Research of dynamic phenomena in a model engine stand

: The highest loads on the elements of the crank – piston system of the internal combustion engine occur during the combustion phase which takes place succes - sively in individual cylinders. Smaller, but also signi ﬁ - cant, loads occur beyond this phase when dynamic forces begin to play a dominant role. The latter depends on the degree of wear of the engine components. The aim of this article was to analyze the stresses in a model stand for testing dynamic phenomena in an internal combustion engine operating without the combustion process. A stand has been developed which includes a combustion engine driven by an electric motor placed on a mobile frame. The coast - down method was used to estimate the average values of the equivalent moment of inertia of the engine for various cylinder con ﬁ gurations with a lack of compression process due to a signi ﬁ cant weak - ening of the valve springs or signi ﬁ cant wear of the valve seats. This lack of compression was simulated on a bench by partially loosening the spark plug mounting. The article presents the values of the determined mean values of the equivalent moment of inertia of the engine and the stress values in the stand frame obtained from its model developed with the use of the ﬁ nite element method. The obtained values were important from the point of view of the engine dynamics simulation process outside the com - bustion area and the safe foundation and operation of the stand frame during the experimental tests.


Introduction
It is commonly known that in various compression ignition and spark ignition combustion engines, piston compressors, and pumps, a slider-crank mechanism is used to convert a rotary motion into a linear motion or vice versa [1]. Their kinematic structure is constituted to transmit the full power from the piston to the crankshaft side and vice versa. The journal bearings are often applied to deal with the high loads transmitted through the system, limiting the possibility of a compact and hermetic solution [2,3].
Nigus [4] numerically formulated the kinematics of components of an internal combustion engine crank mechanism, the forces acting on the crank mechanism, and the torque applied based on the angles of the crank and connecting rod.
Cavalca [5] proposed a mathematical model for the dynamics of the slider-connecting rod-crank system interacting with the lubrication phenomenon in bearings with alternating motion. Such a model included two submodels. The first one, based on the Eksergian equation of motion, represented the system when the connecting rod end was in contact with the rigid bearing surface without clearance. The second one, based on the Lagrange method, represented the system when the connecting rod end was in the hydrodynamic lubrication mode in the slider bore clearance. In this condition, the slider moves with the connecting rod, presenting a problem of multidegrees of freedom.
Several studies focused on the dynamic analysis of such a system, considering the relative motions of its components and loads acting on its joints.
Varedi et al. [6] studied the effect of the clearances in the joints on the dynamics of such a system and proposed an optimization of the mass distribution of the links of a mechanism to reduce or eliminate the impact forces in the clearance joint.
Using 3D simulation software, Han [7] studied the effect of clearance joints of various materials on the dynamic characteristics of the slider-crank mechanism.
Xiao et al. [8] numerically studied the dynamic behavior of the slider-crank mechanism with clearance fault. They found that the displacement and velocity response of the slider-crank mechanism depended on the clearance in a weak way, while the acceleration response of the mechanism depended on it in a significant manner. With the existence of the clearance, the revolute joint of the mechanism generated rub-impact, and the greater the clearance, the higher the impact strength. During the rub-impact process, three kinds of motion states, separation, collision, and contact, were observed.
Cheng et al. [9] elaborated a flexible multi-body system dynamics model of the crank system to model the crank in an internal-combustion engine accurately. The film hydrodynamics model was built up by linking ADAMS software and elasticity hydrodynamics subroutines. Coupling analysis between multi-flexible body system dynamics and hydrodynamic lubrication of the crank system is processed. This model allowed analyzing the effects of pressure, temperature, rotating speed, and load on the locations of journal centers.
Yaqubi et al. [10] studied the possibility of enhancing the performance by using clearance control in joints accompanied by a second actuator on the connecting rod to reduce the vibrations and load on the first actuator.
Yan and Chen [11] applied a stepper motor to step away from the traditional trajectories associated with a constant speed input. By properly designing the input speed of the mechanism, its output motion can pass through a desired trajectory. A similar strategy was utilized by Yan and Yan [12] and Yan and Soong [13] for a four-bar mechanism.
Some studies focused on adequate actuation and torque control strategies to obtain a desired output profile [14,15].
Wang and Sarlashkar [16] presented algorithms recognizing and tracking the engine crankshaft position for arbitrary cam-and crankshaft tooth wheel patterns in both steady-state and transient operating conditions. This is valuable for prototyping engine control systems.
The use of adjustable slider-crank mechanisms was also studied to obtain typical trajectories [17,18].
Beckers et al. [19] experimentally evaluated the local linear actuating principle to obtain a continuous movement of the slider mechanism loaded with a springdamper element where the top dead center and bottom dead center are reached and to minimize the loads transmitted through the mechanical structure. They found that by matching the operating frequency and resonance frequency of the system, a decrease of the loads transmitted through the system by 63% of the nominal spring load can be obtained.
Goudas et al. [20] investigated the dynamic behavior of slider-crank mechanisms with flexible supports and by driving the resisting loads affected by the angular coordinate of the crank rotation.
Alternatively, Sarigecili and Akcali [21] obtained a constant output force on the slider, independent of the crank angle, by adding a second (controlled) input force on the crank-connecting rod joint.
Soong designed the flexible linkage mechanisms with a rotational input and a linear input combined [22] and similarly, in Soong [23], where such a configuration was applied in a hybrid-driven mechanical press. Beckers et al. [1] proposed linear actuation of the slider of a slider-crank mechanism, without a rotational input. This allowed providing the full power to the linear component directly to counteract the loads, instead of providing it rotationally and fully transmitted through the mechanical system. Such a configuration allowed for minimizing the loads in the joints and decreasing the power transmitted through the system significantly, compared to the other solutions [11,22,23]. Additionally, this allowed for the downsizing of the mechanical structure. The imposing of any desired trajectory and associated control strategies under the existing mechanical limits is also allowed. Maintaining such a mechanical link increased failure safety if an excessive force is imposed on the slider component, through simplified control strategies compared to, e.g., free piston compressors [24].
Currently, one of the directions of development of internal combustion engines is the use of a strategy of variable compression ratio, which can be achieved, inter alia, by stepwise or continuously changing the configuration of the crank system [25][26][27][28][29]. In order to be able to assess the impact of such a change on the inertia forces generated during engine operation, it is necessary to conduct tests on a test bench with a known course of such forces as a function of the engine speed, rotational speed and possibly also its angular acceleration, in the event of the occurrence of torsional vibrations of the crankshaft.
One combustion engine with the possibility of making changes in its crank mechanism (e.g., via changes of counterweight masses, use of connecting rods of controlled variable length) can be used for such studies. Particularly, this engine together with a driving electric motor is seated on a common frame of the test stand.
The conditions that the structure of the frame of the model engine stand should meet include the following: providing a rigid structure that allows the drive to be transmitted in a safe and controlled manner, using durable fasteners that enable stable restraint of the internal combustion engine and the electric motor, applying vertical and horizontal adjustment of motors to level and align the drive shaft, ensuring the mobility of structures for easy transport to different classrooms, the use of road wheel locks preventing the structure from moving during the exercise, protection of the structure against corrosion, and construction cost at an acceptable level.
There are many solutions available in the market that enable the mounting of the combustion engine, e.g., workshop cranes, trolleys for servicing internal combustion engines, gantry winches, or engine dynamometers, but none of the designs meets all the assumptions.
The only solution was to design and build the frame to meet all the requirements. It was decided to make a welded structure of closed, cold-bent profiles with a rectangular cross section. To ensure the horizontal adjustment of the drive unit, eccentric holes are used. On the other hand, it is vertical adjustment, threaded rods cooperating with nuts, acting as jacks. The mobility of the structure was ensured by road wheels, which were able to carry a high dynamic load.
However, for the design of the structure, data on the load that acts on it were necessary. These loads include static loads due to gravity, dynamic loads due to the torque of the electric motor, and dynamic loads due to the movement of the crank-piston system of the combustion engine. While the first two load cases were relatively easy to determine, those from the crank-piston system became problematic.
The most important forces acting on the crank system are the forces generated by the gas pressure and the inertia force. In this case, the forces resulting from the gas pressure were neglected, as the stand is intended for testing an engine without compression.
Numerous publications on internal combustion engines deal with the dynamics of the crank-piston system [30][31][32][33][34][35][36]. They describe the method of determining the forces acting on the crank system, including the inertia forces. It turns out that the forces of inertia can be determined straightforwardly, but to do this, it is necessary to know the dimensions and masses of all elements of the crank-piston system. Additionally, each internal combustion engine is balanced at the design stage to balance the forces of the system.
Due to the lack of data on the dimensions and masses of the elements of the crank system and the lack of knowledge about the degree of balance of the considered engine, it was impossible to use the mathematical model described in the literature. Therefore, it was necessary to use a substitute dynamic model.
Various engine stands can be used for the exposition of combustion engines [37] or their repairs [38,39].
Various engine test stands of various complexity levels are also available in the market [40,41]. However, due to costs and individual requirements as to the equipment of a specific stand and the conditions for conducting tests on such a stand, such test stands are made individually. For example, such stands can be made to order according to the developed technological documentation, taking into account, inter alia, the requirements of safe operation during testing (e.g., protection of people against being hit by rotating parts, or electric arc shock, through the use of appropriate shields, individual protective measures, designation of a safe zone) and minimizing the negative impact on the environment (e.g., due to the high level of generated vibrations, noise, emission of solid particles, and exhaust gases). The research stand under analysis belonged to the group of individually designed ones.
The goal of the present study was to estimate the moment of inertia of the crank-piston system, and additionally analyze the stresses in a research stand for testing dynamic phenomena in an internal combustion engine operating without the combustion process.

Research stand studied
The research stand studied ( Figure 1) comprised a combustion engine operated without the combustion process.
The crankshaft of such an engine was driven by an electric motor linked via the driving shaft connected with elastic coupling. An electric motor was fixed to the common frame using the mounting screws. A combustion engine was mounted on the threaded brackets welded to the frame.
The position of the motor could to some extent be varied vertically with these brackets and fixed through fixing nuts. The frame was connected to swivel wheels fitted with solid rubber tires mounted horizontally in brackets. The latter were able to rotate fully about their vertical axes. As a result, the frame could be moved horizontally across the ground with sliding and rotary movements. Simple lever brakes made it possible to block individual wheels, which stabilized the position of the frame during the tests. The combustion engine utilized in the research stand was an Opel Corsa C engine with the basic parameters presented in Table 1.
This possibility of changing the position of the engine with the abovementioned brackets made it possible to adjust the coaxiality of the crankshaft of the engine and the rotor of the electric motor. Moreover, other tests on the stand are also possible, e.g, tests of the influence of the axle misalignment of the rotating elements on the physical phenomena occurring in the flexible coupling or the joint connecting the electric motor rotor with the crankshaft of the internal combustion engine. When determining the average moment of inertia of the piston and crank system of the internal combustion engine, the effect of air compression in the internal combustion engine cylinders was practically eliminated by removing the spark plugs, as mentioned in the previous section.

Static loads of the frame analyzed
As mentioned earlier, the drive unit consisted of an electric motor, a combustion engine, and a drive shaft. Each of these elements generates a load on the frame by gravity. After weighing all the elements and determining the center of gravity of the assembly consisting of the electric motor and the shaft, it was possible to calculate the static load acting on the frame (Figure 2).
The gravity forces from the electric motor were determined using equation (1). It was assumed, to simplify calculations, that the single force is just one-fourth of the weight of all electric motors: The gravity forces from the combustion engine were determined using the following equation: The force of gravity from the drive shaft with coupling was determined using the following equation: For simplicity of calculations, it was assumed that the F NW forces are acting in the same places as F NS . Such an assumption did not introduce too much error, as the center of gravity for the electric motor is shifted related to the center of the set of screws mounting the motor to the frame. Therefore, compensation to some extent has appeared between the moments from the electric motor weight and from the drive shaft with coupling.   Figure 2: Static loads acting on the frame.

Dynamic load from the torque of the electric motor
The torque generated by the electric motor acts on the power unit mounting lugs with an unknown force. However, with the data given on the nameplate, it was possible to read the rated power and rotational speed ( Figure 3). Using the above data, the torque (M obr ) of the electric motor was estimated from the following equation: where P is the power of the electric motor (W), ω is the angular velocity (rad/s), M obr is the torque (Nm), and n is the rotation speed (rpm).
Knowing the value of the torque, it was possible to determine the force value transmitted by the structure. Knowing the location of all fasteners, such a value was determined from the following equation (Figure 4 where z max is the highest distance of the clamping from the axis of rotation along the Z-axis (mm) and ΣZ i is the sum of all mounting distances from the axis of rotation along the Z-axis (mm).
A rotating motor will cause compression on some mounts and tension on others, as can be seen in Figure 5.

A dynamic equivalent model used for
determining the dynamic load from the crank-piston system inertia It was assumed that the sum of the inertia moments of the rotor of the asynchronous electric motor [42] and of the driveshaft [43] with elastic coupling [44,45] was much lower than the inertia moment of the crank-piston system.   To determine the equivalent dynamic model, the dynamic equation for the rotational motion of a system comprising rigid bodies was used. A temporary change in the moment of inertia of the crank-piston system of an internal combustion engine was achieved with an additional rotating mass with a known moment of inertia almost coaxially with the engine crankshaft. The moment of inertia was changeable, i.e., through a system of several interchangeable identical concentric rings. During studies, the system was mounted either by screwing a set of rings to additional holes made in the flywheel or by mounting the set near the flywheel on the previously made cylindrical surface of the drive shaft with coupling. The dynamic equation for the crank-piston system without additional inertial rings took a form (6), while for the case with the additional rings it took a form (7): where M T1 is the average torque of the resistance to motion for the crank-piston system without additional inertial rings (Nm), M T2 is the average torque of the resistance to motion for the crank-piston system with additional inertial rings (Nm), I 1 is the moment of inertia of the crank-piston system of the combustion engine (kg m 2 ), ε 1 is the angular acceleration of the internal combustion engine without the load (rad/s 2 ), I 2 is the moment of inertia with additional inertial rings installed in the crank-piston system (kg m 2 ), and ε 2 is the angular acceleration of the combustion engine with additional inertial rings (rad/s 2 ). It was assumed that the average torque values of the resistance to motion for the crank-piston system without (M T1 ) and with additional inertial rings (M T2 ) are close to each other, the condition of which could be written in the form (7). The torque of the resistance to motion for the crank-piston system of the combustion engine without the combustion process was composed of three parts [46]: -The reciprocating inertia torque is generated by the reciprocating part of the connecting rod system. Reciprocating mechanisms have variable inertia due to the change in the geometry through a crank revolution [47]. The average values and the range of variability of such a torque were practically the same for each measuring series, as no relative moving part of the engine was changed during measurements. -The friction torque resulted from the piston group (about 50%), main bearings and big-end bearings (about 30%), and valvetrain including crankshaft seals and timing drive (about 20%) [48]. The values of this torque were affected by the temperature; the engine speed and the kind of lubricating oil were fixed, as the measurements were conducted at room temperature, the same initial value, the range of engine speed caused by the electric motor driving its crankshaft, and the original engine oil. -The brake torque was practically excluded via dismantling the spark plugs. The holes in the cylinder head exposed to the atmosphere were connected via plastic hoses with plastic containers, which allowed for the collection of oil droplets sprayed out of these holes when rotating the crankshaft of the engine driven by the electric motor.
Based on the above comments, we adopted the assumption of the equality of the torques M T1 and M T2 .
From equations (5)- (7), formula (8) was derived that allowed the calculation of the moment of inertia of the engine crank-piston system: This means that if the additional inertial rings on the crank-piston system are used, the moment of inertia of the inertial rings can be determined, two values of time in which the engine accelerates (or decelerates) separately with and without inertial rings are measured, the average moment of inertia of the crank-piston system can be determined.

Determination of the moment of inertia of the additional inertial rings installed in the crank-piston system
The assembly of inertial rings attached to the crankshaft of the combustion engine comprises a subassembly of six steel discs with a total weight of 6.41 kg and a steel bushing weighing 0.26 kg. The dimensions of such components are shown in Figure 6. It was necessary to use such a bushing, as the attachment of the assembly of inner rings to the crankshaft was made with an M14 bolt with an outer diameter of 14 mm; the inner radius of the cylinder was 38 mm.
Since both a set of steel disks and sleeves form a hollow cylinder, their moments of inertia were determined using the following equation: where m is the mass (kg), R z is the outer radius (mm), and R w is the inner radius (mm).
The moment of inertia of the steel bushing was estimated from the following equation: The moment of inertia of the subassembly comprising six steel pulleys was estimated from the following equation:  The total moment of inertia was obtained from the following equation:

Determination of the angular acceleration of the motor with and without a load
The angular acceleration of the electric motor was also determined from the following equation: where ω is the rated speed of the electric motor (rad/s), ω 0 is the initial speed, but in this case, ω 0 = 0 (rad/s), and t is the time at which acceleration/deceleration occurs (s).
The angular speed could be determined based on the engine speed data on the nameplate and using the following equation: π n π 2 60 2 1,440 60 151 rad s . (15) The only unknown was the time at which the electric motor accelerated. This time can be the one from the motor start until it reaches its rated speed. This means that this time could be easily determined based on measurements and the observation of selected geometric details, e.g., painted markings or characteristic cut-outs made in the material of the rotating rotor or crankshaft. The measurements were recorded using a camera, and the results were recorded using a tachograph giving the number of engine revolutions and a stopwatch ( Figure 7).
As there was a need to determine the angular acceleration of the motor both without and with the application of additional inertial rings, it became obvious that it was necessary to perform measurements for both cases. Moreover, to minimize the measurement error, a series of 20 measurements were performed for each case, based on which the mean value was determined.

Determination of the angular acceleration of the motor with and without a load
An analysis of stress distribution was also conducted in the frame affected by the static and dynamic loadings mentioned. Such an analysis was conducted using the finite element method implemented in Autodesk Inventor Professional software. The geometrical model of the frame was first elaborated when all weldings were created as solid volumes.
Knowing the estimated values of loads acting on the frame, a rectangular profile 80 × 40 × 2 in accordance with the PN-EN10219-2:2019 standard was chosen for its structural components connected by welding. The required core of the threaded rod was chosen to be the one related to the M24 thread, as it provided enough resistance to compression and buckling loading. All components were treated as one elastic body. The grid of tetrahedral finite elements was generated automatically. Each element has four nodes, each of them possessing three degrees of freedom in the form of displacements u x , u y , u z along the X, Y, Z axes of the global coordinate system, respectively. The material model comprises parameters of stainless steel such as Young's modulus with a value of 210,000 MPa and the Poisson number equal to 0.3. The cylindrical surface of holes where the four brackets related to the frame were fixed. The cylindrical holes for mounting screws fixing the electric motor to the frame and the upper top front planes of the threaded rod were loaded by the related resultant forces described in the previous sections. The analysis was conducted under steadystate conditions.

Results and discussion
The resulting values of the engine start-up time are presented in Table 2 for the case without additional inertia rings and those for the case with additional inertia rings are shown in Table 3.
Using the average values of time in which the motor is accelerating and the determined angular velocity values, we have obtained the average values of angular acceleration from equation (16)    Note: t1 is the time the electric motor needs to accelerate from the start to reach the rated speed for the case without additional inertial rings (s). Note: t2 is the time the electric motor needs to accelerate from the start to reach the rated speed for the case with additional inertial rings (s).
From the determined values of the moment of inertia of the additional inertial rings and the angular acceleration values determined for the cases without and with such rings, the obtained average value of the moment of inertia of the crank-piston system of the combustion engine, using equation (18) based on equation (9): The torque of the engine with an additional inertial ring was calculated from the following equation: Then, using the previously determined mounting locations in Figure 4 and again using formula (5), it was possible to determine the values of the forces with which the load from the crank-piston system exerts on the frame, as presented by the following equation: Such forces are presented in Figure 8. After determining all the loads acting on the frame, both static and dynamic, it was possible to determine the resultant forces acting on a given fastening, using equations (21)-(24) (Figures 9 and 10):     The resulting distribution of von Mises stresses is shown in Figure 11. Their values did not exceed 36 MPa and were at least tenfold lower than the value of the yield stress for the stainless steel. The safety factor values obtained are presented in Figure 12. As their values were higher than 5.9, this provided the elevated level of safety of the frame loaded by static and dynamic forces generated during the operation of an electric motor driving a combustion engine on the research stand. The values of displacements of frame components along the Z direction being vertical are shown in Figure 13. They can cause deviation of the crankshaft axis from the horizontal plane by an angle of up to 0.024°and the rotor axis of the electric motor from the horizontal plane by an angle of up to 0.009°. The relatively high deflection of the brackets supporting the combustion engine from the side of the electric motor indicates the possibility of a large misalignment of the rotor of the electric motor and the crankshaft of the    combustion engine and the necessity to use a flexible coupling and even a joint when connecting them through the drive shaft.
To verify the results of the measurements, the calculated average value of the moment of inertia for the combustion engine crankshaft-piston system was compared with those for combustion engines with similar parameters presented in the literature.
Miljic et al. [49], for their research, created a model of the rotating elements of the DV4TD 8HT engine produced by the PSA group, using CAD. According to the research results, the moment of inertia of the entire crankshaft-piston system with similar parameters was equal to 0.1307 kg m 2 . Such a moment of inertia was smaller than the calculated one by only 2% (Table 4).
Pexa et al. [50] proposed an innovative method of evaluating the moment of inertia of the engine using loosely mounted shafts on which the vehicle wheels are guided. The acceleration of the car in the selected gear results in the transfer of torque to the shafts, which causes their rotation. Then, the electric motors connected to the shafts are turned on, which causes a continuous increase in the engine speed without the need to depress the accelerator. Based on these measurements, the instantaneous speed and acceleration waveforms are obtained, based on which it becomes possible to determine the moment of inertia of the engine ( Table 5).
The differences between the moment of inertia values obtained during tests presented in Pexa et al. [50] and the values obtained by the authors were found to be 2%.
Ubysz [51] used the Catia V5 computer program to create models of selected engines and, on their basis, determined the moments of inertia. Among them, there was a unit with the designation ZI 1.2XE. This is the same unit as the moment of inertia was calculated, hence it was a key publication for comparative analysis ( Table 6).
Comparing the calculated moment of inertia values with the values provided by Ubysz [51], a difference of 7% was obtained.

Conclusions
The following are the conclusions from the obtained results: -The average value of the moment of inertia for the crankshaft-piston system for the combustion engine analyzed has been determined experimentally on the elaborated research stand. -The use of an additional rotating mass with a known moment of inertia almost coaxially with the engine crankshaft allowed a temporary change in the moment of inertia of the crank-piston system of an internal combustion engine, similar to previous studies [52,53]. The measurement of the time of acceleration or deceleration of the crankshaft-piston assembly consecutively with and without the additional rotating mass allowed determining the average moment of inertia of the crankshaft-piston system. -The frame of the research stand can be safely loaded both from the weight of the combustion engine, electric motor, and driving shaft with coupling and from the dynamic loading from the electric motor torque and the periodically varying inertial torque of the combustion engine. -The elaborated research stand can be utilized for the determination of the moment of inertia for the crankshaft-piston system for combustion engines with similar parameters and characteristics operating without the combustion process. -Using the same or similar set of the combustion engine, electric motor, and driveshaft, the research stand can be used to study the effect of the axle misalignment of rotating elements on the physical phenomena occurring in the flexible coupling or the joint connecting the electric motor rotor with the crankshaft of the internal combustion engine. -The fact that the value of the moment of inertia obtained from calculations differed from those for similar combustion engines published in the literature in the range of 2-5% supports the correctness of the measurement results and the analytical method utilized in the present study.