On a Gearing Problem in Conventional Harmonic Drives With Involute Toothed Gear Set

Circular pitches of flex spline teeth of a ‘Strain Wave Gearing’, also known as a ‘Harmonic Drive’, are deformed when the Strain Wave Generating Cam is inserted into the flex spline cup. In the present work the deformed pitch distances considering that flex spline teeth remain rigid while the rim deforms, are estimated. No applied load is considered. It is also shown that if the cam is elliptical then the pitch curve is not an ellipse and vice versa. Geometries of such curves can be defined following the analysis presented in this paper. Cases of both undeformed flex spline with circular spline and deformed flex spline with circular spline, with involute teeth, are considered to find out tooth positions. Geometries of involute teeth profiles in mesh are examined and compared considering oval shaped (on deformation) base drum of flex spline where as base circle of circular spline remained circular.

Deformations and Stresses in Face-Hobbed Spiral Bevel Gears

In this study an attempt is made to predict displacements and stresses in face-hobbed spiral bevel gears by using the finite element method. A displacement type finite element method is applied with curved, 20-node isoparametric elements. A method is developed for the automatic finite element discretization of the pinion and the gear. The full theory of the generation of tooth surfaces of face-hobbed spiral bevel gears is applied to determine the nodal point coordinates on tooth surfaces. The boundary conditions for the pinion and the gear are set automatically as well. A computer program was developed to implement the formulation provided above. By using this program the influence of design parameters and load position on tooth deflections and fillet stresses is investigated. On the basis of the results, obtained by performing a big number of computer runs, by using regression analysis and interpolation functions, equations for the calculation of tooth deflections and fillet stresses are derived.

Analytical Model of the Efficiency of Spur Gears: Study of the Influence of the Design Parameters

An analytic model to compute the efficiency of spur gears has been developed. It is based on the application of a non-uniform model of load distribution obtained from the minimum elastic potential criterion and a simplified non-uniform model of the friction coefficient along the path of contact. Both conventional and high transverse contact ratio spur gears have been considered. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. From this model, a complete study of the influence of some design parameters (as the number of teeth, the gear ratio, the pressure angle, the addendum modification coefficient, etc.) on the efficiency is presented.

Comparison of Numerical Methods for Determining Torsion Stiffness of Automotive Chassis

The torsion stiffness of an automotive chassis can be determined using an analytical approach based purely on geometry, using an experimental method, or alternatively by employing a Finite Element Analysis (FEA) process. These three methods are suitable at different design stages and combined together could prove to be practical methods of determining the torsion stiffness of a chassis. This paper describes and compares two distinct FEA processes to determine the torsion stiffness of an automotive chassis during the detailed design stage. The first process iteratively applies forces to the model and records displacements, while the second process gradually applies vertical displacements in place of force to determine the torsional stiffness threshold. Each method is explained and supported with a case study to provide a basis of comparison of the results.

Soil Modeling Using FEA and SPH Techniques for a Tire-Soil Interaction

In recent years, the advancement of computerized modeling has allowed for the creation of extensive pneumatic tire models. These models have been used to determine many tire properties and tire-road interaction parameters which are either prohibitively expensive or unavailable with physical models. More recently, computerized modeling has been used to explore tire-soil interactions. The new parameters created by these interactions were defined for these models, but accurate soil constitutive equations were lacking. With the previous models, the soil was simulated using Finite Element Analysis (FEA). However, the meshless modeling method of Smooth Particle Hydrodynamics (SPH) may be a viable approach to more accurately simulating large soil deformations and complex tire-soil interactions. With both the FEA and SPH soils modeled as elastic-plastic solids, simplified soil tests are conducted. First, pressure-sinkage tests are used to explore the differences in the two soil-modeling methods. From these tests, it is found that the FEA model supports a surface pressure via the tensile forces created by the stretching of the surface elements. Conversely, for the SPH model, the surface pressure is supported via the compressive forces created by the compacting of particles. Next, shear-displacement tests are conducted with the SPH soil (as this test cannot easily be performed with an FEA soil model). These shear tests show that the SPH soil behaves more like clay in initial shearing and more like sand by exhibiting increased shearing due to vertical loading. While both the pressure-sinkage and shear-displacement tests still show that a larger particle density is unnecessary for SPH soil modeling, the shear-displacement tests indicate that an elastic-plastic material model may not be the best choice.

Performance of Injection-Molded Plastic Helical Gears Finished by Hot Rolling

A hot-roll finishing was proposed as a simple finishing method for plastic gears. In the hot-roll finishing, plastic work gears are finished by meshing with a heated copper die wheel. In the previous study, a hot-roll finishing rig for plastic gears was developed, and it was confirmed that tooth profiles of hobbed plastic gears are improved by the finishing. Thus, the hot-roll finishing could also be effective for injection-molded plastic gears. In the present paper, appropriate hot-roll finishing procedures for injection-molded polyoxymethylene (POM) helical gears were pursued. In the injection molding, an inadequate mold easily allows large slope deviations on a tooth profile and trace. The hot-roll finishing can reduce the slope deviations, but induces form deviations especially on the profile. Tests of injection-molded and hot-roll-finished plastic gears were performed on a self-produced gear roller test rig and a self-produced fatigue rig, and a transmission error and load capacity were estimated. Compared with injection-molded gears, hot-roll-finished plastic gears showed small transmission error, while a load capacity was at the almost same level. As a result, the hot-roll finishing is effective for improving a transmission error of injection-molded plastic gears.

Smooth Shutdown Control Strategy of Hybrid Engines for Commercial Vehicle Hotel Mode

Long-haul commercial vehicles provide the hotel mode with a desirable comfort cabin for drivers to have rest. During this mode, sustainable power requirement on the on-board battery asks for occasional engine-on/off to maintain the battery SOC level, neither deeply charged nor overcharged. With the conventional engine-only-driven powertrains, there is a great challenge to deliver smooth engine on/off processes during the hotel mode in order to maintain the cabin as quiet and vibrationless as possible. But for the electric hybrid powertrain system, such a challenge can be addressed with the involvement of the hybrid motor/generator (M/G) to achieve smooth engine crank and shutdown. Apparently it is feasible to control M/G to mitigate discomfortable vibrations inside the cabin caused by periodic engine shutdowns for recharging the battery. In this paper, a pole placement control (PPC) with application of the hybrid M/G is developed to dampen out this kind of adverse vibrations which are transmitted from engine/gearbox to the cabin through the chassis structure and cabin mounts. More specifically, the PPC uses the motor speed as a feedback control signal to create a desirable motor torque command so that the vibration transmission could be abated. In the end of this paper, field testing data from a prototype hybrid truck will be presented to demonstrate the effectiveness of this innovative PPC strategy.

On Failure Problem of Gears Made From Very High Strength Steel

Some typical examples of failure of gears made from very high strength steel are shown and its trigger and whose causes are discussed: Many of such failure are triggered by tooth side edge contact or tooth tip edge contact and meshing-in of the wear debris. The limit of validity of the traditional methods for load carrying capacity of gears exists in the fact that they are based on the theory of contact of tooth flanks that realize conjugate or almost conjugate action of gears. To be able to design reliable gears made from very high strength steel, a principle is shown that suggests a new method for tooth form modification and of longitudinal crowing modification to avoid such failure. Metallurgical problem of gear material and special heat treatment aiming high surface hardness is also discussed.

Tooth Root Stresses of Helical Gear Pairs With Unequal and Offset Face Widths

In this study, tooth root stresses of helical gear pairs with different combinations of face width increase and offsets were analyzed. Contact face width was kept constant. The variables studied were face width and gear faces offset. The well-known LDP – Load Distribution Program was used to calculate tooth root stresses using a finite element model. The results presented show that the face width increase and offset have a significant influence on tooth root stresses. In some cases, increasing face width of one gear pair member resulted in significant increase of tooth root stress of the other member. For gear pairs with unequal and offset face widths, tooth root stresses were mostly affected when face widths were increased to the same direction of the contact line travel direction.

Effect of Gear Tooth Crack on Spur Gear Dynamic Response by Simulation

Geared transmission systems are widely applied to transmit power, torque and high rotational speed, and as well as change the direction of rotational motion. Their performances and efficiencies depend greatly on the integrity of the gear structure. Hence, health monitoring and fault detection in geared systems have gained much attention. Often, as a result of inappropriate operating conditions, application of heavy load beyond the designed capacity or end of fatigue life, gear faults frequently occur in practice. When fault happens, gear meshing characteristics, including mesh stiffness that is one of the important dynamic parameters, can be affected. This sudden change in mesh stiffness can induce shock vibration as the faulty gear tooth passes through the engagement zone. In this study, a finite element model representing the crack at the tooth root of a spur gear is developed. The theory is applied to investigate the effect of different crack sizes and the corresponding change in mesh stiffness. In addition, a lumped parameter model is formulated to examine the effect of tooth fault on gear dynamic response.