The decisive criteria of the quality of machining tools are their productivity and working accuracy.
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One innovated method for improving the technological parameters of manufacturing machines (machine tools) is to optimise the structure of their nodal points and machine components.
Because of the demands on machine tool productivity and accuracy, the spindle-housing system is the heart of the machine tool, Figure 1, [1]. Radial ball bearings with angular contact are employed in ever increasing arrays. The number of headstocks supported on ball bearings with angular contact is increasing proportionally with the increasing demands on the quality of the machine tool [2]. This is because these bearings can be arranged in various combinations to create bearing arrangements which can enable the reduction of both radial and axial loads. The possibility of varying the number of bearings, their preload value, dimensions and the contact angle of bearings used in the bearing nodes, creates a broad spectrum of combinations which enable us to achieve the adequate stiffness and high speed capabilities of the Spindle-Bearings System (SBS) [2], [3]. Adequate stiffness and revolving speed of the headstock are necessary conditions for meeting the manufacturing precision quality and machine tool productivity required by industry.
When designing a machine tool headstock, the starting point is the design of the spindle support, as this limits the stability, accuracy and production capacity of the machine by its stiffness and revolving speed. However, the parameters influencing the stiffness and frequency can act in opposition to each other. The selection of the type of bearing has to take into consideration the optimization of its stiffness and revolving speed characteristics. The maximum turning speed of the bearings is a function of the maximum revolving speed of the individual bearings, their number, pre-load magnitude, manufacturing precision, and the types of lubrication used.
The stiffness of the SBS depends on the stiffness of the bearings and the spindle itself. There are several methods that can be employed for determining the static stiffness of the spindle system, e.g. [1] and [2].
However, one problem which has not yet been solved is the calculation of the stiffness of the bearings, (or nodes of bearings) in the individual housing. Accurate calculation of the stiffness of the bearing nodes requires the determination of the static parameters of each bearing. From a mathematical point of view, this can be solved by using a system of non-linear differential equations, which requires the use of computers. To simplify the design, we need a static analysis which provides the basis for the dynamic characteristics of the mounting, and of the machine itself. Designers often prefer the conventional and proven methods of mounting, without taking into account the technical and technological parameters of the machine.
For the design engineer, it is important to be able to undertake a quick evaluation of various SBS variants at the preliminary design stage. The success of the design will depend on the correct choice of suitable criteria for the SBS, and if the design engineer has adequate experience in this field.
The headstock, whether tool or workpiece carrier, has a direct influence on the static and dynamic properties of the cutting process, Figure 2. The spindle-bearing system (SBS) stiffness affects the surface quality, profile, and dimensional accuracy of the parts produced. It also has a direct influence on machine tool productivity because the width of cut influences the initiation of self-induced vibration;it is directly proportional to machine tool stiffness and damping.
Complex analysis of the SBS is very difficult and complicated, [5]. The analysis requires an advanced understanding of mathematics, mechanics, machine parts, elasto-hydrodynamic theory, rolling housing techniques, and also programming skills. The results of our research into SBS have been divided into three parts:
Theoretical research - dealing with creating mathematical models
Experimental research - verifying theoretical hypotheses and results on testing devices
Application research - dealing with the special software application, Spindle Bearings for SBS design.
According to the Hertz assumptions [13], [14], there is a dependence between load 'P' and deformation 'δ' at the contact point of the ball with the plane, given by the relationship
P = kδ.δ3/2E11the bearings in the nodal points are of the same type and dimensions, with precise geometric dimensions
the value of the contact angle is the same for all directionally-arranged bearings in the nodal point, which delivers equal distribution of strain on these bearings
radial load is equally distributed onto all the bearings in the nodal point
The calculation of the stiffness of a nodal point is based on the stiffness of the bearing itself [15], which is defined as:
Kr1=dFr1dδr0E12As radial displacement δr0 is a function of contact deformation δ0 of the ball with the highest load [13], the equation for calculating the stiffness of bevelled radial bearings will have the form:
Kr1=dFr1dδ0.dδ0dδr0E13When calculating stiffness, the distribution of load among the rollers must be determined, and the dependence between the load on the top ball and external load must be found. The distribution of load in the bearing can be derived from the balance under static conditions [14],
Fr1=Fr1i='j=0zPj.cos(αj).cos(j.γ)E14whereγ=360z is the spacing angle of the balls.
The values of contact deformations δj and angles αj differ from each other around the circumference of the bearing and can be expressed as follows, (Figure 8).
δj=lrj'lp=[lz.sin(αz)+δp]2+[lz.cos(αz)+δr0.cos(j.γ)]2'lpE15cos(αj)=lz.cos(αz)+δr0.cos(j.γ)[lz.sin(αz)+δp]2+[lz.cos(αz)+δr0.cos(j.γ)]2E16By loading the pre-stressed bearing with a radial force, the distance, OAOip, between the centre of the balls is constant, (Figure 8 b, c).
lp.sin(αp)=lrj.sin(αrj)=konst.E17The dependence between the deformation of the jth ball and the top ball can be determined by the relation
δj=δ0.cos(j.γ)E18By derivation of equation (14) we get
dFr1dδ0 =i.'j=0z[dPjdδj.cos(αj)'Pj.sin(αj).dαjdδj].dαjdδ0.cos(j.γ)E19The unknown derivatives in equation (19) can be calculated by changing the relations (11), (17), (18).
dPjdδj=32kδ2/3Pj1/3E20dαjdδj='tg(αj)lrjE21dδjdδ0=cos(j.γ)E22The interdependence of the contact deformation and radial displacement, Figure 8, can be determined from the relation
dδ0dδr0 =(dδjdδ0)'1.dδjdδr0E23Where dδjdδr0 is calculated from equation (15)
dδjdδro=12.2(1zcosαz+δrocos(j.γ))cos(j.γ)(1zcosαz+δrocos(j.γ))2+(1zsinαz+δp)2=cosαjcos(j.γ)E24by inserting equations (24) and (22) into equation (23)
dδ0dδr0 =1cos(j.γ).cos(αj).cos(j.γ)=cos(αj)E25After inserting equations (25) and (19) into equation (13) we get the resulting relation for the stiffness of a pre-stressed nodal point with directionally-arranged bearings.
Kr=i.'j=0z[32.kδ2/3.Pj1/3.cos2(αj)+Pj.sin2(αj)lrj].cos2(j.γ)E26When calculating the nodal point with bearings arranged according to shape, we divide the nodal point into part '1' and part '2' (Table 1), with the same orientation of contact angles in nodes with directionally-arranged bearings, and the stiffness of the parts is calculated as follows:
Kr1=i1.'j=0z[32.kδ2/3.Pj1/3.cos2(α1j)+Pj.sin2(α1j)lr1j].cos2(j.γ)(a)Kr2=i2.'j=0z[32.kδ2/3.Pj1/3.cos2(α2j)+Pj.sin2(α2j)lr2j].cos2(j.γ)(b)E27For example in Figure 9 the total numbers of bearings in the front node SBS is 5:i1 = 3, i2 = 2, contact angles α1 = α2 = 25.
We determine the total stiffness of the nodal point by the addition of both parts of the node with the equation:
Kr=Kr1+Kr2E28In order to optimize the stiffness and load-bearing capacity for specified technological conditions, the manufacturers of machine tools have come out with a new, non-traditional solution for nodal points. By diminishing the contact angle of the bearing in Part 2, the axial stiffness of the nodal point is partially decreased, but at the same time, the value of the radial stiffness and boundary axial load is increased.
When evaluating the overall stiffness of a spindle, the designer must take into account the approximate calculation of the stiffness of the nodal points.
If all the balls are loaded, and there are more than 2 per bearing [14], the following equation can be applied:
'j=0zcos2(j.γ)=z2E29If the bearing angle is loaded only in an axial direction by the pre-stressing force, then the load on the rollers is constant around the whole circumference and can be expressed, for the particular parts of the nodal point [11] in the form
P1j=Fpi1.z.sin(αp1);P2j=Fpi2.z.sin(αp2)E30If the magnitude of the spindle bearing contact angles is not greater than 26 degrees, then the value of the second expression in equations (27a) and (27b) is negligible.
Taking these assumptions into consideration, we obtain the relationship for the approximate calculation of the radial stiffness of a bearing angle with directionally placed bearings in the form:
Kr=3.10-34.z2/3.kδ2/3.i2/3.Fp1/3.cos2(α)sin1/3(α)E31and with bearings arranged according to shape in the form:
Kr=3.10-34.z2/3.kδ2/3.i12/3.Fp1/3.cos2(α1)sin1/3(α1).[1+i22/3.cos2(α2).sin1/3(α1)i12/3.cos2(α1).sin1/3(α2)]E32where the approximate value of the deformation constant is
cδ=105.1,25.dwE33dw' is the diameter of the balls.
The pre-stressing value 'Fp' can be calculated according to the standard, STN 02 46 15. Some foreign manufacturers (for example, SKF, FAG, SNFA...) publish this value in their catalogues. The number of balls 'z' and their diameters 'dw' of some types of bearings are quoted in the literature, e.g. [16].
Based on the equation for the calculation of a nodal point axial stiffness [17]
and substituting the equation in brackets
T1=1+i223cos2α2sin1/3α1i123cos2α1sin1/3α2in equationE35and
T2=1+i223sin53α2i123sin53α1in equationE36the dependence between the axial and radial stiffness can be expressed by the relation
Kr=Ka2.1tg2α1.T2T1E37When α1=α2 in a nodal point with bearings arranged according to shape, or i = 0 in nodal points with bearings arranged according to direction, the quotient of the constants T1, T2 will be equal to 1 and the relation (37) will be simplified. Thus
Kr=Ka2.1tg2αE38Taking equations (32) and (34) into consideration, it is evident that the stiffness of the bearing arrangement depends on the number of bearings (i1andi2) in the arrangement, the dimensions of the bearings (z1, dw1 and z2, dw2), the contact angle (α1 and α2) and the preload value Fp.
The conclusions of the analysis [10] are as follows:
Radial stiffness increases proportionally with increasing values of "z", "dw", "i", "Fp" and decreases when "a" is prolonged, (Figure 10).
The parameters "z" and "dw" must be evaluated in mutual interaction because they characterize the size and dimensions of the bearings. Increasing both of these parameters, and producing the consequent increase of stiffness of the bearing arrangement, can be achieved by increasing the inner bearing diameter. The disadvantage here is that maximum revolving speed will be reduced. A more suitable solution is to decrease the width of the bearing, e.g. from B72 to B70, B719 or B718. In this case the number of rolling elements "z" will be increased and their diameter "dw" will be smaller.
Considering equations (31), (32) and (34), it is evident that "z" has a more important influence on stiffness than "dw". If the diameter of the rolling elements is smaller, their weight will also be decreased, and this fact will allow an increase in the maximum revolving speed.
The number of bearings in bearing arrangement "i" is the significant factor which can favourably influence stiffness. But the increased number of bearings will reduce the maximum revolving frequency and therefore it is possible to use this solution only for low speed spindle-bearing systems.
The preload has a relatively small effect on the stiffness of bearing arrangements. The preload real value also depends on the type of flange used. When fixed flanges are used the preload value can exceed the nominal value by several times. This will cause excessive preload values which produce heat and the bearing arrangement will break down much sooner than expected.
The contact angle "α" has a significant influence on the variation of the stiffness of the bearing arrangement. When the value of the contact angle is increased, the radial stiffness and maximum revolving speed of the bearing arrangement is also decreased. On the other hand, the axial stiffness of the bearing arrangement will be significantly increased.
In addition to the bearing arrangements, the temperature properties of the bearing supporting node have an increasingly greater significance on the high-speed capability of the bearing. The main goal of thissection is to show the SHS design under real operating conditions, taking into consideration the temperature-related behaviour of the spindle and bearing nodes.
The value of the changes in SHS temperature depends on the temperature gradient, the type of bearing arrangement (DB, DF, DT, '), the contact angle of the bearing, and the distance between the bearings arranged in the node.
The stiffness of the given example was analysed using the application software 'Spindle Headstock' [3], developed in our department.
The analysis identified the optimal stiffness, which was then applied to the headstock of the DB 24 fy. Ex-Cell-O GmbH., Eislinger precision boring machine, Figure 11, [18]
The headstock used for analysis had the following parameters:
Output power: P = 3 kW
Maximum speed: ncmax = min-1
Shape inaccuracy at boring Es' 1,5μm
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Surface roughness: Et = 1...1,5μm
Bearings: FAG B C.TPA.P4.UL in 'O' arrangement
Bearing lubrication: grease
AdvertisementThe temperature dilatation of the spindle can be described by the equation:
ΔL=λt.L.ΔtE39If the distance between the bearings in the 'DB' arrangement is short (Figure 13a), the dilatations in a radial direction is greater, [18]. The temperature gradient causes the dilatation of the inner bearing rings to be greater than that of the outer rings. Consequently, the original preload increase in temperature will be higher in the bearing node. The elevated temperature will influence the temperature gradient, and the preload value could cause bearing node failure.
The preload change was defined by the change in the distancebetween the centres of the radii of the rolling raceways:
l0=rA+rI'dwE40The distance lt at given temperature gradient in accordance with Figure 13 is
lt=a2+b2E41where
a=l0.sinα+λt2.[Bm.(tI'tA)+l0.sinα.(tI+tA'2.t0)]E42 b=l0.cosα+λt2.[Dm.(tA'tI)+l0.cosα.(tI+tA'2.t0)]E43The magnitude of deformation will be
Δδ=l0'ltE44and preload change in accordance with [18] will be
ΔF=Δδ.z2/3.cδ2/3.sin8/3αE45where
cδ=105.1,25.dwE46In the twin bearings FAG B C.TPA.P4.UL with 'DB' arrangement, at a temperature gradient of 10 ºC, and with bearing distance Bm = 29 mm, the preload will increase by 13,32 N.
Conversely, if the distance of the bearing in 'O' arrangement is long (Figure 13b), the dilatations in the axial direction prevail and cause a decrease in the value of the preload.
In the twin bearings FAG B C.TPA.P4.UL with 'DB' arrangement, at a temperature gradient of 10ºC, the preload will be decreased by 5,88 N.
In 'DB' arrangement, the main goal of temperature optimization is dependant on the determination of the optimum distance between the bearings at which a change in the preload at the given temperature gradient would be minimal.
In accordance with Figure 13 the condition
l0=ltE47must be satisfied.
By substituting equations (42) and (43) into (46), the optimal bearing separation distance from the point of view of temperature can be deduced from:
Bmopt=Dm.cosαsinα'l0.(tI+tA'2.t0)tI'tA.(1sinα)E48Figure 14 shows the change of optimal bearing distance at various values of the temperature gradient for the analysed SBS, Figure 11.
The recommendations from the point of view of temperature optimisation for the DB 24 SHS boring machine are based on the results of the analysis undertaken. From the perspective of temperature, it can be seen that a change in bearing node arrangement to individual spindle supports from 'DB' to 'DT' would be advantageous, Figure 15.
In comparison with the original bearing node arrangement, the radial stiffness of the rearranged spindle-bearing system will drop slightly, but its axial stiffness will increase. The advantage of the reconfigured SBS is that at real mean values of temperature gradient, the SBS stiffness will be almost fixed.The application software is used for calculating the SBS of machine tools supported on rolling bearings.The programme enables us to determine all elements and calculate the properties of the spindles and shafts which are supported on rolling bearings. The application software enables very fast and user-friendly calculation of the radial spindle stiffness in the bearing arrangement in a bearing unit.
The architecture of the programme contains a number of mathematical formulae which have been experimentally verified. These models respect the conditions of the spindle working accuracy in terms of the external load cutting forces, driving forces, and also spindle rotation speed.
The basic interactive programme offers:
The ability to input user-determined conditions for the calculation and optimisation of the spindle fitting system (Figure 16);
The ability to select the most appropriate bearing or bearing node arrangements (Figure 17, Figure 18, Figure 19). Data about selected bearings can be ganed from extensive databases according to the users requirements within the bearing inner diameter range:
angular contact ball bearings, type 710..150 mm
single row cylindrical roller bearings, type N50..120 mm
full cylindrical roller bearings, type NN30..440 mm
axial angular contact bar, type ..380 mm
thrust ball bearings, single direction, type ..360 mm
thrust ball bearings, double direction, type ..190 mm
deep groove ball bearings, type 63..360 mm;
The identification and selection of the standardized spindle nose for turning, milling, grinding and boring;
The choice of the design parameters and spindle suitability for different working conditions (working accuracy, preloading, flange type, lubrication system, cooling), Figure 20;
The calculation and optimization of the cutting parameters for the required material to be machined (cutting force, torque, feed, power), Figure 21;
Calculation and optimization of the design and fitment with regard to the applied conditions (revolving speed, radial stiffness, axial stiffness, rating life) for the bearing units and the fitting as a whole, for all of the identified bearing types.
Graphical output of partial deflections caused by bearing nodes distance are shown in Figure 21.
The results include:
applied entries
chosen bearing (unit) fit types
rotational speed limit
radial unit stiffness
axial unit stiffness
resultant stiffness for the chosen spindle fit system
load parameter and durability
graphical illustration of the chosen design (Table 1.).
The "Spindle Headstock" software application product is a basic programme which can be modified according to the user's wishes.
The programme has been written in the source code programming language, T-PASCAL v.7, with special additional modules for graphics. A number of interactive modules prepare user-specified data for use in AutoCAD utilising the DXF format. The programme can be used on any IBM/PC compatible computer using a HERCULES, EGA or VGA graphics adapter.
The applied software technology has been used in the industry to improve the working accuracy of the machine tools made by TOS Trenčín-Slovakia, for SN and SPSI type lathes, (2), and to design the boring headstocks for the modular single-purpose machine tools made by TOS Kuřim-Czechoslovakia, (5) TOS Lipník, SKF, GMN and INA Skalica. The programme is very effective and reliable and comparison of the results between experiments and calculations show good correlation, never exceeding 10 %.
Manufacturers across Europe seeking value-added bearing solutions have long relied upon the Neuweg brand for performance and quality as it has been part of the NSK group since . As a result, users of NWG-marked bearings not only benefit from products manufactured according to NSK standards, but can tap into the innovation and customisation capabilities of a global bearing specialist with more than a century of knowledge and expertise.
Double row ball bearings produced at the facility include self-aligning, angular contact and deep groove types. However, beyond the standard range, a specialty of the plant is its ability to manufacture variant designs in short lead times.
Customisation options
In terms of the outer ring, customers are able to request a specific diameter and width, as well as requirements for a groove or threaded bore. It is also possible to select special profiles, such as spherical, Gothic arch, V and groove, while specific diameters, cones, teeth, grooves and threads are among the customisation options for the inner ring bore. In addition, various special seal options are available, like multi-lipped, labyrinth and three-part, along with several coating choices. A new option here is DLC (Diamond-like Carbon) coating, an ultra-thin layer (1-3 µm) that provides superior wear resistance thanks to its high hardness (70 HRc).
Among the major competence areas at the Germany-based NSK plant is the agriculture industry, which has special requirements for protection against dust, dirt and shock loads. NSK has developed solutions that can cope with these harsh conditions, which include not just bearings, but fully built units like Agri Disc Hubs. These ready-to-install bearing units offer high efficiency and a robust sealing system, ensuring their success in machinery such as compact disc harrows.
Retaining the agriculture theme, NSK has developed many special bearings over the years for this demanding sector. A case in point was a special NWG series double row ball bearing (with integrated flange) required by a major agricultural machinery OEM for a high-capacity pneumatic seed drill. Alongside design innovation, high performance and reliability were among the principal factors governing selection.
Pumps and compressors provide another focus market. For these products, the Neuweg plant develops and manufactures double row angular contact ball bearings both in standard and special format, as well as QJ bearings (four-point contact bearings) in a broad range of variants.
To offer a further example, a leading woodworking machine OEM is taking advantage of a special double row angular contact ball bearing for a range of sliding table saws. The bearing features a V groove on the outer ring, along with customised dimensions and axial clearance.
Additional products manufactured at Munderkingen include support rollers and pulleys, which serve high-temperature furnaces in the steel industry, for example.
Supply chain security
A key benefit for European customers of the solutions produced in Munderkingen is rapid delivery. Located in the south of Germany, the plant has excellent access to Europe's wider transportation network, reducing any risk of supply chain disruption.
The manufacturing expertise of NSK has had a huge influence on the Neuweg brand. Thanks to the introduction of modern manufacturing strategies and processes, the Munderkingen plant can offer high levels of flexibility. It is possible to produce a vast range of products, even in small-to-medium batch sizes (from -off), providing yet another benefit for customers seeking bespoke solutions. Using NSK's expertise in engineering and innovation, special designs can progress from concept to production in just 2-5 months.
NSK can cite many, many examples of customised bearing solutions that have been developed and manufactured at Munderkingen. For instance, these products include: a fully integrated flange bearing for an elevator gearbox and a double four-point contact ball bearing with split inner ring for a mobile crane. Further examples of bespoke double row angular contact ball bearings include ones with a 35° contact angle and split inner ring for air conditioner compressors used on commercial vehicles, others offering a 25° contact angle and extended inner ring for surgical power tools, ones featuring a fully integrated flange and special sealing for a vacuum pump, and yet more with a low-friction TM seal and high-temperature plastic cage for a motorcycle gearbox. The plant has even produced support rollers for so-called 'sky cams' that suspend over the playing surface at major sporting events.
It is important for the market to understand that it is possible to propose and manufacture high added-value bearings within the NSK group, helping customers to save money through the provision of solutions that take full lifetime costs into account.
For more information, please visit ZZ Bearing.