Contact Path Research Articles

The kinematic synthesis of involute spiral bevel gears and their tooth contact analysis

In this paper, a mathematical model of the spherical involute tooth surface of a spiral bevel gear whose generating curve is an arc of a circle is built. The parameters on the base cone of the gear are derived from those on the pitch cone of the gear. The algorithm derived can be used for designing the spherical involute surface of straight and spiral bevel gears. The curve of action, the paths of contact and the contact patterns of spiral bevel gears are obtained by the tooth contact analysis (TCA). The TCA results show that: 1) the curve of action is on a spherical surface; 2) the paths of contact do not change with the variation of the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear; 3) the length of the major semi axis of their contact ellipse is determined by the radii of the generating arcs of circles of the tooth surfaces of the pinion and the gear and it does not change during the transmission process. The 3-dimensional (3D) model of the gears is constructed in 3D modeling software based on the proposed method.

Study on ZI worm and helical gear drive with large transmission ratio

A ZI worm and helical gear drive is composed of an involute helicoid worm and a helical gear. Its application is limited due to less studies on the transmission performance with a large transmission ratio. In this paper, the design method of the drive is developed as: the parameters of the ZI worm should be the same as those of the helical gear; the helix angle β1 and the reference diameter factor d1∗ of the ZI worm should be greater than the minimum values proposed. The TCA of the drive shows that: the contact areas on the tooth surfaces are narrow; the effective face width of the ZI worm is larger than that of the helical gear; the contact ratio is less than 2; when the number of threads of the ZI worm changes from 1 to 5, the contact ratio decreases slightly, the effective face width of the worm decreases and that of the helical gear increases correspondingly. The instantaneous transmission ratio is proved theoretically to be constant and the assembly errors cause small shifts of the paths of contact.

Grinding Experiment Research of Face Gear with CNC Machine

A grinding method with CNC machine for face gears is studied. Firstly, the single indexing generating grinding method of face gear is introduced. Then, a grinding experiment of face-gear is performed on a CNC grinding machine with five degrees of freedom, and the tooth deviation is measured on gear measuring center. The tooth surface error is obviously decreased after grinding, and the precision of face gear tooth surface is improved significantly. Finally, a rolling test is performed which indicates that the contact path on face gear before grinding shows discontinuous because the surface deviation is over big. The contact path gets better after grinding.

Computational Framework for Determining Patient-Specific Total Knee Arthroplasty Loading.

The purpose of this work is to describe a computational framework for predicting total knee arthroplasty loads which are necessary for accurate preclinical testing of implant designs. Inputs required include patient knee joint kinematics, and implant type, size, and physiological alignment. Computational models used in the framework include the calculation of knee joint kinematics and kinetics, prediction of the contact path, a model to determine muscle forces, and a force model to obtain parametric solutions for implant forces. The resulting knee implant forces have been validated in two studies, and in both the model accurately predicted differences in knee joint loading. To date, implant contact forces have been predicted for 35 patients with four different implant types. Forces have been calculated for walking, chair, and stair activities.

Method of spiral bevel gear tooth contact analysis performed in CAD environment

Purpose – The purpose of this paper is to present the use of a CAD system for the analysis of meshing of spiral bevel gears. Design/methodology/approach – The TCA computer programs are based on a purely mathematical model and require to get the numerical solution of a set of nonlinear equations. There are situations that the programs fail to obtain the proper solution. In such cases, geometrical gear models defined in CAD environment prove to be a good choice. This paper describes a tool for analyzing tooth contact and transmission errors of spiral bevel gear sets with tooth flanks represented as CAD free-form surfaces. Findings – A new method has been proposed to keep those surfaces in continuous contact in the whole range of meshing of a mating tooth pair. During meshing, the points of contact as well as the corresponding angles of rotation of both the pinion and the ring gear are recorded. Thus, the tooth contact path as well as the motion transmission error graph is determined. Then, the contact pattern that is formed by a set of instantaneous contact ellipses is designated. Practical implications – The TCA results are essential for the assessment of the gear set quality in the early stages of the process of its development. Originality/value – All the results presented in graphical form are very illustrative and easy to interpret.

Tibiofemoral centroid velocity correlates more consistently with cartilage damage than does contact path length in two ovine models of stifle injury

Anterior cruciate ligament (ACL) rupture and/or meniscal injury are known risk factors for post-traumatic osteoarthritis. We tested the hypothesis that increasingly abnormal tibiofemoral centroid path lengths and velocities would correlate with the severity of cartilage damage in injured sheep. Six sheep underwent combined ACL/medial collateral ligament transection (ACL/MCLx), five complete lateral meniscectomy (Mx), and four sham arthrotomy (Sham). Weighted centroids were used to estimate in vivo tibiofemoral cartilage contact path length during stance and the velocity of relative motion. Cartilage morphology was graded at dissection. Ligament transection significantly elongated plateau centroid path lengths and velocities, whereas condyle paths and velocities were reduced. Differences between plateau and femoral velocities (relative centroid velocity) were increased up to 10-fold over baseline values in the medial compartment. Reductions in Mx lateral compartment paths were significantly different from ACL/MCLx paths, but not relative to baseline or Sham values. Importantly, only centroid velocities consistently correlated with cartilage damage in either injury model, suggesting that while path length is valuable in detecting changes in the envelope of joint motion, it may average out meaningful peaks in the rate of relative motion that more closely relate to the mechanisms that might be damaging articular cartilage in these models.

Mode of binding of RNA polymerase α subunit to the phased A-tracts upstream of the phospholipase C gene promoter of Clostridium perfringens

Three phased A5-6-tracts lie upstream of the promoter of plc encoding the α-toxin (phospholipase C) of Clostridium perfringens. The α subunits of C. perfringens RNA polymerase bind directly to the phased A-tracts via the C-terminal domain of the α subunit (αCTD). To identify the amino acid residues involved in the binding of C. perfringens α subunits to the phased A-tracts, 27 amino acid residues in C. perfringens αCTD were substituted with alanine. The affinities of the mutated α subunits for the phased A-tracts were examined by gel shift assays and surface plasmon resonance (SPR). The SPR analyses revealed that the phased A-tracts themselves facilitated a complex formation between the phased A-tracts and C. perfringens α subunits [Kd was 6.1 (±0.3) × 10−8 M], and that Arg261, Asn264, Gly292 and Lys294 in C. perfringens αCTD were critical for the binding to the phased A-tracts. The topology of these amino acid residues on the predicted structure of C. perfringens αCTD indicated a contact path with the phased A-tracts that was similar to that of Escherichia coli αCTD with the upstream (UP) element. On the other hand, SPR analyses at different temperatures (15, 25 and 37 °C) indicated that the affinity of the C. perfringens α subunits for the phased A-tracts increased in a low-temperature-dependent manner, whereas that of the E. coli α subunit for the UP element did not. This suggests that the phased A-tracts may not simply be a subset of the UP element, and that they show specific binding activity with the RNA polymerase α subunit.

Contact processes with random connection weights on regular graphs

In this paper we study the asymptotic critical value of contact processes with random connection weights, sitting on a degree-increasing sequence of r-regular graph Gr. We propose a method to generalize the asymptotics results for λc(Zd) and λc(Td) of classical contact processes as well as of recent work for contact processes on complete graphs with random connection weights. Only the lower bound is rigorously proved; it is conjectured, however, that the lower bound gives the right asymptotic behavior. For comparison purposes we also introduce binary contact path processes with random connection weights, whose asymptotic behavior of the critical value is obtained.

Microstructure and Residual Stresses in Surface Coatings with PTFE Reservoirs

The paper presents the results of experimental study into the microstructure and changes in residual stresses resulting from sliding and rolling/sliding loaded interaction between metallic surface coatings with embedded PTFE reservoirs and various counter faces. It was found that before testing surface coatings had compressive residual stresses. Molybdenum coating with all types of PTFE reservoirs displayed, as a result of testing, decrease in residual stress level unevenly distributed within the contact path. On the other hand, aluminum–bronze coating, regardless the shape of PTFE reservoirs embedded into it, did not show any appreciable change in the residual stress level due to testing. Residual stresses generated under testing conditions in counter materials were typically of the compressive nature.

Reverse engineering of machine-tool settings with modified roll for spiral bevel pinions

Although a great deal of research has been dedicated to the synthesis of spiral bevel gears, little related to reverse engineering can be found. An approach is proposed to reverse the machine-tool settings of the pinion of a spiral bevel gear drive on the basis of the blank and tooth surface data obtained by a coordinate measuring machine(CMM). Real tooth contact analysis(RTCA) is performed to preliminary ascertain the contact pattern, the motion curve, as well as the position of the mean contact point. And then the tangent to the contact path and the motion curve are interpolated in the sense of the least square method to extract the initial values of the bias angle and the higher order coefficients(HOC) in modified roll motion. A trial tooth surface is generated by machine-tool settings derived from the local synthesis relating to the initial meshing performances and modified roll motion. An optimization objective is formed which equals the tooth surface deviation between the real tooth surface and the trial tooth surface. The design variables are the parameters describing the meshing performances at the mean contact point in addition to the HOC. When the objective is optimized within an arbitrarily given convergence tolerance, the machine-tool settings together with the HOC are obtained. The proposed approach is verified by a spiral bevel pinion used in the accessory gear box of an aviation engine. The trial tooth surfaces approach to the real tooth surface on the whole in the example. The results show that the convergent tooth surface deviation for the concave side on the average is less than 0.5 μm, and is less than 1.3 μm for the convex side. The biggest tooth surface deviation is 6.7 μm which is located at the corner of the grid on the convex side. Those nodes with relative bigger tooth surface deviations are all located at the boundary of the grid. An approach is proposed to figure out the machine-tool settings of a spiral bevel pinion by way of reverse engineering without having known the theoretical tooth surfaces and the corresponding machine-tool settings.

Erratum

Takagaki, K., Okajima, I., Kunisato, Y., Nakajima, S., Kanai, Y., Ishikawa, S-I., & Sakano, Y. (2013)) Preliminary assessment of the behavioral activation model in Japanese undergraduate students. Psychological Reports, 112, 1, 47–59. The last seven lines of page 54 and the first four lines of page 55 should be cor-rected to read as follows: “The results suggest that depressive mood has a moderate positive relation-ship with avoidance (path coefficient = .44), a small but negative relationship with activation (path coefficient = −.25), and no significant relationship to attenuation of social contact. Avoidance was positively related to attenuation of social contact (path coefficient = .78). Activation had a moderate negative correlation with attenuation of social contact (path coefficient = −.41). Attenuation of social contact had a moderate negative correlation with frequency of positive reinforcement (path coefficient = −.53). In addition, frequency of positive reinforcement had a moderate negative correlation with depressive mood (path coefficient = −.48; Fig. 4).

Contact stress calculation of high transverse contact ratio spur and helical gear teeth

For contact stress calculations of spur and helical gears, the Hertz equation can be used in combination with a model of load distribution along the line of contact. This load distribution is not uniform due to the changing rigidity of the pair of teeth along the path of contact and has decisive influence on the location and the value of the critical contact stress to consider for calculations. Moreover, the load distribution can be highly influenced for non-standard gearing conditions as the presence of undercut, enlarged tooth addendum or reduced center distance, often present in high transverse contact ratio gears. In this paper, a new calculation method of the contact stress of spur and helical gears with transverse contact ratio greater than 2 is developed. It is based on the Hertz equation and an enhanced model of load distribution, obtained from the minimum elastic potential criterion, suitable for non-standard gearing conditions. A complete study on the critical load conditions and the value of the critical contact stress has been carried out. As a result, a recommendation for pitting load capacity calculations is proposed.

Characteristics of grasping movements in a laboratory and in an everyday-like context

To understand the principles of motor control, it is useful to know whether movements with the same physical constraints can be governed by different rules depending on the behavioral context. We therefore have recently introduced a paradigm in which subjects grasp from the same starting position to the same final object, once as a typical laboratory task and once as part of everyday-like behavior. In the laboratory context, grasping was repetitive, externally triggered and purposeless; in the everyday-like context, it was embedded in a complex activity, intentionally initiated, and served a purpose. Here we present a comprehensive analysis of data from that paradigm. Among 38 response parameters that reflected hand transport, grip shaping and object manipulation, 20 differed significantly between groups. Factor analysis further reduced them to four orthogonal factors: response speed, finger-object contact, response variability, and hand path curvature. This shows, for the first time, that behavioral context influences the execution of grasping movements in four independent ways, possibly reflecting four distinct functional modules in the motor system. This fits well with the view – derived from neurological data – that grasping is controlled by a set of interconnected brain areas which are differentially recruited to achieve different behavioral goals.

Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears

Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.). Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc.) on the efficiency is also presented.

Influence of Thermal Segregation on Asphalt Pavement Compaction

Aggregate and thermal segregation during asphalt compaction can cause premature failures in asphalt pavements. Although aggregate segregation can be identified by visual observation, thermal segregation is impossible to locate in this manner. A thermal imaging technique was used to evaluate thermal segregation. Continuous profiles of mat temperature were recorded during field compaction to identify possible locations of cold spots and rate of temperature loss. The temperature difference was found to be approximately 14°C immediately after laying the material, with scattered cold spots and faster heat loss at the lane interface and edges. Laboratory investigations on roller-compacted asphalt slabs showed that this difference resulted in 5% to 7% higher voids at the edge compared with the center, indicating inferior compaction. The effect of layer interface was also evaluated, and it was found that air void contents were 6% to 10% higher at the interface. The compaction level in these places was improved when slabs were produced in heated molds (simulating a heated adjoining layer): this result indicated that better compaction could be achieved if temperatures at the interface were elevated while laying the material. Three-dimensional finite element modeling was conducted for transient thermal analysis to evaluate heat loss at the interface when a hot mixture (150°C) was laid on a cold layer (5°C) and on a layer at ambient temperature (22°C). The temperature at the contact path between new and existing layers showed that the inner part of the adjoining layer had considerably lower temperature compared with the upper part, with resulting nonuniform compaction between the top and bottom of the layer.

Multibody dynamic models in biomechanics: modelling issues and a new model

In the surgical process of total knee replacement (TKR), it is well known that the three types of failureswhich are; a) unable to reproduce normal knee function, b) bone-implant interface failure c) wear duringuse. These failures are certainly due to the motion and the load that influence the prosthesis components.In this study, the modelling questions of the human knee joint will be discussed in relation only to themultibody dynamics models. Firstly, a summary is presented about the relevant literature, where themodels with their different features are presented and evaluated. The existing models are mainly focusedon the investigation of the ligaments (linear of non-linear properties), the description of the contact path,and contact forces during the motion, kinematics (rotation, abduction and adduction) and even the wearmechanism of the knee joint. The primal advantages of the multibody dynamics models are the easyadaptability in the mechanical parameters to carry out simulations and the connection with CAE programsthat helps the design of new prostheses. A new multibody model is also presented by the authors.

Tool Path Calculation Based on the Actual Tool Profile

Due to tool wear and making errors, calculating the tool path based on the tool theory model has a great deal of influence on the accuracy of surface finishing machining. In order to solve the above problem, a photogrammetry method is used to extract the rotary cutter profile, and then the tool surface is get by letting the fitting profile curve revolves about the cutter axis, finally the cutter contact path is obtained based on the minimal orientation-distance algorithm. Experiments prove the cutter contact path is just on the theory surface of the workpiece. Therefore the accuracy of surface finishing machining will be greatly improved by the method.

Analysis on Isothermal Elastohydrodynamic Lubrication of Orthogonal Face Gear

Face-gear drives have been applied in aviation transmissions, in particular, helicopter transmissions, and the lubrication characteristics are an important indicator for estimating the load-carrying capacity of face-gear teeth. In order to analyze the lubrication performance of the face gear under load, equations for the contact path of the face gear loaded tooth contact analysis (LTCA) were established on the basis of the load equivalent error of alignment (LEEA) and the load distribution among the teeth was calculated. Then a method for calculating the contact area and tooth surface velocity of face-gear drives was studied. Face-gear isothermal elastohydrodynamic lubrication (EHL) dimensionless equations are presented. A multigrid algorithm was used to complete the solution of the minimum film thickness and film pressure of face-gear drives. The lubricant film thickness and film pressure variation in the mesh cycle are expressed using example calculations that provide a theoretical basis for face-gear lubrication design.

Bi-unicondylar knee replacement laxity with changes to simulated soft tissue constraints

Unicondylar knee replacement systems have been shown to perform comparably to total knee replacements, while being much less surgically invasive. Proper ligament balancing, as well as knee laxity, has been shown to play an important role in optimizing kinematic behavior of these implant systems and improving long-term survival of the implant. This study investigates the effect of different simulated ligament laxity conditions of the anterior cruciate ligament and the posterior cruciate ligament on the resulting anteroposterior and mediolateral contact kinematics for medial and lateral pairs of UKR implants with flat and symmetric ultrahigh-molecular-weight polyethylene inserts during force-controlled ISO-14243-1 knee testing simulation. A novel method of capturing the tibiofemoral lowest point contact path was used to calculate the shear plane lowest point contact path kinematics in both the anteroposterior and the mediolateral directions. The results illustrated that multiple clinically relevant soft tissue configurations produce statistically different measured knee kinematics in unicondylar knee replacement systems than is seen in accepted "standard" knee simulator protocols with 95% confidence interval. The observed kinematic differences in anteroposterior and mediolateral movement from what was observed using standard wear testing protocols could aid in the development of unicondylar knee replacement design enhancements that are resistant to varying soft tissue deficiencies.

Enhanced model of load distribution along the line of contact for non-standard involute external gears

The presence of undercut at the tooth root, non-equal addendum on pinion and wheel, non-standard tooth height or non-standard center distance may have decisive influence on the load distribution along the line of contact of spur and helical gear teeth. The curve of variation of the meshing stiffness along the path of contact, quite symmetric respect the midpoint of the interval of contact, loses its symmetry for non-standard geometries and operating conditions. As a consequence, the critical contact points for bending and wear calculations may be shifted from their locations for standard gears. In this paper, a non-uniform model of load distribution along the line of contact of standard spur and helical gears, obtained from the minimum elastic potential criterion, has been enhanced to fit with the meshing conditions of the above mentioned non-standard cylindrical gear pairs. The same analytical formulation of the initial model may be used for the non-standard gears by considering appropriate values of a virtual contact ratio, which are also presented in the paper.