Materials Testing for Mechanical Properties—Problems and Solutions

This appendix provides readers with worked solutions to 25 problems involving calculations associated with tensile testing and the determination of mechanical properties and variables. The problems deal with engineering factors and considerations such as stress and strain, loading force, sample lengthening, and machine stiffness, and with mechanical properties and parameters such as elastic modulus, Young’s modulus, strength coefficient, strain-hardening exponent, and modulus of resilience. They also cover a wide range of materials including various grades of aluminum and steel as well as iron, titanium, brass, and copper alloys.

Theoretical and experimental investigations of mechanical vibrations of hot hammer forging

The characterization of mechanical vibrations in a hammer forging process is a tremendously important parameter for machine design and production engineering. The dynamic response of a forging hammer to the reaction forces is affected by material behaviour, time, spring-damper system and foundation. In this research firstly, the effect of mass ratio and coefficient of restitution on the forging efficiency were theoretical characterized. The interesting influence of anvil initial velocity on the forging efficiency is also analytically presented. The mechanical vibrations of a LASCO HO U-315 hammer were experimentally investigated. Two steel grades a S355 and a 42CrMo4 were used to forge trial parts. The velocity of the ram and acceleration of the anvil during a hot die forging process were measured using a laser velocity meter type LSV-2000-45. The influences of forging time, coefficient of restitution, energy loss and time interval (delay) between blows on the efficiency of the forging process were examined. The energy loss before die contact was determined to be approximately 10%. The investigations also showed that a variation of the time interval between blows within the usual range has no effect on the intensity of the vibrations of the anvil nor on the energy loss of the hammer. The dependence of the free damped vibrations of the anvil on machine stiffness, damper coefficient and mass of machine has been confirmed. Additionally, the loss of energy due to hammer movement as well as the free damped mechanical vibrations of the anvil were theoretically analysed in order to verify the experimental findings. Theoretical analysis showed an anvil initial velocity of approximately 0.2 m/s results in a 4% increase of forging efficiency. A good agreement between the experimental and theoretical results was observed.

The Effect of Grinding Wheel Contact Stiffness on Plunge Grinding Cycle

This paper presents the effect of grinding wheel contact stiffness on the plunge grinding cycle. First, it proposes a novel model of the generalized plunge grinding system. The model is applicable to all plunge grinding operations including cylindrical, centerless, shoe-centerless, internal, and shoe-internal grinding. The analysis of the model explicitly describes transient behaviors during the ramp infeed and the spark-out in the plunge grinding cycle. Clarification is provided regarding the premise that the system stiffness is composed of machine stiffness and wheel contact stiffness, and these stiffnesses significantly affect productivity and grinding accuracy. The elastic deflection of the grinding wheel is accurately measured and formulas for representing the deflection nature under various contact loads are derived. The deflection model allows us to find the non-linear contact stiffness with respect to the normal load. The contact stiffnesses of four kinds of grinding wheels with different grades and bond materials are presented. Both cylindrical grinding and centerless grinding tests are carried out, and it is experimentally revealed that the time constant at ramp infeed and spark-out is significantly prolonged by reducing the grinding force. It is verified that a simulation of the grinding tests using the proposed model can accurately predict critical parameters like forces and machine deflection during plunge grinding operations. Finally, this paper provides a guideline for grinding cycle design in order to achieve the required productivity and grinding accuracy.

Mathematical Model of a Vertical Six-Axis Cartesian Computer Numerical Control Machine for Producing Face-Milled and Face-Hobbed Bevel Gears

Prior to the development of sophisticated computer numerical control (CNC), both face milling (FM) and face hobbing (FH), the two most popular technologies for bevel gear production, required cradle-type machines with diverse and complicated mechanisms. In the last two decades, however, the gear industry has replaced these traditional machines with six-axis CNC bevel gear cutting machines that have superior efficiency and accuracy. One such machine is a vertical six-axis machine with a vertical spindle arrangement, which offers two industrially proven advantages: compact design and maximum machine stiffness. The technical details of this machine, however, remain undisclosed; so, this paper proposes a mathematical model that uses inverse kinematics to derive the vertical machine's nonlinear six-axis coordinates from those of a traditional machine. The model also reduces manufacturing errors by applying an effective flank correction method based on a sensitivity analysis of how slight variations in the individual machine setting coefficients affect tooth geometry. We prove the model's efficacy by first using the proposed equations to derive the nonlinear coordinates for pinion and gear production and then conducting several cutting experiments on the gear and its correction. Although the numerical illustration used for this verification is based only on FM bevel gears produced by an SGDH cutting system, the model is, in fact, applicable in the production of both FM and FH bevel gears.

A Surface Generation Mechanism of Grinding

This paper presents a surface generation mechanism of grinding that captures the microscopic interaction between the abrasive grains and work-surface. The mechanism utilizes both deterministic and stochastic formulations and deals with such realistic constraints as loss/wear and uneven distribution of abrasive grains, roughness of already-ground work-surface, and machine stiffness. Apart from the theoretical treatments, numerical examples are cited showing how the topography of the work-surface evolves because of the proposed mechanism. The work will help build computerized systems ensuring a reliable prediction of the surface roughness due to grinding under the realistic constraints.