Domestic market overview of precision non-standard cutting tools

The screw micrometer has high precision, which is closely related to the nature of the screw.Today, I will talk about something related to the college entrance examination -- spiral micrometer and vernier caliper.When it comes to these two length measurement tools, many little cuties are familiar with them (after all, they have to take the college entrance exam), especially the precautions when reading them.

Not only are these two lengths tricky to read, but their principles are even more subtle.I can't help but wonder how the people who invented them actually came up with this idea.

Let's start with the helical micrometer. The name of the helical micrometer explains how it works -- the helical. Let's start with the helical.

"Spiral"

A screw is a twisting curve, such as a spiral and a screw. Screws and bolts are often found to work with a screw.

If you rotate an inclined plane around a cylinder, you get a helix, so a helix has some of the properties of an inclined plane.In fact, ancient Greek scientists defined a helix by rotating an inclined plane around a cylinder.

A slope is a labor-saving device. The smaller the slope of the slope (the smaller the Angle between the slope and the horizontal plane), the less the force required to be exerted on the object [1].Similarly, the helix can also save effort, in addition to the helix can also transform rotation motion into linear motion, torque into linear force.By means of the helical mechanism, the force can be amplified, and a smaller torque applied to the shaft can be converted into a larger axial force, which can be used to make jacks.

● Screw micrometer

Having said all that, what is the relationship between the spiral micrometer and the spiral?Don't worry, let's get down to business.In fact, the spiral micrometer is a "spiral pair".A cylinder with uneven surface and spiral stripes is called a "screw", while a round hole with uneven surface and spiral stripes is called a "nut".The nut and screw with internal and external threads matching each other form a pair of "screw pairs" [2].The bolt mentioned in the opening picture is a "screw pair". Take a look at the profile of the screw micrometer.

Helical micrometer structure

Micrometer screw and differential cylinder are one. Micrometer screw plays the role of screw in the "screw pair", while fixing sleeve is equivalent to "nut".The fixed sleeve is tightly packed on the periphery of the micro-measuring screw. When the differential cylinder is twisted, the micro-measuring screw and the differential cylinder will rotate along the thread and pass through the nut in a straight line along the shaft of the screw, forming a "spiral motion".

The higher precision of the helical micrometer is based on the principle of turning the rotary motion into a straight line motion.The concept of "lead" needs to be added here.The lead is the straight-line distance of the rotation of the helix.We know that when the differential cylinder rotates once and the measuring screw moves 0.5mm forward or backward, the lead of the measuring screw is 0.5mm.The rotation of the differential cylinder is equal to 0.5mm. If the circumference of the differential cylinder is equally divided into 50 parts, does it mean that 0.5mm is equally divided into 50 parts?Then, each portion on the differential cylinder is equivalent to 0.01 mm, which gives a higher accuracy.

This principle is known as "helical amplification" : the use of a helix to turn the motion of a rotation into a linear motion, and the less obvious changes in the distance of the linear motion, to the more obvious changes in the circumference of the rotation motion.So be careful not to damage the inside screw when using the screw micrometer.

According to this principle, someone has made a toy with a screw micrometer, like this one, but not very accurate.

● Vernier caliper ●

The principle of the screw micrometer is easy to understand from its section view, and the reading method is actually similar to that of our ordinary ruler.Vernier calipers, on the other hand, often find them strange and counter-intuitive when they are first used: trying to find the right line.It's a wild guess. It's not serious at all.What's more, the scale on the cursor and the scale of the main ruler are not in line at zero, which makes it uncomfortable to watch.

Although the vernier scale does not match the master ruler scale, this is the reason why the vernier caliper can be more accurate than the ruler.Take the following 50-degree grid vernier caliper for example. When the cursor is set back to zero, it can be found that the length of the 50 index grid on the cursor is 49 mm, which is exactly 1 mm shorter than 50 mm, so the length on each index grid is actually 0.98 mm.We have all learned how to read a vernier caliper. The 29th scale on the vernier looks the most correct, so the indicator of this caliper is: 3 + 29× 0.02mm = 3.58mm.

So how does this work?If you see that the 29th scale on the upper scale of the figure matches the 32mm scale best, divide the 32mm into three parts.The first part is 3mm on the master ruler, the second part is the distance between 3mm of the master ruler and the vernier zero scale, and the third part is the distance between the vernier zero scale and 32mm.The second part is the length we want to know.The distance between the second part and the third part adds up to 29mm, so the third part contributes 29× 0.98mm = 28.42mm, and the second part contributes 29-28.42mm = 0.58mm.

Or another way to think about it, if you look to the left from 32 mm, think about how the second part of the distance is generated.The second part is actually because each index lattice on the cursor is shorter than 1 mm. The length of the second part is shorter when adding up 29 index lattice.What about these shorter lengths?Directly add up the 0.02mm short of each of the 29 indexing lattice, that is 29 × 0.02mm = 0.58mm.

In fact, it is easy to understand that the cursor is slightly shorter in each index case on purpose, which is to make use of the shorter length to achieve more precise measurement.Then the vernier caliper of tenths and 20ths is the same principle. Each grid of tenths is 0.1mm shorter than 1 mm, and each grid of 20ths is 0.05mm shorter than 2 mm.The reading is simply the sum of the total number of fractions (0.02mm, 0.05mm, 0.1mm).