New machine Build - Motor torque required

Hello All, I am a newbie here so please be gentle.

I am designing a machine to test vertical applied loads on a sliding table and need help to determine the correct motor size (Torque rating) to handle the load and stop start action.

Essentially it is a linear sliding table using 4x HGH35HA blocks on 2 rails.
It will have 250kg and 900kg vertical loads applied to the table (fixed castor wheel to give rolling motion) as it travels fore and aft.
It will have a 300mm stroke at 50mm/second stroke rate and each 'test' will comprise 1000 cycles/passes.
Approx 25 tests with 250kg and 6 tests with 900kg.
I am planning on using a 3205 single ball screw which is probably an overkill but better safe than sorry.
I am wanting assistance in determining the best sized motor, at this stage I am thinking of Nema52 stepper motor with 50nm torque rating and hybrid stepper driver, is 50nm sufficient or too big.
The machine will probably only conduct 40-50 tests in its entire lifetime.

Hi Tony - so the rails are horizontal? The stroke is short so to size the motors it revolves around the acceleration and deceleration distance. The most distance is 150mm ie accel for 150mm then decel for 150mm then repeat. Or you may want it to accel in 20mm? More detail about what you are testing for is helpful. This potentially has very high accels (maybe that's what you are interested in?) Could be a shaker type table? Anyways once the accel distance is specified the motor size can be calculated . Peter

a 5mm pitch screw with 50Nm torque can apply 6403kgf which is a huge load. If the rails are horizontal the friction ratio for the load is 900x0.004=3.6kgf needed to move the 900kg load. So a tiny motor will move the load. Its the required acceleration of the load (translational inertia) and rotational inertia of a large 32mm ballscrew that needs to be calculated for. In high acceleration applications an belt is often used as the ballscrew can be 80% of the required torque. Whereas a belt is nearly negligible in the inertia. I once designed a belt system to fling a piano across the room in a Titanic experience in a theme park... That was fun.. Peter

your speed is 1min for the 300mm run which is slow I'd expect a crank arm mechanism would be easier and better than a ballscrew system. But is a harmonic motion suitable? Using the slowest acceleration ie over 150mm means to achieve 50mm/s the peak speed needs to be 100mm/s this gives an acceleration of 0-0.1m/s of 0.002m/s/s say. Thats 0.002/9.81=0.0002g which is tiny. Thinking about it a very small motor will do this job easily... unless your mass is being raised vertically then that's entirely different!! Sop specify your test a little better and I can figure out the motor size. Consider using a 150mm crank (ie 300mm stroke) very easy....

The ballscrew will require electronics and programming but the crank is completely mechanical just put a variable speed motor on it... and a cycle counter... plus your 35mm rail and cars are a bit oversized. A 20mm rail will take several tonnes...

Is this a one way test or a reciprocating test? if reciprocating the crank is definitely the go.

sorry error in above the target cycle time is 6sec not 1min. Peter

32mm is overkill for 300mm travel

You can use a much smaller screw, such as 16mm, which will require much less torque to spin.

From my understanding of your description:
You are moving a plate horizontally (back and forwards) repeatedly.
There is a load applied vertically down on top of the plate.
(Is this to test wheel endurance/ performance?

A picture tells a thousand words.

Hi,

Quote:

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32mm is overkill for 300mm travel

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I'm not sure I agree. If OP is attempting to accelerate a 900kg load back and forth the thrust on the small thrust bearings of a 16mm ballscrew will wreck them in short order.
32mm ballscrews have BK25 or FK25 support bearings, the '25' signifying the internal diameter of the angular contact bearings and is a much better size for the loads that OP is talking about.

Craig

Hi Tony,
the size of the motor requires that you calculate the momentum equation.

the angular acceleration of a rotating assembly is:

dw/dt= T/J_total

where:
dw/dt is the angular acceleration in radians/ sec²
J_total is the total first moment of inertia of the assembly in kg.m²
T is the torque in N.m

In your circumstance the total first moment of inertia is the sum of smaller factors, the first moment of the ballscrew, the first moment of the armature of the servo and the first moment of the linearly accelerationg axis mass
refered to the rotating ballscrew

J_total=J_ballscrew + J_servo + J_linear

J_ballscrew= 1/2. rho. r⁴. PI. l

where:
r=radius of ballscrew in m
rho=density of steel (aprrox 8000kg/m³)
l= length of ballscrew in m

J_servo is published by the servo manufacturer. For example my 750W Delta B2 series servos have a first moment of 1.16 x 10^-4kg.m²

J_linear= 1/40 p². m

where:
m= axis mass in kg
p is the pitch of the ballscrew in m

I will start by reviewing the calaculation I made for my machine. I have 32mm 5mm pitch C5 ground ballscrews. They have a travel of 350mm but are 700mm long. The double nut reduces the travel somewhat.
These screws would be similar in size to what you would require for a 300mm travel. I have 750W delta B2 servos, as above. I assumed a linear axis mass of 150kg. The cast iron bed is 115 kg, and the balance is the
weight of the vice and the part.

J_ballscrew= 0.5 x 3.141 x 0.016⁴ x .7
=5.76 x 10^-4kg.m²

J_servo=1.16 x 10^-4kg.m²

J_linear=1/40 x 0.005² x 150
=0.94 x 10^-4kg.m²

J_total= (5.76 + 1.16 + 0.94) =7.86 x 10^-4kg.m²

This is an exceptionally important result, and one you must understand, the rotational momentum is dominated(72%) by the ballscrew....not the linear axis mass(12%).

If you choose to use a 32mm diameter screw then it is likely that the momentum will be dominated by the screw, not the 900kg you pile on the top!!! In this regard pippin's comment about a 32mm screw being
overkill warrants consideration. The momentum of a screw is proportional to the fourth power of its diameter. Thus if you were to decrease the size of the ballscrew to 20mm (rather than 32mm) the
ballscrew momentum would diminish by 85%!!!!

The first moment of the linear axis mass is proportional to the second power of pitch...so pitch is an important design parameter also but much less so than the ballscrew diameter.

Lets say you use the same servo and ballcrew as in my machine (32mm diameter, 5mm pitch,700mm long and 750W Delta B2) and recalculate for 200kg axis mass and 900kg axis mass respectively.

J_{total,200kg axis}= (5.76 + 1.16 + 1.25) x 10^-4kg.m² ......so the linear axis is only 15% of the total momentum.
J_{total,900kg axis}=(5.76 + 1.16 + 5.52 ) x 10^-4kg.m²........so the linear axis mass is now 44% of the total momentum.

Despite a heavy axis mass the rotating parts (the ballscrew and servo) still dominate the momentum. Is this what you were expecting?

All you have to decide now is what you want your acceleration to be and that will determine the torque required and therefore the servo required. Lets imagine you chose the Delta B2 as I have....what
would the acceleration be with the 900kg axis, the worst case?

dw/dt= 2.4 / 12.44 x 10^-4.....where the rated servo torque is 2.4Nm
=1930 radians/sec²

This corresponds to a linear acceleration (determined by the pitch) of:
accel=1.53 m/sec² or .15g
Note that this is the acceleration achieved with just the rated torque of the servo....not its overload rating which would be 0.45g!!!

My machine is somewhat lighter than yours and I get 0.27g at rated servo torque, but that is too scary fast for me. I dial it back to 0.15g and it's still scary bloody fast. Thus depending on what you want
to do even a 900kg axis can be accelerated by a 750W servo to 0.15g with a 32mm diameter screw and 5mm pitch. Is that enough?

Craig

Hi Tony et al - I think for this application a ballscrew is a poor choice. A flywheel and crank will do this much easier. But it comes down to what Tony is actually trying to test. So Tony what are you actually trying to get out of the test? or what are you actually testing for? or what is the actual motion profile you need? Peter

Hi Tony,
were you to reduce the ballscrew diameter to 20mm, which I think would be pretty marginal for a 900kg axis, and retain the same pitch (5mm), then with the same servo (Delta B2)
the acceleration at rated servo torque would increase to 0.24g...an improvement certainly and well into 'scary bloody fast' territory.

Quote:

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at this stage I am thinking of Nema52 stepper motor with 50nm torque rating and hybrid stepper driver, is 50nm sufficient or too big.

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A 52 size stepper motor with 50Nm??? What's the bet it will be way WAY too slow. To do 50mm/sec the motor needs to spin 10 revs/sec, and you'd only ever get
that with a low, very low inductance stepper, not a 50Nm behemouth.

Craig

Quote:

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Originally Posted by joeavaerage

Hi,



I'm not sure I agree. If OP is attempting to accelerate a 900kg load back and forth the thrust on the small thrust bearings of a 16mm ballscrew will wreck them in short order.
32mm ballscrews have BK25 or FK25 support bearings, the '25' signifying the internal diameter of the angular contact bearings and is a much better size for the loads that OP is talking about.

Craig

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From my understanding the 900kg is a vertical load on top of the plate with a rolling element (caster wheel) between the moving plate and the load.

I.e. the 900kg load is fixed horizontally, and just applying vertical pressure on the driven moving plate.

My guess is this is all to test caster wheels with a load.

The opening poster needs to clarify what is actually being done, with a picture / model.

Hi pippin,
I read the same description but came to a different conclusion. Namely that the accelerating mass (worst case) is 900kg,
it is moving on a platform formed by the four linear cars and accelerated back and forth by a ballscrew. Exactly what OP means
is still a mystery.

Craig

Thanks for your comments, and those of others in the forum. I will try and explain what I am doing.

The machine is to endurance/wear test aluminium floor mats when wheeled trolleys are rolled across them.
A section of mat will be attached to the top of the sliding table.
The table will move horizontally, (backwards and forwards).
The castor wheel will be fixed horizontally and have a vertical load applied to it, thus 'rolling' across the mat. Attached picture shows the general concept.

The 250kg and 900kg load will be static so doesnt have to be accelerated, but the surface of the mat will bumpy which will cause problems as well.

I had thought about a crank but am concerned about the thrust angle causing load binding issues, which the ball screw would not have.

In a real world situation the trolley would roll across the mat at a steady speed of approx 50-100mm/sec. I dont want the speed to be too slow so as to allow the castor wheel to get caught in the furrows of the mat, or too fast which might make it jump, ideally I think 50-70mm/sec.

Thanks for the feedback

Hi Tony - The crank is the simplest I think. The crank arm needs to be long say 3x or 4x the stroke (1000mm or longer the better) Its not speed that stops the wheel it lack of push. Is the test load applied via hydraulics or pneumatics or dead load? Peter

Hi Peter

The load will be applied via pneumatics (airbag).

When I was originally thinking of a crank I was going to use a 750w motor running 1400rpm through a worm drive gearbox to get a 90rpm output at the crank. I was trying to not overload the motor but getting the ratio correct is difficult with worm drive which is why I started looking at ball screw.