Talk:Balance wheel

Untitled
This article seems to focus on one narrow part of the subject: compensated, bimetallic balance wheels. When and where were balance wheels invented? Why was the spring added? Were balance wheels used in anything besides watches? What do modern balance wheels look like? How accurate are they? --Chetvorno 00:22, 15 June 2007 (UTC)


 * Good points. One issue is that the balance wheel is a component of a system (the mechanical watch).  Some of what we'd want to discuss relates to the system, not the component. For example, you can't speak of accuracy of a balance.  A watch has accuracy, and the way the balance is constructed is a factor, but it also depends on the balance spring, the escapement and so on.


 * Mechanical watch might be a good spot for this. Paul Koning 10:59, 15 June 2007 (UTC)
 * I've taken off some of the tags since those issues have now been cured. That was a nice rewrite, Chetvorno.  Paul Koning 14:51, 19 June 2007 (UTC)

Mechanical chess clocks are still being manufactured using balance wheels. However, the prevalence of tournaments which specify time controls with delay time are decreasing the mechanical clock's usefulness. Louis Reed (talk) 21:06, 20 June 2013 (UTC)


 * Yeah, balance wheels are still used in a variety of cheap timers, such as kitchen timers. -- Chetvorno TALK 21:36, 20 June 2013 (UTC)

Modern balance wheels
I have a photo of a chronometer (in my father's collection), built during world war 2 by the Hamilton Watch Company. It clearly has an elinvar balance spring because the balance wheel has no cuts in it. But apart from that, the balance wheel looks like the classic kind, with screws at various points around the circumference.

I was told (but don't have a reference at hand) that elinvar still has a (very small) temperature coefficient, so it is desirable for the balance wheel to compensate for that. And supposedly that's done by using a bimetallic rim whichs is not cut, or perhaps a rim of one material with spokes of another. Supposedly, the result is that the wheel changes shape slightly (from circular to elliptical) when temperature changes, a smaller effect than the Earnshaw pattern classic compensation balance. And if that's correct, then the screws would indeed be compensation adjustment screws.

I'll see if I can get more data, and perhaps permission to include the photo. Paul Koning 20:32, 22 June 2007 (UTC)


 * That's fascinating! I've heard the same thing, about uncut alloy balance wheels being temperature compensated, but I was unable to find anything about it.  I have a Bulova 23j watch from 1956 with an uncut balance with weights, and it says 'adjusted to heat and cold' on the movement, so I always wondered.  If you could find a reference, that would be a good thing to include.


 * I have an image of an alloy balance on Wikipedia Commons, Benrus_Watch_Balance_Wheel.jpg that I was going to include in the article, but your photo sounds better. --Chetvorno 02:09, 23 June 2007 (UTC)


 * One key difference is that I don't have permission yet to make that photo available.... so use yours. Even if I do get permission it will take a while (months not days).  Paul Koning 14:50, 25 June 2007 (UTC)

Mathematical Model
I was thinking of adding a section on the math of balance wheels at the end, similar to below. Comments? Too boring? --Chetvorno 00:39, 23 June 2007 (UTC)

(See definition of terms at end)

A balance wheel is a lightly damped impulse driven harmonic oscillator. The equation of motion is:


 * $$ I \ddot \theta + c \dot \theta + k\theta = \tau(t)$$

A 'perfect' balance, with no friction $$c\,$$ or drive torque $$\tau\,$$ has the solution:


 * $$\theta = A\cos{(\omega_0t+\phi)} \,$$      where   $$\omega_0 = \sqrt {k/I} \,$$

So it oscillates at a constant amplitude with the frequency $$f_0 = 2\pi\omega_0 = 2\pi\sqrt{k/I}\,$$, called the natural resonant frequency. The goal of balance wheel design is to approach the behavior of this 'perfect' balance.

The general unforced (homogeneous) solution is:


 * $$ \theta = A e^{-\alpha t} \cos {( \omega t + \phi )} \, $$


 * Where:
 * $$ \alpha = c / 2I \,$$


 * $$ \omega = \sqrt { k/I - (c/2I)^2 } = \sqrt { \omega_0^2 - (c/2I)^2 }$$

The friction $$c\,$$ of real balances is low enough that they are very underdamped, sharply resonant systems. Under these conditions, where $$ c << (kI)^{1/2} \,$$, a common dimensionless parameter used to characterize the timekeeping ability of balance wheels and other resonators is the Q, or quality factor:


 * $$Q = (2\pi) \frac {\mbox{energy stored in balance}}{\mbox{energy lost during one period}}

= (2\pi) \frac {\mbox{energy stored in balance}}{\mbox{energy provided by escapement during one period}}\,$$
 * $$= \frac {\sqrt{4kI}}{c} = \frac{2I\omega_0}{c}\,$$

The higher the Q, the less energy is required from the escapement per period to replace the energy lost to friction. Since the escapement is the main source of disturbances to the motion of the balance, a balance's possible precision as a timekeeper is roughly proportional to it's Q.

It can be seen that to get higher Q, other things being equal, requires a larger, heavier balance (I), a faster beat ($$\omega_0$$), or lower friction (c). This is the direction balance design has taken over the years. The Q of modern watch balances is around 100 to 300. This is why they are not as good timekeepers as pendulums (Q ~ 10^4), or quartz crystals (Q ~ 10^4 – 10^6).
 * ==Definition of terms==
 * $$\theta = \,$$ Angle of rotation of balance wheel from rest position (radians)
 * $$I = \,$$ Moment of inertia of balance wheel (Kg-m)
 * $$c = \,$$ Coefficient of angular friction from all sources (Kg-m^2/radian-s)
 * $$k = \,$$ Spring coefficient of angular elasticity (Newton-m/radian)
 * $$\tau = \,$$ Drive torque on balance from escapement (Newton-m)
 * $$A = \,$$ Maximum amplitude of vibration (radians)
 * $$\omega = \,$$ Angular frequency of vibration (radians/sec)
 * $$f =\,$$ Beat/2 = Frequency of vibration (Hz)


 * Interesting. The difference in Q seems to correspond reasonably well to the difference in achievable accuracy (order of a second a year for a high quality quartz clock vs. maybe 10x that for a good mechanical chronometer).  But there are other aspects that I don't see here.  For example, it's a rule of escapement design that you want to apply the impulse at the zero crossing.  Why (mathematically) is that? Paul Koning 14:49, 25 June 2007 (UTC)

Temperature compensation section
Chetvorno, you reverted an edit of mine on temperature compensated balance wheels. I noted in my edit that the compensation doesn't cause the balance to turn faster or slower and you replied "Yes, it does. Lower moment of inertia = higher acceleration = higher angular velocity = higher freq, compensating for freq lowering effect of spring."

I understand what you mean, but the balance can't actually be allowed (by the designer) to oscillate at a higher frequency to compensate for the frequency lowering effect of spring, because if it did, then the watch would not keep accurate time. The objective of the designer of the watch is to keep the balance oscillating, as nearly as possible, at the *same* frequency all the time, whatever the temperature.

What actually happens is that as the higher temperature causes the spring to become weaker, the moment of inertia of the balance is reduced by the curving in of the bimetallic arms of the balance. These two effects happen together, and the reduction in the moment of inertia of the balance is designed to keep in step with (to "compensate" for) the reduced strength of the balance spring, so that as the spring becomes weaker it can still accelerate the balance at the same rate as before, and the balance then oscillates at the same frequency, preserving the timekeeping of the watch.

I hope this clarifies things and the reason for my edit. I don't want to get into a to and fro reverting each others edits so I hope we can reach an agreement that we are both happy with.

David.Boettcher 18:15, 19 January 2014 (UTC)


 * Sorry, I didn't mean to be abrupt or callous in reverting your edit. I agree with your analysis above.  But I felt that your wording, "A temperature increase makes the arms bend inward toward the center of the wheel, and the shift of mass inward reduces the moment of inertia of the balance, compensating for the reduced couple produced by the weaker balance spring" was not as clear for readers lacking a science background as the ice skater analogy.  However I take your point that the original wording promotes the misconception that the compensation causes the balance frequency to "change".  Let me look at it again. -- Chetvorno TALK 20:25, 19 January 2014 (UTC)

I don't think that the ice skater analogy is appropriate in the context of a balance wheel, and in fact it could lead to the misunderstanding that the balance wheel speeds up in the same way that the skater does. However, I agree that the wording could be a bit challenging for some readers so I have expanded it to make it easier to understand. I have also linked to the moment of inertia page where the ice skater analogy is well used. David.Boettcher 11:10, 21 January 2014 (UTC)
 * I think the additional explanation is a little confusing, and your original edit was better. I restored it, except for changing the rather technical term "couple" to the slightly more accessible "torque".   -- Chetvorno TALK 16:42, 21 January 2014 (UTC)

Temperature error
The opening para of this section has now been copyedited to death (including by me). It used to read;
 * After the balance spring was added, a major remaining source of inaccuracy was the effect of temperature changes. Early watches had balance springs made of plain steel, and balances of brass or steel, and these were affected by temperature to the extent that the rate of even the earliest balance spring watches watch was noticeably affected.

This could have been intended to mean that early balance spring watches were inaccurate for reasons other than temperature effects, but even so, the temperature error was still very noticeable. If so, that point has been entirely lost in the copyediting. However, I have not put it back because I am not knowledgable enough on the subject to know if that is true and it is kind of self-contradictory with the opening sentence saying the remaining major source of inaccuracy was temperature changes.  Spinning Spark  14:04, 6 March 2014 (UTC)

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Harmonic oscillator vs...
This article mentions that a balance wheel is a harmonic oscillator. It might also be worth mentioning that the verge and foliot escapement, of which the balance wheel was an improvement, was a kind of relaxation oscillator. In a harmonic oscillator, the dynamic interplay between the inertia of the balance wheel and the restoring force provided by the spring obeys a simple and predictable physical law. A relaxation oscillator, on the other hand, continually and abruptly switches back and forth between two different states. Insignificant-seeming variations in the timing of the mechanism that underlies those abrupt changes can accumulate, making the rate of a relaxation oscillator somewhat variable and difficult to predict. — Preceding unsigned comment added by 74.111.96.172 (talk) 16:46, 16 December 2021 (UTC)


 * Agree, good idea. It requires a source that says the verge and foliot escapement was a relaxation oscillator.  Do you know of one?  I'll look around. --ChetvornoTALK 19:25, 16 December 2021 (UTC)

Recent changes to introduction
User:109.70.40.55 recently  changed the introduction wording from:
 * A balance wheel, or balance, is the timekeeping device used in mechanical watches and small clocks, analogous to the pendulum in a pendulum clock.  It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring, known as the balance spring or hairspring.   It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel.  Each swing of the wheel (called a "tick" or "beat") allows the gear train to advance a set amount, moving the hands forward.  The balance wheel and hairspring together form a harmonic oscillator, which due to resonance oscillates preferentially at a certain rate, its resonant frequency or "beat", and resists oscillating at other rates.   The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or "tick" very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present.

To:
 * "A balance wheel together with the balance spring, or hairspring, forms the balance, the timekeeping device used in mechanical watches and small clocks. The weighted balance wheel rotates back and forth, being returned toward its equilibrium position by the spring; analogous to the pendulum in a pendulum clock. Thus it is a harmonic oscillator between the angular momentum of the wheel, and the elasticity of the spring. With each sweep of the wheel (tick or beat), the escapement is released a single step and the wheel receives a single impulse of power from the watch wheel train. That the resonant frequency is determined by the intrinsic mass properties of the wheel and elasticity of the spring accounts for its nearly universal use as the timekeeper in mechanical watches through to the present."

Which is better?
 * I feel the original wording (top), which has been unchanged for years, was better and should be restored. It is important that the introduction be clear and comprehensible, as it may be the only part of the article that nontechnical readers will read. The objections I have to the new wording are:
 * "The weighted balance wheel rotates back and forth, being returned toward its equilibrium position by the spring; analogous to the pendulum in a pendulum clock."  A pendulum is not returned toward its equilibrium position by a spring. The misplacement of the central phrase makes it seem like the phrase "analogous to the pendulum" refers to "returned by the spring", not "balance wheel".
 * "Thus it is a harmonic oscillator between the angular momentum of the wheel, and the elasticity of the spring." This is confusing. Is the harmonic oscillator physically located between the angular momentum and the elasticity?  Also, what makes it a harmonic oscillator is the "moment of inertia" of the wheel, not "angular momentum".
 * "With each sweep of the wheel (tick or beat), the escapement is released a single step..." "Swing" is a better word for what the wheel does than "sweep". Escapements don't have "steps".
 * The single purpose of an escapement is to have a step. 109.70.40.55 (talk) 14:40, 4 April 2022 (UTC)
 * "That the resonant frequency is determined by the intrinsic mass properties of the wheel and elasticity of the spring accounts for its nearly universal use as the timekeeper in mechanical watches through to the present." No, the reason for its wide use as a timekeeper is its constant oscillation rate. The constant oscillation rate is due to the factors mentioned.  And what are "intrinsic mass properties"? "Moment of inertia" would be better.  Also the long  prepositional phrase at the beginning makes the sentence awkward.
 * The wording doesn't really make clear that the wheel and spring together constitute the harmonic oscillator.
 * The wording doesn't mention the key reason why a harmonic oscillator is used: that it oscillates preferentially at a certain frequency, and resists oscillating at other rates.
 * For the most part the new wording just says the same thing in a more confusing way.--ChetvornoTALK 14:19, 2 April 2022 (UTC)


 * I agree, I think the original one is better, and I generally agree with your objections. The second one does confuse me more. — Danre98 ( talk ^ contribs ) 18:59, 2 April 2022 (UTC)
 * I also agree, the original text is clearer and more understandable. SailingInABathTub (talk) 21:00, 2 April 2022 (UTC)
 * I agree too. The new wording is obviously confusing right from the start.  Since this is pretty much unanimous, I'm going to restore the original wording
 * I have taken the liberty of removing all statements that do not agree with the near unanimous discussion here. I hope the remaining text meets with your approval, and concurs with the goals of the process you are undertaking. 109.70.40.55 (talk) 14:56, 4 April 2022 (UTC)
 * Thanks. I didn't mean to imply your ideas were without merit. You seem to have lots of expertise in this area, and there are a lot of other areas in this article, and other articles on Wikipedia about clocks and watches, that need improvement. I'll return the intro to the way it was. --ChetvornoTALK 19:27, 4 April 2022 (UTC)
 * On your removal of the term "resonance", a balance wheel is driven by a periodic force, from the escapement, so the word "resonance" applies. --ChetvornoTALK 19:34, 4 April 2022 (UTC)

simple animated diagram
The article is kinda unintuitive with describing how it works at the beginning. It requires an animated diagram. I feel it correctly describes a flywheel but doesn't actually explain the flywheel for someone who doesn't already know what a flywheel is. There is a distinction. — Preceding unsigned comment added by 101.98.178.115 (talk) 04:34, 1 June 2022 (UTC)


 * A balance wheel is not a flywheel; they work differently --ChetvornoTALK 09:54, 1 June 2022 (UTC)


 * I think you’re right though. There is a video, but a diagram would be helpful. I’ll look around --Chetvorno<i style="color: Purple;">TALK</i> 23:23, 1 June 2022 (UTC)