## 3 Materials and Methods  
As previously highlighted, the discussed control system is complex, making it quite expensive. Thus, testing was undertaken to find a solution that would stabilize the reaction forces to simplify the support control system by changing the shaft structure to identify a design that distributes the reaction force over individual main journals with small variations. First, we used a specific shaft design presented in Figure 8, where the center of gravity of the crank-web and journal system were located in the axis of the shaft, which ensured that the calculated reaction forces at individual main journals were constant. Based on simulation results, a shaft was engineered so that its center of gravity was located in the main axis of the shaft to ensure minimal changes in the reaction forces at individual main journals during shaft rotation. The shaft's design was modified compared with the nominal design by attaching counterweights to crank webs opposite them. Moments of inertia of counterweights were not considered because the measurements were quasi-static. The counterweight masses were calculated from the requirement for the equilibrium of torques of gravity forces from all masses (crank webs, crankpins, additional counterweight masses) with respect to the shaft rotation axis. In practice, the solution required the determination of counterweight parameters, which, after being applied to the shaft design, caused the counterweights to balance the torques of the cranks. Three counterweight shapes (Figure 9) were considered. These counterweight shapes made it possible to distribute their masses and position their centers of gravity to obtain the torque of counterweight gravity forces that balanced the moment of the gravity forces of cranks. Solution \"c\" was chosen as the most advantageous because of its slenderness and compactness and manufacture and assembly technology. An analysis was performed for the shaft of a ship's Buckau Wolf R8 DV136 main engine, the model of which is shown in Figure 10.  
The crankshaft is 3630-mm long, weighs 9360 N, and is fitted with ten main journals, each 149 mm in diameter. It also has eight crankpins, each 114 mm in diameter. The shaft model was engineered with a design that was modified compared with the nominal one in Figure 11.  
Each crank was equipped with a pair of counterweights to compensate for the elastic deflection of the shaft rotation during measurements. The measurement procedure using the proposed solution should follow the activity diagram in Figure 12.  
Figure 8: The design of the “ideal” shaft that ensured zero deflection at journals as the shaft rotates. Figure 10: View of the crankshaft of the Buckau Wolf R8 DV 136 medium-speed main propulsion engine [39]. Figure 9: Analyzed counterweight design variants: (**a**) square/rectangle counterweight; (**b**) half-circle counterweight; (**c**) “hammer”-shaped counterweight. According to the assumptions, the procedure consists of the following steps:  
1. Calculating the reaction forces at the supports of the analyzed shaft for specified increments of the rotation angle from 0-360\({}^{\circ}\), e.g., every 15 degrees. 2. Determining balancing masses, the locations of their centers of gravity, and the position of masses on the crank to obtain the minimum changes in reaction forces for a full shaft rotation (as shown in the example). In practice, a reaction force deviation equal to approx. 0.1-0.5% prevents a shaft's elastic deformation from affecting the accuracy of profile measurements. 3. Fitting the crank with a correction device with weights that correspond to the calculated reaction forces. The device should be installed in the crank's plane of symmetry, perpendicular to the longitudinal axis of the crankshaft. The weight must be located symmetrically, opposite the crankspin, for which the indications of the correction device's displacement sensor may be helpful. 4. Adjusting weights so that the center of gravity of the device with the weights is as recommended in point 2.