Continuous Change of Direction of Rotation

You've just invented a mechanical sine wave generator

<Ahem>

Assuming the drawing is showing an elevation of the machine looking at the natural horizon, the output on the pinion shaft is not sinusoidal, as the position of the pin on the RH end of the rack varies with both the vertical and the horizontal coordinates of the pin on the drive wheel.

Were the connecting rod only free in the horizontal, then the output of the pinion shaft would indeed be sinusoidal, however that is not the case here as drawn.

</Ahem>

It looks like the same situation you would have with a standard piston engine. The angular acceleration of the shaft would be equivalent to an additional mass mounted on the rack in place of the gear and shaft. (You could calculate this amount of mass from the radius of the gear and the moment of inertia of the shaft.)

So, does shaking a mass back and forth (such as a piston in an engine) require energy? Energy is force times displacement. During the time when the motor is accelerating the mass, force and displacement are opposed and energy is being transferred from the motor to the mass. During the time when the mass is decelerated, force and displacement are in the same direction, and energy is being transferred from the mass back to the motor.

I think that you can see that due to symmetry, these two actions would be equal. Half of the time, the motor is pushing the mass, and half of the time the mass is pulling the motor. No energy is required to accelerate the mass back and forth. Any energy required from the motor would be to overcome friction, a force that is always opposed to displacement.

I might suggest you add an idle hold-down gear above the gear rack centered above the lower support closest to the motor. Some side guides may be prudent as well.

Oh, and the connection of the rod to the gear rack could be through a clevis adaptor so as the hole 'wallers out' as my Grandpa use to say.... you need only replace the clevis and not the gear rack.

What about the effect on bearing???

Looks OK to me.

If the mass of the disk overcomes the mass of the rack and the rest of the assembly is properly designed for the forces involved, it should be fine.

As a wild guess, you might lose 5-10% of the motor power to frictional losses in this mechanism (depending on how well lubricated it is). Most of the power will go to whatever the reversing shaft is driving.

The 2000 rpm is not constant. Half the time the disc is causing the rack to accelerate the other half it is decelerating. There is always power loss in mechanical system do to friction. It also takes more power to move a mass from a stop then to maintain the motion. Your going to do that about 33 times a second. But power lost there is not important if the device does useful work.

A couple things:

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If the disk is turning at a steady 2000 rpm the pinion can have an instantaneous rate of 1000 rpm at intermittent moments, but only at intermittent moments.

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This next part is more about the description than the mechanism (Words are important.; those who do not share that conviction need not read any further).

The pinion will change direction of rotation continually, but it will be accelerating continuously. 'Continuous' means without cease. 'Continual' means frequently reoccurring but not without interruption.

The pinion and shaft would turn clockwise, stop, turn counterclockwise, stop... 1000 times every minute. I suppose that is what he meant by 2000 rpm?

Ah yes. I probably just misinterpreted 'rpm' as 'revolutions per minute' instead of the intended 'reversals per minute'.

Such a badly worded question, or is it?

"This pinion is fixed on a shaft which rotates at 2000rpm and it is supported with ball bearings."

The drive motor is on the disc!

Leaves a big question mark on my side!

I don't think the gearing would hold up under this kind of stress....better to have an opposing dual spring mechanism that would wind from center for both sides and a switching ratcheting flywheel for either side so that the drive motor is just used as a power booster....sort of like a mechanical clock works...

OP does not say how long the mechanism has to last. I agree that the rack would wear pretty quickly, even with proper lubrication and probably wouldn't take too long before the teeth at the ends of the "stroke" and on the pinion would fatigue if it is run continuously. Life could be extended by the selection of the proper materials in the design.

Do you really want the pinion to reverse direction? How many revolutions must it do before it changes direction?

Jim

Then your arithmetic is off. Way off.

And then it reverses?

I'd take a good look at a few electric toothbrushes before you go any further.

Any place where energy is converted or transferred, there will be power lost as heat. in the arrangement shown there are friction sources as follows:

• The bearings on the drive shaft on the right, including the crankpin bearing, which can be reduced by applying a lubricant
• Friction due to parts moving through a viscous fluid called air, which can be reduced by aerodynamic principles
• The bearing on the LH end of the connecting rod/RH end of the rack, which can be reduced by lubrication
• The support rollers for the rack, which can be reduced by lubrication
• The mesh between the rack and the pinion gear, which can be reduced by lubrication
• The bearings on the pinion shaft, which can be reduced by lubrication

Whether it is worth applying any of the above to this device is a function of size, which is not shown, and the aims of the Designer.

• The bearings supporting the rack
• The

Your pinion shaft does not rotate at 2000 rpm it ramps up to that speed over 5 revolutions and then ramps down again over the next 5 revolutions. The average speed of your pinion shaft is 1414 rpm but because the ramp curve is sinusoidal in the worst case you are changing the speed of the pinion shaft by 618 rpm in a single revolution. Given the torque imposed on the spindle shaft your quoted moment of inertia seams low. I think you will need to increase both the diameter and weight of the shaft. This and the load imposed by the unspecified external work that the shaft is doing will increase the wear on the rack and pinion, if it does not strip them completely. While your design works in theory I have serious reservations about it's durability if incorporated into any machinery.

Here is a website with "food for thought" on various mechanical movements.

There are many ways shown to convey one type of movement to another.

http://507movements.com/toc.html

Please consider that the mouvement you get is not a simple sinus curve. Due to the connecting rod finite length it will be a more complex combination of different frequencies. It must be as well considered the flank change which will reduce the life expectancy due to an alternative loading in comparison with usual gears where in most cases the load is for teeth pulsating thus offering a longer life.

As for bearings it depends what type you intend to use. Changes in direction are - depending on load- reducing the life expectancy due to a destruction of lubricating film.

In order to obtain the expected 10 rotations the stroke has to be 10*pi*D and this is also the double of the radius on the big wheel where the connecting rod is connected. You have thus 2*R=10*pi*D it does not look as your sketch

rpm is 2000 not 31400

See post #24 for derivation of 31400 based on your earlier statements.

(1. that the main motor rotates at 1000 rpm, and, 2. that you want the pinion to do 10 revs. in each direction).

Which rpm of which shaft? None of the arithmetic so far makes any sense. Please describe accurately what you are trying to do.

rpm of pinion is 2000

On your sketch it is written that the wheel at the right makes 1000 rpm.

You say that the pinion has to turn 10x for every half rotation of the motor.

This means that the pinion makes 20 rotations for 1 turn of motor you have only to MULTIPLY 20 by 1000 and you get 20*1000 = 20,000 rpm and NOT 2000 as you claim. It is only a factor 10 you missed or lost some where.

The rack and pinion is designed such that for 100 rpm of disc the pinion makes 2000 rpm

100 RPM for the disc is a whole lot better than 1000 RPM, but I think you are confusing the calculations for a belt and pulley system with those for a rack and pinion driven by a crank.

With 100 RPM for the disc, a 20:1 diameter ratio for pulleys would give a constant 2000 RPM for the small wheel, with no slippage.

With the rack and pinion, it is significantly more complicated: Assuming, as I did in the previous drawing, a 2.0 cm pitch diameter (1.0 cm pitch radius) of the pinion, then the attachment point on the disk would have to be at a 20.0 cm radius on the disc for a 20:1 ratio. Then the rack would move back and forth a distance of 40.0 cm. The pitch circumference of the pinion is 6.28 cm, so in one half revolution of the disc, the pinion would rotate 40/6.28=6.37 revolutions (not 10). At the instant when the attachment point of the connecting rod on the disc is at top dead center, the attachment point and the rack are both traveling horizontally in the shaft view, so the pinion would be rotating 2000 RPM, but that is NOT the peak velocity.

I'm not certain, but I suspect the maximum velocity may occur when the connecting rod is perpendicular to the radius of the connecting point. I won't waste my time verifying that, since it has no real bearing on your machine...If you would tell us what you are trying to accomplish, I might spend more time on it, but that seems unlikely.

The pinion comes to rest twice in every cycle as the direction reverses. It never attains a constant speed but varies speed following an approximation of the sine curve output of the crank. Do you require a peak speed of 2000 rpm which gives an average speed of 1414 rpm, or an average speed of 2000 rpm which gives a peak speed of 2829 rpm?

Assuming you have a 17mm nominal diameter shaft you could hob the pinion into the shaft the form of a single piece spline gear so problems associated with fixing the pinion to the shaft are eliminated. It also allows you to adjust the length of your spline/width of your pinion to match the imposed torque. The rack can then be machined to the optimum width to minimize it's weight and inertia. Cutting 20 teeth on a 2mm pitch gives you a 13.37mm pcd and an od. of about 15mm. If you case hardened the spline you would be looking at a torque of about 0.4Nm per mm of spline length with this size of pinion. You would need a rack length of 400mm with a total travel of 800mm per cycle. I agree with the opinion that your power shaft is only rotating at 100 rpm not 1000 rpm so you rack is moving 80m/minute. The rack is moving at a peak speed of 1.33'm/s or 1.883'm/s depending on your requirements in paragraph 1.

Your main problems are going to be lubrication, heat removal, wear and reliability. I would suggest immersing the rack and pinion in a circulating oil bath with a heat exchanger but I suspect that at those velocities the oil would cavitate

As Randall and Tornado indicate, your numbers don't compute, and you haven't told us what you are trying to accomplish. I said nothing about the load, because you haven't said where the load is located or what the device does to the load. I really can't imagine a practical use for this motion, other than for stirring something, and that would have to be at a vastly slower speed.

If the maximum speed of the pinion is to be 2000 RPM, then either (1) you'll have to be satisfied with only 2/∏ of a revolution of the pinion in each direction, and have a 2:1 ratio between the motor wheel and pinion pitch diameters, or (2) slow the main wheel down to approximately 63 RPM.

A great deal is learned by making a correct scale drawing. Here is one, using a pinion with a 2cm pitch diameter. notice that the complete device is just under 2 meters across. This is the minimum size for 10 revolutions of a Ø 2cm pinion.

I'll let you figure out how to get the connecting rod past all the rollers necessary to support the rack as it travels back and forth. Notice that the drawing shows the rack at its center position, and the connecting point to the wheel is NOT at top dead center. The OD of the main wheel is 65cm. A wheel that large spinning at 1kRPM better be very carefully balanced, and counterbalanced for the rack, connecting rod, and load.

The only way to reduce the size is to scale everything proportionately, or give up on that 10 revs of the pinion. If you went to a 1cm pitch diameter on the pinion, you could get the overall size just under a meter, but a pinion that small better be moving something like 5 or 10 grams, not 500!

Define RPM.

The only continuous rotation is made by the motor on the drive wheel.

The pinion, rack and shaft will reverse rotation.

rpm = rotation per minute

not to be mixed up with reverses per minute which should be strokes per minute for the rack.