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Conditions of the Ball Screw

Lead angle accuracy

The lead angle accuracy of the ball screw is controlled in accordance with the JIS standard JIS B 1192 (ISO 3408).
Accuracy grades C0 to C5 are defined in the linearity and the directional property, and C7 to C10 in the travel distance error in relation to 300 mm.

Actual Travel Distance

An error in the travel distance measured with an actual Ball Screw.

Reference Travel Distance

Generally, it is the same as nominal travel distance, but can be an intentionally corrected value of the nominal travel distance according to the intended use.

Target Value for Reference Travel Distance

You may provide some tension in order to prevent the screw shaft from runout, or set the reference travel distance in "negative" or "positive" value in advance given the possible expansion/contraction from external load or temperature. In such cases, indicate a target value for the reference travel distance.

Representative Travel Distance

It is a straight line representing the tendency in the actual travel distance, and obtained with the least squares method from the curve that indicates the actual travel distance.

Representative Travel Distance Error (in ±)

Difference between the representative travel distance and the reference travel distance.

Fluctuation

The maximum width of the actual travel distance between two straight lines drawn in parallel with the representative travel distance.

Fluctuation/300

Indicates a fluctuation against a given thread length of 300 mm.

Fluctuation/2π

A fluctuation in one revolution of the screw shaft.

Table1 Lead Angle Accuracy (Permissible Value)
Unit: μm
Note) Unit of effective thread length: mm
Precision Ball Screw
Rolled Ball Screw
Accuracy grades C0 C1 C2 C3 C5 C7 C8 C10
Effective thread
length
Representative
travel distance
error
Fluctuation Representative
travel distance
error
Fluctuation Representative
travel distance
error
Fluctuation Representative
travel distance
error
Fluctuation Representative
travel distance
error
Fluctuation Travel
distance
error
Travel
distance
error
Travel
distance
error
Above Or
less
- 100 3 3 3.5 5 5 7 8 8 18 18 ±50/300mm ±100/300mm ±210/300mm
100 200 3.5 3 4.5 5 7 7 10 8 20 18
200 315 4 3.5 6 5 8 7 12 8 23 18
315 400 5 3.5 7 5 9 7 13 10 25 20
400 500 6 4 8 5 10 7 15 10 27 20
500 630 6 4 9 6 11 8 16 12 30 23
630 800 7 5 10 7 13 9 18 13 35 25
800 1000 8 6 11 8 15 10 21 15 40 27
1000 1250 9 6 13 9 18 11 24 16 46 30
1250 1600 11 7 15 10 21 13 29 18 54 35
1600 2000 - - 18 11 25 15 35 21 65 40
2000 2500 - - 22 13 30 18 41 24 77 46
2500 3150 - - 26 15 36 21 50 29 93 54
3150 4000 - - 30 18 44 25 60 35 115 65
4000 5000 - - - - 52 30 72 41 140 77
5000 6300 - - - - 65 36 90 50 170 93
6300 8000 - - - - - - 110 60 210 115
8000 10000 - - - - - - - - 260 140
Table2 Fluctuation in Thread Length of 300 mm and in One Revolution (permissible value)
Unit: μm
Accuracy grades C0 C1 C2 C3 C5 C7 C8 C10
Fluctuation/300 3.5 5 7 8 18 - - -
Fluctuation/2π 3 4 5 6 8 - - -
Table3 Types and Grades
Type Grade Remarks
For positioning 0, 1, 3, 5 ISO compliant
For transport 0, 1, 3, 5, 7, 10

Example: When the lead of a Ball Screw manufactured is measured with a target value for the reference travel distance of ‒9 μm/500 mm, the following data are obtained.

Table4 Measurement Data on Travel Distance Error
Unit: μm
Command position (A) 0 50 100 150
Travel distance (B) 0 49.998 100.001 149.996
Travel distance error (A-B) 0 -0.002 +0.001 -0.004
Command position (A) 200 250 300 350
Travel distance (B) 199.995 249.993 299.989 349.985
Travel distance error (A-B) -0.005 -0.007 -0.011 -0.015
Command position (A) 400 450 500
Travel distance (B) 399.983 449.981 499.984
Travel distance error (A-B) -0.017 -0.019 -0.016

The measurement data are expressed in a graph as shown in Fig.2 .
The positioning error (A-B) is indicated as the actual travel distance while the straight line representing the tendency of the (A-B) graph refers to the representative travel distance.
The difference between the reference travel distance and the representative travel distance appears as the representative travel distance error.

[Measurements]
Representative travel distance error: -7μm
Fluctuation: 8.8μm

Accuracy of the Mounting Surface

The accuracy of the Ball Screw mounting surface complies with the JIS standard JIS B 1192 (ISO 3408).

Accuracy of the Mounting Surface

Table5 to Table9 show accuracy standards for the mounting surfaces of the precision Ball Screw.

Table5 Permissible Radial Runout of the Grooved Surface of the Screw in Relation to the Screw Shaft Support Axis and the Permissible Radial Runout of the Part-Mounting Surface
Unit: μm
Note) The measurements on these items include the effect of the runout of the screw shaft diameter. Therefore, it is necessary to obtain the correction value from the overall runout of the screw shaft axis, using the ratio of the distance between the fulcrum and measurement point to the overall screw shaft length, and add the obtained value to the table above.
Screw shaft outer
diameter (mm)
Runout (maximum)
Above Or less C0 C1 C2 C3 C5 C7
- 8 3 5 7 8 10 14
8 12 4 5 7 8 11 14
12 20 4 6 8 9 12 14
20 32 5 7 9 10 13 20
32 50 6 8 10 12 15 20
50 80 7 9 11 13 17 20
80 100 - 10 12 15 20 30

Example: model No. DIK2005-6RRGO+500LC5

Note) For the permissible overall radial runout of the outer diameter of the screw in relation to the screw shaft support axis, refer to JIS B 1192 (ISO 3408).

Table6 Permissible Axial Runout of the Support End Face in Relation to the Screw Shaft Support Axis
Unit: μm
Screw shaft outer
diameter (mm)
Permissible Axial runout
(maximum)
Above Or less C0 C1 C2 C3 C5 C7
- 8 2 3 3 4 5 7
8 12 2 3 3 4 5 7
12 20 2 3 3 4 5 7
20 32 2 3 3 4 5 7
32 50 2 3 3 4 5 8
50 80 3 4 4 5 7 10
80 100 - 4 5 6 8 11
Table7 Permissible Axial Runout of the Flange Mounting Surface in Relation to the Screw Shaft Axis
Unit: μm
Nut diameter (mm) Permissible Axial runout
(maximum)
Above Or less C0 C1 C2 C3 C5 C7
- 20 5 6 7 8 10 14
20 32 5 6 7 8 10 14
32 50 6 7 8 8 11 18
50 80 7 8 9 10 13 18
80 125 7 9 10 12 15 20
125 160 8 10 11 13 17 20
160 200 - 11 12 14 18 25
Table8 Permissible Radial Runout of the Nut Circumference in Relation to the Screw Shaft Axis
Unit: μm
Nut diameter (mm) Permissible radial runout
Above Or less C0 C1 C2 C3 C5 C7
- 20 5 6 7 9 12 20
20 32 6 7 8 10 12 20
32 50 7 8 10 12 15 30
50 80 8 10 12 15 19 30
80 125 9 12 16 20 27 40
125 160 10 13 17 22 30 40
160 200 - 16 20 25 34 50
Table9 Permissible Parallelism of the Nut Circumference (Flat Mounting Surface) to the Screw Shaft Axis
Unit: μm
Mounting reference
length (mm)
Permissible parallelism
Above Or less C0 C1 C2 C3 C5 C7
- 50 5 6 7 8 10 17
50 100 7 8 9 10 13 17
100 200 - 10 11 13 17 30

Method for Measuring Accuracy of the Mounting Surface

Radial Runout of the Circumference of the Motor-mounting Shaft-end in Relation to the Bearing Journals of the Screw Shaft (see Table5)

Support the end journal of the screw shaft on V blocks. Place a probe on the circumference of the motor-mounting shaft-end, and record the largest difference on the dial gauge as a measurement while rotating the screw shaft through one revolution.

Radial Runout of the Circumference of the Raceway Threads in Relation to the Bearing Journals of the Screw Shaft (see Table5)

Support the end journal of the screw shaft on V blocks. Place a probe on the circumference of the nut, and record the largest difference on the dial gauge as a measurement while rotating the screw shaft by one revolution without rotating the nut.

Axial Runout of the Support End Face in Relation to the Screw Shaft Axis Support (see Table6)

Support the bearing journal portions of the screw shaft on V blocks. Place a probe on the screw shaft’s supporting portion end, and record the largest difference on the dial gauge as a measurement while rotating the screw shaft through one revolution.

Axial Runout of the Flange Mounting Surface in Relation to the Screw Shaft Axis (see Table7)

Support the thread of the screw shaft on V blocks near the nut. Place a probe on the flange end, and record the largest difference on the dial gauge as a measurement while simultaneously rotating the screw shaft and the nut through one revolution.

Radial Runout of the Nut Circumference in Relation to the Screw Shaft Axis (see Table8 on A15-16 )

Support the thread of the screw shaft on V blocks near the nut. Place a probe on the circumference of the nut, and record the largest difference on the dial gauge as a measurement while rotating the nut through one revolution without rotating the screw shaft.

Parallelism of the Nut Circumference (Flat Mounting Surface) to the Screw Shaft Axis (see Table9)

Support the thread of the screw shaft on V blocks near the nut. Place a probe on the circumference of the nut (flat mounting surface), and record the largest difference on the dial gauge as a measurement while moving the dial gauge in parallel with the screw shaft.

Overall Radial Runout of the Screw Diameter Relative to the Shaft Support Axis

Support the supporting portion of the screw shaft on V blocks. Place a probe on the circumference of the screw shaft, and record the largest difference on the dial gauge at several points in the axial directions as a measurement while rotating the screw shaft through one revolution.

  • Note) For the permissible overall radial runout of the outer diameter of the screw in relation to the screw shaft support axis, refer to JIS B 1192 (ISO 3408).

Axial Clearance

Axial Clearance of the Precision Ball Screw

Table10 shows the axial clearance of the precision Ball Screw. If the manufacturing length exceeds the value in Table11 , the resultant clearance may partially be negative (preload applied).
The manufacturing limit lengths of the Ball Screws compliant with the DIN standard are provided in Table12 .For the axial clearance of the Precision Caged Ball Screw, see Precision Caged Ball Screw .

Table10 Axial Clearance of the Precision Ball Screw
Unit: μm
Clearance symbol G0 GT G1 G2 G3
Axial Clearance 0 or less 0 to 0.005 0 to 0.01 0 to 0.02 0 to 0.05
Table11 Maximum Manufacturing Length of Precision Ball Screws by Axial Clearance
Unit: μm
*When manufacturing the Ball Screw of precision-grade accuracy C7 with clearance GT or G1, the resultant clearance is partially negative.
Screw shaft
outer diameter
Clearance GT Clearance G1 Clearance G2
C0 C1 C2・C3 C5 C0 C1 C2・C3 C5 C0 C1 C2 C3 C5 C7
4・6 80 80 80 100 80 80 80 100 80 80 80 80 100 120
8 230 250 250 200 230 250 250 250 230 250 250 250 300 300
10 250 250 250 200 250 250 250 250 250 250 250 250 300 300
12・13 440 500 500 400 440 500 500 500 440 500 630 680 600 500
14 500 500 500 400 500 500 500 500 530 620 700 700 600 500
15 500 500 500 400 500 500 500 500 570 670 700 700 600 500
16 500 500 500 400 500 500 500 500 620 700 700 700 600 500
18 720 800 800 700 720 800 800 700 720 840 1000 1000 1000 1000
20 800 800 800 700 800 800 800 700 820 950 1000 1000 1000 1000
25 800 800 800 700 800 800 800 700 1000 1000 1000 1000 1000 1000
28 900 900 900 800 1100 1100 1100 900 1300 1400 1400 1400 1200 1200
30・32 900 900 900 800 1100 1100 1100 900 1400 1400 1400 1400 1200 1200
36・40・45 1000 1000 1000 800 1300 1300 1300 1000 2000 2000 2000 2000 1500 1500
50・55・63・70 1200 1200 1200 1000 1600 1600 1600 1300 2000 2500 2500 2500 2000 2000
80・100 - - - - 1800 1800 1800 1500 2000 4000 4000 4000 3000 3000

Axial Clearance of the Rolled Ball Screw

Table12 shows axial clearance of the rolled BallScrew.

Table12 Axial Clearance of the Rolled Ball Screw
Unit: μm
Screw shaft outer diameter Axial clearance (maximum)
6 to 12 0.05
14 to 28 0.1
30 to 32 0.14
36 to 45 0.17
50 0.2

Preload

A preload is provided in order to eliminate the axial clearance and minimize the displacement under an axial load.
When performing a highly accurate positioning, a preload is generally provided.

Rigidity of the Ball Screw under a Preload

When a preload is provided to the Ball Screw, the rigidity of the nut is increased.
Fig.4 shows elastic displacement curves of the Ball Screw under a preload and without a preload.

Fig.5 shows a single-nut type of the Ball Screw.

The A and B sides are provided with preload (Fa0) by changing the groove pitch in the center of the nut to create a phase. Because of the preload, the A and B sides are elastically displaced by δa0 each. If an axial load (Fa) is applied from outside in this state, the displacement of the A and B sides is calculated as follows.

In other words, the loads on the A and B sides are expressed as follows:

Therefore, under a preload, the load that the A side receives equals to Fa‒Fa'. This means that since load Fa', which is applied when the A side receives no preload, is deducted from Fa, the displacement of the A side is smaller.
This effect extends to the point where the displacement (δa0) caused by the preload applied on the B side reaches zero.
To what extent is the elastic displacement reduced? The relationship between the axial load on the Ball Screw under no preload and the elastic displacement can be expressed by δa∝Fa2/3 . From Fig.6 , the following equations are established.

Thus, the Ball Screw under a preload is displaced by δa0 when an axial load (Ft) approximately three times greater than the preload is provided from outside. As a result, the displacement of the Ball Screw under a preload is half the displacement (2δa0 ) of the Ball Screw without a preload.
As stated above, since the preloading is effective up to approximately three times the applied preload, the optimum preload is one third of the maximum axial load.
Note that an excessive preload adversely affects the service life and heat generation. The maximum preload should be set at 10% of the basic dynamic load rating (Ca) in the axial direction.

Preload Torque

The preload torque of the Ball Screw is controlled in accordance with the JIS standard JIS B 1192 (ISO 3408).

Dynamic Preload Torque

A torque required to continuously rotate the screw shaft of a Ball Screw under a given preload without an external load applied.

Actual Torque

A dynamic preload torque measured with an actual Ball Screw.

Torque Fluctuation

Variation in a dynamic preload torque set at a target value. It can be positive or negative in relation to the reference torque.

Coefficient of Torque Fluctuation

Ratio of torque fluctuation to the reference torque.

Reference Torque

A dynamic preload torque set as a target.

Calculating the Reference Torque

The reference torque of a Ball Screw provided with a preload is obtained in the following equation (4).

Example: When a preload of 3,000 N is provided to the Ball Screw model BIF4010-10G0 + 1500LC3 with a thread length of 1,300 mm (shaft diameter: 40 mm; ball center-to-center diameter:41.75 mm; lead: 10 mm), the preload torque of the Ball Screw is calculated in the steps below.

Calculating the Reference Torque
Calculating the Torque Fluctuation

Thus, with the reference torque in Table14 being between 600 and 1,000 N・mm, effective thread length 4,000 mm or less and accuracy grade C3, the coefficient of torque fluctuation is obtained as ±30%.
As a result, the torque fluctuation is calculated as follows.
865×(1±0.3) = 606 N・mm to 1125 N・mm

Result
Reference torque 865 N・mn
Torque fluctuation 606 N・mm to 1125 N・mm
Table13 Tolerance Range in Torque Fluctuation
Reference torque
N・mm
Effective thread length
4000mm or less Above 4,000 mm and
10,000 mm or less
-
Accuracy grades Accuracy grades Accuracy grades
Above Or less C0 C1 C3 C5 C7 C0 C1 C3 C5 C7 C3 C5 C7
200 400 ±30% ±35% ±40% ±50% - ±40% ±40% ±50% ±60% - - - -
400 600 ±25% ±30% ±35% ±40% - ±35% ±35% ±40% ±45% - - - -
600 1000 ±20% ±25% ±30% ±35% ±40% ±30% ±30% ±35% ±40% ±45% ±40% ±45% ±50%
1000 2500 ±15% ±20% ±25% ±30% ±35% ±25% ±25% ±30% ±35% ±40% ±35% ±40% ±45%
2500 6300 ±10% ±15% ±20% ±25% ±30% ±20% ±20% ±25% ±30% ±35% ±30% ±35% ±40%
6300 10000 - ±15% ±15% ±20% ±30% - - ±20% ±25% ±35% ±25% ±30% ±35%