Infinities larger than others

 Hei Inspektører

Speaking of mathematics, can we say that there are infinities larger than others?

Lately I have been delving into these issues that, although they have a direct applicability in the engineering area where we develop as inspectors, I also believe that they are adapted to practically any daily concept.

For example, I was reading a while ago about a mathematician named Georg Cantor who in the 20th century showed that not all infinities are equal. (speaking clearly, of numbers, excluding a certain well-known eponymous business in my hometown)

What was Georg Cantor's explanation? Simple. He first wanted to match odd and even numbers by discovering that both sets of numbers are infinitely equal.

Then he wanted to match rational numbers with whole numbers and here he noticed that there are more rational numbers than whole numbers, since there are infinitely many decimals between 1 and 2 for example. (That is, the number of decimal numbers is directly more infinite than whole numbers)

The idea in general was rejected at the time by other scientists contemporary to Cantor such as Kronecker who believed more that this topic belonged to the field of philosophy or the Swede Gösta Mittag-Leffler who questioned Cantor's reputation in the field of the maths.

So, we have more than one infinity (finding infinity then infinities) and we also deduce that there does not exist as such a set of numbers (infinities) that is greater, there will always be a greater one.

As far as I read, this statement is true but cannot be proven.

Hall effect & coils P3

 Hei Inspektører!

A few days ago I was writing a bit about a type of sensor called Hall effect and its general application in MFL. I tell you that there are others, one of them is a little better known and used; The reels.

This is the most widely used MFL sensor, due to the large surface areas of the inspected ferromagnetic parts and can be used with their faces parallel or perpendicular to the inspected surface.

Arrays (Arrays) of these devices are also used to increase coverage and these can be connected physically or electronically so that only discontinuity signals are selected and noise is minimized.

The advantage of coils is that they are strong and relatively inexpensive to manufacture. They can also be molded or rolled to fulfill the inspection task. Their disadvantages are their size, the need to encapsulate them in non-conductive material with good wear characteristics, and their dependence on speed.

There are various factors that influence or affect its operation, but we will elaborate on this issue later.

Magnetic Field Characteristics.

When Magnetic domains remain aligned or extended after the influence of a magnetic field is removed, he material is said to be magnetized. This residual field is called Remanence or a Residual magnetic field. The ability of materials to retain magnetism after the magnetic force has been removed is called retentivity.

Although described as magnetic lines, the magnetic field within and surrounding magnetized materials is continuous. When a paper is placed over a magnet and fine iron particles are sprinkled on the paper, the iron particles align with the magnetic field in distinct lines of equipotential magnetic intensity and appear to form lines. Therefore, the magnetic field is referred to as lines or lines of force.

All magnets have two poles, North and South. A permanent bar magnet exhibits polarity; if freely suspended, one end of the bar will point toward the earth's magnetic North Pole. This north-seeking end of the magnet is called the South Pole; the opposite end is the North Pole.

If a bar magnet is U-shaped (horseshoe), the polarity remains but the magnetic field and the lines of force are more concentrated in the gap between the ends of the bar. If the magnetized bar is formed into a close or fused loop, the magnetic field is fully contained within a closed circuit in the magnetic material and no external magnetic lines of field exists.

Magnetic lines of force have the following properties:

• They formed closed loops
• They do not cross one another
• They seek paths of least magnetic resistance
• Their density decreases as distance from the poles increases
• They are considered to have direction by convention, from north to south external to the magnet.

When two magnets are moved into close proximity to each other, a reaction occurs. The like poles repel each other and unlike poles attract one another.

Principles of Bubble Testing

 Principles of Bubble Testing


In leak testing by the bubble test technique, a gas pressure differential is first established across a pressureboundary to be tested. A test liquid isthen placed in contact with the lower pressure side of the pressure boundary. (This sequence prevents the entry andclogging of leaks by the test liquid.) Gas leakage through the pressure boundary can then be detected by observation of~ub\Jles formed in the detection liquid atthe exit points of leakage through thepressure boundary. This technique provides immediate indications of theexistence and location of large leaks, 10-3to 10-s Pa-m3-s-1 (10-2 to lo-4 std cm3·s-1).Longer inspection time periods may be needed for detection of small leaks, 10-5to lQ-6 Pa·m3-s-1 (10-4 to 10-5 std cm3-s-1),whose bubble indications form slowly.
In bubble tests, the probing medium isthe gas that flows through the leak due to the pressure differential. The test indication is the formation of visible bubbles in the detection liquid at the exitpoint of the leak. Rate of bubble formation, size of bubbles formed and rate of growth in size of individual bubbles provide means for estimating the size of leaks (the rate of gas flow through leaks).

Bubble Test Liquids

Bubble test techniques for detecting or locating leaks can be divided into three major classifications related to thetechnique of using the test liquid.
1. In the liquid immersion technique,the pressurized test object or system is submerged in the test liquid. Bubbles are then formed at the exit point of gas leakage and tend to rise toward thesurface of the immersion bath.
2. In the liquid film application technique, a thin layer of test liquid is flowed over the low pressure surface of the test object. An example of this solution film leak test is the well known soap bubble technique used byplumbers to detect gas leaks. Films of detection liquid can be readily appliedto many components and structuresthat cannot be conveniently immersedin a detection liquid. For detection ofsmall leaks, this liquid should form a thin, continuous, wetted film covering all areas to be examined.

3. The foam application technique is used for detection of large leaks in which the applied liquid forms thick suds or foam. When large leaks are encountered, the rapid escape of gas blows a hole through the foam blanket, revealing the leak location.

Pressure Control in Bubble Testing
Subclassifications of these basic techniques of bubble testing refer todifferent techniques for controlling thepressure differential acting across thepressure boundary. Several techniques are used to raise the pressure differential andso to increase the rate of gas leakage and the rate of formation of bubbles.
1. Pressurize the interior volume of thetest object or system before and duringthe leak test. Internal gas pressure should be applied across the pressure boundary before test liquid contacts the external surface. This tends to prevent entry of liquid into leaks, which might possibly clog the leaks togas flow. Protection against hazards ofoverpressure must be provided.
2. Control the heating of sealed test objects and small components tocause internal gas expansion. This increases the pressure differential andcauses outward gas flow throughpossible leaks in the pressure boundary.
3. Apply a partial vacuum above thesurface of the test liquid (immersion liquid or solution film). This reduces external pressure to the pressure boundary. The resultant increase inpressure differential across the system boundary acts to cause gas flow through any leaks that are present.

Grinding cracks

Grinding cracks can be attributed to glazed wheels, inadequate coolant, excessive feed rate or attempting to remove too much material in one pass.
Grinding cracks develop where there is localized overheating of the base material.
Surface cracks in hardened objects can be caused by improper grinding operations. Thermal cracks are created by stresses from localized overheating of the surface under the grinding wheel. 
Overheating can be caused by using the wrong grinding wheel, a dull or glazed wheel, insufficient or poor coolant, feeding too rapidly or cutting too heavily. Grinding cracks are especially detrimental because they are perpendicular to the object surface and have sharp crack tips that propagate under repeated or cyclic loading. 
Grinding cracks are typically at right angles to the grinding direction, are very shallow and are often forked and sharp at the root.
When located in high stress areas, such cracks may result in fatigue failures caused by residual stresses. 
Materials that have been hardened or heat treated are susceptible to grinding cracks because uncracked they retain high residual stresses from quenching. 
During grinding, localized heating added to entrapped stresses can cause surface ruptures. The resulting cracks are usually more severe and extensive than typical grinding cracks.