## Screw Jack Calculation - Power

Kelston has created an online System Builder for customers to quickly and easily determine an appropriate screw jack system. It achieves this by calling on customer specified requirements and established component and system data whilst taking account of the various combinations, orientations, efficiencies and fixture options of Kelston screw jacks. For more information regarding screw jacks please refer to Screw Jack Working Principles in our Knowledge Base.

**To Calculate Screw Jack System Power and Select a Suitable Motor**

Here you will be able to follow the key calculations undertaken by the system builder when determining appropriate screw jacks and a drive motor by calculating the power requirement of the system. The formulae used here are not unique to our system builder and the theory can be applied to all screw jack power calculations.

The following formula shows the relationship between Power, Torque and Speed. These factors are explored here.

$$P_{in}=T_{in}S_{in}$$

**Where:**

P_{in}= Input power (kW)

T_{in} = Input torque (Nm)

S_{in} = Worm shaft input speed (RPM)

**Worm Shaft Input Speed, S _{in}:
**

The worm shaft input speed equals the motor drive speed.

Our screw jacks come in a range of load ratings and within this range we can accommodate a large variation of travel speeds and lengths.

The speed of rotation of the worm shaft (RPM) necessary to provide the required linear travel speed is given by:

$$S_{in}={S_{t}\over S_{r}}$$

**Where:**

S_{t} = Linear travel speed (mm/min)

S_{r} = Travel rate (mm/rev)

The travel rate, S_{r}, is determined by the ratio of worm wheel teeth to worm shaft starts and the pitch of the lead screw. As an example a worm wheel with 40 teeth and a worm shaft with 2 starts would have a reduction of 20.

All combinations of ratios, starts etc and the resulting travel rates are held in a database and are called upon by the system builder. For more information on worms, wheels and travel rates, refer to the Kelston Knowledge Base.

**Input Torque for the Dynamic Load, T_{in}
**

The required torque for a given screw jack is determined by:

-The load it acts to lift,

-The effective distance from which the input force acts (the lever arm),

-The efficiency of the system.

Kelston has created a database of input torque for all appropriate combinations and sizes of screw jack. So, to calculate the required torque for a customer specified dynamic load, we take the appropriate torque and speed values for the identified screw jack and worm drive combination and calculate as follows:

$$T_{in}={T_{c}L_{d}\over L_{n}}$$

**Where:
**

T_{in} = Input torque for customer specified dynamic load (Nm)

T_{c} = Input torque for nominal capacity (Nm)

L_{d} = Dynamic load applied to jacks (kN)

L_{n} = Nominal capacity (kN)

**Power for a Single Jack:
**

From the above equation for power input, P_{in}, our units of torque (Nm) and worm input speed (RPM) would give power units of Nm.RPM. This is not particularly useful so we convert to the SI equivalent of kW as follows:

The SI units of angular speed are Radians/Second so we multiply our worm shaft input speed (RPM) by 2pi to convert to radians per minute and divide by 60 to give radians per second. A kW is 1000 Watts so we divide by 1000:

$$P_{in}=T_{in}S_{in}{2\pi\over 60\times1000}$$

Therefore, the power requirement of a single screw jack is given by:

$$P_{in}={T_{in}S_{in}\over 9550}$$

**Where:
**

P_{in} = Input power for a single screw jack (kW)

T_{in} = Input torque for customer specified dynamic Load (Nm)

S_{in} = Worm input speed (RPM)

**Screw Jack System Power Requirement:
**

The power requirements of the system determines the necessary drive motor and is found as follows:

$$P_{s}={P_{in}\times(no. of jacks)\over \eta}$$

**Where:
**

P_{s} = Required power for a system of screw jacks (kW)

P_{in} = Input power for a single screw jack (kW)

Number of Jacks = The number of jacks in the system sharing the load

eta = The system efficiency factor. This is previously determined through physical measurement and relates to the losses due to the number of screw jacks in a the system.

From the calculated system power requirements a suitable motor can be determined.