Spiral steam. Restoration of screw pairs. Application areas of ball screws

Ball screws

A ball screw is a linear mechanical drive that converts rotation into linear motion and vice versa. Structurally, it is a long screw along which a ball nut moves. Inside the nuts between it internal thread and the screw threads roll the balls along a spiral path, then falling into the return channels - internal or external.

The ends of the screw are usually mounted on bearing supports, and the nut is connected to the moving unit. As the propeller rotates, the nut moves linearly along the propeller along with the payload. But there are also ball screws with a rotating nut - in this design the screw moves linearly relative to the nut.

An ordinary screw drive consists of a screw and a nut, which have a trapezoidal thread. In such a transmission, sliding friction occurs during movement, and about 70% of the energy is dissipated in the form of heat.

Unlike a screw-nut drive, a ball screw drive contains rolling elements (balls) that transfer mechanical energy between the nut and the screw. This provides the ball screw with significant advantages:

Efficiency can exceed 80%

the required power and torque of the drive motors is much less

wear rate is minimized

service life is much longer than that of sliding helical gears and can be determined by rolling fatigue calculations

Less heat promotes continuous operation

However, due to the low coefficient of friction, ball screws are susceptible to rolling, especially with large thread pitches. Therefore, in some cases it is necessary to use a braking device to prevent spontaneous movement of the mechanism.

Range of main characteristics of ball screws:

Nominal screw diameter – from 6 to 150 mm

Dynamic load capacity – from 1.9 to 375 kN

Static load capacity – from 2.2 to 1250 kN

Linear speed – up to 110 m/min.

There are two types of ball screws, differing in the technology of manufacturing the threaded screw: rolled (thread rolling) and ground (thread cutting followed by grinding the surface). Rolled screws are easier to produce and therefore more affordable. Ground ones are more expensive, but have significantly better thread manufacturing accuracy, and, consequently, positioning accuracy and repeatability.

An important parameter is also the thread pitch. The larger it is, the higher the maximum linear speed, but the lower the positioning accuracy and axial force.

We offer an extensive range of precision ball screws with rolled and ground screws. Corresponding accessories such as flange nuts and bearing supports are also available.

Rolled Ball Screws

SKF Ball Screws are a high-performance solution for a wide range of applications where precision, reliability and value for money are particularly important.

The use of high-tech equipment in the production of rolled screws has made it possible to achieve almost the same performance and accuracy as ground ones, but at a lower cost. The standard accuracy class is G9, according to ISO 286-2:1988. From a nominal diameter of 20 mm, rolled screws from SKF meet G7 precision. Screws with G5 precision according to ISO 3408-3:2006 are available on request, corresponding to the G5 precision of ground screws for positioning applications.

From SKF's wide range of precision rolled ball screws you can choose exactly what you need for your application:

Miniature ball screws (with a nominal diameter of 6 mm, external or internal ball recirculation) – compact, efficient system drive.

Most miniature ball screws are available in stainless steel.

Rolled ball screws with larger nominal diameters (16 to 63 mm) are available with various types nuts, with or without axial play, with preload – both for normal drive applications and for precision positioning.

These screws offer a variety of optional accessories, such as optional nut flanges and bearing supports, to simplify assembly of the complete system.

Rolled high pitch ball screws provide the highest linear speeds for specific applications.

SKF also offers ball screws with rotating nuts to reduce system inertia. You can contact us for more detailed information.

Precision Ground Ball Screws

SKF offers a comprehensive range of ground ball screws for applications where high precision and rigidity. Since the rolling surfaces are processed with special high-precision equipment, ground ball screws are easy to adapt to almost any requirement. Standard thread accuracy is G5, G3 and G1 are available upon request.

How to make the right choice?

With SKF's wide range of ground ball screws, you are sure to find exactly what you need for your application:

Metric and imperial

DIN nut or cylindrical flange

Internal or external return channels

Flange in the middle of the nut or at one of the ends

Nut with axial clearance, without clearance, with preload

Single or double nut

Standard processing of screw ends or according to customer requirements

Custom nuts can be made to order

Optional - shaft with shoulders cut from a metal plate

All accessories, including bearing supports, can be supplied already installed on the ball screw assembly.

SKF Ball Screw Catalogs

Let us consider the relationships between the forces acting in a screw pair with a rectangular thread. Let's turn the round of rectangular thread of the screw along the average diameter d 2 into an inclined plane, and replace the nut with a slider (Fig. 1). The lifting of the slide along an inclined plane corresponds to screwing the nut onto the screw.

Rice. 1 - Replace the nut with a slider

As is known from theoretical mechanics, the interaction force F between the inclined plane and the slider, which arises when it moves along the inclined plane, represents the resultant of the normal force and the friction force between them and is inclined to the normal n of the surface of their contact at a friction angle φ.

Let's break down the force F into two components: axial force F a, acting on the screw pair, and the circumferential force F t rotating the nut when screwing it on (in other cases, rotating the screw when screwing it in).

From the diagram of the distribution of forces (Fig. 1) it follows that
where ψ is the thread lead angle.

Obviously the torque T in thread, created by force F t , when tightening a nut or screwing in a screw,

or

The descent of the slider along an inclined plane (Fig. 2) corresponds to the unscrewing of a nut or screw. In this case, when expanding the interaction force F between the inclined plane and the slider on the axial force F a and circumferential force F′ t we have

Rice. 2 - Unscrewing the nut

It is obvious that when F′ t ≥0 [which corresponds to the condition tg(φ-ψ)≥0] the thread will be self-braking. Consequently, the self-braking condition of a rectangular thread is mathematically determined by the condition ψ≤φ. When lifting the slider along an inclined plane with a driving force F t (Fig. 1) to a height equal to the thread stroke P h, work of driving forces

and the work of useful resistance forces

Coefficient useful actionη of a screw pair with a rectangular thread when screwing on a nut or screwing in a screw.

or

From the analysis of the formula it follows that for a self-braking screw pair, where ψ Let us consider the power relations, self-braking conditions and efficiency of a screw pair with a triangular or trapezoidal thread. Since the reasoning and conclusions for the indicated threads are the same, we will consider them in relation to a triangular thread. If in the considered screw pair we replace the rectangular thread with a triangular one, then the friction force in the thread, and therefore the circumferential force of the screw pair, will have different values. Let us determine the friction forces and establish the relationship between the friction forces in rectangular and triangular threads. To simplify the conclusions, we will take the thread inclination angle equal to zero. Friction force for rectangular thread (Fig. 3)

where ƒ is the friction coefficient. Friction force for triangular (Fig. 4) or trapezoidal thread

where α is the thread profile angle,
ƒ′ - reduced friction coefficient:

Rice. 3 - Friction force for rectangular threads

It follows from the formula that, compared to rectangular threads, triangular and trapezoidal threads have more friction. For normal metric threadα=60° and ƒ′=1.15ƒ, for trapezoidal thread α=30° and ƒ′=1.04ƒ, therefore, in this thread the friction is greater than in a rectangular thread, but less than in a triangular thread.

Rice. 4 - Trapezoidal thread friction force

It is obvious that the relationship between the friction coefficients ƒ and ƒ′ corresponds to the relationship between the friction angles φ and φ′ where φ′ is the reduced friction angle:

The relationships between forces in rectangular and triangular threads are similar. Therefore, by analogy with the formulas, it follows that for a triangular or trapezoidal thread, the circumferential force
thread torque
the self-braking condition is determined by the expression ψ≤φ′, efficiency
and for a self-braking screw pair, where ψ Rice. 5 - End bearing surface of the nut

The frictional moment T f at the end of a nut or screw head when screwing them is determined as follows. The end bearing surface of the nut or screw head (Fig. 5) is assumed to be ring-shaped with an outer diameter D, equal to the key opening, and internal diameter d 0 equal to the diameter holes for a bolt, screw or stud. It is generally accepted that the pressure on the supporting surface is distributed evenly, i.e.

Thus, the frictional moment at the end of a nut or screw head

or finally

To simplify calculations, it is often assumed that the resultant friction force ƒF on the supporting surface of the nut or screw head acts tangentially to the circle of average diameter d c , the supporting surface and the moment

Where

The last formula provides quite sufficient accuracy for technical calculations.

It is obvious that the moment of tightening the nut or screwing in the set screw

Wear-resistant screw (screw) pairs of gerotor screw pumps.

Gerotor or single-screw pumps are positive displacement pumps; their operating principle is based on the movement of a product by a rotating rotor along the internal spiral of a two-thread fixed stator. In this case, no pressure surges are created, and the structure of the transported product is not subjected to mechanical impact. Foam concrete does not delaminate. Screw pumps are used in many industries. The pumping working element of the pump is a screw gerotor or screw pair. The screw pair consists of a single-thrust rotor rotating inside a stationary elastic double-thrust stator (cage). Geometric parameters screw pair, such as the length and diameter of the rotor and stator, pitch of the screw surface, number of steps, axial eccentricity, etc. determine the volume of the resulting working cavity between the rotor and stator and the number of such cavities. The ability of the screw pair to develop a certain pressure of the product at the outlet, pump a strictly defined amount of product per revolution of the screw (rotor) and pump solutions with a certain size of the solid fraction (2-16mm) depends on the design characteristics. A vacuum is created at the inlet of the screw pair, so the pumps are self-priming. Screw pairs of a gerotor pump are capable of pumping various abrasive solutions, thick and gas-containing liquids and are a wearing consumable part of the pump unit. When pumping abrasive plaster and concrete mortars, the working surfaces of the rotor and stator are subject to intense abrasive wear, so the rotor is made of a wear-resistant hard alloy, and the stator is made of a wear-resistant elastic material.

Scope of application of screw gerotor pumps:

— Construction industry: plastering, puttying, painting units and stations, concrete and mortar pumps, machines for concrete shotcrete and injection cement mortars in wells for building foundations, units for self-leveling floors and roofs

— Pumps for chemical production

— Multiphase pumps for pumping thick, sandy and gassy oil

— Pumps treatment facilities, sludge, storm water for wastewater, fecal for pumping manure in livestock farming, etc.

— Pumping of mine water during mining

— Food pumps for pumping pastes, creams, minced meat, molasses, purees, ketchups, chocolate, dough, perfume creams, etc.

— Pumps for pumping explosives, peat and coal chips, paper pulp, lime, clay, bitumen

Measuring dosing pumps

Advantages of screw gerotor pumps.

— The large range of screw pairs used determines a wide range of screw pumps in terms of application, performance and discharge pressure.

— The pump discharge pressure is determined only by the design of the screw pair and is constant at any rotor speed and pump performance.

— Pump performance varies with rotor speed.

— The product is supplied evenly without pressure pulsations.

— High efficiency pump

— Effectively pump thick, viscous, viscous liquids, suspensions and solutions with high content(up to 60%) gas and solid or fibrous components.

For one revolution of the rotor, a strictly fixed (up to grams) amount of liquid is pumped. Function of precise volume dosing or measurement

— Screw pumps are self-priming.

— Simplicity of the pump design - there are no rotating seals.

— Silent operation of the screw pair.

— Easy maintenance - replacing the screw pair without disassembling the pump.

The company's engineers are able to calculate, design and manufacture screw pairs with a specific set of technical characteristics or analogues of any imported screw pair according to the Customer's instructions. We produce wear-resistant screws and clamps D6-3, D8-1.5 and 2L74 for imported plastering, puttying and shotcrete units of companies Putzmeister, m-tec, Maltech, P.F.T., Putzknecht, Turbosol, Utiform, Borneman, Brinkman, Edilizia, Kaleta, MAI, Chemgrout, Foerdertechnik, Lutz,Filamos, Knoll, Power-spray, KTO,ATWG, Hi-Flex, Tumac, etc.

The company produces screw pairs to order SO-115, D-4, D-5, SO-87 with improved technical characteristics for plastering MASH-1-01, puttying SO-150B and painting units, etc. manufacturers KSOM And JSC "MISOM OP" And Oryol Construction Equipment Plant. We have modernized the designs of some screw pairs, which has increased their durability, discharge pressure, and others. technical specifications. The company manufactures screws (rotors) from wear-resistant alloys with a high content of hard carbides, so they have working life 3 times or more KSOM screws, machined from 40X steel.

The technology for producing Even Wall stator cages for screw pairs made of wear-resistant polymers has been mastered. Screw pairs we produce SO-115, D-4, D-5, SO-87 at lower prices, and in durability they are significantly superior to KSOM analogues. The price/quality ratio is unrivaled, the price is 20-30% lower, durability is 3 times higher. By purchasing and operating our pair, you will appreciate its undeniable advantages and save significant money on the screw pair and its delivery.

To create machines with computer numerical control, it is necessary to use ball screws. They differ not only appearance, but also by design. For selection a certain model You should familiarize yourself with the structure and components of the ball screw in advance.

Purpose of ball screws

All types of ball screws for CNC machines are designed to convert rotational motion into translational motion. Structurally they consist of a housing and a lead screw. They differ from each other in size and technical characteristics.

The main requirement is to minimize friction during operation. To achieve this, the surface of the components undergoes a thorough grinding process. As a result, during the movement of the lead screw there are no sharp jumps in its position relative to the housing with bearings.

Additionally, to achieve a smooth ride, not sliding friction relative to the pin and body is used, but rolling. To achieve this effect, the principle of ball bearings is used. Such a scheme increases the overload characteristics of ball screws for CNC machines and significantly increases efficiency.

Main components of ball screw:

lead screw Designed to convert rotational motion into translational motion. A thread is formed on its surface, the main characteristic is its pitch;
frame. As the lead screw moves, displacement occurs. Various machine components can be installed on the body: cutters, drills, etc.;
balls and liners. Necessary for smooth movement of the housing relative to the axis of the lead screw.

Despite all the advantages of this design, CNC ball screws are used only for medium and small machines. This is due to the possibility of screw deflection when the housing is located in its middle part. In on standing time the maximum permissible length is 1.5 m.

The screw-nut transmission has similar properties. However, this scheme is characterized by rapid wear of components due to their constant friction with each other.

Application areas of ball screws

The relative simplicity of the design and the possibility of manufacturing a ball screw with different characteristics expands the scope of its application. Nowadays, ball screws are integral components of homemade milling machines with numerical control. Well, the scope of application is not limited to this.

Due to their versatility, ball screws can be installed not only in CNC machines. Smooth running and virtually zero friction make them indispensable components in precision measuring instruments, medical installations, and mechanical engineering. Often for bundling homemade equipment they take spare parts from these devices.

This was made possible thanks to the following properties:

minimizing friction losses;
high coefficient load capacity with small dimensions of the structure;
low inertia. The movement of the body occurs simultaneously with the rotation of the screw;
no noise and smooth running.

However, the disadvantages of ball screws for CNC equipment should also be taken into account. First of all, they include complex design housings. Even if one of the components is slightly damaged, the ball screw will not be able to perform its function. There are also restrictions on the speed of rotation of the propeller. Exceeding this parameter may result in vibration.

To reduce the axial clearance, the assembly is performed with interference. To do this, balls of increased diameter or two nuts with axial displacement can be installed.

Characteristics of ball screws for CNC equipment

For selection optimal model ball screw for numerically controlled machines, please read the technical specifications. In the future they will influence performance equipment and the time of its maintenance-free operation.

The main parameter of ball screws for CNC machines is the accuracy class. It determines the degree of position error of the moving system according to the calculated characteristics. The accuracy class can be from C0 to C10. The displacement error must be given by the manufacturer, indicated in technical passport products.

Accuracy class	C0	C1	C2	C3	C5	C7	C10
Error at 300 µm	3,5	5	7	8	18	50	120
Error per screw revolution	2,5	4	5	6	8

In addition, when choosing, you need to consider the following parameters:

the ratio of the maximum and required motor speed;
total thread length of the lead screw;
average load on the entire structure;
axial load value - preload;
geometric dimensions - diameter of the screw and nut;
electric motor parameters - torque, power and other characteristics.

These data must be previously calculated. It should be remembered that the actual characteristics of ball screws for CNC equipment cannot differ from the calculated ones. Otherwise it will lead to malfunction machine

The number of revolutions of the balls in one circle will determine the degree of transmission of torque from the shaft to the housing. This parameter depends on the diameter of the balls, their number and the cross-section of the shaft.

Installing a ball screw on a CNC machine

After choosing the optimal model, it is necessary to think over the installation scheme of the ball screw on the CNC machine. To do this, a design drawing is first drawn up, and other components are purchased or manufactured.

When performing work, it is not only the technical characteristics of the ball screw that should be taken into account. Its main purpose is the movement of machine elements along a certain axis. Therefore, you should think in advance about attaching the processing unit to the ball screw housing for CNC machines. Dimensions need to be checked mounting holes, their location on the body. It should be remembered that any machining ball screw may lead to negative changes in its characteristics.

Installation procedure in the body of a CNC machine.

Determination of optimal technical characteristics.
Shaft length measurement.
Creation of a diagram for coupling the mounting part of the shaft with the motor rotor.
Installing the gear on the machine body.
Checking the functionality of the node.
Connecting all main components.

After this, you can perform the first test run of the equipment. There should be no oscillations or vibrations during operation. If they appear, perform additional component calibration.

If the ball screw breaks down during operation of a CNC machine, you can repair the transmission yourself. You can order a special kit for this. You can see the specifics of the restoration work in the video:

1. Specifications
Ball screws such as NBS are characterized by strict quality control carried out during each production process.
High performance screws allows torque reductions of up to 70% compared to traditional trapezoidal screws in applications general purpose(conversion of rotational motion into translational motion) and in special applications (conversion of translational motion into rotational movement).

1.1 Contact geometry
The Gothic arch provides significant strength to the screw while providing precision and low torque values.

2. Selection parameters of NBS ball screws (with recirculating balls)

The choice of a ball screw (with ball circulation) is determined by the following parameters:

- Accuracy class

-Thread pitch

-Nominal service life

-Method of fastening

-Critical rotation speed

-Rigidity

-Operating temperature

-Lubricant

2.1 Accuracy class
NBS ball screws (recirculating balls) are available in the following accuracy classes:

CO. C1. C2. C3. C5. C7. C10

Each accuracy class is determined by the following parameters:

E. e. ezoo. e2∏

The graph below provides a description of their meanings.

Table - Terminology for indicating accuracy class

Term	Link	Definition
Stroke compensation	T	Stroke length compensation - the difference between the theoretical and nominal stroke length; small compensation value (if compared to nominal stroke) often necessary to compensate for elongation caused by increased temperature or external loads. If this compensation is not necessary, the theoretical stroke is equal to the nominal one.
Actual stroke length	-	The actual stroke length is the axial displacement between the screw and the nut.
Average stroke length	-	The average stroke length is the straight line that comes closest to the actual stroke length; the average stroke length represents the slope of the actual stroke length.
Average stroke length deviation	E	Average stroke length deviation is the difference between average and theoretical stroke length.
Changing the course	e ezoo e2п	A stroke change is a strip with two parallel lines of average stroke length. Maximum range of changes over stroke length. Range of changes measured over a typical stroke length of 300mm. Runout error, range of change per revolution (2 radians).

Table - Values ±E and e [unit. µm]

Accuracy class			C0		C1		C2		C3		C5		C7	C10
Length progress [mm]	from:	to:	±E	e	±E	e	±E	e	±E	e	±E	e	e	e
		100	3	3	3.5	5	5	7	8	8	18	18	±50/ 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
	10000	12500									320	170

Table - Values of e zoo and e 2π [units. µm]

Accuracy class	C0	C1	C2	NW	C5	C7	C10
e zoo	3.5	5	7	8	18	50	210
e 2π	2.5	4	5	6	8

2.2 Preload and axial clearance
The preload and axial clearance of NBS ball screws are shown in the table below.

Table - Combination of preload and axial clearance

Preload class	P0	P1	P2	RZ	RA
Axial clearance	Yes	No	No	No	No
Preload	No	No	Easy	Average	Strong

The following tables list the basic guidelines for selecting the accuracy class, preload and axial clearance of NBS ball screws.

Table - Accuracy class, preload and axial clearance

Accuracy class	Preload and axial clearance	Nut type	Lead screw type
From 10	RO (with axial clearance)	Single	Knurled
C 7	P1 or RO	On demand	Rolled or straightened
C 5	On demand; standard 0TNBS-P2	On demand	step errors
C 3	On demand; standard 0TNBS-P2	On demand	Straightened, with control certificate step errors

Table - Preload force for class P2

Model	Single nut	Double nut
1605	1±3N	3 ± 6 N
2005	1±3N	3±6N
2505	2 ± 5 N	3±6N
3205	2 ± 5 N	5±8N
4005	2 ± 5 N	5±8N
2510	2 ± 5 N	5±8N
3210	3 ± 6 N	5±8N
4010	3 ± 6 N	5±8N
5010	3 ± 6 N	8 ± 12 N
6310	6 ± 10 N	8 ± 12 N
8010	6 ± 10 N	8 ± 12 N

2.3 Thread pitch
The choice of propeller pitch depends on the following formula:

Where:
Ph = screw pitch [mm]
Vmax = maximum system travel speed [m/min]
n max = maximum propeller rotation mode [min 1]

If the result of the equation is not the whole result, you should choose a value rounded up, choosing between the available steps.

Taking into account the possible variability of axial loads, caused, for example, by the presence of inertial forces, it is necessary to calculate the load value designated as “average dynamic load Pm”, which determines the same variable load coefficients.

2.4.1 Average dynamic load
To calculate a ball screw subject to variable operating conditions, the average values of Pm and n m are used:

Р m = average dynamic axial load [N]
n m = average speed[min -1 ]

Under continuous load and variable speed conditions the following values can be achieved:

Under variable load and continuous speed conditions the following values can be achieved:

Under variable load and variable speed conditions the following values can be achieved:

The choice of propeller depending on the acting and (or) required traction forces is determined by the following values:

Static load capacity Soa
Dynamic load capacity Ca

The static load capacity Coa (or load capacity factor) is defined as a load of constant intensity acting on the axis of the screw, which, at the point of maximum impact between the contacting parts, establishes a permanent deformation equal to 1/10000 of the diameter of the rolling element.

Coa values are given in the size tables.

2.5.1 Static safety factor a s The static safety factor a s (or static safety factor) is determined by the following equation:

2.5.2 Hardness factor f H
The hardness coefficient takes into account the surface hardness of the raceways:

Where:
raceway hardness HsV10 = actual raceway hardness expressed in Vickers units with a test load of 98.07 N

700HV10 = hardness equal to 700 Vickers at test load equal to 98.07 (700HV10 ≈ 60 HRC)

2.5.3 Accuracy factor f ac
The accuracy coefficient takes into account the processing tolerances of the screw, and therefore the accuracy class corresponding to the standard.
The table shows some examples.

The need for a static safety factor a s > 1 is due to the possible presence of shocks and (or) vibrations, starting and stopping torques, and random loads that can lead to system malfunction.
The table below shows the static safety factor values based on the type of application.

Load dynamic capacity Ca (or dynamic load coefficient) is a constant intense dynamic load acting on the screw axis, which determines the service life of 10 6 revolutions.

The C a values are given in the size tables.

2.7 Nominal life L

The rated life L (this is the theoretical mileage completed by at least 90% of a representative number of identical ball screws (with recirculating balls) subjected to the same load conditions without showing signs of material fatigue) is determined by the following conditions:

Nut without preload
Nut with preload

2.7.1 Nut without preload
For ball screws (with recirculating balls) with a nut without preload, the calculation of the rated life, expressed in number of revolutions, is determined by the following formula:

Where:

P m = average dynamic axial load involved [N]

Screw accuracy class from 1 to 5
Reliability up to 90%

Where:
a 1 = safety factor

2.7.2 Coefficient a 1
Coefficient a 1 takes into account the possibility of non-deflection C%.

Table - Non-deflection coefficient a 1

C%	80	85	90	92	95	96	97	98	99
a 1	1.96	1.48	1.00	0.81	0.62	0.53	0.44	0.33	0.21

It should be noted that for C% = 90 a 1 = 1.00

2.7.3 Preloaded nut
The validity of the following formulas depends on maintaining a constant preload; otherwise, the case with a nut without preload should be taken into account.
For ball screws (recirculating ball screws) with a preloaded nut, the calculation of the rated life, expressed in number of revolutions, is determined by the following formula:

Where:
L 10 = rated life [rev]
L 10 b - (C a / Pm 2) x 10 6

L 10a and L1 0b are the nominal resources for two halves of the nut.

Raceway hardness = 60HRC
Screw accuracy class from 1 to 5;
Reliability up to 90%.

If the operating conditions do not meet the above conditions, the following formula should be used:

Where:
L 10 = rated life [rev]
L 10 a = (C a /P m1) 3 X 10 6
L 10 b - (C a / Pm 2) x 10 6

a 1 = reliability coefficient;
f ho = hardness factor (see static safety factor a s)
f ac = accuracy factor (see static safety factor a s)

P m1 and P m2 - average axial dynamic loads for the two halves of the nut;

P r = preload force [N]

2.7.4 Rated service life in hours Lh

Having L 10 (nominal life, expressed in number of revolutions), you can calculate the nominal life in hours of operation L h;

Where:
L m = operating time [hours]
n m = average rotation speed [min -1 ]

m i = speed [MIN -1 ]
qi = percentage distribution [%]

2.7.5 Nominal service life in km Lkm

Having L 10 (nominal resource, expressed in number of revolutions), you can calculate the nominal resource of the distance traveled in km L km.

Where:
L km =nominal life [km]
P h = screw pitch [mm]

The following table provides an indication of typical ball screw life for general purpose applications.

2.8 Mounting method
As a rule, there are following types ball screw mounting:

The fastening method used is a function of the application conditions, ensuring rigidity and the required accuracy.

2.9 Critical rotation speed

The maximum rotation speed of the ball screw should not exceed 80% of the critical speed.
The critical rotation speed is the point at which the propeller begins to vibrate, producing a resonant effect caused by the vibration frequency matching the natural frequency of the propeller.

The value of the critical speed depends on the internal diameter of the lead screw, the method of fastening the edges and the length of the free deflection.
The critical speed is measured by the following formula:

Where:
n cr = critical speed [min -1 ]
f kn = fastening method factor
d 2 = internal diameter of the lead screw [mm]
l n = length of free deflection [mm]

Depending on the type of fastening, f kn values are supplied:

Where:
do = nominal diameter[mm]
da = ball diameter [mm]
a = contact angle (= 45)

The length of the free deflection l n is determined depending on:

-Nuts without preload

l n = distance between fastenings [mm] (in the case of “one-piece - free” fastening, the distance between the free edge of the screw and the socket must be taken into account)

-Nut with preload

l n = maximum distance between the nut half and the fastening [mm] (in the case of a “one-piece - free” fastening, the maximum distance between the nut half and the free edge of the screw must be taken into account)

n max = maximum propeller speed [revolutions/min]

The critical load is the maximum axial load that the propeller can be subjected to without affecting the stability of the system; in the event that the maximum axial load acting on the propeller reaches or exceeds the critical load value, a new form impact on the screw, which is called “peak load”, causing additional deflection in addition to simple compression.

This phenomenon, associated with the elastic properties of the component, becomes more sensitive when the large length of the free deflection of the screw has significant values in relation to its cut. The critical load value is determined by the following formula:

Where:
P cr = Critical load [N]
f kp = fastening method factor
d 2 = internal diameter of the lead screw [mm] (see critical speed)
l cr = length of free deflection [mm]

Depending on the type of fastening, fkp values are supplied:

One-piece - One-piece	f kр = 40.6
One-piece - Support	f kp = 20.4
Reference - Reference	f kp = 10.2
One-piece - Free	f kp = 2.6

To calculate the critical load, the value of la is determined by the maximum distance between the nut half and the fastener.

For greater safety, the maximum permissible axial load should be considered equal to half the critical load:

P max = maximum permissible axial load [N]

2.11 Hardness

The axial stiffness of a moving system equipped with a ball screw is determined by the following formula:

Where:
K = axial stiffness of the system
P = axial load [N]
e = axial deformation of the system [µm]

The axial stiffness of a K system is a function of the axial stiffness of the individual components that make it up: lead screw, nut, supports, connecting supports and nut.

Where:
K s = axial stiffness of the lead screw
K N = axial stiffness of nut
K in = axial stiffness of supports
Kn = axial stiffness of connection supporting elements and nuts

2.11.1 Ks - Axial stiffness of the lead screw

The stiffness value Ks is a function of the fastening system.

Mounting method: One-piece - One-piece

Where:
d 2 = internal diameter (see critical rotation speed)
l s = distance between the middle axis of two fastenings

Mounting method: One-piece - Support

Where:
d 2 = internal diameter [mm] (see critical speed)
l s = maximum distance between the center axes of the fastening and the nut [mm].

2.11.2 K N - Axial stiffness of the nut

Double nut with preload

Where:
K = table stiffness
F pr = preload force [N]

Simple nut without preload

The value of K N is determined by the following formula:

Where:
P = axial load [N]
C a = dynamic load capacity [N]

2.11.3 Kv - Axial rigidity of supports

The axial rigidity of the screw supports is determined by the rigidity of the bearings.
In the case of rigid angular contact radial ball bearings, the following formulas apply:

Where:
bv = axial deformation of the bearing
Q = load on each ball [N]
β = contact angle (45°)
d = diameter of balls [mm]
N = number of balls

The rigidity of the connecting support elements and nuts is a characteristic of the machine, which means it does not depend on the system of screw, nut, and supports.

2.12 Operating temperature

In the case of permanent-on-one-piece fastening, the possible thermal expansion caused by the increase in temperature of the screw during operation must be taken into account; such expansion, if properly provided for, imposes an additional axial load on the system, which can lead to malfunction of the system. To solve problems, it is necessary to preload the screw sufficiently.

Where:
AL = change in length [mm] a = coefficient of thermal expansion
(11.7 x 10 -6 [°C -1 ])
L = screw length [mm]
AT = temperature change [°C]

2.13 Lubrication

To lubricate NBS ball screws, the following instructions must be observed.

2.13.1 Lubrication with liquid lubricant

Should be preferred this type lubrication in case of operation at high rotation speeds. The liquid lubricants that can be used have the same characteristics as the substances used for the lubrication of rolling bearings (from VG 68 to VG 460). The choice of viscosity is a function of operating characteristics and operating environment: temperature, rotation speed, operating loads; It is only recommended to use high viscosity classes (approx. VG 400) for low-speed screws.
In this case there is no need to pay special attention for maintenance except for the constant provision of lubricating oil in the system (relubrication intervals are shorter than in grease-lubricated installations).
In any case, the liquid oil manufacturer's instructions should be followed.

2.13.2 Grease

Grease lubrication is intended for low rotational speeds.
When selecting a lubricant, the regulations applicable for the lubrication of rolling bearings must be taken into account; Therefore, it is recommended to use lithium soap-based grease rather than greases with solid additives (such as MoS2 or graphite greases), except at very low rotational speeds; however, it is recommended that you follow the grease manufacturer's instructions.

3. Torque and rated power

To approximately calculate the torque and power values of the motor for converting rotational motion into linear motion, you need to use these formulas:

Where:

Pmax = maximum effective load [N]
Ph = thread pitch [mm]
ɳ v = mechanical efficiency of the propeller (approx. 0.9)
ɳ t = mechanical efficiency of the engine-propeller transmission
(transmission with gears ɳ t = 0.95+0.98);
z = gear ratio engine - propeller

In case direct connection engine - propeller, z=1 and ɳ 2 =1.

Where:
Nm = rated motor power [kW]
Mm = rated torque [Nm]
Pmax = maximum propeller rotation [min]
z = gear ratio motor - propeller (Ptah X Z = P motor)

In the case of converting linear motion into rotational motion, there is:

M r = load torque [Nm]
P max = maximum effective load [N]
P h = thread pitch [mm]
ɳ r = mechanical efficiency (approx. 0.8

4. Installation examples

Table - Order designation

Nut type code			Direction screw	Nominal diameter screw [mm]	Pitch [mm]	Flange type	Processing code	Class accuracy	General length screw [mm]	Code preload
Single or double	Flanged or not flanged	Type
V = single W = double	F = flanged C = flanged	U I E TO M	R = right L = left	_	-	N = no cut S = single cut D = double cut	C = Straightened F = Knurled	From 0 C 1 C 2 C 3 C 5 C 7 From 10	-	P0 P1 P2 RZ P4