Here's an overview of some key design considerations when selecting and sizing roller screws.

Life. Expected life of a roller screw is defined as the linear travel distance that 90% of the screws are expected to meet or exceed before experiencing metal fatigue. For a single, nonpreloaded nut:

L10 = (C/F ) 3 S

where L10 = travel life in millions of mm; C = dynamic load rating, N; F = cubic mean applied load, N; and S = lead, mm.

Critical speed. Critical speed depends on screw length and the type of bearing supporting the screw. The rotational speed of a roller screw should always be less than the critical speed, determined by the following relationship.

where nc= critical rotational speed under zero axial load, rpm; do = screw diameter, mm; fs= support bearing factor (from accompanying figures); and l = screw length, mm.

Compressive axial loads reduce critical speeds while tensile loading increases them.

Mechanical speed limit. Screw length and mounting configuration are not the only parameters that affect roller-screw speed. The nuts have mechanical speed limits that applications must not exceed. Maximum speed depends on screw diameter and lubrication. Maximum mechanical speed in rpm for a single, nonpreloaded nut is:

Oil lubrication = 140,000/d0,

Grease lubrication = 90,000/do,

where d0 = screw diameter, mm.

Buckling force. Excessive compressive loads can buckle roller screws. Like critical speeds, buckling force is a function of screw length, diameter, and type of bearing supporting the screw. When sizing roller screws, the maximum applied compressive load must be less than the buckling force Fb, determined by:

where fb= buckling force bearing factor (from accompanying graphic); do= screw diameter, mm; and l = screw length, mm.

Torque. Engineers should size the roller screw's torque to match the motor. These numbers are then compared against the torque rating of the motor/drive controlling the roller-screw velocity and position. Both load torque and acceleration torque must be less than the motor's torque rating.

Calculate torque under load from:

λ = SF/(2π η)

where λ = torque, Nm; F = applied load, N; S = screw lead, m; and = motor efficiency, %.

Torque under acceleration is calculated from:

λ = (Il + Im)α

where λ = torque, Nm; Im = inertia of the proposed motor's armature (from motor specifications), N-m-sec 2 ; and = motor acceleration, rad/sec 2 .

Il = reflected inertia due to load, N-m-sec 2 , is determined from:

where S = screw lead, m; m = mass of the applied load, N; and g = gravitational constant, 9.75 m/sec 2 .

Linear speed. Linear speed of the follower (nut) is a function of the shaft's rotational speed and the roller-screw lead. Calculate linear speed of the follower from:

V = nS

where V = linear velocity, mm/sec; n = follower rotational speed, rev/sec; and S = screw lead, mm.