**4.3. Spindle headstock**

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:**

1. The ability to input user-determined conditions for the calculation and optimisation of the spindle fitting system (Figure 16);

**Figure 16.** Entering the input data

74 Performance Evaluation of Bearings

*Optimal calculated values* 

SBS stiffness will be almost fixed.

**4.3. Spindle headstock** 

rotation speed.

Bearings

**Rear support** **Front support** 



Bearings distance: L = 297 mm

Optimal bearing length: Lopt = 283.6 mm Optimal displacement at the end LOpt: yrmin = 0.00372686 mm Optimal stiffness: Krcopt = 268 322 Nmm-1

stiffness in the bearing arrangement in a bearing unit.

**The basic interactive programme offers:** 

the spindle fitting system (Figure 16);

Total displacement at the end: yr(L+a) = 0.00372931 mm **Total stiffness: Krc = 268 146 Nmm-1**


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

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

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

1. The ability to input user-determined conditions for the calculation and optimisation of


**Figure 17.** Selection of the bearing arrangement and type of bearings

Radial Ball Bearings with Angular Contact in Machine Tools 77

yC yL yO yF

**Figure 20.** Entering preliminary data for the bearings conditions

Figure 21.

**y (mm)**

The results include: applied entries

0 0,001 0,002 0,003 0,004 0,005 0,006 0,007

chosen bearing (unit) fit types

 rotational speed limit radial unit stiffness

be machined (cutting force, torque, feed , power), Figure 21;

units and the fitting as a whole, for all of the identified bearing types.

**Figure 21.** Graphical output of the dependence of partial deflection on bearing node distance

0 50 100 150 200 250 300 350 **L (mm)**

5. The calculation and optimization of the cutting parameters for the required material to

6. 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

Graphical output of partial deflections caused by bearing nodes distance are shown in

**Figure 18.** Dimensional design data of the spindle housing

**Figure 19.** Changing data of the bearings mounting



**Figure 20.** Entering preliminary data for the bearings conditions


Graphical output of partial deflections caused by bearing nodes distance are shown in Figure 21.

**Figure 21.** Graphical output of the dependence of partial deflection on bearing node distance

The results include:

76 Performance Evaluation of Bearings

**Figure 18.** Dimensional design data of the spindle housing

**Figure 19.** Changing data of the bearings mounting

grinding and boring;

3. The identification and selection of the standardized spindle nose for turning, milling,

4. The choice of the design parameters and spindle suitability for different working conditions (working accuracy, preloading, flange type, lubrication system, cooling), Figure 20;



The "Spindle Headstock" software application product is a basic programme which can be modified according to the user's wishes.

Radial Ball Bearings with Angular Contact in Machine Tools 79

We use this device to measure the deformation characteristics of the bearing node with different combinations of bearing arrangement, pre-stressed values, contact angles, loads and revolution frequencies. We use this experimental measuring head for verifying the theoretical calculation and real performances of the bearing node (stiffness, precision

running and temperature).

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 %.
