the full-scale shaking table test of an E-Defense 2018 ten-story RC structure. The vision-based damage detection method effectively detected multicategory seismic damage on the component surfaces, and the damage states estimated by the vision-based method were consistent with the results estimated by the measured plastic hinge rotation. The proposed inter-story drift-based damage inference method reasonably estimated the reduction factors of components in the stories without damage photos. The numerical model updated by the reduction factors of damaged components provided accurate estimates of the fundamental vibrational frequencies after different levels of seismic shaking, and the drift-based inference method significantly improved the results compared with the trivial linear interpolation method. The residual capacity curves provided by pushover analysis of the updated model using the reduction factors as per FEMA 306 & Chiu et al. reasonably captured the hysteretic responses of the structure.

Study on seismic behavior and collapse risk of super high-rise braced mega frame-core tube structural system

The braced mega frame-core tube (BMFCT) structure could provide an efficient lateral-force resisting (LFR) system for high-rise or super high-rise buildings, especially for those higher than 500 m. The BMFCT structure is a dual LFR system, including the outer braced mega frame and the inner core tube. The seismic behavior and design method of this structural system is not clear. In this study, a parametric study based on collapse risk-targeted analysis is conducted to clarify seismic mechanism and performance and to make clear means of matching reasonable stiffness and setting energy-dissipation components. Five comparable BMFCT structures with different mega brace stiffness proportions and frame-tube stiffness ratios are designed. An efficient elasto-plastic modeling method is introduced to establish the accurate FE models. The corresponding collapse risks are calculated through Incremental Dynamic Analysis and fragility theory. The results show that the structural collapse risk increases with the increased frame-tube stiffness ratio. Therefore，the stiffness and bearing capacity of peripheral frames should be strengthened to ensure the structural collapse margin. On the other hand, the collapse resistance capacity gradually decreases with the increasing of the mega brace stiffness. Thus, the stiffness proportion of mega braces should be recommended to meet the basic lateral stiffness requirements, which shall not exceed 35 % of the overall structural stiffness. Moreover, the distribution feature and ideal arrangement of the energy dissipation components are proposed. The seismic design recommendation based on the uniform collapse risk is also proposed for the BMFCT system, which serves a reference for the structural design of super high-rise buildings.

An analytical approach to the stiffness calculation of statically indeterminate 3-DOF delta parallelogram-type parallel robot

This paper introduces an analytical approach entailing a clear physical meaning for calculating the stiffness of the 3-DOF Delta parallel robot. By defining suitable linear and torsion springs, the stiffness of the robot components in different postures and the stiffness coefficients of the indeterminate parallelogram under conceivable wrenches are comprehensively obtained. Moreover, the stiffness coefficients for each limb chain are assigned, and then by considering the assigned stiffness coefficients and static equilibriums the indeterminate problem of 3-RUU DPRs is solved. By reformulating the forward kinematics which takes into account the deflected components and based on the elastic properties, the deflection in each manipulator component is calculated and the amount of moving platform twist is obtained. The proposed approach is validated by the FEA method and results reveal that the maximum error of the proposed method is 0.1489° in the orientation and 0.1420 mm in translation compared to the FEA. Then to avoid the problem of different units of translation and orientation in indexing, the virtual work concept is used for assigning an index number.

Mechanical forces quench frontal polymerization: Experiments and theory

Frontal polymerization is a promising energy-saving method for rapid fabrication of polymer components with good mechanical properties. In these systems, a small energy input is sufficient to convert monomers, from a liquid or soft solid state, into a stiff polymer component. Once the reaction is initiated, it propagates as a self-sustaining front that is driven by the heat released from the reaction itself. While several studies have been proposed to capture the coupling between thermodynamics and extreme chemical kinetics in these systems, and can explain experimentally observed thermo-chemical instabilities, only few have considered the potential influence of mechanical forces that develop in these systems during fabrication. Nonetheless, some experiments do indicate that local volume changes induced by the competing effects of thermal expansion and chemical shrinkage, can lead to significant deformation or even failure in the resulting component. In this work, we present a unique experimental approach to elucidate the effect of mechanics on the propagation. Our experiments reveal that residual stresses that arise in frontal polymerization are not only a potential cause of undesired deformations in polymer products, but can also quench the reaction front. This thermo-chemo-mechanically coupled effect is captured by our theoretical model, which explains the mechanical limitations on frontal polymerization and can guide future fabrication. Overall, the findings of this work suggest that mechanical coupling needs to be taken into consideration to enable industrial applications of frontal polymerization at large scales.

Unification: Emergent universe followed by inflation and dark epochs from multi-field theory

A two scalar field model that incorporates non Riemannian Measures of integration or usually called Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. In the Einstein frame a K-essence is generated and as a consequence for the early universe, we can have a Non Singular Emergent universe followed by Inflation and for the present universe dark epochs with consistent generation of dark energy (DE), dark matter (DM) and stiff matter. The scale invariance is introduced and then is spontaneously broken from the integration of the degrees of freedom associated with the modified measures. The resulting effective potentials and K-essence in the Einstein frame produce three flat regions corresponding to the different epochs mentioned before. For the first flat region we can associate an emergent and an inflationary universe. Here for a parameter-space region this flat plateau possesses a non singular stable emergent universe solution which characterizes an initial epoch of evolution that precedes the inflationary scenario. Also assuming this first plateau, we study the inflation in the framework of the slow-roll approximation. In this scenario under the slow roll approximation we obtain a linear combination that is a constant. The corresponding cosmological perturbations in our model are determined and we also obtain the different constrains on the parameter-space from the Planck data.In the following flat region DE and also the DM, which does not need to be introduced separately, it is instead a result of a K-essence induced by the multi measures, multi field theory. Also stiff matter component is automatically generated from the K-essence theory from two scalar fields. From the perturbative analysis associated to the perturbation solution of background, we find a correlation between the two scalars. Besides, we obtain that our model during the dark epoch has a behavior of tracking freezing model.

Latching control: A wave energy converter inspired vibration control strategy

Latching control is a phase optimization control mechanism for improving the energy conversion efficiency of a wave energy converter (WEC). This paper, for the first time, extends the latching mechanism to vibration control to improve energy dissipation efficiency. An innovative semi-active latched mass damper (LMD) is proposed in this paper by integrating conventional tuned mass dampers (TMD) and the latching mechanism. First, the theoretical models of WEC and TMD are compared. Second, the mathematical model of an LMD installed on a single-degree-of-freedom structure is established, and three latching control strategies with different latching time instants, latching durations, unlatching time instants, and required information feedback are tested. Subsequently, the performance of the LMD is evaluated through the comparison with the detuned and optimally tuned TMDs. The characteristics of the latching control force are analyzed in terms of phase, component, energy dissipation, and damping enhancement effect. Lastly, the feasibility and effectiveness of the proposed LMD with three different latching strategies are proven. The latching control can reduce the stiffness component and increase the damping component of the control force, thereby optimizing the phase lag between the control force and the structural response. The proposed latching mechanism and strategies for vibration control can provide an innovative solution to improve the effectiveness of high-frequency detuned dampers, facilitate the design of long-period dampers, and develop adaptive semi-active dampers in the future.

Seismic behavior of partially encased composite columns-steel plate shear wall structure with different semi-rigid joints

Seismic performance of partially encased concrete (PEC) column-steel plate shear wall (SPSW) structure is significantly affected by the characteristics of beam-column connections. Three component models of semi-rigid beam-column connections, including the bidirectional bolt extended end-plate connection, the flush end-plate connection, and the web double-angle steel connection, are designed according to Eurocode 3. Afterward, three 1/3-scale two-story single-span PEC column-SPSW structures with the three types of semi-rigid connections are tested under quasi-static cyclic loading. The test results indicate that all three structures satisfy the design requirement of “strong frame-weak wall plate”. The PEC-SPSW structure with the bidirectional bolt extended end-plate connections exhibits a higher bearing capacity and stiffness than the other two structures. Compared with the web double-angle connection, the adoption of bidirectional bolt extended end-plate connection increases the yield bearing capacity by 14.32% and the initial stiffness by 16.16%, but ductility decreases by 17.65%. The energy dissipation of each story of the structure with flush end-plate connections is relatively balanced. The energy dissipated by the second-story of SPSW is less than that of its first-story due to the higher rotational stiffness of the bidirectional bolt extended end-plate connections. The PEC-SPSW structures fracture at the column foot. The reliability of the initial rotational stiffness component models is verified by comparing the finite element (FE) and test results.

The sensitivity of the stiffness and thickness of a titanium inlay in a cementless PEEK femoral component to the micromotions and bone strain energy density

Polyetheretherketone (PEEK) has been proposed as alternative material for total knee arthroplasty implants due to its low stiffness, which may reduce stress-shielding. In cementless fixation, a proper primary fixation is required for long-term fixation. Previous research showed that the lower stiffness of a cementless PEEK femoral component results in larger micromotions at the implant-bone interface compared to a cobalt-chrome femoral component. A titanium inlay on the PEEK implant surface may improve the primary fixation while maintaining the favourable stiffness properties. Therefore, the effect of thickness and stiffness of a titanium inlay on the primary fixation and stress-shielding was investigated. A finite element model of the femur and femoral component was created with five titanium inlay variants. The micromotions and strain energy density (SED) were quantified as outcome measures. The distal thin – proximal thick variant showed the largest resulting micromotions (51.2 µm). Relative to the all-PEEK femoral component, the addition of a titanium inlay reduced the micromotions with 30 % to 40 % without considerably affecting the stress-shielding capacity (strain energy difference of 6 % to 10 %). Differences in micromotions (43.0–51.2 µm) and SED between the variants were relatively small. In conclusion, the addition of a titanium inlay could lead to a reduction of the micromotions without substantially affecting the SED distribution.

Material extrusion additive manufacturing of dual material composite thermoset silicone components

AbstractAdditive manufacturing (AM) is a disruptive manufacturing process that gives designers freedom to create highly complex shapes through free‐form fabrication. The majority of polymers used in extrusion AM are thermoplastics because they are easy to process in affordable machines. While there are a number of moderate modulus thermoplastics in regular use in AM, thermoplastics are known to weaken with increases in temperature or exposure to solvents and many commodity thermoplastics used in AM are brittle. On the other hand, there are few elastomers, and even fewer elastomer reinforcement schemes, that are accessible using standard AM technologies. In this work, we report a novel dual extrusion process that integrates elastomeric silicone with reinforcing thermoplastic. By developing and demonstrating a dual extrusion 3D printer that can process common thermoplastics with commercially available thermosetting silicones, new types of composite elastomers are reported with good mechanical performance. The 0°/20°/−20° grid pattern thermoplastic reinforced samples achieved 2.5 MPa tensile strength in low extension region (0.5 strain), which improves the initial stiffness of the composite component. Desired mechanical responses of composite structures can be realized by tuning the reinforcement volume ratio and infill percentages, and applying various types of reinforcement mesh patterns and thermoplastics.Highlights A dual extrusion process integrates fus filament fabrication and direct ink writing technologies. Thermoplastic reinforced silicone composite with stiff/soft properties. Tunable volume ratio, infill percentage, mesh pattern, and material option.

Performance Optimization for Bionic Robotic Dolphin with Active Variable Stiffness Control.

Aquatic animals such as fish and cetaceans can actively modulate their body stiffness with muscle to achieve excellent swimming performance under different situations. However, it is still challenging for a robotic swimmer with bionic propulsion mode to dynamically adjust its body stiffness to improve the swimming speed due to the difficulties in designing an effective stiffness adjustment structure. In this paper, based on the special torque mode of a motor, we propose an active variable stiffness control method for a robotic dolphin to pursue better swimming speed. Different from a variable stiffness structure design, a torque control strategy for the caudal motor is employed to imitate the physical property of a torsion spring to act as the variable stiffness component. In addition, we also establish a dynamic model with the Lagrangian method to explore the variable stiffness mechanism. Extensive experiments have validated the dynamic model, and then the relationships between frequency and stiffness on swimming performance are presented. More importantly, through integrating the dynamic model and torque actuation mode-based variable stiffness mechanism, the online performance optimization scheme can be easily realized, providing valuable guidance in coordinating system parameters. Finally, experiments have demonstrated the stiffness adjustment capability of the caudal joint, validating the effectiveness of the proposed control method. The results also reveal that stiffness plays an essential role in swimming motion, and the active stiffness adjustment can significantly contribute to performance improvement in both speed and efficiency. Namely, with the adjustment of stiffness, the maximum speed of our robotic dolphin achieves up to 1.12 body length per second (BL/s) at 2.88 Hz increasing by 0.44 BL/s. Additionally, the efficiency is also improved by 37%. The conducted works will offer some new insights into the stiffness adjustment of robotic swimmers for better swimming performance.

Testing spasticity mechanisms in chronic stroke before and after intervention with contralesional motor cortex 1 Hz rTMS and physiotherapy

BackgroundPrevious studies showed that repetitive transcranial magnetic stimulation (rTMS) reduces spasticity after stroke. However, clinical assessments like the modified Ashworth scale, cannot discriminate stretch reflex-mediated stiffness (spasticity) from passive stiffness components of resistance to muscle stretch. The mechanisms through which rTMS might influence spasticity are also not understood.MethodsWe measured the effects of contralesional motor cortex 1 Hz rTMS (1200 pulses + 50 min physiotherapy: 3×/week, for 4–6 weeks) on spasticity of the wrist flexor muscles in 54 chronic stroke patients using a hand-held dynamometer for objective quantification of the stretch reflex response. In addition, we measured the excitability of three spinal mechanisms thought to be related to post-stroke spasticity: post-activation depression, presynaptic inhibition and reciprocal inhibition before and after the intervention. Effects on motor impairment and function were also assessed using standardized stroke-specific clinical scales.ResultsThe stretch reflex-mediated torque in the wrist flexors was significantly reduced after the intervention, while no change was detected in the passive stiffness. Additionally, there was a significant improvement in the clinical tests of motor impairment and function. There were no significant changes in the excitability of any of the measured spinal mechanisms.ConclusionsWe demonstrated that contralesional motor cortex 1 Hz rTMS and physiotherapy can reduce the stretch reflex-mediated component of resistance to muscle stretch without affecting passive stiffness in chronic stroke. The specific physiological mechanisms driving this spasticity reduction remain unresolved, as no changes were observed in the excitability of the investigated spinal mechanisms.

THE CURRENT STATE OF BLADE MACHINING WITH BLOCK-MODULAR TOOLS ON HEAVY-DUTY CNC MACHINES

The article analyzes the current state of the problem of blade machining, considers ways to improve the efficiency of the machining process on heavy unique machine tools, prefabricated tool systems, tool reliability, evaluates methods for ensuring satisfactory chip formation and their technological capabilities, considers methods of multicriteria optimization, identifies areas of scientific research, and formulates the purpose and objectives of the study. For the first time, the scientific principles of creating block-modular tooling systems for heavy machine tools were published, which include: principles of creating block-modular tooling systems based on qualimetric assessment of the states of the machining process, possible failures of the technological system, properties and criteria for their optimization, determination of the criteria weights; principles of designing block-modular tool elements taking into account the assessment of the stress-strain state and stiffness of the main components, creation of a mathematical model.

New possibilities for laser welding of highly loaded transmission components by strategic use of simulation methods

Laser welding in transmission manufacturing opens up completely new kinds of product solutions with excellent properties in terms of wear, corrosion resistance, and service life. Current welding designs are characterized in particular by difficult-to-weld material combinations (e.g., steel versus cast iron) and a high component stiffness, which is correlated with high residual welding stresses. The major challenge for these mass-produced components remains both their crack-free weldability and their complex cyclic load capacity [U. Stamm, “Rissfreies Laserstrahlschweißen von Mischverbindungen aus Gusseisen und Einsatzstahl, Jahresbericht Fraunhofer IWS 2006” (2006); X. Shu, “Untersuchungen zum Laserstrahlschweißen von Werkstoffkombinationen aus Gußeisen und Stahl,” Dissertation, Shaker, Band 4/94 (1994), ISBN: 3-8265-0098-9; G. Göbel, “Erweiterung der Prozessgrenzen beim Laserstrahlschweißen heißrissgefährdeter Werkstoffe,” Dissertation, Fraunhofer-IRB-Verlag (2007), ISBN: 978-3-8167-7671-0]. Therefore, this contribution presents practical solutions for weld-compatible joint constructions and the reduction of residual stresses on the basis of a representative transmission design. Specifically, a systematic study is being conducted to understand and qualitatively evaluate effective methods for reducing residual weld stresses in circumferential welds. The recommendations developed as part of this study take particular account of the influence of process modifications, material conditions, and geometric aspects on weldability and component distortion. Here, structural welding simulations are performed and verified by experimental welding trials, including metallographic examinations. To ensure the required component fatigue strength, a practical concept for determining Wöhler curves is presented, which is based on structural mechanical simulations and multiaxial fatigue strength tests on simplified test specimens. The adaptations developed in this way facilitate the production of difficult-to-weld and highly stressed transmission components. In particular, time-consuming and cost-intensive iterations of laser welding tests can be significantly reduced or even eliminated [Brenner et al., “Neuere Ergebnisse zum Schweißen von Eisenbasiswerkstoffen mit Faserlasern, 5. Laser-Anwenderforum,” Strahltechnik Band 28 (2006), pp. 139–148, ISBN: 3-933762-18-9, S]. Furthermore, the systematic investigations provide effective recommendations for phenomenological understanding and solving typical welding challenges in practice [J. Standfuß, “Ganzheitliche innovative fügetechnische Konzepte am Beispiel des PKW-Antriebsstranges,” Fraunhofer Verlag (2010), ISBN: 978-3-8396-0125-9]. This applies, in particular, to load-transmitting components in the fields of e-mobility, aerospace, and industrial engineering [Wagner et al., “Entwickeln und Auslegen von lasergeschweißten Getriebe-komponenten für die Luftfahrt,” DVS-Berichte Band 365 (2020), pp. 62–69, ISBN: 978-3-96144-098-6].

Axially Encoded Mechano-Metafiber Electronics by Local Strain Engineering.

Multimaterial integration, such as soft elastic and stiff components, exhibits rich deformation and functional behaviors to meet complex needs. Integrating multimaterials in the level of individual fiber is poised to maximize the functional design capacity of smart wearable electronic textiles, but remains unfulfilled. Here, this work continuously integrates stiff and soft elastic components into single fiber to fabricate encoded mechano-metafiber by programmable microfluidic sequence spinning (MSS). The sequences with programmable modulus feature the controllable localization of strain along metafiber length. The mechano-metafibers feature two essential nonlinear deformation modes, which are local strain amplification and retardation. This work extends the sequence-encoded metafiber into fiber networks to exhibit greatly enhanced strain amplification and retardation capability in cascades. Local strain engineering enables the design of highly sensitive strain sensors, stretchable fiber devices to protect brittle components and the fabrication of high-voltage supercapacitors as well as axial electroluminescent arrays. The approach allows the scalably design of multimaterial metafibers with programmable localized mechanical properties for woven metamaterials, smart textiles, and wearable electronics.

Axial compressive behavior of low steel–concrete composite walls with multi-partition steel tubes and concrete

Herein an innovative steel–concrete composite walls (SCW) with multi-partition steel tubes and concrete was proposed, and the axial compressive behavior for eliminating the overall stability was firstly investigated based on three axial compression tests. The test parameters included overall height and width-to-thickness ratio of single cavity. The test results validated that low SCW component obtained considerably large axial compressive strength and axial stiffness. Experimental observations demonstrated that under the axial compression, SCW specimens did not occur apparent overall stability, and developed the step-like multi-wave local buckling in the free-weld region of steel faceplate and core-filled concrete crush at the buckling location. Based on the test results, a refined finite element model (FEM) of SCW component was built and validated, and the influences of span-to-height ratio, faceplate thickness, concrete strength, and steel strength were evaluated according to the parametric analysis. The axial compressive strength and axial stiffness of the SCW component were enhanced significantly with increasing span-to-height ratio, steel faceplate thickness, concrete strength, and steel strength. Theoretical equations were proposed based on the SCW component mechanism and parametric simulated results, and the proposed equations offer accurate predictions on the peak axial compressive resistance.

Experimental investigation of 3D printed infill structures for crash absorbing applications

In recent years additive manufacturing technologies have rapidly evolved and are now an effective tool adopted for final components production. 3D printing techniques allow to realize complex geometries that are difficult if not impossible to fabricate by means of conventional production methods. This peculiarity can be exploited to design and manufacture infill structures that can be used in various engineering applications. Combining lightweight 3D printed infill structures with conventional laminate carbon-epoxy composites can be an efficient way to realize light and stiff components that find their optimal use in crash absorbing applications. Plain polymers and fiber reinforced polymers composites represent an interesting solution for additive manufacturing, offering light weight and ductility of the polymeric matrix with the possible enhancement of mechanical properties with the addition of fibers. This work focuses on the study of commercially available 3D printed infill structures via compression tests on cubic samples, deepening understanding about different densities and different strain rates effects on material’s behavior.

A geometric-based method for the mesh stiffness evaluation of spur gears with spatial cracks

Bending fatigue is one of the most common failure modes of gear-based transmissions. Bending fatigue often manifests in the form of cracks at the gear tooth root, which propagates over the time, until a part of the tooth or the whole tooth is removed. Many papers have been published to determine the effect of this failure mode on the gear system dynamics, specifically, the gear mesh stiffness. But the majority of them considered uniform propagation paths and distribution of the crack profile. Moreover, as we know, the effect of the crack initiation point on the mesh stiffness deformation has not been investigated previously.In this study, a geometric-based method is proposed to investigate the effect of non-uniform crack faults on the gear mesh stiffness. This is realized by uncoupling the crack geometry modeling from the stiffness calculation equations, which will enable us to model any crack geometry without any change in the mathematical expressions of the stiffness components. Furthermore, limiting lines of a specific crack shape and initiation point are customized in this study to better consider the effect of random propagated cracks including reascending cracks on the mesh stiffness variation. Simulation results showed that the crack shape, length, and initiation point have a significant effect on the final deformation of the gear mesh stiffness.