force, torque, power

[blockhed]

Hi guys,

need a bit of help with a project

i have to work out the power required for a motor in a hand blender, the
hardest fruit i need to cut is an apple,

i put a long knife on the apple and a weight of 1.2kg on the knife cut the
apple

using the equation for torque i get

Torque = r x F x sin(theta)
r = distance from pivot of the knife to the cutting point on the apple
F = force
theta = angle at which force is applied perpendicular to r

so
Torque = .31m x 1.2kg x 9.81m/s x sin(90) = 3.65 Nm

estimated time to cut the apple was 0.1s
Power = Torque / time = 3.65 / 0.1 = 36.5 W

so I need a 36.5W motor to cut the apple,

why are the hand blenders on the market all 300-600 W ?
are my calculations correct?

Thanks

 

[daestrom]

Hi guys,

need a bit of help with a project

i have to work out the power required for a motor in a hand blender, the
hardest fruit i need to cut is an apple,

i put a long knife on the apple and a weight of 1.2kg on the knife cut the
apple

using the equation for torque i get

Torque = r x F x sin(theta)
r = distance from pivot of the knife to the cutting point on the apple
F = force
theta = angle at which force is applied perpendicular to r

so
Torque = .31m x 1.2kg x 9.81m/s x sin(90) = 3.65 Nm

estimated time to cut the apple was 0.1s
Power = Torque / time = 3.65 / 0.1 = 36.5 W

For Power = Torque / time to be true, the time you're using must be the time
it takes to turn 1 radian, not the time to cut through one apple. So you're
turning your rotor assembly at 10 radians / second. That's about 95 RPM. I
think most blenders turn faster than that when switched to full power.

so I need a 36.5W motor to cut the apple,

Most blenders can cut/chop through several 'chunks' at the same time. Take
two 'beaters' and assume two of the four blades on each 'beater' is
slicing/cutting at the same time. So torque is four times higher. Now
assume it spins at about 300 RPM (31.4 radians/sec).

That works out to 4*3.65*31.4 = 459 W

daestrom

 

[Phil Scott]

--
Phil Scott
Ideas are bullet proof.

Hi guys,

need a bit of help with a project

i have to work out the power required for a motor in a hand
blender, the
hardest fruit i need to cut is an apple,

i put a long knife on the apple and a weight of 1.2kg on the
knife cut the
apple

using the equation for torque i get

Torque = r x F x sin(theta)
r = distance from pivot of the knife to the cutting point on
the apple
F = force
theta = angle at which force is applied perpendicular to r

so
Torque = .31m x 1.2kg x 9.81m/s x sin(90) = 3.65 Nm

estimated time to cut the apple was 0.1s
Power = Torque / time = 3.65 / 0.1 = 36.5 W

so I need a 36.5W motor to cut the apple,

why are the hand blenders on the market all 300-600 W ?
are my calculations correct?

Thanks

You left speed of the total disintigration out of your
equation, and assumed that the apple masher machine used knife
blades perpendicular to the apple.. it cant of course.

 

[Phil Scott]

--
Phil Scott
Ideas are bullet proof.

They also have to cut carrots, tofu, and on up to ice. While
most veggies might not be any harder to cut up than an apple
I'll bet ice sure is.

Doug T

there is also the issue of cost/vs reliablity and warranty
claims.. you wouldnt size the motor to the bare minimim...
that would be like sizing a car engine to do max 65 mph...