Ballscrew Selection 1.1

8/13/2019 Ballscrew Selection 1.1

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Selection criteria for ball screws

The following factors should be considered when selecting the ball screw for

a given application:

Degree of accuracy required e (lead deviation)

It is the difference between the actual mean travel and the nominal or

specified travel.

Ball screw classified to tow types according to accuracy

1-Positioning ball screw type (p)

Ball screw used for precision positioning which enables to indirect

measurement of axial travel from the angle of rotation and the lead, without

backlash (preloaded).

Backlash is total free axial displacement between the nut and the ball screw

shaft when there is no rotation between the components

2-Transport ball screw type (T)

Ball screw the travel of which is measured by a separate measuring system

independent of angle of rotation and lead of the ball screw.

Permissible deviations


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The ball screws accuracy tested in six standard tolerance grades (table

.) in conformance with International Tolerance grade numbers (IT)

(ISO 286-2:1988).

Standard tolerance grade 0

Standard tolerance grade 1 Increasing requirements on

Standard tolerance grade 3 accuracy and function




Table standard tolerance grade

Tolerances

Tolerances on specified travel ( e p) for the useful travel (l u) taken directly

from ISO 286-2 1988, table 1. Value of ( e p ) for useful travel (l u) of greater

than or equal to 3150 mm were calculated be linear extrapolation .

Tolerances on travel variation, v up, in micrometers, within useful travel l u

were evaluated using the following equations:

- Grade 0: v up = 0,0035 * l u + 2,4


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- Grade 1: v up = 0,0045 * l u + 4,6

- Grade 3: v up = 0,009 * l u + 9,2

- Grade 5: v up = 0,018 * l u + 18,4

Where l u is the geometrical mean, in millimeters, of the extreme lengths of

each step of measured travel given in Table ():

lu = (l umax *lumin )1/2


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In service load condation

Basic static load rating C o

The static load rating is an axial, concentrically acting force that

induce s a permanent deformation of 0.0001 x the ball diameter between the

ball and the ball raceway.

Basic dynamic load rating C

The dynamic load rating is an axial concentrically acting force of

constant magnitude and direction under which 90 % of a sufficiently large

amount of identical ball screws can achieve a nominal service life of one

million revolutions.

Service life

The nominal life is expressed by the number of revolutions

(number of operating hours at constant speed) that will be attained or

exceeded by 90 % of a representative sample of identical ball screws before

the first signs of material fatigue become evident. The nominal life is

designated as L or Lh depending on whether it is specified in revolutions or

hours.

Critical speed


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Rotation speed of the ball screw nut or ball screw shaft that produces

resonant vibrations of the ball screw

Buckling load

Maximum compressive axial load that can be applied to the ball screw

without resulting in its permanent structural deformation.

Rigidity of ball screws

Measure of the resistance of a ball screw to deformation (load per unit

of deformation ). Rigidity is function of the components of the ball screw

and the preload applied.

Calculation formulas

Average speed and Average load

Average speed where the speed fluctuate

Nav = average speed (rpm) , n = angular speed of ball screw shaft (rpm) ,

t = discrete time ( %)

Where load fluctuate and the speed is constant


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Where both the load and the speed fluctuate

Service life in revolutions

L = service life (revolutions)

Fm = average load (N)

C = dynamic load (N)

Service life in hours

Lh = service life (h)

L = service life (revolutions)

nav = average speed (rpm)

Drive torque and drive powerDrive torque for conversion of rotary motion into linear motion:-

Transmitted torque for conversion of linear motion into rotarymotion

M ta = drive torque (Nm)


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M te = transmitted torque (Nm)F = operating load (N)P = lead (mm) = mechanical efficiency (approx. 0.9) = mechanicalefficiency (approx. 0.8)

Drive power P a

Pa = drive power (kW) M ta = drive torque (Nm)n = speed (rpm)

ISO 3408-1:1991 Ball screws - Part 1: Vocabulary and designationISO 3408-2:1991 Ball screws - Part 2: Nominal diameters and nominal leads - Metricseries

ISO 3408-3:1992 Ball screws - Part 3: Acceptance conditions and acceptance testsISO/DIS 3408-4 Ball screws - Part 4: Axial rigidityISO/DIS 3408-5 Ball screws - Part 5: Static and dynamic axial load ratings andoperationallifetimeselection ball screw for z axis :

Step 1:- positioning accuracy

Selection according to international standard of accuracy grade for ballscrew, selected grade 3 (table )

Step 2:- ball screw lead

Lead screw = Rapid feed rate (Vmax) / Max speed of motor (N max)

Assumed rapid feed rate 5000 mm/min


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Max speed of motor 1000 rpm

Lead screw 5000/ 1000 = 5 mm

Lead screw = 5 mm

Step 3 :

Total length = thread length+ journal end length

Thread length = stroke + nut length + unused thread

The total length of z axis is 400mm

Step 4 :- Load condition

According to plasma cutting procedure there is no fluctuating load likelathes machines and milling machines the load just the weight of the axiscomponents, if the load is fluctuating , used equation no... to calculate themean load.

Assume the load of the axis component is 20kg or (200 N)

Speed condition

Assume

Step 5 :- Preload calculating

In this design used nut without preload

Step 6


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Calculating basic dynamic load

Design for 30000 hours of working

[ ] [ ]

* + Step 7 :- Screw diameter

Selected screw diameter depended on

-basic dynamic load (2258.5 N)

-ball screw lead (5 mm)

-critical speed

Critical speed depends on the of the screw diameter, the type of the endfixing and the free length.

As general critical speed of shaft Where:

g = gravity acceleration (9.81 m/s2)

st = total maximum static deflection

Critical speed can calculate from formulas which supplies from the ballscrew companies.


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Fixed - free For this design assumed

Screw diameter = 12mm

Lead = 5 mm

Length = 400 mm

Fixed - supported

HIWIN Company formula

For Rexroth Company

Buckling load:-

As general buckling

where

F = maximum or critical force (vertical load on column),

E = modulus of elasticity,


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I = area moment of inertia,

l = unsupported length of column,

K = column effective length factor, whose value depends on the conditions

of end support of the column, as follows.

Supported Supported K = 1.0.

Fixed Fixed K = 0.50.

Fixed Supported K = 1.0 /2.0.

Fixed Free K = 2.0.

The ball screws companies manufacturing ball screws from different

material so that supplied the formula and charts of the buckling for the

customers .

HIWIN Company

( )

permissible load ( )

maximum permissible load ( ) .

= factor of different mounting type

Fixed fixed


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fixed Supported

Supported supported

Fixed free

( )

Rexroth Company

( ) ( )

Supported Supported = 10.2.

Fixed Fixed = 40.6.

Fixed Supported = 20.4.

Fixed Free = 2.6.

in the both selection (HIWIN & Rexroth) the load(200 N) is less than

buckling load.


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Step 8:- Drive torque

For this axis :-

Drive Power:-

Take factor of safety = 2

Total motor power = From the HIWIN Ball screws technical information catalog, selected FSI nuttype.

The ball screw specified: - 1R16-5T3-FSI-400-500-0.012

Selection ball screw for X axis

Step 1 : positioning accuracy


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Step 2 : ball screw lead



Max speed of motor 1000 rpm

Lead screw 10000/ 1000 = 10 mm

Lead screw = 10 mm

Step 3 :Total length = thread length+ journal end length



Step 4:- Load condition


Speed condition

Assume


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Step 6 :- Calculating basic dynamic load


[] [ ] * +

Step 7 :- Screw diameter

For this design assumed


Lead = 10 mm


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Length = 1500 mm

Fixed - supported


For Rexroth Company

Buckling load:-

HIWIN Company

( ) ( )


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Rexroth Company

( ) ( )


For this axis :-

Drive Power:-


Total motor power = From the HIWIN Ball screws technical information catalog, selected FSI nuttype.

The ball screw specified: - 1R32-5T3-FSI-1500-1600-0.012


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Selection ball screw for y axis

Step 1 : positioning accuracy


Step 2 : ball screw lead



Max speed of motor 1000 rpmLead screw 10000/ 1000 = 10 mm

Lead screw = 10 mm

Step 3 :

Total length = thread length+ journal end length



Step 4:- Load condition


Speed condition

Assume


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Step 6 :- Calculating basic dynamic load


[]

[ ] * + Step 7 :- Screw diameter

For this design assumed


Lead = 10 mm

Length = 2500 mm

Fixed fixed


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For Rexroth Company

Buckling load:-

HIWIN Company

( )

( )


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Rexroth Company

( ) ( )


For this axis :-

Drive Power:-


Total motor power =


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Ballscrew Selection 1.1

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