Tooth Contact Pattern Research Articles

A Clinical Study To Evaluate Tooth Contact Patterns And Correlation With Masticatory Efficiency in Dentulous Subjects.

A variety of functional tooth contact patterns exist in population of young adult patients.The purpose of the present study is to find the relationship between different lateral tooth contact patterns and dental morphology and their effect on masticatory efficiency. Forty young dentulous subjects were selected and their impression with irreversible hydrocolloid was made. Polyvinyl silicone bite registration paste was used to record lateral tooth contact patterns in functional range of mandibular movement. Overjet and overbite including mesiodistal relation of tooth recoded with cast secured in the intercuspal position and masticatory efficiency was determined by calorimetric method by using raw carrot. Among all subjects 15% having canine protection, 55% group function, and 30% balance occlusion. There is positive correlation between age and masticatory efficiency [r=+0.656, p<.01] and negative correlation between overjet and masticatory efficiency [r=-0.409, p<0.01]. In the present study Canine protection occlusion had significantly lower mean masticatory efficiency than group function and balanced occlusion group. This signifies that the masticatory efficiency is dependent on lateral tooth contact patterns.

Analytical and Experimental Tooth Contact Pattern of Large-Sized Spiral Bevel Gears in Cyclo-palloid System

Demand for large-sized spiral bevel gears has increased in recent years and a trend expected to continue. The large-sized spiral bevel gears with equi-depth teeth are usually manufactured based on Klingelnberg cyclo-palloid system. In this paper, the tooth contact pattern of large-sized spiral bevel gears in this system are investigated analytically and experimentally. First, the tooth contact pattern and transmission errors of such gears are analyzed. The analysis method is based on simultaneous generations of tooth surface and simulations of meshing and contact. Next, the large-sized spiral bevel gears are manufactured and the tooth contact pattern of these gears is investigated experimentally. Moreover, the real tooth surfaces are measured using a coordinate measuring machine and the tooth flank form errors are detected using the measured coordinates. It is possible to analyze the tooth contact pattern of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically and experimentally. These analyzed results were compared with experimental ones. As a result, the two results showed a good agreement.

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth microtopography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here, the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

1112 歯面膜要素による円錐ころ軸受の剛性評価(テクスチャリングと低摩擦(1),一般講演)

In order to permit gear units to have higher performance ; e.g., higher efficiency and lower driving noise level, an appropriate tooth contact pattern is required. The tooth contact pattern is affected by the stiffness of bearings, shafts and a gear case. Therefore, it is important in design process of gear units to evaluate the stiffness of these elements precisely. Stiffness of bearings is generally calculated using the method proposed by Harris. However, the stiffness of a tapered roller bearing subject to axial and radial load calculated by the method is different from the our measured one. Thus, the stiffness of tapered roller bearings under axial and radial load was analyzed and evaluated by using Tooth Flank Film Elements (TFFEs) for the contact problem. As a result, the calculated stiffness by TFFEs coincided with measured one. Furthermore, the appropriate bearing stiffness was obtained in consideration of the clearance between the inner and outer raceway and the deviation in the diameter of each tapered roller.

Contact Characteristics of Circular-Arc Curvilinear Tooth Gear Drives

Abstract In this paper, the circular-arc curvilinear tooth gear drive is proposed. The gear and pinion tooth surfaces are generated by two complemented circular-arc rack cutters with curvilinear tooth-traces. According to the theory of gearing, the mathematical model of the proposed gear is developed. The tooth contact analysis technique is utilized to investigate the kinematical errors of circular-arc curvilinear tooth gear drives under different assembly errors. Contact patterns of the circular-arc curvilinear tooth gear drive are simulated by the developed computer-aided tooth contact analysis programs and surface topology method. Numerical examples are presented to show the kinematical errors of the circular-arc curvilinear tooth gear set under different assembly conditions. Relations among the circular-arc tooth profile, curvilinear tooth-trace, contact ratio, contact pattern, and kinematical error are also demonstrated by numerical examples.

Computerized Modeling and Loaded Tooth Contact Analysis of Hypoid Gears Manufactured by Face Hobbing Process

The face hobbing process has been widely applied in automotive industry. But so far few analytical tools have been developed. This makes it difficult for us to optimize gear design. To settle this situation, this study aims at developing a computerized tool to predict the running performances such as loaded tooth contact pattern, static transmission error and so on. First, based upon kinematical analysis of a cutting machine, a mathematical description of tooth surface generation is given. Second, based upon the theory of gearing and differential geometry, conjugate tooth surfaces are studied. Then contact lines are generated. Third, load distribution along contact lines is formulated. Last, the numerical model is validated by measuring loaded transmission error and loaded tooth contact pattern.

Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification

Systematic optimization of the tooth contact pattern under load is an open problem in the design of spiral bevel and hypoid gears. In order to enhance its shape and position, gear engineers have been assisted by numerical tools based on trial-and-error approaches, and/or they have been relying on the expertise of skilled operators. The present paper proposes a fully automatic procedure to optimize the loaded tooth contact pattern, with the advantage of eventually reducing design time and cost. The main problem was split into two identification subproblems: first, to identify the ease-off topography capable of optimizing the contact pattern; second, to identify the machine-tool setting variations required to obtain such ease-off modifications. Both of them were formulated and solved as unconstrained nonlinear optimization problems. In addition, an original strategy to quickly approximate the tooth contact pattern under load was conceived. The results obtained were very satisfactory in terms of accuracy, robustness, and computational speed. They also suggest that the time required to optimize the contact pattern can be significantly reduced compared with typical time frames. A sound mathematical framework ensures results independent of the practitioner’s subjective decision-making process. By defining a proper objective function, the proposed method can also be applied to affect other contact properties, such as to improve the motion graph or to decrease the sensitivity of the transmission to assembly errors. Furthermore, it can be easily adapted to any gear drive by virtue of its systematic and versatile nature.

Simulation of Hypoid Gear Lapping

In the lapping process of hypoid gears, a gear set is run at varying operating positions and under a light load in order to lap the complete tooth surface. Because of the rolling and sliding motion inherent to hypoid gears, the lapping compound acts as an abrasive and refines the tooth surface to achieve smoothness in rolling action and produce high quality gear sets. In this paper, the lapping process is reproduced using advanced modeling tools such as gear tooth vectorial simulation for the tooth surfaces and reverse engineering to analyze the tooth contact pattern of existing gear sets. Test gear sets are measured using a coordinate measurement machine prior to a special lapping cycle where the position of the gear sets on the lapper does not change, and then are remeasured after lapping in order to establish how much and where material was removed. A wear constant named “wear coefficient” specific to the lapping compound is then calculated. Based on the obtained wear coefficient value, an algorithm for simulating the lapping process is presented. Gear sets lapped on the production line at AAM are used for simulation case studies. Initial results show significant scattering of tooth distortion from tooth to tooth and from gear set to gear set, which makes the simulation process difficult. However, it is possible to predict a confidence range within which actual lapping should fall, thereby opening the door to the optimization of the lapping process.

Centrifugal load and its effects on bending strength and contact strength of a high speed thin-walled spur gear with offset web

Abstract This paper discusses effects of centrifugal load on bending strength and contact strength of a thin-walled spur gear used at high speed. A three-dimensional (3D), finite element method (FEM) is presented in this paper for analyzing centrifugal deformations and centrifugal stresses of the thin-walled gear at high speed and the responsive FEM software are developed through many years’ efforts. It is verified that the developed FEM software can calculate correct centrifugal deformations and centrifugal stresses of the thin-walled gear by a cantilever model. Then centrifugal deformations and centrifugal stresses of a thin-walled spur gear with offset web are analyzed with the FEM software at speed range 5000–40,000 rpm. It is found that effects of centrifugal load on deformations and stresses of the thin-walled gear can be neglected when gear speed is below 10,000 rpm. But it is necessary to consider the effects of centrifugal stresses on strength design of the thin-walled gear when the gear speed exceeds 10,000 rpm. Effects of the centrifugal load-deformed thin-walled spur gear on tooth contact pattern, surface contact stress, root bending stress and tooth load-sharing ratio of the gear are also investigated through performing loaded tooth contact analyses of the gear when it is engaged with a solid mating gear under a torque. It is found that centrifugal deformation of the gear at high speed has greater effects on tooth contact pattern, tooth surface contact stress, root bending stress and tooth load-sharing ratio of the pair of gears. Finally it is pointed out that strength calculation methods of a thin-walled gear are quite different from a solid gear. Methods for exact bending strength and contact strength calculations of a thin-walled gear at high speed are presented in this paper.

213 ハイポイドギヤの歯当り移動特性に関する実用研究(OS09-1 ハイポイドギヤ・ウォームギヤI)

The movement behavior of tooth contact pattern is one of major characteristics for hypoid gears. Especially, the VH behavior (i.e. the movement of tooth contact pattern for Vertical and Horizontal displacement) is extremely important not only for mesh quality but also for lapping productivity. This paper visualized the VH behavior of heat-treated hypoid gears by analyzing their ease-off directly using the measured tooth flanks. As a result, it is clarified that the lapping productivity depends upon the VH behavior: (1) bad lapping productivity shows the identical movement directions of tooth contact pattern for the vertical and horizontal displacement. (2) good lapping productivity has a crossed movement directions of tooth contact pattern for vertical and horizontal displacement. (3) Large cutter radius has a good lapping productivity. All analysis results are confirmed by test.

Relationship between occlusal tooth contact patterns and tightness of proximal tooth contact

The aim of this study was to investigate the relationship between occlusal tooth contact patterns and the tightness of proximal tooth contact (TPTC) during clenching. Twenty young adult volunteers with healthy dentition participated in the study. TPTC between the left second premolar (P2) and the first molar (M1) was measured during clenching at the 50% maximum voluntary contraction level in the intercuspal position (ICP). A silicone impression material was used to make an interocclusal record at the ICP in each subject, and interocclusal records were analysed using an image-processing system. Subjects were classified according to the presence or absence of each type (A, B or C) of occlusal contact. Statistical analysis was performed using the Mann-Whitney U-test. The results of this study exhibited a relationship between B-type contact and the TPTC of maxillary teeth. The experimental group with a lack of B-type contact on maxillary P2 and/or M1 showed a statistically greater TPTC than the group with B-type contact on both of these teeth (P < 0.01). These results suggest that occlusal tooth contact patterns have an influence on TPTC during clenching.

Evaluating the Interlobe Clearance and Determining the Sizes and Shapes of All the Leakage Paths for Twin-Screw Vacuum Pump

The maximum sphere method and the minimum cross-section method are proposed to calculate the interlobe clearance between two mating screw rotors and to determine the shapes and sizes of all the leakage paths. These two methods are inspired by the red-lead and tooth-contact pattern and can be used to evaluate the interlobe leakage and to design the mating rotor profiles. The combined results of these two methods provide the basis for an exact evaluation of the fluid leakage, and this feature increases flexibility in geometrical designing and manufacturing of the screw rotors. These methods are also suitable for non-conjugate rotors and contribute to thermal analysis and optimum programming.

Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly errors and tooth modifications

This paper presents three-dimensional (3-D), finite element methods (FEM) to conduct surface contact stress (SCS) and root bending stress (RBS) calculations of a pair of spur gears with machining errors (ME), assembly errors (AE) and tooth modifications (TM). In this paper, firstly positions of a pair of parallel-shaft spur gears with ME, AE and TM are defined in a 3-D coordinate system. Then tooth contact of the pair of gears is assumed on a reference face around the geometrical contact line. This tooth contact on the reference face is called face-contact model of the gears. With this face-contact model, contact reference points on the reference face of one gear are assumed firstly, then a geometrical method that can consider the effects of ME, AE and TM on tooth contact is presented to find the responsive contact reference points on tooth surface of the second gear (the mating gear). Deformation influence coefficients of the pairs of contact points are calculated by 3-D, FEM and loaded tooth contact analysis (LTCA) of the pair of gears with ME, AE and TM is conducted by mathematical programming method. FEM programs are developed to do LTCA, tooth load, SCS and RBS calculations of the pair of spur gears with ME, AE and TM automatically in a personal computer. Tooth contact lengths of a pair of spur gears with lead crowning are calculated by the programs and compared with the measured results. Also, tooth contact pattern and root stains of a pair of spur gears with AE are analyzed by the programs and compared with experimental results. It is found that the calculated results are agreement with the measured ones well. Finally, an example of calculating the real SCS and RBS of a pair of spur gears with ME, AE and TM is given in the paper. It is found that ME, AE and TM exert great effects on SCS and RBS of the gears. SCS and RBS of the same pair of gears are also calculated by ISO and JGMA standards for comparing with the FEM results.

Malocclusion and temporomandibular disorder: a comparison of adolescents with moderate to severe dysfunction with those without signs and symptoms of temporomandibular disorder and their further development to 30 years of age.

A total of 1018 subjects were examined at the age of 11 years, 791 were reexamined at 15 years, 456 at 19 years, and 337 at 30 years. Anamnestic and clinical recordings of temporomandibular disorder (TMD) were made. Morphology, including calculation of peer assessment rating (PAR) scores, was recorded. Previous history of orthodontic treatment was assessed. Muscular endurance was recorded. The subjects completed four psychological measures. The malocclusion prevalence, occlusal contacts, psychological factors, and muscular endurance in subjects with no recorded signs and symptoms of TMD were compared with those with the most severe dysfunction at 19 years of age. The further development of TMD to 30 years of age was followed. PAR scores were significantly higher in the subjects with the most severe dysfunction. Apart from crowding of teeth, no other significant differences were found between the groups with regard to separate malocclusions, tooth contact pattern, orthodontic treatment, or extractions. A greater proportion of subjects with low endurance were found in those with TMD. Significant associations between TMD and general health and psychological well-being as well as the personality dimension of neuroticism and self-esteem were found. During the period from 19 to 30 years, the prevalence of muscular signs and symptoms showed considerable reduction, whereas clicking showed a slight increase. Locking of the joint showed a decrease from 19 to 30 years. One-quarter of the TMD subjects showed complete recovery. Thus, orthodontic treatment seems to be neither a major preventive nor a significant cause of TMD.

Mesh Stiffness and Its Non-Linearity of a Pair of Spur Gears with Machining Errors, Assembly Errors and Tooth Modifications

Three-dimensional (3D), finite element method (FEM) and face-contact model of gear teeth are combined with mathematical programming method to do loaded tooth contact analysis (LTCA) and mesh stiflhess (MS) calculation of a pair of spur gears with machining errors (ME), assembly errors (AE) and tooth modifications (TM). MS of the gears without ME, AE and TM are calculated by the presented method and compared with the results calculated by Ishikawa's equations. It is found that the two results are agreement with each other roughly. Also, tooth contact pattern and root strains of gears with AE are calculated and compared with the measured ones. It is found that the calculated results are agreement with the measured ones well. Then, MS of a pair of spur gears with ME, AE and TM are analyzed with the presented method and effects of ME, AE and TM on MS of the gears are investigated. It is found that ME, AE and TM reduce MS of the gears greatly. It is also found that MS is a 6-order non-linear function of the loaded torque; a 2-order non-linear function of the misalignment error on the plane of action; 2-order non-linear function of the machining errors and a 3-order non-linear function of the quantity of lead crowning. These non-linear relationships of the MS shall be used for exact vibration analysis of a pair of gears with ME, AE and TM in the future research.

べベルギヤ歯面のマスターギヤ基準測定(O.S.04-1 歯車の検査(1),O.S.08-2 ハイポイド・ウォーム(1))

Recently hypoid gear tooth form can be measured with reference to the kinematical surface defined by cutting machine settings. But in most of the cases hypoid gears are still being checked by tooth contact pattern using the master gears. For the straight bevel gears, whose geometric surface is hard to define, situations are the same. In this report the method of creating coordinate data of the existing master tooth are proposed. And the example of bevel gear tooth form measurement reference to it introduced.

Simplified Model for Deformation of Gear Tooth and Meshing Simulation (For Spur Gear Pairs)

A simplified model for calculating deformation of a gear tooth is proposed. In this model, the gear tooth is expressed by many thin gears that appear at the sections perpendicular to the tooth helix. Each thin gear deforms as a cantilever by the tooth load, and load transmission between the thin gears is made by shearing. Therefore, the tooth deformation that generally falls into a three-dimensional problem can be calculated as a two-dimensional problem. Using the proposed model, the transmission errors and tooth contact patterns of the spur gear pairs under the loaded conditions are analyzed in consideration with interference between the tooth tip and the mating tooth root. To confirm the calculated results, the loaded meshing tests were conducted on the gear-testing machine. The test results gave good agreement with the calculated ones.

Optimized Bearing Ellipses of Hypoid Gears1

For given machine tool settings of a universal hypoid gear generator, the tooth contact patterns are computed for the coast and drive side of a hypoid gear drive. Each contact pattern is replaced by a determined tooth-bearing ellipse. The position, shape, and inclination of each bearing ellipse is calculated. By the help of these data, an influence function is designed that describes the influence of supplemental kinematic flank correction motions (modified motions) on the gear-tooth contact. Examples show the influence of helical motion and modified roll. An evaluation function permits the calculation of modified motions which improve the tooth contact either at coast and drive side simultaneously, or only at one of the sides. For a given pair of start-bearing ellipses at coast and drive side, and for given importance weights to the sides, we describe how modified motions can be computed that best fit a given target pair of bearing ellipses.

Tooth contacts at the mandibular retruded position, influence of operator's skill on bite registration.

Occlusal conditions at the retruded contact position (RCP) have been thought to be among the aetiological factors for temporomandibular disorders. However, the role of these occlusal factors still remain unclear. The purpose of a series of studies was to investigate the locations of RCP contacts and to discuss their implication by the authors. In the study reported here, the influence of the operator's skill on bite registration was surveyed. Eighty-six dental students were selected as subjects. One specialist in prosthetic dentistry moved the subject's mandible up and down while guiding it gently backward until it rotated on its retruded axis. Once the initial tooth contacts were established, the operator checked them by using a thin articulating paper (direct method). On the other hand, six younger operators following precise instruction from the specialist about the technique of jaw guidance examined each of the subjects for location of RCP contacts using the indirect method. Silicone-based impression material was used for bite registration while the subject kept the jaw at this contact position (indirect method). Wilcoxon signed rank test was applied to evaluate differences between the expert operator and six younger operators regarding locations of RCP contacts. Results from the expert operator (direct method) showed that tooth contact at the first premolar was most frequently observed and the number of subjects who possessed unilateral tooth contacts was more than that with bilateral tooth contacts. On the other hand, in the case of the indirect method performed by younger operators, tooth contact patterns significantly differed from those of the direct method.

Gear Contact Model and Loaded Tooth Contact Analysis of a Three-Dimensional, Thin-Rimmed Gear

This paper performs loaded tooth contact analysis of a three-dimensional, thin-rimmed gear (3DTRG) by presenting a method that combines the mathematical programming method with the three-dimensional, finite element method (3DFEM). Also, a face-contact and whole gear deformation model is used for the 3DTRG. 3DFEM programs for the contact analysis and strength calculation of the 3DTRG are developed successfully in a personal computer. By using this program, 3D tooth load distributions, tooth root strains and the tooth contact pattern of the 3DTRG are obtained. Calculation results are proved to be correct by experiments.