Ball Screw Selection and Calculations - University of Utah

Ball Screw Selection and Calculations

ME EN 7960 ? Precision Machine Design Topic 4

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-1

Ball Screw Selection Criteria

Applied Load Thrust force Required torque

Maximum Rotational Speed

Resonance (bending) of threaded shaft DN value

Ball Screw Life Basic dynamic load rating

Ball Screw Selection

Accuracy

Stiffness

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-2

1

Based on Load

? A ball screw transforms rotational motion into translational motion. As a result, the shaft is subject to loads:

? Thrust force (the sum of all external forces such as machining load, gravity, friction, inertial forces, etc.).

? Torque required to generate the thrust force.

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-3

Driving Torque to Obtain Thrust

T = Fal 2

T: driving torque [Nm]

Fa: thrust force [N] l: screw lead [m] : efficiency

Source: THK Co., Ltd.

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-4

2

Required Thrust

? The thrust is the sum of all forces acting in the axial

direction.

Fa = FM + Ff + Fi + Fg

FM: Machining force [N]

Ff:

Frictional force [N]

Fi:

Inertial force [N]

Fg: Gravitational force [N]

Source: THK Co., Ltd.

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-5

Stresses from Applied Loads

axial

=

Fa rtr2

torsional

=

2T rtr3

The equivalent (Von Mises) stress:

eq =

+ 3 2

axial

2 torsional

eq

=

4Fa dt2r

1

+

12l 2 2dt2r

2

max: Permissible stress [147 MPa]

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-6

3

Von Mises Stress [Pa]

Graphic Solution

3 .108 2. 5 .108

2 .108 1. 5 .108

1 .108 5 .107

Von Mises Stress in Shaft (Fa = 2344N)

1mm lead 2mm lead 4mm lead 5mm lead

max = 147 MPa

0 0. 00 1

0. 00 2

0. 00 3

0.004 0.005 0.006 0.007

Root Diameter [m]

0. 00 8

0. 00 9

1mm lead -> dtr > 4.6mm 2mm lead -> dtr > 4.8mm 4mm lead -> dtr > 5.2mm 5mm lead -> dtr > 5.5mm

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-7

Permissible Compressive Load

? Buckling Load

P1

=

2EI lb2

P1: Buckling load [N]

lb:

Distance between mounting positions [m]

E:

Elastic modulus [Pa]

I:

Second moment of inertia [m4]

:

Support factor

Fixed ? free:

= 0.25

Fixed ? supported:

= 2.0

Fixed ? fixed:

= 4.0

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-8

4

Fixed-Free Mount

Source: THK Co., Ltd.

Inexpensive but only applicable for short ball screws and/or slow speeds.

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-9

Fixed-Supported Mount

Most commonly used mounting setup.

Source: THK Co., Ltd.

ME EN 7960 ? Precision Machine Design ? Ball Screw Calculations

4-10

5

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