Applied Mechanics Commons^™

Experiments And Multi-Field Modeling Of Inelastic Soft Materials, Shuolun Wang

Dissertations

Soft dielectrics are electrically-insulating elastomeric materials, which are capable of large deformation and electrical polarization, and are used as smart transducers for converting between mechanical and electrical energy. While much theoretical and computational modeling effort has gone into describing the ideal, time-independent behavior of these materials, viscoelasticity is a crucial component of the observed mechanical response and hence has a significant effect on electromechanical actuation. This thesis reports on a constitutive theory and numerical modeling capability for dielectric viscoelastomers, able to describe electromechanical coupling, large- deformations, large-stretch chain-locking, and a time-dependent mechanical response. This approach is calibrated to the widely-used …

Soft-Microrobotics: The Manipulation Of Alginate Artificial Cells, Samuel Sheckman

Mechanical Engineering Research Theses and Dissertations

In this work, the approach to the manipulation of alginate artificial cell soft-microrobots, both individually and in swarms is shown. Fabrication of these artificial cells were completed through centrifugation, producing large volumes of artificial cells, encapsulated with superparamagnetic iron oxide nanoparticles; these artificial cells can be then externally stimulated by an applied magnetic field. The construction of a Permeant Magnet Stage (PMS) was produced to manipulate the artificial cells individually and in swarms. The stage functionalizes the permanent magnet in the 2D xy-plane. Once the PMS was completed, Parallel self-assembly (Object Particle Computation) using swarms of artificial cells in complex …

Blunt And Ballistic Impacts On Human Head Models: An Analytical And Numerical Study, Yongqiang Li

Mechanical Engineering Research Theses and Dissertations

Head injuries, as a leading cause of death, have become a major health care issue for civilians and soldiers. There has been an urgent need to understand mechanisms of such injuries. The objective of this dissertation research is to study some head injuries and related mechanisms using analytical and computational models.

In Chapter 2, a new analytical (non-linear) model for the impact of a solid sphere on a fluid-filled spherical shell is developed by including the stress wave propagation effect in addition to the Hertzian contact deformations and the shell membrane and bending actions. A simplified (linearized) model incorporating the …

Modeling Of Swimming Cells From Nano-Scale To Micro-Scale, Yicheng Zhao

McKelvey School of Engineering Graduate Student Theses & Dissertations

Certain human genetic diseases -- primary ciliary dyskinesia, infertility, and hydrocephalus -- are characterized by changes in beat frequency and waveform of cilia and flagella. Chlamydomonas reinhardtii, which is a single-cell green alga about ten micrometers in diameter that swims with two flagella, serves as an excellent biological model because its flagella share the same structure and genetic background as mammalian cilia and flagella. This study uses the finite element method to investigate the behavior of C. reinhardtii swimming from nano-scale to micro-scale. At the device-level, micro-scale modeling indicates that well-designed acoustic microfluidic devices can be used to trap groups …

Digital Enhancement Of Analog Measurement Systems For Temperature Compensation Of Strain Gages, Islombek Karimov

Electrical Engineering Theses

Generally known temperature compensation techniques for strain gages (like the use of a dummy gage or the implementation of half- and full-bridge configurations) are not applicable to all strain-measurement situations and cannot fully compensate for all sources of error. Digital Enhancement of Analog Measurement Systems presents a universal method of corrections for these effects in which temperature is measured independently of other variables and ex post facto corrections are computed and applied to digitized readings of the analog measurement system.

A single, linear-pattern strain gage, self-temperature-compensated for steel 1018, has been utilized in a quarter-bridge to measure tensile strain in …

Microheater Array Powder Sintering (Maps) For Printing Flexible Electronics, Nicholas Holt

Graduate Theses and Dissertations

Microheater array powder sintering (MAPS) is a novel additive manufacturing process that uses an array of microheaters to selectively sinter powder particles. MAPS shows great promise as a new method of printing flexible electronics by enabling digital curing of conductive inks on a variety of substrates. MAPS operation relies on establishing a precision air gap of a few microns between an array of microheaters, which can reach temperatures of 600°C, and a layer of conductive ink which can be deposited onto a flexible substrate. This system presents challenges, being: the fabrication of a microheater that can reach suitable temperatures in …

A Nanoindentation Study Of The Fatigue Properties Of Al/A-Si Core-Shell Nanostructures, Jason Steck

Mechanical Engineering Undergraduate Honors Theses

Nanostructure-textured surfaces can reduce friction and increase the reliability of micro- and nanoelectromechanical systems (NEMS/MEMS). For MEMS incorporating moving parts, the fatigue properties of nanostructures pose a challenge to their reliability in long-term applications. In this study, the fatigue behavior of hemispherical Al/a-Si core-shell nanostructures (CSNs), bare hemispherical Al nanodots, and a flat Al/a-Si layered thin film have been studied using nanoindentation and nano-scale dynamic mechanical analysis (nano-DMA) techniques. Fatigue testing with nano-DMA shows that the deformation resistance of CSNs persists through 5.0 × 10⁴ loading cycles at estimated contact pressures greater than 15 GPa. When the a-Si shell …

Phase Transitions In Monochalcogenide Monolayers, Mehrshad Mehboudi

Graduate Theses and Dissertations

Since discovery of graphene in 2004 as a truly one-atom-thick material with extraordinary mechanical and electronic properties, researchers successfully predicted and synthesized many other two-dimensional materials such as transition metal dichalcogenides (TMDCs) and monochalcogenide monolayers (MMs). Graphene has a non-degenerate structural ground state that is key to its stability at room temperature. However, group IV monochalcogenides such as monolayers of SnSe, and GeSe have a fourfold degenerate ground state. This degeneracy in ground state can lead to structural instability, disorder, and phase transition in finite temperature. The energy that is required to overcome from one degenerate ground state to another …

A High-Magnification Uv Lens For High-Temperature Optical Strain Measurements, Robert S. Hansen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Digital Image Correlation (DIC) is an experimental method used to produce full-field strain maps of specimens undergoing deformation. In this measurement, images of a specimen are taken before and after mechanical and thermal loading, then software is used to track deformation and compute strains. DIC has been recently adapted for high-temperature tests by using ultraviolet (UV) range cameras, lenses, and filters to produce the images.

Application of DIC to small length scales and at high temperatures can be performed with proper equipment. However, for these measurements, there is no commercially available high-magnification lens that will allow images to be taken …

Novelis Teaching Table, Phillip Laplante, Robert Hemker, Taylor Mcgriff, Juan Restrepo, Shelly Abraham

KSU Journey Honors College Capstones and Theses

Novelis is a company that specializes in metal casting, recycling, and rolling. They primarily focus on aluminum rolling for cans and car bodies but are an industry leader in numerous related areas. As the rolling process is not taught in most general engineering courses, Novelis periodically teaches new engineers and technicians about the specifics of this relatively mathematically complex process. Most of the current teaching methods are through PowerPoint presentations and group exercises, with minimal hands-on involvement. One of the most useful tools for teaching the rolling process is an actual jeweler’s rolling mill, which Novelis currently possesses, but is …

Numerical Simulation Of A High Strain Rate Biaxial Compression Apparatus, Michael Lagieski

McKelvey School of Engineering Graduate Student Theses & Dissertations

Few experimental methods today are capable of exploring the strength of materials at high strain rates (10⁵ s^-1). Those that are capable, such as the Split Hopkinson Bar, Taylor Anvil and Plate Impact suffer from instability and are generally limited to one dimensional wave propagation. Of particular interest is material response under biaxial compression, similar to that seen in inertial confinement fusion. Laser fusion fuel pellets typically undergo large strain rates as well as plastic deformation and non-linear behavior. This work briefly outlines an experimental procedure designed to replicate these large strain rates under biaxial compression using …

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle

Master's Theses

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing …

Investigation Of Discrete Element Methods For Stud To Turf Interactions, Justin Rittenhouse

Masters Theses

Artificial turf is frequently used in sports today and attempts to advantageously replicate a natural grass/soil playing surface. Despite numerous advantages, the technology is correlated with an increase in injuries. The concept behind this research is to create and validate a discrete element model (DEM) for the ground/foot interaction through the use of open source software. After validation, the goal is to analyze an arrangement of studs to determine what role stud geometry plays on torque [N-mm] and force [N] generation. The validation data was provided through laboratory experiments. Three football studs attached to a rigid bracket were turned at …

Determination Of Chemical Notch, KChem On Aluminum And Steel When Subjected Under Slow Strain Rate Test In Corrosive Environment, Joshua Teo Lee Kuok

Masters Theses

When designing for any mechanical components or system, the question would arise as to how the material would react to the loads subjected on it? Would the component survive its service load? How would it react to environmental corrosion? To answer these questions, the technique used in this thesis paper is the Slow Strain Rate Test (SSRT) method. Aluminum and steel were chosen as the material to be tested in this paper. Al 7075-T651, and Al 6061-T651 was chosen due to its wide range of application, high strength to weight ratio and ease of machinability. It is highly used in …

Experimental Investigation Of A New Spiral Wingtip, Naseeb Ahmed Siddiqui, Mohammed Aldheeb, Waqar Asrar, Erwin Sulaeman

International Journal of Aviation, Aeronautics, and Aerospace

Experiments on the relative merits and demerits of slotted wingtips mimicking a bird’s primary feathers have been performed. The real emargination length of feather tips, their flexibility and curved shapes during cruise are considered in the present study. The experiments were performed at a Reynolds number of 3.7 x 10⁵ on a symmetric flat plate half wing of aspect ratio 3. Lift, drag and pitching moments were measured using a six component aerodynamic balance. Four different shapes inspired by bird primary feathers have been analysed. The rigid curved tip performed the best increasing the L/D ratio by 20%. This …

A 2-D Finite Element Modeling And Simulation Of 3-Roll Forming, Wenbo Zhao

LSU Master's Theses

Medium to large diameter carbon steel pipes are widely used in various applications such as gas and fluid transportation, tunnels construction and building construction. Based on manufacturing techniques and characteristics, they are mainly categorized into three categories: Seamless pipe, Butt-welded pipe and Spiral pipe. The forming of butt-welded and spiral pipe is often performed by a technique called 3-roller bending. While traditional trial-and-error method is costly, the geometry complexity, along with material nonlinearity makes exact theoretical analysis difficult unless heavy simplified assumptions are made. While the forming parameters in the 3-roller forming process of butt-welded pipe has been studied in …

H.F. Hauff Electric Pruner Drive Train, Grady Graff

All Undergraduate Projects

The H.F. Hauff Company invests a large amount of money in developing a quality pruner used in everyday agriculture. Modern electric pruners tend to be expensive while manual tree pruning is very physically demanding. A battery assisted pruner that is light-weight, ergonomic, inexpensive to build and powerful enough to cut branches that a nominal apple tree would possess is the direct affiliation that H.F. Hauff devotes its funding too. A team of engineering students from Central Washington University developed a product with consideration to each of these circumstances. Since hand drills have proven to be user friendly and of abundance …

Exercise Machine Generator, Duane Harbick

All Undergraduate Projects

Exercise “spinning bikes” and bicycle training stands are common ways to maintain fitness and train for cycling. This exercise necessitates the user putting work into the machine by means of pedaling. In many instances the work put into exercise bikes and training stands is not taken advantage of. The objective of this project is an attempt to make use of some of the energy that a person would usually expend during exercise by building a generator that interfaces with multiple spinning bikes and training stands. It uses a synchronous pulley system to interface with the exercise machine and spin a …

Cassette Lockring Removal Tool, Kyle Wright

All Undergraduate Projects

Removal of a bicycle cassette requires additional tools to hold the cassette in place while loosening the cassette lockring. Typically a tool called a chain whip is used to stabilize the cassette, but is difficult to quickly and correctly apply to the cassette. Due to the need for an additional tool to hold the cassette, the user is faced with utilizing both hands while still needing to somehow hold the wheel in place. The lockring is torqued relatively tight and the overall combination of force, ergonomics, and number of tools required makes the task difficult to perform quickly. The objective …

Equibiaxial Flexural Strength Testing Of Advance Ceramics, Ryan T. Jordan

Honors Undergraduate Theses

Ceramics are very important materials with many unique properties used in numerous industrial applications. Ceramics could be very hard and very strong in comparison to metals; however, they are very brittle, thus they are prone to instantaneous and catastrophic failure. Therefore, their reliability is compromised and it is very important to have advanced techniques that allow evaluating their mechanical behavior in many unusual stress states. One of such testing methods is biaxial strength method, that allows to measure properties not only unidirectional, but also in a biaxial way. The research work for this thesis will be built on design and …

Raman Spectroscopy Of The Skeleton Of The Coral Acropora Cervicornis, Zachary C. Shepard

Honors Undergraduate Theses

Coral reefs are an important element of marine ecosystem that are critical to maintain a healthy environment. Unfortunately, in recent years coral reefs are doing poorly and many in parts of the ocean are simply dying. Therefore, study of coral’s structural response to external loads could answer what will happen with their structures, while they exhibit different types of loading. Therefore, the proposition of using in-situ micro-Raman spectroscopy to study skeletons of Acropora cervicornis was used. Coral skeleton samples I subjected to mechanical loading studied their vibrational properties by exciting the material with 532nm visible light. A uniaxial compressive load …

Mimicking Blood Rheology For More Accurate Modeling In Benchtop Research, Lindsey Webb

Honors Undergraduate Theses

To confirm computer simulations and Computational Fluid Dynamics (CFD) analysis, benchtop experiments are needed with a fluid that mimics blood and its viscoelastic properties. Blood is challenging to use as a working fluid in a laboratory setting because of health and safety concerns. Therefore, a blood analogue is necessary to perform benchtop experiments. Viscosity is an important property of fluids for modeling and experiments. Blood is a shear thinning fluid, so it has a decreasing viscosity with higher shear rates. This project seeks to create a blood mimicking fluid for benchtop laboratory use. Numerous fluids with different combinations of water, …

Design And Analysis Of A 3d-Printed, Thermoplastic Elastomer (Tpe) Spring Element For Use In Corrective Hand Orthotics, Kevin Thomas Richardson

Theses and Dissertations--Mechanical and Aerospace Engineering

This thesis proposes an algorithm that determine the geometry of 3D-printed, custom-designed spring element bands made of thermoplastic elastomer (TPE) for use in a wearable orthotic device to aid in the physical therapy of a human hand exhibiting spasticity after stroke. Each finger of the hand is modeled as a mechanical system consisting of a triple-rod pendulum with nonlinear stiffness at each joint and forces applied at the attachment point of each flexor muscle. The system is assumed quasi-static, which leads to a torque balance between the flexor tendons in the hand, joint stiffness and the design force applied to …

Modeling And Analysis For Driveline Jerk Control, Prince Lakhani

Dissertations, Master's Theses and Master's Reports

In modern-day automotive industry, automotive manufacturers pay keen attention to driver’s safety and comfort by ensuring good vehicle drivability, feel of acceleration, limiting jerk and noise. The vehicle driveline plays a critical role to meet these criteria. By using high-fidelity simulation tool such as AMESim®, it is now possible to accurately model the vehicle driveline to be tested for different scenarios. With Simulink®, one can develop an efficient torque-based control system to limit the driveline oscillations and the generated noise. So, a joint simulation is used which provides a platform to evaluate the estimators and control system while considering the …

การประมาณค่าในช่วงเชิงพหุนามลากรานจ์ร่วมกับตัวประกอบถ่วงน้ำหนักนอกช่วงแบบใหม่เพื่อแก้ปัญหาการไหลภายในช่องว่างสี่เหลี่ยมผืนผ้า, อุทัย ประสพชิงชนะ

Chulalongkorn University Theses and Dissertations (Chula ETD)

งานวิจัยนี้มีวัตถุประสงค์เพื่อนำเสนอแผนแบบใหม่ที่มีชื่อว่าแผนแบบ LIP (Lagrange Interpolating Polynomial scheme) และการประมาณค่านอกช่วงแบบใหม่ที่มีชื่อว่าการประมาณค่านอกช่วงแบบ WF-LIP (Weighting Factors with Lagrange Interpolating Polynomial extrapolation) โดยแผนแบบ LIP ถูกใช้สำหรับการประมาณค่าของตัวแปรและอนุพันธ์ของตัวแปรทั้งเทียบกับระยะและเวลาในระเบียบวิธีไฟไนต์วอลู่ม ข้อดีของแผนแบบ LIP คือ เป็นแผนที่มีความแม่นยำลำดับสี่ เป็นแผนที่ง่ายต่อการพัฒนาโปรแกรมที่ใช้การแก้ปัญหาด้วยเม็สซ์ที่ไม่สม่ำเสมอ และเป็นทั้งแผนทางระยะและแผนทางเวลา สำหรับการประมาณค่านอกช่วงแบบ WF-LIP ถูกนำมาใช้ในการหาค่าคาดเดาเริ่มต้นของตัวแปรในแต่ละช่วงเวลาย่อยของปัญหาที่สภาวะไม่คงตัว ซึ่งใช้วิธีการหาคำตอบของแต่ละช่วงเวลาย่อยด้วยวิธีการทำซ้ำ จากผลการตรวจสอบความถูกต้องของคำตอบที่คำนวณจากแผนแบบ LIP และการทดสอบประสิทธิภาพของการประมาณค่านอกช่วงแบบ WF-LIP พบว่า คำตอบที่คำนวณจากแผนแบบ LIP มีความถูกต้องและมีความสอดคล้องกับคำตอบที่นำมาใช้ในการเปรียบเทียบความถูกต้อง ขณะที่การประมาณค่านอกช่วงแบบ WF-LIP สามารถช่วยลดระยะเวลาที่ใช้ในการคำนวณเพื่อหาคำตอบของปัญหาได้สูงสุดถึงร้อยละ 49.69 เมื่อเทียบกับกรณีที่การคำนวณหาคำตอบ โดยไม่ได้ใช้การประมาณค่านอกช่วงแบบ WF-LIP

Garbage Disposal, Madison Popa, Tyler Miller, Mitchell Wheeler, Johnathon Klebe

Williams Honors College, Honors Research Projects

The purpose of this report is to outline a new design for a sink garbage disposal system. The goal of this design is to develop a garbage disposal that could be made for less money, which would turn into a cost savings for the consumer and would lead to an increase in the amount of garbage disposal systems being used throughout the world. This allows the garbage disposal system to be marketed to different parts of the world that currently can’t afford the systems available on the market.

The increased use of garbage disposals, help reduce the amount of organic …

Human Powered Vehicle Design Team: Speed Variable Steering Stabilizer, Eric Miller, Matt Kraml

Williams Honors College, Honors Research Projects

The Human Powered Vehicle Competition (HPVC) is held annually by ASME at a few locations. The University of Akron has competed in the ASME-East and ASME-West competitions over the past handful of years against universities from all over the world. Objectives of each team for the competition are three-fold: vehicle design, racing performance, and innovation. Our senior design project involved working on the innovation concept for ASME-East 2018 held at Penn State University during the weekend of 4/13. Speed variable steering was decided upon by the entire HPVC team early in the design process as the innovation choice for this …

Study Of Asymmetry Configuration Effects On Plate Heat Exchanger Performance, Pearachad Chartsiriwattana

Chulalongkorn University Theses and Dissertations (Chula ETD)

Plate heat exchanger is wildly used in engineering application. Previous studies indicated that flow profile effects to plate heat exchanger overall heat transfer coefficient with various factors that manipulate flow profile. This study aims to observe the effect of manipulation flow by creating non-uniform cross-section area along with the flow by applied asymmetry configuration to plate heat exchanger. The experimental results categorize into two groups. The first group is an asymmetric configuration that enhances the overall heat transfer coefficient by 6.54% compared to symmetric configuration due to promoting heat convection. The other group is an asymmetric configuration that ineffective to …

A Numerical Investigation Of Augmented Heat Transfer In Rectangular Ducts With Ribs, Warissara Tangyotkhajorn

Chulalongkorn University Theses and Dissertations (Chula ETD)

The application of roughness structure of ribs inside a smooth channel is one effective way of heat transfer augmentation, but the accompanied pressure drop could be high. A novel V-rib design with branches was introduced and numerical simulations on the thermo-fluid impact of heat transfer and pressure drop were investigated. The parameters of investigation include the branching number and the pitch ratio of the V-ribs. It appears that increasing the relative pitch ratio serves to improve the overall performance of a roughened channel. The effect of the branching number is only experienced at low pitch ratio. At high pitch ratio, …

สมการเชิงประจักษ์สำหรับความแข็งเกร็งของคู่เฟืองตรงด้วยผลจากระเบียบวิธีไฟไนต์เอลิเมนต์, ทิวา นันตะภักดิ์

Chulalongkorn University Theses and Dissertations (Chula ETD)

ความแข็งเกร็งของเฟืองตรงเป็นพารามิเตอร์สำคัญที่ใช้ในการศึกษาการสั่นสะเทือนของเฟือง หากทราบค่าที่แม่นยำจะสามารถนำไปใช้ในแบบจำลองเพื่อทำนายลักษณะการสั่นสะเทือนของเฟืองตรงได้อย่างถูกต้อง การหาความแข็งเกร็งของเฟืองตรงโดยส่วนใหญ่มักใช้วิธีการวิเคราะห์ หรือใช้ระเบียบวิธีไฟไนต์เอลิเมนต์ ถึงแม้ว่าวิธีเหล่านี้จะสามารถใช้หาค่าความแข็งเกร็งได้ แต่เนื่องจากการคำนวณโดยวิธีการวิเคราะห์มีความซับซ้อน ส่วนการคำนวณด้วยโปรแกรมไฟไนต์เอลิเมนต์มีความยากลำบากในการจัดการสัมผัสของฟันเฟืองและใช้เวลาคำนวณมาก วิธีทั้งสองจึงยังไม่สะดวกในการนำไปใช้งานจริง ในวิทยานิพนธ์นี้จึงมีเป้าหมายที่จะสร้างสมการอย่างง่ายเพื่อคำนวณค่าความแข็งเกร็งของเฟืองตรง สมการที่สร้างขึ้นแบ่งออกเป็น 2 ส่วน ได้แก่ 1) สมการคำนวณความแข็งเกร็งส่วนทรงกระบอกเฟือง ซึ่งสร้างโดยใช้สมการพื้นฐานกลศาสตร์ของแข็ง และ 2) สมการคำนวณความแข็งเกร็งของคู่ฟันเฟือง ซึ่งสร้างโดยใช้ผลการคำนวณพื้นฐานจากระเบียบวิธีไฟไนต์เอลิเมนต์ การสร้างสมการในส่วนที่ 2 ทำโดยเลือกพารามิเตอร์ที่เกี่ยวข้องกับความแข็งเกร็งของฟันเฟือง และจัดรูปแบบสมการให้เหมาะสม ต่อจากนั้นหาความสัมพันธ์ของความแข็งเกร็งของฟันเฟืองที่มีพารามิเตอร์รูปร่างต่างๆ กับตำแหน่งการขบด้วยวิธีการถดถอยแบบพหุนาม โดยใช้ข้อมูลผลการคำนวณด้วยระเบียบวิธีไฟไนต์เอลิเมนต์ของชุดเฟืองจำนวน 8 ชุดที่มีพารามิเตอร์แตกต่างกัน และมีภาระกระทำต่างๆ กัน ความแข็งเกร็งของคู่เฟืองหาได้โดยรวมความแข็งเกร็งทั้งสองส่วนเข้าด้วยกันแบบอนุกรม การตรวจสอบความแม่นยำของสมการที่สร้างขึ้นทำโดยเปรียบเทียบความแข็งเกร็งที่คำนวณได้กับผลจากระเบียบวิธีไฟไนต์เอลิเมนต์ โดยเปรียบเทียบทั้งกรณีความแข็งเกร็งของชุดเฟืองตั้งต้นที่ใช้สร้างสมการ และชุดเฟืองอื่นที่มีค่าพารามิเตอร์ต่างจากชุดเฟืองตั้งต้น รวมทั้งตรวจสอบผลกับงานวิจัยอื่นด้วย ผลที่ได้พบว่าค่าความแข็งเกร็งที่ได้มีค่าใกล้เคียงกัน และมีความคลาดเคลื่อนสูงสุดไม่เกิน 10% ซึ่งแสดงให้เห็นว่าสมการที่สร้างขึ้นสามารถทำนายค่าความแข็งเกร็งได้อย่างถูกต้องและสามารถนำไปใช้กับคู่เฟืองอื่นๆ ได้