# Measurement of Static Stiffness after Motion on a Three-Axis CNC Milling Table
## 2 Proposed Measurement Schemes
### Second Experiment (Scenario)--Modified Static Stiffness Measurement across All Positions  
When applying load to positions on the table, the work procedure will involve alternating load and load-free cycles. The reason for such a procedure was to estimate the thermal expansion of the table against the base during one cycle. During the cycle under load both, deformation by force and by the change in temperature, is likely to occur. During the load-free cycle, only the deformation resulting from temperature change is likely to occur. Figure 5 shows that one cycle consists of a gradual sliding of the table from position 1 to position 9 and back to position 1. Using the laser interferometer, the exact position will be captured. During the load cycle, a fixed static force \(\mathrm{F_{r}}\) will be applied to the table by means of a string transmission. The applied load will gradually increase with every other cycle. Table sliding working speed rate was the same in all experiments (F = 300 mm/min). The distances between individual positions are the same (l = 75 mm).  
Measuring scenario, see in Figure 5:  
* Running of one cycle over all positions load-free (\(\mathrm{F_{r}}\) = 0)
* SaS stiffness measurement
* Running of one cycle over all positions with the application of load (\(\mathrm{F_{ri1}}\))
* SaS stiffness measurement
* Repeating of previous steps under increased load (\(\mathrm{F_{ri2}}\), \(\mathrm{F_{ri3}}\),... )  
Third Experiment (Scenario)--Measurement by Repeated Application of Load to the Table Position with Small Back Slidings  
With the third stiffness measurement method, several repetitive return slidings at the given position of the table from both sides in the +X and \(-\)X axis will be done. Figure 6 shows that the runs will start 5 mm apart from each other and they will be executed in immediate succession alternately from both directions. A load will be added after each cycle. The maximum load was \(\mathrm{F_{r}}\) = 126 N. This repeated measurement procedure is the shortest in time. Therefore, the impact of temperature on the measurement is smaller compared to the first experiment.  
Figure 5: Second measurement scenario scheme. \(\mathrm{F_{rij}}\)—Force in the “r” direction, in the “i” position, with the load “j”. \(\mathrm{F_{ri1}}\)—Load value as a force applied in the first cycle.  
Each point of load is obtained as the mean of deviations from the five alternating runs. Thus, the stiffness course is obtained. As in previous cases of experiments number 1 and 2 respectively, the trend line slope here, too, indicates stiffness. The courses in these experiments are likely to be approximately linear. Therefore, a single value is sufficient to define the SSaS stiffness.  
Measuring scenario, see in Figure 6:  
* Forward and backward motion around one position with application of the first load (F\({}_{\rm ri1}\))
* SSaS stiffness measurement
* Repeating of the first step with gradual load addition around the position (F\({}_{\rm ri2}\), F\({}_{\rm ri3}\),... )
* SSaS stiffness measurement
* Sliding to a new position and repeating the procedure