Operating Conditions of the Ball Screw

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 by error in relation to a 300 mm travel distance.

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 apply tension in order to prevent screw shaft runout or set a negative or positive reference travel distance value in advance to account for possible expansion or contraction from an external load or temperature change. In such cases, indicate a target value for the reference travel distance.

Representative Travel Distance

Is a straight line representing the trend of 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 ±)

Is the difference between the representative travel distance and the reference travel distance.

Fluctuation

Represents 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 in a given threaded portion of length of 300 mm.

Fluctuation/2_π

Indicates the fluctuation in one revolution of the screw shaft.

Table 1: 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	Up to
-	100	3	3	3.5	5	5	7	8	8	18	18	±50/300 mm	±100/300 mm	±210/300 mm
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	1,000	8	6	11	8	15	10	21	15	40	27
1,000	1,250	9	6	13	9	18	11	24	16	46	30
1,250	1,600	11	7	15	10	21	13	29	18	54	35
1,600	2,000	-	-	18	11	25	15	35	21	65	40
2,000	2,500	-	-	22	13	30	18	41	24	77	46
2,500	3,150	-	-	26	15	36	21	50	29	93	54
3,150	4,000	-	-	30	18	44	25	60	35	115	65
4,000	5,000	-	-	-	-	52	30	72	41	140	77
5,000	6,300	-	-	-	-	65	36	90	50	170	93
6,300	8,000	-	-	-	-	-	-	110	60	210	115
8,000	10,000	-	-	-	-	-	-	-	-	260	140

Table 2: Fluctuation in a 300 mm Threaded portion 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	-	-	-

Table 3: Types and Grades

Type	Grade	Remarks
For positioning	0, 1, 3, 5	ISO compliant
For transport	0, 1, 3, 5, 7, 10

Example: The following data were obtained by measuring the lead of a ball screw manufactured with a target reference travel distance of ‒9 μm/500 mm.

Table 4: 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 the actual travel distance while the straight line representing the trend of the (A-B) graph indicates 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: -7 μm
Fluctuation: 8.8 μm

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

Accuracy Standards for the Mounting Surface

Table 5 to Table 9 show accuracy standards for the mounting surfaces of the precision ball screw.

Table 5: Permissible Radial Runout of the Grooved Surface of the Screw and the Motor Coupling Journal in Relation to the Bearing Journals
Unit: μm

Note: The measurements for these items include the effect of the screw shaft's runout. Therefore, it is necessary to use the ratio of the overall screw shaft length to the distance between the fulcrum and the measurement point to obtain the correction value from the overall runout of the screw shaft axis, and then add that value to the value from 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 axis at the journal, refer to JIS B 1192 (ISO 3408).

Table 6: Permissible Axial Runout of the Journal End Face in Relation to the Bearing Journals

Unit: μm

Screw shaft outer diameter (mm)		Permissible axial runout (maximum)
Above	Up to	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

Table 7: 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	Up to	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

Table 8: 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

Table 9: Permissible Parallelism of the Nut Circumference (Flat Mounting Surface) to the Screw Shaft Axis

Unit: μm

Mounting reference length (mm)		Permissible parallelism
Above	Up to	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 Motor Coupling Journal in Relation to the Bearing Journals (See Table 5)

Support the journals of the screw shaft on V blocks. Place a probe on the circumference of the motor coupling journal and record the largest difference measured by the dial gauge while rotating the screw shaft through one revolution.

Radial Runout of the Grooved Surface of the Screw in Relation to the Bearing Journals (See Table 5)

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

Axial Runout of the Journal End Face in Relation to the Bearing Journals (See Table 6)

Support the journals of the screw shaft on V blocks. Place a probe on the screw shaft’s journal end face, and record the largest difference measured by the dial gauge 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 threaded portion of the screw shaft on V blocks near the nut. Place a probe on the flange end, and record the largest difference measured by the dial gauge 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 Table 8 )

Support the threaded portion of the screw shaft on V blocks near the nut. Place a probe on the circumference of the nut, and record the largest difference measured by the dial gauge 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 Table 9)

Support the threaded portion 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 measured by the dial gauge while moving the dial gauge in parallel with the screw shaft.

Overall Radial Runout of the Screw Diameter Relative to the Bearing Journals

Support the journals of the screw shaft on V blocks. Place a probe on the circumference of the screw shaft, and record the largest difference in the axial direction measured by the dial gauge at several points 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 axis at the journal, refer to JIS B 1192 (ISO 3408).

Axial Clearance of Precision Ball Screws

Table 10 shows the axial clearance of the precision ball screw. If the manufacturing length exceeds the value in Table 11, the resultant clearance may partially be negative (preload applied).
The manufacturing limit lengths of the ball screws compliant with the ISO standard are provided in Table 12. For the axial clearance of precision Caged Ball ball screws, see Precision Caged Ball Screw .

Axial Clearance of Rolled Ball Screw

Table 12 shows axial clearance of rolled ball screw.

A preload is applied in order to eliminate the axial clearance and minimize the displacement under an axial load.
A preload is generally used in applications requiring highly accurate positioning.

Rigidity of the Ball Screw under a Preload

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

Fig. 5 shows a single-nut type of 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 Fa‒Fa'. This means that the displacement of the A side is smaller because load Fa', which is applied when the A side receives no preload, is deducted from Fa.
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∝Fa^2/3. From Fig. 6, the following equations are established.

Thus, the ball screw under a preload is displaced by δa₀ when an axial load (F_t) 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).

Note: The values listed above and the preload indicated on the delivery specification drawing are without retainers, grease, or seals.

Example: When a preload of 3,000 N is provided to the Mall 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 Table 14 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 1,125 N･mm

Result

Reference torque	865 N･mn
Torque fluctuation	606 N･mm to 1,125 N･mm

Table 13: Tolerance Range in Torque Fluctuation

Reference torque N･mm		Effective thread length
		4,000mm or less										Above 4,000 mm and up to 10,000 mm
												-
		Accuracy grades					Accuracy grades					Accuracy grades
Above	Up to	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	1,000	±20%	±25%	±30%	±35%	±40%	±30%	±30%	±35%	±40%	±45%	±40%	±45%	±50%
1,000	2,500	±15%	±20%	±25%	±30%	±35%	±25%	±25%	±30%	±35%	±40%	±35%	±40%	±45%
2,500	6,300	±10%	±15%	±20%	±25%	±30%	±20%	±20%	±25%	±30%	±35%	±30%	±35%	±40%
6,300	10,000	-	-	±15%	±20%	±30%	-	-	±20%	±25%	±35%	±25%	±30%	±35%