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Term Description Unit
d Diameter m
F Force N
g Acceleration due to gravity ms-2
J Total inertia kgm2
JL Load inertia kgm2
JM Motor inertia kgm2
m Mass kg
M Motor torque Nm
Ma Accelerating torque Nm
ML Load torque Nm
n Rotational frequency rpm*
n1 - input rpm*
n2 - output rpm*
Δn Change of rotational frequency rpm*
p Pitch m
P Motor power kW
Pa Accelerating power kW
PL Load power absorbed kW
r Radius m
s Distance m
t Acceleration time s
Δt Acceleration period s
v Linear velocity m/min*
Δv Change of linear velocity m/min*
V Traction capacity M3s-1
W Energy J (Joule)
η Efficiency -
μ Coefficient of friction -

Note: For practical convenience, some of the units in the formulae following are not S1 units; for example, rotational frequency is commonly measured in revolutions per minute, although the S1 unit is revolutions per second. In these servo drive formulae, the terms used are as tabulated above.Those which are in non-S1 units are marked *.

Linear Motion

Linear Motion
Fig. A

Consider a body mass m acted upon by a single force F, Fig A. The body accelerates in the direction in which the force is acting, at a rate given by:

A = F/m

After a time t has elapsed, the body has achieved a velocity v, where:

v = u + at

(u is the initial velocity, before the force F was applied. If the body was initially at rest, u is zero)

The distance, s, travelled by the body during time t is

s = ut + at2/2

Distance and velocity are related by the following equation, derived from the two previous ones:

v2 - u2 = 2as

The work done by the force in accelerating the body is the product of force and distance:

W = Fs

The kinetic energy of the body, ie the energy which it possesses by virtue of its motion, is the product of its mass and the square of its velocity:

Ek = mv2/2

Furthermore, since energy is conserved, the work done by the force is equal to the change in the body's kinetic energy (neglecting losses):

W = m(v2 - u2)/2

Power is the rate at which work is done, therefore it is the product of force and velocity:

P = Fv

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Kubler Displays

The Measured Values of Inputs A and B are associated mathematically. Thus the result can also be multiplied, divided or added to an offset value, in order to obtain the desired display value. The user can consequently obtain up to three display values with just one device: Display A, Display B and a display based on the calculation of A and B. The analogue output ranges from 0/4 to 20 mA, +/-10 V or 0 to 10 V.

Danfoss Drives

As Individual Harmonics also fulfill toughest harmonic requirements, the VLT Low Harmonic Drive meets all present harmonic standards and recommendations. Unique features such as sleep mode and back channel cooling offers unmatched energy efficiency for Low Harmonic Drives. The Total Harmonic Current Distortion is reduced to less then 3% at ideal conditions and to less than 5% at heavy distortion grids with up to 2%