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General Quantities in Metal Drawing

In various engineering disciplines, drawing plays a pivotal role in the creation and analysis of components and products. Understanding the fundamental quantities that are encountered during drawing processes is crucial for achieving accurate designs and efficient production. This article delves into the realm of general quantities in drawing, including dimensions, force, work, energy, power, stress, strain, and temperature. These parameters form the foundation of drawing engineering and contribute to the success of manufacturing processes.

General Quantities in Metal Drawing

  1. Dimensions:

Commonly encountered dimensions include the diameter of round bars, rods, or wires. Such diameters are regularly given in millimetres (mm) or inches (in.). One inch equals 25.4 mm, and it is important to be facile in both SI (International System) and UK/US measurement systems. Wire diameters are also frequently quoted in gauge numbers, with higher gauge numbers corresponding to smaller diameter values. For instance, the American Wire Gage (AWG) system is widely used for nonferrous wires.


  1. Force:

This is usually referred to as drawing force. While the detailed physics of force involve intricate concepts, drawing analyses generally focus on steady-state dynamics, where drawing force relates to drawing speed, work, and power. The standard unit of force is the newton (N) in the SI system and pounds (lb) in the UK/US system.


  1. Work and Energy:

When force is applied over a distance, work is done, and energy is expended. The SI unit for work and energy is the joule (J), while the UK/US system commonly employs foot-pounds (ft-lb) and British thermal units (Btu). These quantities are pivotal in assessing the energy requirements of drawing processes.


  1. Power:

Power represents the rate at which work is done or energy is expended per unit time. In drawing, the SI unit for power is the watt (W), while the UK/US system employs horsepower (hp). Understanding power is crucial, as it ties drawing force to drawing speed, giving insights into the efficiency of the process.


  1. Stress:

Stress, a fundamental concept in drawing engineering, is the force applied per unit area. It is a critical parameter that influences material behavior and performance during the drawing process. The stress experienced by a material can be categorized into different types based on its direction and magnitude.

The SI unit for stress is the pascal (Pa), which is equivalent to a newton applied to a square meter of surface area. However, since drawing processes often involve significant stresses, the megapascal (MPa) is commonly used, where 1 MPa equals 10^6 Pa. In the UK/US system, stress is usually expressed in pounds per square inch (psi) or kilopounds per square inch (KSI), with 1 KSI equal to approximately 6.894 MPa.

Drawing or pulling stresses are tensile tresses and are designated with a positive sign.   Pushing stresses are called compressive stresses and are designated with a negative sign.   However, pushing tresses are often called pressures, such as the die pressure in a drawing. Notably, pushing stresses and pressures are considered positive.

When the applied force is perpendicular to the surface, it gives rise to normal stresses, designated by the Greek letter σ (sigma). On the other hand, shear stresses, designated by the Greek letter τ (tau), occur when the force is parallel to the surface. Shear stresses are exemplified by friction in the drawing process.

Sometimes, the area to which the force is applied undergoes changes during deformation. Stress computed based on the “current” or “instantaneous” area is termed a true stress (σt), while a stress calculated using the initial area is called an engineering stress (σe). This distinction becomes crucial when considering the effects of deformation on stress values.


  1. Strain:

Strain is a measure of how much a material is deformed in response to applied forces. It plays a significant role in understanding material behavior during drawing processes. Strain is dimensionless, as it involves the ratio of length changes to the original length, making it a critical parameter for evaluating material deformation.

Two primary types of strain are encountered in drawing analysis: normal strain (ε) and shear strain (γ). Normal strains involve changes in dimensions that are parallel to the original dimension, which commonly occurs during tension or compression. Shear strains, on the other hand, arise from changes in dimensions that are perpendicular to the original reference dimension.

One widely used measure of normal strain is engineering strain (εe), which is the change in length divided by the original length. It can be calculated using the formula:

εe = (l1 – l0) / l0

Where l1 is the new length and l0 is the original length.

However, in cases where significant changes in reference dimensions are encountered, a more accurate measure of strain is required. True strain (εt) takes into account the progressive changes in reference dimensions by using the natural logarithm of the length ratio:

εt = ln(l1 / l0)

Additionally, considering that the volume of a workpiece remains constant during drawing, the product of workpiece length and cross-sectional area is constant. This observation leads to the concept that true strain can be related to the change in cross-sectional area. The cross-sectional area of a round wire, for example, is given by (π/4)d^2, where d is the diameter.

It’s worth noting that drawing strains, calculated using these methods, often assume uniform flow of the workpiece. In practice, nonuniform strain is introduced when passing through dies, known as redundant strain, which affects the overall deformation process.


  1. Strain Rate:

In drawing, the rate of strain is crucial, measured in units of s⁻¹. The average strain rate can be determined by the product of drawing strain, drawing speed, and the length of the deformation zone.


* Relations Between Stress and Strain:

Below certain stress levels, stress and strain are related elastically, with stress proportional to strain and the elastic strain returning to zero when the stress is removed. The simplest relation of this kind is Hooke’s Law for simple tension or compression:

σ = E ε,

where E is Young’s modulus. The units of Young’s modulus are the same as those of stress. There is a stress level, however, above which strain does not return to zero when stress is removed. Such remaining strain is called plastic, and the stress level is called the yield strength, (σy). Nearly all of the strain of interest in drawing is of the plastic type and the stress in the drawing zone is, in effect, at or above the yield strength of the workpiece. The strength that the bar, rod, and wire present during drawing will be called the flow stress, designated σ0.


  1. Temperature:

Temperature and its variations significantly impact the drawing process. Different temperature units, including degrees Celsius (°C) and degrees Fahrenheit (°F), are used in different systems. Conversions between these units are crucial for accurate thermal analyses.

One can convert from Fahrenheit to Celsius as follows:

°C = ( °F – 32 ) * ( 5 / 9 )

Some thermal analyses are based on absolute zero or the lowest possible temperature (at which point thermal energy ceases). In the Celsius system, this temperature is  273.15, and the absolute temperature in degrees Kelvin (K) is °C+273.15. In the Fahrenheit system, this temperature is 459.67 and the absolute temperature in degrees Rankine (°R) is °F +459.67.


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