Tooth Geometry Research Articles

Lateral cutting forces for different tooth geometries and cutting directions

Lateral (sideways) cutting forces were measured for 6 different tooth geometries when cutting green spruce and pine heartwood. The teeth were intended for use on circular saw blades for the rip sawing of logs. The 6 tooth geometries were designated straight, pointed, bevelled, rounded, trapezoidal and hollowed out. Cutting speed was 15 m/s, feed per tooth was 0.3 mm and the cutting directions were 90°–90° (rip sawing) and 90°–0° (milling), with two different variants of growth ring angles for each direction. The tools were tested in sharp conditions, in dull conditions and in a dull condition with a corner broken off. All lateral forces were small when cutting with sharp teeth, except for the rounded and bevelled teeth. Lateral forces increased with wear, except for a period of initial wear where the lateral forces were reduced. High wear resulted in greater lateral forces, most probably due to unsymmetrical wear. Growth ring direction did not generally affect lateral forces. The teeth with acute corners, which were the straight and hollowed out tooth, were most sensitive to a broken off corner. The lateral forces in the cases of wood cutting at 90°–90° increased less with wear compared to the 90°–0° cases.

A Mathematical Model of Tooth Geometry and Undercutting Condition and Contact Ratio Analysis of the Cosine Gear Drive Generated by a Cosine Rack Cutter

This paper proposes a cosine gear drive provided with a pair of cosine gears which are generated by a cosine rack cutter. Based on the coordinate transformation theory and the theory of gearing, a mathematical model of tooth geometry of the cosine gear drive is developed. The condition of undercutting for the cosine gear generated by a cosine rack cutter is established to determine the minimum number of teeth of non-undercutting. An analytic mathematical model for evaluating contact ratio of the cosine gear drive is built. A cause-and-effect analysis for contact ratio is executed under considering gear module, gear ratio, addendum coefficient, and dedendum coefficient as causes. Results of the analysis show that gear module does not affect contact ratio at all but the other causes do affect contact ratio. The proposed cosine gear drive is able to reduce the size of gear box since the minimum number of teeth of non-undercutting is only 6. Furthermore, the production cost and production lead time of the proposed cosine gear drive are low because it can be manufactured efficiently and economically by regular hobbing machines. The use of CNC machines is not necessary.

Sea urchin tooth mineralization: Calcite present early in the aboral plumula

In both vertebrate bone, containing carbonated hydroxyapatite as the mineral phase, and in invertebrate hard tissue comprised of calcium carbonate, a popular view is that the mineral phase develops from a long-lived amorphous precursor which later transforms into crystal form. Important questions linked to this popular view are: when and where is the crystallized material formed, and is amorphous solid added subsequently to the crystalline substrate? Sea urchin teeth, in which the earliest mineral forms within isolated compartments, in a time and position dependent manner, allow direct investigation of the timing of crystallization of the calcite primary plates. Living teeth of the sea urchin Lytechinus variegatus, in their native coelomic fluid, were examined by high-energy synchrotron X-ray diffraction. The diffraction data show that calcite is present in the most aboral portions of the plumula, representing the very earliest stages of mineralization, and that this calcite has the same crystal orientation as in the more mature adoral portions of the same tooth. Raman spectroscopy of the aboral plumula confirms the initial primary plate mineral material is calcite and does not detect amorphous calcium carbonate; in the more mature adoral incisal flange, it does detect a broader calcite peak, consistent with two or more magnesium compositions. We hypothesize that some portion of each syncytial membrane in the plumula provides the information for nucleation of identically oriented calcite crystals that subsequently develop to form the complex geometry of the single crystal sea urchin tooth.

Tooth geometry and bending stress analysis of conjugate meshing face-gear pairs

The conjugate meshing face-gear pairs are implemented to high shaft angle intersecting axis gears such as the pericyclic transmission system. The meshing face-gear pair tooth surfaces are generated with a mutually conjugate spur shaper. The established tooth geometry and the dimensions of the conjugate face-gear pairs are summarized in this article. Four different example face-gear pairs are generated at various shaft angles and numbers of tooth combinations. Tooth bending stresses of these face-gear pair teeth are investigated based on finite element analysis methods. In these analyses, only single pairs of teeth are investigated. These results are compared to analog the spur gear tooth bending stresses calculated by finite element analysis and standard spur gear stress formulas. Meshing face-gear pair single tooth bending stress levels show approximately 3% to 6% difference from same size spur gear tooth.

Mode-splitting and quasi-degeneracies in circular plate vibration problems: The example of free vibrations of the stator of a traveling wave ultrasonic motor

In systems with rotational symmetry, bending modes occur in doubly-degenerate pairs with two independent vibration modes for each repeated natural frequency. In circular plates, the standing waves of two such degenerate bending modes can be superposed with a 1/4 period separation in time to yield a traveling wave response. This is the principle of a traveling wave ultrasonic motor (TWUM), in which a traveling bending wave in a stator drives the rotor through a friction contact. The stator contains teeth to increase the speed at the contact region, and these affect the rotational symmetry of the plate. When systems with rotational symmetry are modified either in their geometry, or by spatially varying their properties or boundary conditions, some mode-pairs split into singlet modes having distinct frequencies. In addition, coupling between some pairs of distinct unperturbed modes also causes quasi-degeneracies in the perturbed modes, which leads their frequency curves to approach and veer away in some regions of the parameter space. This paper discusses the effects of tooth geometry on the behavior of plate modes under free vibration. It investigates mode splitting and quasi-degeneracies and derives analytic expressions to predict these phenomena, using variational methods and a degenerate perturbation scheme for the solution to the plate’s discrete eigenvalue problem; these expressions are confirmed by solving the discrete eigenvalue problem of the plate with teeth.

Design of Laser Treatment Protocols for Bacterial Disinfection in Root Canals Using Theoretical Modeling and MicroCT Imaging

Theoretical simulations of temperature elevations in root dentin are performed to evaluate, how heating protocols affect the efficacy of using erbium, chromium; yttrium, scandium, gallium, garnet (Er,Cr;YSGG) pulsed lasers for bacterial disinfection during root canal treatments. The theoretical models are generated based on microcomputer tomography (microCT) scans of extracted human teeth. Heat transfer simulations are performed using the Pennes bioheat equation to determine temperature distributions in tooth roots and surrounding tissue during 500 mW pulsed Er,Cr;YSGG laser irradiation on the root canal for eradicating bacteria. The study not only determines the heat penetration within the deep dentin but also assesses potential thermal damage to the surrounding tissues. Thermal damage is assumed to occur when the tissue is subject to a temperature above at least 47 °C for a minimum duration of 10 s. Treatment protocols are identified for three representative tooth root sizes that are capable of maintaining elevated temperatures in deep dentin necessary to eradicate bacteria, while minimizing potential for collateral thermal tissue damage at the outer root surfaces. We believe that the study not only provides realistic laser heating protocols for various tooth root geometries but also demonstrates utility of theoretical simulations for designing individualized treatments in the future.

Elastohydrodynamic Lubrication Analysis of Conjugate Meshing Face Gear Pairs

This paper investigates the nominal elastohydrodynamic lubrication (EHL) characteristics of the conjugate meshing face gears and predicts the mesh efficiency of the pericyclic transmission system. The meshing face-gear tooth geometries and meshing kinematics are modeled. Hertzian contact and the isothermal non-Newtonian lubricant film characteristics of the meshing face-gear pair are investigated. The friction coefficient is calculated with the effects of lubricant behavior and mesh kinematics. Finally, the pericyclic transmission efficiency is calculated as a function of friction coefficient, mesh loads, and mesh kinematics. The Hertzian contact behavior, film thickness, and friction coefficient values are simulated for an example fixed axis face-gear pair rotating at 1000 rpm with 3.4 kN-m torque. The EHL film thickness ranges from 0.1 to 0.25 μm in this example. The average friction coefficient is predicted as 0.05. The efficiencies of three different 24:1 reduction ratio 760 HP pericyclic transmission designs are investigated. The minimum and maximum efficiency in the given design space are 97% and 98.7%, respectively.

Finite element analysis of thermo-mechanical loaded teeth

This paper presents the possibility of applying the finite element method for the analysis of stress level in hard dental tissues, restored with class I dental filling and exposed to thermal and mechanical load. The studies were made on a geometrical model imitating the real geometry of a premolar tooth obtained using the X-ray microtomography technique and CAD software. The distributions of reduced stress defined in accordance with the Huber–Mises–Hencky (H–M–H) hypothesis in hard dental tissues were analyzed, and assessment of the degree of strength of the adhesive layer at the border of the composite restoration and biological tissue was attempted. The application of numerical simulations (Abaqus) enables real assessment of the tooth tissue strength, which allows assessing the risk of unsuccessful dental treatment, and helps prepare rational methods of preventing tooth damage resulting from load. Maximum reduced stresses were located in areas of the external load attachment and exceeded 668.8MPa with the force loading and 34MPa and 58.4MPa with temperature loading of 55°C and 5°C respectively. Superposition of loadings has produced maximum stresses of 669.4MPa in the case of 5°C.

Comparison of tooth profiles and oil formulation focusing lower power losses

Environmental awareness, lower consumption of raw materials and longer life of equipment are main concerns nowadays and are leading to the research and development of lubricants and equipment to access those requirements. In this study, the power loss performance of three different tooth profile geometries, developed with the purpose of decreasing power losses while keeping the predicted life, were tested and evaluated in a FZG test rig. The path to reduce power losses was based on the decrease of the module, the increase of the helix angle and increase of the addendum modification coefficients in order to reduce the path of contact, i.e. the sliding velocity. The power loss behaviour of two different lubricants was also evaluated for each tooth profile geometry considered. The influence of the oil level in the gearbox was also evaluated. One of the lubricants has an ester base while the other has a polyalphaolefin base and both are fully formulated. An energetic model was developed for the FZG test gearbox and applied to these tests to improve the knowledge about the influence of tooth geometries as well as lubricant formulation in the power losses and coefficient of friction between gear teeth. The developed geometries showed that the path followed for the reduction of power losses produced the expected results and can be implemented with success on gear design.

Feasibility study on roller-cone bit wear detection from axial bit vibration

Previous studies reported that the peaks of a power spectrum for roller-cone bit axial vibration move to higher frequencies with the progression of bit-tooth wear. This result implies that monitoring and analyzing roller-cone bit vibration could be a new real-time detection method for downhole bit wear conditions.In this study, the dynamics of roller-cone bit axial vibration were modeled to quantitatively evaluate bit-tooth wear. The model includes the kinematics of roller-cone bit motion and a model for bit-tooth/rock interaction that considers the detailed geometry of a worn tooth. By sequentially solving the equation of motion with increments of cone rotation angles, the time history of axial bit vibration was simulated.The developed model was validated by comparing the power spectral densities for the simulated time histories of axial bit vibration with the experimental results of full-scale drilling tests. Detection of bit-tooth wear, bearing failure, and broken teeth was studied from a feasibility perspective.

Development of Advanced Broaching Tool for Machining Titanium Alloy

Broaching is a precision multipoint metal removal operation normally employed for manufacturing variety of complex parts having either internal or external features. Broaching can produce high precision and good surface finish at a high metal removal rate. The unique feature of a broach tool is that the feed/depth of cut for the teeth is built into the broach unlike other cutting tools. The tool design (e.g., rise per tooth and tooth geometry) play a vital role in the broach performance. A specially adapted machine tool modified to investigate a single broach tooth has been used. Cutting forces and material removal rate have been measured during experimental work for different combination of broaching parameters and broach tool geometry. The effect of the parameters on the surface quality produced has been established. The characteristics of chips formed have also been defined. Finally, optimum tooth geometry and rise per tooth have been recommended for tool performance, broached surface quality and efficient chip formation. The information provided in this paper will be beneficial for broach tool designers and manufacturing engineers.

Influence of Gear Design on Tool Load in Bevel Gear Cutting

During gear design, the tooth geometry is optimized towards the required running behavior. Pressure angle and tooth root radius of the gearset are among the influencing factors. As the tools in bevel gear cutting are specially designed for each gearset, the tool profile geometry is defined by the gear geometry. The objective of this work is to analyze the influence of the tool profile geometry on thermal and mechanical tool load during bevel gear machining. By means of a finite element based machining simulation the chip formation in bevel gear cutting of ring gears is calculated. The simulation results show a significant thermal and mechanical load maximum at the tool corner, where the maximal wear occurs. The variation of the tool profile geometry shows a high influence of the tool pressure angle and the tool corner radius on the tool load at the tool corner.

Development of Advanced Broaching Tool for Machining Titanium Alloy

Broaching is a precision multipoint metal removal operation normally employed for manufacturing variety of complex parts having either internal or external features. Broaching can produce high precision and good surface finish at a high metal removal rate. The unique feature of a broach tool is that the feed/depth of cut for the teeth is built into the broach unlike other cutting tools. The tool design (e.g., rise per tooth and tooth geometry) play a vital role in the broach performance. A specially adapted machine tool modified to investigate a single broach tooth has been used. Cutting forces and material removal rate have been measured during experimental work for different combination of broaching parameters and broach tool geometry. The effect of the parameters on the surface quality produced has been established. The characteristics of chips formed have also been defined. Finally, optimum tooth geometry and rise per tooth have been recommended for tool performance, broached surface quality and efficient chip formation. The information provided in this paper will be beneficial for broach tool designers and manufacturing engineers.

Stresses in Teeth and Overlying Crowns

A complete cast crown allows the operator to modify axial tooth contour. The margin should be smooth and distinct and its width has to allow adequate bulk of metal at the margin. The objective of this study was to evaluate, by finite element analysis, the influence of different degree of taper and marginal designs for cast crown preparations, on the stress distribution in teeth and crowns. As experimental model an upper first molar was used. The geometry of the intact tooth were obtained by 3D scanning. The tooth preparations and the complete cast crowns were designed. Models were exported in a finite element analysis software for structural simulations. Von Mises equivalent stresses were calculated and their distribution was plotted graphically. Numerical simulations provide a biomechanical explanation for stress distribution in prepared teeth and overlying crowns.

A Note on Flow Regimes and Churning Loss Modeling

The purpose of this study is to investigate the various fluid flow regimes generated by a pinion running partly immersed in an oil bath and the corresponding churning power losses. In a series of papers, the authors have established several loss formulae whose validity depends on two different flow regimes characterized via a critical Reynolds number. Based on some new measurements for transient operating conditions, it has been found that the separation in two regimes may be not accurate enough for wide-faced gears and high temperatures. An extended formulation is therefore proposed which, apart from viscous forces, introduces the influence of centrifugal effects. The corresponding results agree well with the experimental measurements from a number of gears and operating conditions (speed and temperature). Finally, the link between churning and windage losses is examined and it is concluded that the physical mechanisms are different thus making it difficult to establish a general correlation between the two phenomena. In particular, it is shown that tooth geometry is of secondary importance on churning whereas, the air-lubricant circulation being different for spur and helical gears, it substantially impacts windage.

Personalized Tooth Shape Estimation From Radiograph and Cast

Three-dimensional geometric information of teeth is usually needed in pre- and postoperative diagnoses of orthodontic dentistry. The computerized tomography can provide comprehensive 3-D teeth geometries. However, there is still a discussion on computed tomography (CT) as a routine in orthodontic dentistry due to radiation dose. Moreover, the CT is useless when a dentist needs to extract 3-D structures from old archive files with only radiographs and casts, where patient's teeth changed ever since. In this paper, we propose a reconstruction framework for patient-specific teeth based on an integration of 2-D radiographs and digitized casts. The reconstruction is under a template-fitting framework. The shape and orientation of teeth templates are tuned in accordance with patient's radiographs. Specially, the tooth root morphology is controlled by 2-D contours in radiographs. With ray tracing and a contour plane assumption, 2-D root contours in radiographs are projected back to 3-D space, and guide tooth root deformations. Moreover, the template's crown is deformed nonrigidly to fit digitized casts that bear patient's crown details. The system allows 3-D tooth reconstruction with patient-specific geometric details from just casts and 2-D radiographs.

Evolutionary Morphology, Platyrrhine Evolution, and Systematics

This special volume of the Anatomical Record focuses on the evolutionary morphology of New World monkeys. The studies range from three-dimensional surface geometry of teeth to enamel ultrastructure; from cranioskeletal adaptations for eating leaves and seeds to the histology of taste bud proxies; from the architecture of its bones to the mechanoreceptors of the tail's skin; from the physical properties of wild foods to the feeding biomechanics of jaws and skull; from the shapes of claws and fingertips, and of elbows, to the diversity and morphology of positional behavior; from the vomeronasal organ and its biological roles to links between brains, guts, sociality, and feeding; from the gum-eating adaptations of the smallest platyrrhines to the methods used to infer how big the largest fossil platyrrhines were. They demonstrate the power of combining functional morphology, behavior, and phylogenetic thinking as an approach toward reconstructing the evolutionary history of platyrrhine primates. While contributing new findings pertaining to all the major clades and ecological guilds, these articles reinforce the view that platyrrhines are a coherent ecophylogenetic array that differentiated along niche dimensions definable principally by body size, positional behavior, and feeding strategies. In underlining the value of character analysis and derived morphological and behavioral patterns as tools for deciphering phylogenetic and adaptational history, doubts are raised about a competing small-bore morphological method, parsimony-based cladistic studies. Intentionally designed not to enlist the rich reservoir of platyrrhine evolutionary morphology, an empirical assessment of the costs incurred by this research stratagem reveals inconsistent, nonrepeatable, and often conflicting results.

Low torque loss gears: austempered ductile iron versus carburized steel

Low-loss power transmission gears operate at lower temperature than conventional ones because their teeth geometry is optimized to reduce friction. The main objective of this work is to compare the operating stabilization temperature and efficiency of low-loss austempered ductile iron (ADI) and carburized steel gears. Three different low-loss tooth geometries were adopted (types 311, 411 and 611, all produced using standard 20° pressure angle tools) and corresponding steel and ADI gears were tested in a FZG machine. The results obtained showed that low-loss geometries had a significant influence on power loss, gears 611 generating lower power loss than gears 311. At low speeds (500 and 1000 rpm) and high torque ADI gears generated lower power loss than steel gears. However, at high speed and high torque (high input power and high stabilization temperature) steel gears had better efficiency.

Research on Overlying Strata Movement and Deformation under the Conditions of Shortwall and Longwall Mining

We simulate the rock’s movement and defoemation process in the coal mining, and research the overlying strata movement and deformation under the conditions of shortwall and longwall mining. The conclusion of the experiment indicates: with the method of double deck mining, the rock’s damage level in caving layer is more serious, the final subsidence curve presents a tooth geometry. The subsidence curve of fissure and flexure zone is simily with the longwall mining condition.

Evaluation of the Integrity of a Human Molar under Compressive Loading Using 3-D Axial Tomography

This paper reports a structural integrity analysis of a first human molar tooth. In this study, the loading condition caused by different sort of food was simulated. In order to cover a wide range, the resultant stress field evaluation was evaluated when a compressive load varied between 70N and 150 N. The finite element model was created using 3-D Computed Tomography and SCAN IP V.4 software. In the experimental analysis, reflective photoelasticity was used and the specimens were loaded with a Universal Testing Machine. The results show that stress concentrations are developed over the crown surface. The range of the top von Mises stress, for the loading cases mentioned above, is between 1.05 MPa and 3.46 MPa. The tooth geometry distributes gently the resultant stress on its root.