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In a modern age full of smart devices, it may be hard to imagine that just a few decades ago, the most convenient timing device in the world was a mechanical watch. Unlike quartz watches and smartwatches, it does not require any batteries or other electronic components. In this article, I will talk about the working principle of the mechanical watch shown in the following figure.

What is revealed here is the movement-the interior of the mechanical watch, which is usually encapsulated in a metal shell. This article does not care about the shell, but focuses on the movement inside, after all, that is the soul of this work. The whole watch movement has many parts, just the professional name of each part will make people big, but you don't have to rush to remember them, I will use the same color to mark the professional name and the corresponding parts on the picture. The timing system of any mechanical watch is made up of seven main parts, which can be arranged in a row for display.

The seven parts don't look like much, but they have a lot of interesting details that make the second hand rotate at the right speed. Let's start with the power source and explore how this whole wonderful device works.

Power source pure mechanical equipment has several different ways of supplying energy, one of the simplest ways is to store the energy in the spring. The most common spring we see is solenoid.

For example, when you press down a load hanging from a spring, it will store energy, and then release the spring, and it will release energy and bounce. Mechanical watches usually use another kind of spring-a spiral torsion spring. When it is twisted, it stores energy, and when released, it twists in the opposite direction and oscillates back to its natural state of relaxation.

In the mechanical watch, we finally want the pointer to rotate to indicate the time, and the rotation torque provided by the torsion spring is just to meet this need. In general, the clockwork spring in a mechanical watch has a more complex shape, just like the initial relaxation in the image below. If you hang it in the air, roll it, and then release it, it will quickly return to its original shape.

As you can see, this winding spring is so strong that it can easily unfold into that complex shape quickly. In order to install the winding, we need to put it into the shell, which is called the winding box.

Once placed in the winding box, although the winding still wants to unfold back to its original shape, the wall of the winding box will fix it in the box. In this way, the clockwork stores energy for the mechanical watch. This is very important, so this clockwork is also called "main clockwork".

But it's not all right yet, because now that the main spring has spread to the maximum extent in the box, we can't extract energy from the spring in this state to drive the mechanical watch. In order for the main spring to shrink back to store more energy, we need to add a clockwork axis on the inside of it.

If you look closely, you will see a small hole at the end of the main winding in the center of the picture. There is a small hook on the clockwork shaft that can hook the hole.

Turn the clockwork axis and it will drive the main clockwork around together. In the following picture, we fix the winding box, wind it up and release it.

Fix the clockwork box and release the clockwork axis. You can see that once the development axis is placed, the main clockwork will turn back with the axis. But this is not what we want. What we want is the winding box to rotate so that the gears on the edge of the box can drive the other parts of the watch. In order for the main winding to work honestly, we need to fix the winding axis instead of the winding box when extracting energy.

Fix the winding axis and release the winding box immediately we will know how to use it in practice, but for now, let's assume that the winding axis is firmly fixed, and the main winding will drive the winding box, as shown in the image above. Then, let's put aside the main winding and the winding box to see two other gadgets that can make the mechanical watch work more reliably. First of all, review the state of the clockwork when it is relaxed.

The metal strip attached to the main winding provides extra tension to the outside. The metal bar wants to bounce back to the shape of a straight line, so it pushes the wall of the winding box to create a huge friction to keep the winding of the metal end fixed relative to the wall of the box.

In this way, when the clockwork axis rotates the inner end of the clockwork, the outer end of the clockwork is fixed. In addition, if we keep turning the winding, when the tension exceeds its maximum elastic range, the friction will be overcome, and the outer end of the main winding will slide inward against the box wall, which plays a security role to prevent the parts from breaking.

We have seen that the main spring is S-shaped in the relaxed state, and its local curvature is constantly changing, which helps the main winding to balance the tension of different parts in the box. Note that the radius of curvature of the inner end of the winding is smaller than that of the outer end. If the naturally relaxed clockwork is a straight metal strip, the inner end of the spring bends more than the outer end after turning. The outer end of the S-shaped clockwork will have a tension similar to that of the inner end, because the section of the S-shaped it wants to restore is bent in the opposite direction.

In order to protect the main winding and prevent dust from entering, we use a lid to cover the winding box.

We have succeeded in getting some parts to turn, and some people will naively think that we only need to add a pointer to the winding box to time it. What do you think? what you get in this way is the picture below, which doesn't work at all.

Did you find that the pointer turns so fast that it uses up the energy stored in the main winding in the winding box after a few turns, and this device cannot time reliably. So obviously, we still have a lot of room for improvement.

If we want the mechanical watch to work continuously for 40 hours after the last winding, we need the minute hand to turn 40 laps during that time. In addition, the second hand has to be turned 40 × 60 = 2400 laps. We need to find a way to convert the short rotation of the winding box into the lasting rotation of the pointer, which requires gears.

Gears can be used to change the speed between two shafts, and you can feel this effect by observing the small black spots on each gear in the image below. The larger red gear in the picture drives the smaller yellow gear so that the yellow gear can turn around in less time.

For two matching gears, their number of teeth determines the speed relationship. For each tooth on one gear, it fits with the backlash on the other gear, so the number of teeth turned by the two gears is the same in a unit of time. If the number of teeth of the two gears is not the same, then the time for them to turn around will be different. In the following picture, red is the driving gear and yellow is the driven gear. By changing the tooth ratio of the two gears, you can see how the tooth ratio affects the speed of the yellow gear.

These gears are designed to mesh with each other, so the tooth number ratio is equal to the ratio of the gear radius. When the driving gear has more teeth, the driven gear rotates faster. Using this property, we can make the second hand rotate at several times the speed of the winding box.

Now let's think about how much we need to increase the speed. The last winding could make the winding box turn close to 7 laps, but during this time, we want to turn the second hand 2400 laps. We need to make the ratio of the number of teeth, or the ratio of the radius of gears, about 343 to 1. Let's see what it would be like to make such a gear in practice.

As you can see, such a huge radius ratio is absurd. In order for the red gear to fit into a reasonable-sized watch, the yellow gear will become very small, and the teeth of the two gears will become small and fragile. Therefore, the mechanical watch uses a different scheme, which uses a series of pairs of gears, each pair of which can increase the speed to a certain extent. Take four gears as an example, notice that there are two gears on most shafts:

The first wheel is the winding box, which drives the second wheel, then the third wheel, and finally the fourth wheel. Notice that each big gear drives the pinion, so pinion is specially used to refer to the pinion in English. The pinion and the big gear in the next pair are installed on the same shaft, so we can constantly increase the speed of each shaft. This method has a significant advantage-it can make the whole mechanism smaller and can use intermediate gears to drive the minute hand and hour hand at a lower speed.

Before we finish the chapter on gears, let's take a look at the shape of the teeth. Most large machines use involute teeth, but mechanical watches usually use cycloidal teeth.

Pull down a rope attached to the circle to form an involute, and the normal of each point above it is tangent to the generating circle, which meets the requirements of the transmission law of the force on the gear. The shape of the tooth starts from the root circle (dedendum circle), then to the base circle (base circle) that is generated as an involute, and then the involute passes through the pitch circle (pitch circle) as the equivalent circle of the two gears meshing, and finally ends with the crown circle (addendum circle). The cycloid is constructed in another way:

One circle scrolls on the surface of another circle to form a cycloid | Source: tec-science

The cycloid makes the meshing point move more smoothly, and the normal of the meshing point always points to node C, which can reduce the surface pressure and wear, but it requires high machining accuracy. Tec-science: let's get back to the point and turn the clockwork axis to tighten the main clockwork to see how the mechanical watch works after adding the gear set:

Succeed! We have achieved the goal of turning the second hand several times when the winding box turns around, but the speed of the needle is completely uncontrollable. We need to find a way to control the energy release rate of the main winding, which is about to get out of the escapement.

The escapement consists of two parts-an escape wheel and an escape fork. Pay attention to the special shape of the escapement teeth, which is very different from the gears we have seen before. It has a regularly shaped gear at the top, which is used to receive the force from the drive to drive the entire escapement wheel. The escape fork itself is made of metal, but the two light red transparent parts at its top are made of artificial rubies. This material is not only hard and wear-resistant, but also has a very low coefficient of friction with steel. From the way the two parts work with each other, you can see why these two properties are important.

The escape wheel wants to rotate in the direction indicated by the red arrow, and the escape fork hinders the movement. When we swing the escapement fork back and forth, we let the escape wheel briefly "open" the bondage, and then be "caught" by the escapement fork.

We'll take a closer look at how they interact later. Now, this escapement allows us to control the rotation of the escapement wheel by swinging the escapement fork. Let's wind up and manually swing the escapement fork to see how the mechanism fits with the rest of the device.

The spring of the main spring drives the escapement wheel, but the escape fork only allows it to move in a very short period of time. Under the action of gear deceleration, the rotation of the winding box is almost invisible. However, if you look at the pointer on the fourth gear, you can see that it rotates gently as the escape fork swings.

This little timing device is almost complete, and the remaining last step is how to make the escape fork swing automatically. However, in order for the watch to time accurately, the swing must have an appropriate rhythm. This is necessary to introduce the beating heart of the mechanical watch-the pendulum wheel group.

Let's review the torsion spring shown at the beginning. When you twist it, it starts to oscillate and stops after a while.

We can control this vibration period by adjusting two parameters. The first is the stiffness coefficient of the spring, which mainly depends on the width, thickness, length and composition material of the spring. The second is the mass and mass distribution, or, more accurately, the moment of inertia of the object that the spring rotates. The greater the mass, the farther the matter is from the axis, and the greater the moment of inertia.

By carefully adjusting these parameters, we can make the system vibrate at the desired rate. The periodicity of the torsion spring vibration can be used as the basis for the accurate timing of the mechanical meter. The pendulum wheel group in the mechanical table is composed of the pendulum wheel attached to the upstream wire, and it can be seen that the vibration frequency of the pendulum wheel in the mechanical watch is quite high.

There is another light red transparent gem at the bottom of the pendulum wheel, called the core. Small as it is, it is important-when the wheel turns, the core hits the other end of the escapement fork, causing it to tick. Let's take a look at how the pendulum wheel works with other parts.

Take a closer look at what's going on.

When the swinging wheel comes with the core, the core will hit the escapement fork, thus opening the escapement wheel. Once flung open, the escapement wheel driven by the main spring pushes the escapement fork, which in turn pushes the swing wheel itself through the core. This allows the pendulum wheel to gain some energy so that it does not stop for a period of time-which is equivalent to giving the swing player a push. When the pendulum wheel comes back, it does the same thing, but in the other direction.

You may also have noticed that the disc on the pendulum wheel has a notch and a delicate dance-like movement pattern between it and the small corner at the end of the escapement fork. These parts ensure that the escapement fork can only be placed aside at the right time-a safety mechanism that prevents the watch from being locked when it shakes or falls.

Once the escape fork opens the escape wheel, the wheel has to start turning quickly. This is why there are holes in the gear sets-this reduces the moment of inertia and allows the winding box to drive them faster.

Another important point is that the gear set not only magnifies the speed of the gear, but also reduces the force acting on the pendulum wheel set. The winding box itself will have a lot of rotating torque, but when it comes to the escape wheel, this torque is greatly reduced, which prevents the escape wheel from pushing the escape fork and pendulum wheel too violently.

Let's take a last look at the entire organization that has been built so far. I'm setting it to normal running speed.

In the movement of this watch, the pendulum wheel makes four complete swings per second, hitting the escapement fork twice in each cycle, so it hits a total of eight times per second and 28800 times per hour. Of course, different watches may have different speeds, but their second hands make several small turns per second to make the pointer movement of the mechanical watch very smooth.

In theory, all the parts we have built here are enough to make a watch work, but we are still missing hundreds of millions of details. More importantly, the parts we have completed are all placed in the air, so in the next issue, we will assemble them into a complete watch movement.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Ciechanowski, translator: shepherd, revision: Tibetan idiot

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