Dynamic Loading Analysis of Involute Gears Considering Lubrication Performance

PurposeThe safety assessment of engineering structures under repeated variable dynamic loads such as seismic and wind loads can be considered as a dynamic shakedown problem. This paper aims to extend the stress compensation method (SCM) to perform lower bound dynamic shakedown analysis of engineering structures and a double-closed-loop iterative algorithm is proposed to solve the shakedown load.Design/methodology/approachThe construction of the dynamic load vertexes is carried out to represent the loading domain of a structure under both dynamic and quasi-static load. The SCM is extended to perform lower bound dynamic shakedown analysis of engineering structures, which constructs the self-equilibrium stress field by a series of direct iteration computations. The self-equilibrium stress field is not only related to the amplitude of the repeated variable load but also related to its frequency. A novel double-closed-loop iterative algorithm is presented to calculate the dynamic shakedown load multiplier. The inner-loop iteration is to construct the self-equilibrated residual stress field based on the certain shakedown load multiplier. The outer-loop iteration is to update the dynamic shakedown load multiplier. With different combinations of dynamic load vertexes, a dynamic shakedown load domain could be obtained.FindingsThree-dimensional examples are presented to verify the applicability and accuracy of the SCM in dynamic shakedown analysis. The example of cantilever beam under harmonic dynamic load with different frequency shows the validity of the dynamic load vertex construction method. The shakedown domain of the elbow structure varies with the frequency under the dynamic approach. When the frequency is around the resonance frequency of the structure, the area of shakedown domain would be significantly reduced.Research limitations/implicationsIn this study, the dynamical response of structure is treated as perfect elastoplastic. The current analysis does not account for effects such as large deformation, stochastic external load and nonlinear vibration conditions which will inevitably be encountered and affect the load capacity.Originality/valueThis study provides a direct method for the dynamical shakedown analysis of engineering structures under repeated variable dynamic load.

To address the frequent occurrence of rock burst disasters in areas with wide coal pillars during mining in the western mining area of China, the wide coal pillar area of the Tingnan coal mine in Shanxi Province was used as the research background. Theoretical analysis, numerical simulation, and field tests were used to establish the mechanical criterion and the energy criterion for the dynamic instability of wide coal pillars. The process and mechanism of wide coal pillar dynamic instability under dynamic and static load disturbances were revealed, and a wide coal pillar rock burst prevention and control scheme was proposed. The results indicated that when the load above a coal pillar reached the stress failure index and the energy failure index was met, the coal pillar reached the critical conditions for rock burst. With increasing static load, the stress, energy, and range of the plastic zone all showed increasing trends on both sides of the coal pillar. Under a given dynamic load, the stress and plastic zone range of the coal pillar significantly increased compared to those without a dynamic load. Under a given static load, the greater the dynamic load, the more likely the coal pillar was to undergo dynamic instability. The evolution of coal pillar dynamic instability was divided into three stages: energy accumulation, local instability, and dynamic instability. When the critical stress and energy conditions for coal pillar dynamic instability are exceeded, rock burst will occur. To reduce the static and dynamic loads of coal pillars, a rock burst prevention and control scheme of energy release and load reduction was proposed and applied onsite. The monitoring results showed that this control plan effectively reduced the stress of the coal pillar and the dynamic load generated by the fracture of the overlying rock layer, indicating safe mining in this area of wide coal pillars.

Vehicle traction control is the cornerstone for enhancing driving performance, ensuring road safety, and enabling intelligent driving. For off-road vehicles, variable road roughness imposes varying degrees of vertical dynamic loads on the wheels and affects changes in vehicle traction. Through simulation experiments, this paper found that the slip rate control performance of vehicle traction control systems traditionally designed for static loads exhibited significant variations when dynamic loads were introduced. To address this issue, vertical dynamic wheel load data under different vehicle speeds and road classifications were subjected to clustering, leading to the determination of three as the optimal number of clusters. The integration of the immune whale algorithm for the design of corresponding traction control systems for different dynamic load categories, and their subsequent comparison with traditional controllers, revealed a significant enhancement in slip rate control performance. Under Class I dynamic loads, the control performance on all road surfaces achieved the best results, reaching a maximum of 63.4%. Consideration of the dynamic variations in dynamic loads caused by changes in vehicle speed led to the design of a global controller capable of adapting to different dynamic load conditions, based on the aforementioned classification controller. The final simulation verification confirmed the maintained excellent control performance of this adaptive controller under various operating conditions.

The stability control of surrounding rock for large or super-large section chamber is a difficult technical problem in deep mining condition. Based on the in-site geological conditions of Longgu coal mine, this paper used the dynamic module of FLAC3D to study the response characteristics of deep super-large section chamber under dynamic and static combined loading condition. Results showed that under the static loading condition, the maximum vertical stress, deformation and failure range are large, where the stress concentration coefficient is 1.64. The maximum roof-to-floor and two-sides deformations are 54.6 mm and 53.1 mm, respectively. Then, under the dynamic and static combined loading condition: (1) The influence of dynamic load frequency on the two-sides is more obvious; (2) The dynamic load amplitude has the greatest influence on the stress concentration degree, and the plastic failure tends to develop to the deeper; (3) With the dynamic load source distance increase, the response of surrounding rock is gradually attenuated. On this basis, empirical equations for each dynamic load conditions were obtained by using regression analysis method, and all correlation coefficients are greater than 0.99. This research provided reference for the supporting design of deep super-large section chamber under same or similar conditions.

Almost all of road damage can be caused by dynamic loads of vehicles that fluctuate according to the type of vehicle that passes through. This study aims to calculate the vertical dynamic load of the vehicle actually occurs on road construction by the mechanism of vehicle wheel suspension. Pneumatic cylinders driven by pressurized air directly load the spring and shock absorber installed on the wheels of the vehicle. The load fluctuations of the medium weight categorized vehicles are determined by the regulation of the amount of pressurized air that enters into the pneumatic cylinder chamber, pushing the piston and connecting rods. The displacement that occurs during compression on the spring and shock absorber, is substituted into the equation of vehicle dynamic load while taking into account the spring stiffness constant, and the fluid or damper gas coefficient. The results show that the magnitude of the displacement when the compression force works has significant influences to the amount of vertical dynamic load of the vehicle that overlies the road construction. The presence of dynamic load of vehicles that fluctuates and repeats, also affects on the reduction of road ability to receive the load. Experimental results using pneumatic actuators instead of real dynamic vehicle loads illustrate the characteristics of the relationship between work pressure and dynamic load. If the working pressure of P2 (bar) is greater, the vertical dynamic load Ft (N) that overloads the road structure is also greater. The associate graphs show that the shock absorber has a greater ability to reduce dynamic load vertically that burden the road structure when compared with the ability of screw spring.

All the loads in the real world act dynamically on structures. Since dynamic loads are extremely difficult to handle in analysis and design, static loads are utilized with dynamic factors. The dyna mic factors are generally determined based on experiences. Therefore, the static loads can cause problems in precise analysis and design. An analytical method based on modal analysis has been proposed for the transformation of dynamic loads into equivalent static load sets. Equivalent static load sets are calculated to generate an identical displacement field in a structure with that from dynamic loads at a certain time. The process is derived and evaluated mathematically. The method is verified through numerical tests. Various characteristics are identified to match the dynamic and the static behaviors. For example, the opposite direction of a dynamic load should be considered due to the vibration response. A dynamic bad is transformed to multiple equivalent static loads according to the number of the critical times. The places of the equivalent static load can be different from those of the dynamic load. An optimization method is defined to use the equivalent static loads. The developed optimization process has the same effect as the dynamic optimization which uses the dynamic loads directly. Standard examples are solved and the results are discussed

Performance of spur gears largely depends on the magnitude and nature of variation of dynamic loads occuring between mating teeth. Variable tooth mesh stiffness is one of the primary sources causing parametric excitations resulting in dynamic loads. The usual method of varying the mesh stiffness to reduce dynamic loads is to use high contact ratio and profile modified gears. In this paper, a new type of tooth design to improve the dynamic performance of spur gears is presented. In this, a through hole is drilled in each tooth in a direction parallel to the gear axis. The diameter of the hole and its position on the tooth centre line are variable. Such a gear is called a hollow gear. Dynamic analysis is carried out for the mesh of hollow pinions mating with solid gears. The results are compared with solid pinions (no holes in teeth) meshing with solid gears. Finite element method is used for the analysis. For estimation of the dynamic load variation in hollow-solid and solid-solid gear meshes, a model incorporating the varying mesh stiffness and damping of gear teeth is used. Governing differential equations are solved using unconditionally stable Newmark-beta algorithm. The dynamic loads obtained are used as an input time varying loads for the determination of dynamic fillet and hole stress response of solid and hollow gear teeth whichever is applicable. Modal superposition technique is used for transient response analysis. The study shows that for the same damping ratio, dynamic loads in hollow-solid meshes are nearly the same as in a solid-solid mesh. In reality, the dynamic loads in a hollow-solid mesh are less than a solid-solid mesh due to its inherent higher material damping.

This study aimed to evaluate peri-implant bone reactions to dynamic and static loads in a rat model. Two cylindrical titanium implants were placed in the left tibia diaphysis of 39 rats, which were divided into three groups: static load for 4 weeks (S4), static load for 8 weeks (S8), and static load for 4 weeks followed by dynamic load for 4 weeks (S4D4). All implants received a mechanical lateral load. After the experiment, the implants were extracted to determine the attachment strength around the bone and implant. The new bone formation and bone-to-implant contact were measured using plain and polarized light microscopy. Histologic tissue analysis revealed good contact between the bone and implant, and new bone formation around all implants. The S4D4 group had the greatest attachment strength, new bone formation, and complex collagen fiber orientation in the new bone tissue, compared with the other groups. No statistically significant differences in bone-to-implant contact were observed among the three groups. Applying dynamic and static loads to osseointegrated implants increased the amplification of new bone. The attachment strength was significantly improved when dynamic load was used for 4 weeks, compared with when static load was used.

The optical fiber has been extensively used as a sensor in some special fields. Because the optical fiber exists crackles itself and also produce the micro-crack as well as local damage, the fatigue behavior of the optical fiber become the main problem we care about. This paper presents the experimental study on the fatigue performance of bare fiber under static, dynamic and cyclic load. The corresponding fatigue life index (Stress corrosion index) n can be obtained, which are 17.14, 11.83 and 5.88, respectively. The experiment data reveal that fatigue life index is related to loading mode and is treated as the indicator of crack propagation resistance of materials. Because dynamic and cyclic loads can induce additional damage, the fatigue life declines dramatically under the same stress levels.

Dynamic experiments were carried out on instrumented model aluminium single piles embedded in clay of different consistencies to study its bending behaviour under lateral loads. Piles with different length to diameter ratios were used. Dynamic lateral load of different magnitudes ranging from 7 to 30 N at wide range of frequencies from 2 to 50 Hz were applied. The load transferred to the pile, pile head displacement and the strain variation along the pile length were measured using a dedicated data acquisition system. Static lateral load tests were also performed to investigate the magnification of dynamic response of piles in clay. It is found that the maximum bending moment due to dynamic load is magnified by about 1.5–4 times in comparison to the static load for short piles but about 9 times for long piles. Depth of fixity and effective pile length is also largely amplified under dynamic loads, thus indicating that a pile which behaves as a flexible pile under static load, may not exhibit flexible behaviour under dynamic load.

Geosynthetic reinforced and pile-supported (GRPS) provide an economic and effective solution for embankments. To investigate the load-bearing mechanism of the GRPS embankment in loess, experimental and numerical studies under static and dynamic loading are carried out. The characteristics of soil arch effect and tensile membrane effect of GPRS embankment under static and dynamic loading are revealed by analyzing pile–soil stress ratio, tension of geogrid, and stress distribution of pile. The test results show that the pile–soil stress ratio under dynamic loading is reduced by 2.3 compared with static loading. In comparison to static load, the soil arching effect is attenuated under dynamic load, and the stronger the static load soil arching effect, the greater the degree of weakening under dynamic load. In addition, under dynamic loading, the tensioned membrane effect is still effective, but its enhancement is not as pronounced as under static loading. Furthermore, by using the finite element software, the numerical model is developed and validated with the experimental results. The parameter analysis of the load-bearing performance of the GRPS embankment is accomplished using the finite element model as well.

Evaluation of dynamic loads on a skew box girder continuous bridge Part II: Parametric study and dynamic load factor

In this paper, a predictive current control technique is utilized to generate switching pulses for four-leg-shunt active power filter (FL-shunt active power filter). The d-q theory technique is executed for removing the reactive and harmonic components of load current. MATLAB-based simulation and FPGA-controlled experimentation have been carried out to evaluate the behavior of predictive current control technique under dynamic and heterogeneous loading conditions. The 3-phase induction machine is considered as a dynamic load, and the capability of FL-shunt active power filter is assessed for compensating the reactive power. The compensation behavior of FL-shunt active power filter is observed with heterogeneous load, which is an amalgamation of dynamic and unstable static loads. Under steady-state and transient conditions, the simulation and experimentation results demonstrate that the proposed technique makes the supply current sinusoidal as well as balanced; compensates the reactive power; maintains near to unity power factor at the point of common coupling (PCC); and annuls the current flow in neutral conductor.

The determination of dynamic characteristics of soil-pile system by full-scale lateral dynamic pile load testing is an important aspect in the design of pile foundations subjected to dynamic loads. Field test results are very useful for validating existing linear/nonlinear models which are used to predict the dynamic stiffness and damping of the soil-pile system. This paper presents the results of field lateral dynamic load tests conducted at two different petrochemical complex sites in India and the measured dynamic constants of the soil-pile system. A three-dimensional finite element (FE) analysis is performed using ABAQUS to predict the nonlinear response of the soil-pile system under dynamic lateral loads. The lateral stiffness estimated from the FE analysis is compared with stiffness measured from field tests and it shows good agreement.

Purpose. Development of a mathematical model of a heavy loaded gear transmission with a self-aligning drive gear; evaluation of the dynamic load on the gear transmission in the gear alignment process. Methodology. The calculation schematic and equations of the relative motion of the self-aligning drive gear are formed using the methods of rigid body dynamics. Analytical expressions for the gear self-alignment time, collision velocity during the alignment and dynamic load factor are obtained by integrating an ordinary differential equation. Methods of the linear theory for oscillations are used to determine the dynamic factor. Findings. The article investigates the state-of-art design and mathematical models of the self-aligning gear. An equation for the relative motion of the moving part of the gear has been formed using the methods of rigid body dynamics. It is shown that by using the proposed hypotheses, the movement of the gear can be reduced to rotation about the instantaneous axis. The influence of geometric and dynamic parameters of the ball mill drive on dynamic loads in the open gear transmission is investigated. The gear alignment speed dependences on the tooth mesh misalignment angle in the gear transmission and the inertial parameters of the gear have been obtained. The obtained dependencies were used to calculate the time and speed of the gear alignment in the open gear transmission of the ball mill 5.5 6.5 (central discharge ball mill). It is shown that in the real range of mesh misalignment angles and gear parameters, the time of the gear alignment is several orders of magnitude less than the time of teeth re-engagement. In the presence of the variable component of the mesh misalignment angle, the gear will constantly make a relative motion with strikes; depending on the current value of the mesh misalignment angle, the dynamic load on the gear transmission can be significant. It is shown that when assessing the efficacy of self-aligning gears, it is necessary to take into account a possible increase in dynamic loads. The dynamic factor and the load factor are calculated for the nominal value of the mesh misalignment angle in the open gear transmission of 5.5 6.5 ball mills. Originality. A mathematical model of the dynamics of a self-aligning gear transmission in heavy duty machine drives has been developed. A quantitative assessment of internal dynamic load factor in an open gear transmission of 5.5 6.5 ball mills has been carried out. Practical value. A method for determining the dynamic component of the load on a gear transmission containing a self-aligning drive gear has been developed.