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A contact stress capacity expression is derived for cylindrical worm sets by considering the worm as a helical rack mating with a helical gear. The concept of the equivalent spur gear for a helical gear defined by the instantaneous radius of curvature in the virtual plane of the helical gear is utilized in the contact stress capacity model formulation. All the basic design parameters of worm and gear are incorporated in the expression which explicitly shows the influence of the base and nominal helix angles on the contact stress. By considering the geometry of the worm and gear in engagement, active gear face width and active threaded length of the worm are defined and used to estimate load sharing among gear teeth. This allows the interaction of motion and forces in wormset meshes to be captured by a semi-empirical factor, an aspect not previously considered. The new model also accounts for multiple threaded worms which seem not to have been treated till now. The service load factor expression for cylindrical gears is modified for wormsets to take account of different worm thread profile designs and mesh friction. Four illustrative examples of contact stress computations are carried out using the new contact stress capacity model for wormset designs from different references. The contact stress estimates from the new model are compared with previous solution values. The estimated percentage variances between the previous and new model values are within the range of -4.5% to 0.3%. These variances indicate excellent to a very favorable comparison that should inspire some confidence in using the new model for preliminary design tasks of cylindrical wormsets.

Expressions for the pulsating or beam strengths of many popular metallic gear materials are derived based on the tensile strength and endurance ratio. The strength values predicted are for a reliability of 99% at load cycles corresponding to that of the endurance strength of the materials. The expressions are based on the consideration of the revised Lewis gear root stress formula by treating the design parameters as random variables associated with the lognormal probability density function and application of the Gerber fatigue failure rule. Pulsating strength predictions are compared with those of AGMA estimates for through-hardened steels and other materials. The variances between model predictions and AGMA values for steel and ductile cast iron materials are reasonably low. Low variances between model and AGMA values for high-strength gray cast iron and cast bronze were also observed. However, high variances between model and AGMA values for low-strength gray cast iron and cast bronze were found. Overall, the model estimates are considered sufficiently accurate for preliminary design applications where initial sizes of gears are generated. The study showed that for many metallic gear materials, the average pulsating strength ratio is 0.36 at 99% reliability. Therefore, the suggestion by Buckingham, that the fatigue strength of a gear tooth is approximately one-third (0.333) of the tensile strength of the material is justified.

Helical bevel gears have inclined or twisted teeth on a conical surface and the common types are skew, spiral, zerol, and hypoid bevel gears. However, this study does not include hypoid bevel gears. Due to the geometric complexities of bevel gears, commonly used methods in their design are based on the concept of equivalent or virtual spur gear. The approach in this paper is based on the following assumptions, a) the helix angle of helical bevel gears is equal to mean spiral angle, b) the pitch diameter at the backend is defined as that of a helical gear, and c) the Tredgold's approximation is applied to the helical gear. Upon these premises, the contact stress capacity of helical bevel gears is formulated in explicit design parameters. The new contact stress capacity model is used to estimate the contact stress in three gear systems for three application examples and compared with previous solutions. Differences between the new estimated results and the previous solutions vary from -3% and -11%, with the new estimates being consistently but marginally or slightly lower than the previous solution values. Though the differences appear to be small, they are significant because the durability of gears is strongly influenced by the contact stress. For example, a 5% reduction in contact stress may result in almost 50% increase in durability in some steel materials. The equations developed do not apply to bevel crown gears.

An attempt is made to predict the pitting strength of cast iron and copper alloy materials from their compressive yield or compressive proof strength for a reliability of 99% at 107 load cycles. The compressive yield or compressive proof strength is related to the tensile strength of ductile cast iron and copper alloy materials by a proportionality factor. Two proportionality factors are used for brittle cast iron materials. The pitting strength formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the predictions are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources. The predicted values for gray cast irons had variances in the range of -11.28% to 25%. Ductile cast iron pitting strength estimates deviated from those of AGMA by -30.28% to 1.73% and 16.76% to 36.34% for Austempered ductile irons. The variances obtained for cast bronze were from 11.17% and 14.73%, but the sample size was small. These variances appear to be reasonable due to the many factors that can influence pitting resistance. Since pitting strength data for many grades of cast iron and copper alloys are not available (especially in the public domain), they may be estimated by the expressions developed in this study for initial design sizing. Also, the pitting strength of new cast iron and copper alloy materials could likewise be estimated for initial design sizing. This will eliminate long and costly contact fatigue testing at the initial design phases, which of course is necessary for design validation.

A single expression for estimating the nominal pitting strength of steel materials, based on surface hardness, is developed from first principles for a reliability of 99% at 107 load cycles. It requires the hardness values to be measured in Vicker's hardness scale. The expression may be used for any steel material processed by hot rolling, cold drawing, quenching and tempering or case-hardening. The formulation incorporates a nominal design factor at 99% reliability which is estimated from a probabilistic model based on the lognormal probability density function. Pitting strength estimates from the expression are compared with those of American Gear Manufacturers Association (AGMA) estimates and data from other sources as indicated in Tables 3 and 4. The expression predicts lower values at low hardness but higher values at high hardness. The variance is between - 15.21% and 10.13% for through-hardened steels. For case-hardened steels, the variances range from 14.23% to 20.26% between the estimates and available data. These variances appear to be reasonable considering the many factors involved in pitting resistance. The main advantage of this study is that pitting strength of new steel materials may be estimated for initial design sizing without long and costly contact fatigue testing which of course is necessary for design validation. Also, the estimation method developed may be applied to other materials, metallic and non-metallic. Suggestions are made for estimating some pertinent pitting strength adjustment factors when considering field or service pitting strength.

The open source Field Operation and Manipulation (OpenFOAM) software was used to investigate the performance of a fully premixed, modern high-performance 4-valve, ISO-octane, dual overhead cam (DOHC) engine with quasi-symmetric pent roof combustion chamber running at 1500 revolutions per minute. The peak pressure occurred at the TDC and had a value of about 30 bar. The results from this study show that the maximum combustion temperature occurred at approximately 95 degrees crank angle ATDC and has a volume averaged value of about 2700°K , whereas the actual computed peak temperature was found to be about 3000ºK and it occurred at grid point 12630. The other temperatures which were found to be higher than the volume averaged temperature were found to be in the range 2968.81 ° K to 2974.01 ° K and correspond to grid point positions 12630 to 12633.The flame-wrinkling factor, X = St / Su was found to be in the range 1.0 ≤ X ≤ 3.8. The dynamics of the regress variable b was accurately predicted.

A method for the design sizing task of cylindrical worm gearsets is presented that gives an estimate of the initial value of the normal module. Expressions are derived for the worm pitch diameter of integral and shell worms as well as for the active face width of the gear and the threaded length of the worm. An attempt is made to predict the contact strength of bronze materials against scoring resistance. Four Examples of design sizing tasks of cylindrical worm gears are carried out using the approach presented and the results are compared with previous solutions from other methods. The results for first three examples show excellent comparisons with previous solutions of American Gear Manufacturers Association (AGMA) method. The results of the fourth example are slightly more conservative than those of DIN3999 but are practically similar. Therefore, it appears that a systematic, reliable and more scientifically based method for cylindrical worm drive design sizing has been developed.

A revised Lewis bending fatigue stress capacity model for spur gears is presented and used to study the influence of mesh friction on root stress. It took the original Lewis formula and made modifications for dynamic loads, shear stress, and mesh friction in spur gear design. The study reveals that mesh friction may increase bending stress by up to 6% in enclosed cylindrical gear drives when an average mesh friction coefficient of 0.07 is assumed. A possible increase of 15% in root stress may occur in open gear drives when the mesh friction coefficient is taken as 0.15, a value considered to be representative for properly maintained open drives. To account for mesh frictional load and other factors directly influencing mesh friction, a friction load factor of 1.1 is suggested and introduced to gear service load estimation for enclosed gear drives and 1.15 for open gear drives.

A numerical simulation code was used to conduct a systematic study of the effects of fuel-air equivalence ratios in the range 0.7 ≤ φ ≤ 1.4 and compression ratio, rc = 8.0 on key operating parameters, such as pressure, rate of change of pressure, '/dt' flame extinction temperature, burn rate frequency, combustion efficiency, ηb, source term, mass burn fractions and heat loss in a simulated 5.734 liter, V8 spark-ignition engine. The data shows that the burn rate characteristics of the fuel and oxidizer are qualitatively perfectly correlated. The results also show that as flame extinction/flameout is approached, the fuel consumption rate, Rfu increases rapidly with temperature for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4. The average burn rate frequency (per second), fbr(1/s) varies from 11.2 ≤ fbr ≤ 137.0 for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 The results further show that the fastest fuel consumption rate was for fuel-air equivalence ratio, φ = 1.4 in the time interval, t such that 0.0 ≤ t ≤ 0.61 ms while the slowest corresponds to φ - 0.7 and the corresponding time interval was 0.0 ≤ t ≤ 3.98 ms. Moreover, the data shows that for fuel-air equivalence ratios, φ in the range 0.7 ≤ φ ≤ 1.4 the fuel consumption rate increases monotonically after the initial ignition delay period. The combustion efficiency, ηb of the engine under investigation were found to be in the range of 94.1% ≤ ηb ≤ 94.4% for lean mixtures, that is, for φ < 1.0;the corresponding values of combustion efficiency, ηb for fuel-rich mixtures were in the interval 93.8% ≤ ηb ≤ 94.1%. The other results from this study are summarized in the conclusion.

A zero-dimensional spark ignition engine model was used to conduct a systematic study of combustion dynamics at the top dead center (TDC) position of a 5.734 liter, V8 spark-ignition engine. The model captures all the experimentally observed essential features concerning combustion at the TDC. The combustion dynamics at compression ratios, rc = 9.5, 10.5, 11.5 and 15.5 and fuel-air equivalence ratio, φ = 1.0 were investigated with the numerical model. The results show that for rc = 15.5, the fueloxidizer charge was consumed almost instantaneously. Furthermore, the data shows that it took about 153.0, 52.6, 21.0 and 1.43 ms at compression ratios, rc of 9.5, 10.5, 11.5 and 15.5 respectively for the in-cylinder combustion dynamics to reach a value T* = 1.0. In the last 0.01 ms, for all compression ratios, the rate of change of pressure, dp/dt lies in the range 108 < dp/dt < 1014 Pa/s while the corresponding temperature varies from 2230 ≤ T ≤ 2700 K. The study also shows that as the compression ratio increases both the adiabatic flame temperature and heat of combustion at the top dead center increases monotonically as well.