Ideal spiral bevel gears: A new approach to surface geometry

The fundamental geometrical characteristics of spiral bevel gear tooth surfaces are discussed. The parametric representation of an ideal spiral bevel tooth is developed based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics

Compliance and stress sensitivity of spur gear teeth

The magnitude and variation of tooth pair compliance with load position affects the dynamics and loading significantly, and the tooth root stressing per load varies significantly with load position. Therefore, the recently developed time history, interactive, closed form solution for the dynamic tooth loads for both low and high contact ratio spur gears was expanded to include improved and simplified methods for calculating the compliance and stress sensitivity for three involute tooth forms as a function of load position. The compliance analysis has an improved fillet/foundation. The stress sensitivity analysis is a modified version of the Heywood method but with an improvement in the magnitude and location of the peak stress in the fillet. These improved compliance and stress sensitivity analyses are presented along with their evaluation using test, finite element, and analytic transformation results, which showed good agreement

Dimpling process in cold roll metal forming by finite element modelling and experimental validation

The dimpling process is a novel cold-roll forming process that involves dimpling of a rolled flat strip prior to the roll forming operation. This is a process undertaken to enhance the material properties and subsequent products’ structural performance while maintaining a minimum strip thickness. In order to understand the complex and interrelated nonlinear changes in contact, geometry and material properties that occur in the process, it is necessary to accurately simulate the process and validate through physical tests. In this paper, 3D non-linear finite element analysis was employed to simulate the dimpling process and mechanical testing of the subsequent dimpled sheets, in which the dimple geometry and material properties data were directly transferred from the dimpling process. Physical measurements, tensile and bending tests on dimpled sheet steel were conducted to evaluate the simulation results. Simulation of the dimpling process identified the amount of non-uniform plastic strain introduced and the manner in which this was distributed through the sheet. The plastic strain resulted in strain hardening which could correlate to the increase in the strength of the dimpled steel when compared to plain steel originating from the same coil material. A parametric study revealed that the amount of plastic strain depends upon on the process parameters such as friction and overlapping gap between the two forming rolls. The results derived from simulations of the tensile and bending tests were in good agreement with the experimental ones. The validation indicates that the finite element analysis was able to successfully simulate the dimpling process and mechanical properties of the subsequent dimpled steel products

How to determine spiral bevel gear tooth geometry for finite element analysis

An analytical method was developed to determine gear tooth surface coordinates of face milled spiral bevel gears. The method combines the basic gear design parameters with the kinematical aspects for spiral bevel gear manufacturing. A computer program was developed to calculate the surface coordinates. From this data a 3-D model for finite element analysis can be determined. Development of the modeling method and an example case are presented

On Hirth Ring Couplings: Design Principles Including the Effect of Friction

Rings with Hirth couplings are primarily used for the accurate positioning of axial-symmetric components in the machine tool industry and, generally, in mechanical components. It is also possible to use Hirth rings as connection tools. Specific industries with special milling and grinding machines are able to manufacture both tailor made and standard Hirth rings available on stock. Unfortunately, no international standard (for instance ISO, DIN or AGMA) is available for the production and the design of such components. In the best-case scenario, it is possible to find simplified design formulae in the catalogue of the suppliers. The aim of this work is to provide some accurate formulae and computational methods for design to provide better awareness on the limitations and the potential of this type of connection. The work consists of five parts: (i) a review of the base calculation derived mainly from the catalogues of manufacturers; (ii) an improved calculation based on a new analytical method including the friction phenomenon; (iii) an experimentation run for validating the method; (iv) a case study applied to a machine tool; and, (v) a closed form formulation to determine an upper threshold for friction, thus ensuring the Hirth coupling regular performance

The biomechanical function of periodontal ligament fibres in orthodontic tooth movement

Orthodontic tooth movement occurs as a result of resorption and formation of the alveolar bone due to an applied load, but the stimulus responsible for triggering orthodontic tooth movement remains the subject of debate. It has been suggested that the periodontal ligament (PDL) plays a key role. However, the mechanical function of the PDL in orthodontic tooth movement is not well understood as most mechanical models of the PDL to date have ignored the fibrous structure of the PDL. In this study we use finite element (FE) analysis to investigate the strains in the alveolar bone due to occlusal and orthodontic loads when PDL is modelled as a fibrous structure as compared to modelling PDL as a layer of solid material. The results show that the tension-only nature of the fibres essentially suspends the tooth in the tooth socket and their inclusion in FE models makes a significant difference to both the magnitude and distribution of strains produced in the surrounding bone. The results indicate that the PDL fibres have a very important role in load transfer between the teeth and alveolar bone and should be considered in FE studies investigating the biomechanics of orthodontic tooth movement. © 2014 McCormack et al

An Investigation of the Dynamic Response of Spur Gear Teeth with Moving Loads

Two concepts relating to gear dynamics were studied. The first phase of the analysis involved the study of the effect of the speed of a moving load on the dynamic deflections of a gear tooth. A single spur gear tooth modelled using finite elements was subjected to moving loads with variable velocities. The tooth tip deflection time histories were plotted, from which it was seen that the tooth tip deflection consisted of a quasistatic response with an oscillatory response superimposed on it whose amplitude was dependent on the type of load engagement. Including the rim in the analysis added flexibility to the model but did not change the general behavior of the system. The second part of the analysis involved an investigation to determine the effect on the dynamic response of the inertia of the gear tooth. A simplified analysis using meshing cantilever beams was used. In one case, the beams were assumed massless. In the other, the mass (inertia) of the beams was included. From this analysis it was found that the inertia of the tooth did not affect the dynamic response of meshing cantilever beams

Modeling dynamics and stability of 5-axis milling processes

5-axis milling is an important machining process for several industries such as aero-space, automotive and die/mold. It is mainly used in machining of sculptured surfaces where surface quality is of extreme importance. Being one of the most important prob-lems in machining, chatter vibrations must be avoided in manufacturing of these com-ponents as they result in high cutting forces, poor surface finish and unacceptable part quality. Chatter free cutting conditions for required quality with higher productivity can be determined by using stability models. Up to now, dynamic milling and stability models have been developed for 3-axis milling operations; however the stability of 5-axis proc-esses has never been modeled. In this paper, a stability model for 5-axis milling opera-tions is proposed. The model can consider the 3D dynamics of the 5-axis milling proc-ess including effects of all important process parameters including lead and tilt angles. Due to the complex geometry and mechanics of the process, the resulting analytical equations are solved numerically in order to generate the stability diagrams

Machining strategy development in 5-axis milling operations using process models

Increased productivity and part quality can be achieved by selecting machining strategies and conditions properly. At one extreme very high speed and feed rate with small depth of cut can be used for high productivity whereas deep cuts accompanied with slow speeds and feeds may also provide increased material removal rates in some cases. In this study, it is shown that process models are useful tools to simulate and compare alternative strategies for machining of a part. 5-axis milling of turbine engine compressors made out of titanium alloys is used as the case study where strategies such as flank milling (deep cuts), point milling (light cuts) and stripe milling (medium depths) are compared in terms of process time by considering chatter stability, surface finish and tool deflections