Load Distribution Ratio Research Articles

Theoretical research on load distribution of composite pre-tightened teeth connections embedded with soft layers

Abstract It has been proved by experiments that the soft layers can effectively adjust the load distribution ratio of composite pre-tightened tooth connection, but theoretical research on the composite pre-tightened tooth connection embedded with soft layers has not been carried out. Therefore, in this work, the load distribution theory of composite pre-tightened tooth connection embedded with soft layers is studied by spring stiffness method. First, based on deformation compatibility condition, the theoretical calculation formula of load distribution ratio of each tooth is derived by spring stiffness method. Then, load distribution ratio is obtained by experiments, and the theoretical calculation results are verified. Finally, through the derived formula, the load distribution ratio of the composite pre-tightened tooth connection embedded with soft layers is parameterized. Research shows that (1) The theoretical value is in good agreement with the experimental value, and the maximum error of calculation result of the load distribution of the joint is 8%; (2) Under the action of soft layers, each tooth of two-teeth and three-teeth joints are damaged at the same time, the ultimate bearing capacity is increased by 29.0 and 21.6%, respectively, compared with the traditional two-teeth and three-teeth joints; (3) The elastic modulus and thickness of soft layers have a significant impact on the load distribution ratio of each tooth.

A new method for visually and real-timely measuring stress and load distributions in bolt with photoelastic technology

After analyzing the stress characteristics of the bolt, we determined that it can be regarded as experiencing a planar stress state due to the absence of circumferential stress. Consequently, a photoelastic bolt specimen was fabricated by taking a slice across its diameter. Using a photoelastic bench, we collected interference fringe images of the photoelastic specimen under different loads. This method enabled us to visually and continuously measure the stress distributions within the specimen in real-time. Additionally, the load distribution ratio of each tooth was derived. By comparing these results with those obtained through numerical simulation, we were able to validate the reasonability of the theoretical assumption regarding the load distribution of each tooth in the bolt. Our method establishes a solid foundation and can be effectively utilized for precise thread connection design.

Calculation methods of load distribution ratio for spiral bevel gear

The tooth strength of spiral bevel gear is compromised with decreased tooth thickness along the cone distance to transfer power between intersected axes. Its stress condition and transmission performance are generally studied by approximating the meshing process as an equivalent spur gear pair. This paper developed a mathematical model to bridge the meshing characteristics of spiral bevel gear and its basic parameters with no approximate simplification in the derivation process. It is constituted with the equations for the calculation of contact ratio, determining the track of contact areas, and describe the primary geometric parameters. The meshing model indicates that the contact profile of the teeth pair is determined by its spiral angle in certain working conditions. The multi-state meshing characteristic and stress condition of spiral bevel gear are analysed by dividing the tooth surface into different meshing regions. A calculation method of load distribution ratio for spiral bevel gear is proposed while two methods are developed for comparative analysis based on the length of the contact line and the potential energy principle, respectively. They are suitable for different working conditions. The results show that the stability of the spiral bevel gear drive is sensitive to the alternating of the meshing state, which is generally believed only appear in the gear drives with straight teeth. Additionally, an excitation source from the varying length of the contact line has been unveiled exists in the spiral bevel gear drive. The two types of excitations will occur simultaneously in some cases and become apparent with the increase of the meshing stiffness. The distribution law of the load is obtained and illustrated on the tooth surface. It provides a theoretical basis for the dynamic analysis and optimal designs of spiral bevel gear.

An improved load distribution model for involute helical gear pairs considering an actual contact ratio

With the increasing requirements of helical gears for high strength and low noise, it is significant to improve the accuracy of the load distribution ratio depending on the minimum elastic potential energy (MEPE) model. In this paper, an improved distribution model is developed to replace the theoretical contact ratio with the actual contact ratio and introduce the potential energy of the fillet foundation for comparison. Then, the operation process of the helical gear is divided into seven cases. Finally, combined with the finite element method, the accuracy of the improved model is confirmed. Results indicate that the load distribution model with fillet foundation energy is only effective under the front or the full tooth meshing. When the gear meshing includes the rear part of a tooth, the inclusion of the actual contact ratio and fillet foundation energy should be considered.

Analysis on the stress mechanism of the exposed steel anchor box composite cable–pylon anchorage structure

For the exposed steel anchor box cable–pylon anchorage structure, there is a good application prospect in urban bridges of medium and small span due to its good mechanical behavior, easy construction and beautiful overall appearance. This paper reveals the stress-transfer mechanism of the exposed steel anchor box cable–pylon anchorage structure through a segmental model test with a scaled-down ratio of 1:2, and focused on the effect of prestress in the pylon. Three calculation modes for the anchorage structure are proposed, and simplified calculation equations of the horizontal load distribution relationship and the vertical shear force of the stud are derived. The effects of various design parameters on the load distribution ratio, the pylon wall tension caused by shrinkage and the vertical shear force of the studs are discussed by using the simplified calculation equation. The research results show that the exposed steel anchor box cable–pylon anchorage structure has good applicability in medium and small span bridges. Prestress can significantly reduce the tensile stress of the pylon wall concrete, and improve its crack resistance. There is no significant difference between the results of the simplified calculation equations and the finite element calculation, and the simplified calculation equations meet the design requirement.

Analysis of load and stress distribution of a bolted joint composite plate

The determination of the load distribution between bolts is a crucial step in predicting the failure of bolted joints. In this paper, the purpose is to investigate the effects of stacking sequence on the load distribution and the stress distribution around hole of a double lapped and three bolted joint composite plate with shearing force. The accuracy and reliability of the finite elements model was verified by the spring method results and test results at first. Subsequently, the load distribution among bolts and the stress distribution around hole of six structural combinations of two stacking sequence composites were studied. Results indicate that the load distribution ratio of the sequential structure is more even than that of the symmetrical structure. And the symmetrical stacking structure can bear greater stress than that of the sequential stacking structure, which is about three times that of sequential stacking structure. As the external loading increases, the hole-edge stress is relatively stable at ±45° layer, while the hole-edge stress of the orthogonal layer is varied and occurs damage failure at 90° around the hole.

Modeling and analysis of load distribution ratio and meshing stiffness for orthogonal spur-face gear drive under point contact

Analytical models of load distribution ratio (LDR) and meshing stiffness for orthogonal spur-face gear drive under point contact are established to provide the parameter basis for dynamics studies in this paper. Meshing point tracks and contact line ranges on tooth surfaces are strictly divided according to the point contact ratio. Local contact stiffness at meshing point is calculated based on Hertz contact theory and calculation approaches of global tooth stiffness under line and point contact are proposed and compared. Then, models of LDR and meshing stiffness are constructed and analyzed. The results show that the global tooth stiffness decreases after considering point contact on the basis of line contact. LDR is significantly affected by the error on tooth surface. The meshing stiffness increases with the increase in meshing force. The contact deformation accounts for a high proportion in the total deformation. It expands the existing modeling methods to cover line and point contact, and lays the foundation of studies for orthogonal spur-face gear drive.

Dynamic characteristics of helical gear with root crack and friction

Helical gear transmission is smooth and has many advantages. However, long-term operation will cause root cracks, which will reduce the time-varying meshing stiffness (TVMS) of the gears, increase the transmission error (LSTE), and reduce the load distribution ratio (Lsr). According to the slice method and the energy method, a TVMS calculation model for a helical gear pair with cracks was established, and the effects of the crack initiation width, termination width, effective contact length and crack propagation angle on the gear were studied. Then, the changes of TVMS, LSTE, and Lsr under the time-varying friction and crack are considered. Build failure dynamics model, and fourth-order Runge-Kutta solution for vibration and amplitude-frequency characteristics. And wavelet transform and variational mode decomposition (VMD) are used to analyze the vibration signal, and statistical indicators are used to analyze the sensitivity of vibration. The results show that the TVMS with tooth root cracks will gradually decrease, LSTE will increase, the Lsr will decrease, and the vibration displacement (VD) will increase. When the two faults are combined, due to the damping characteristics of friction, the TVMS will increase, the LSTE and the VD will decrease. This offers a theoretical foundation for studying the dynamic characteristics of the coupling of gear cracks and friction faults, as well as vibration and noise reduction.

Load distribution of composite pre-tightened teeth connections embedded with soft layers

Due to the brittleness of composite materials, the load distribution of each tooth in the force transmission process of the composite pre-tightened tooth joint is uneven, so that the strength of the composite material cannot not be brought into full play. Based on the mechanism of force transfer in natural biological structures, the mechanism of soft layers with different stiffness in the composite pre-tightened tooth joints affecting the load distribution ratio of each tooth was studied. First, experiments were performed to investigate the influence law of soft layers with different thickness and elastic moduli on the bearing capacity, damage mode, and load distribution ratio of the specimens. Then, a progressive damage model of the joint was established and modified according to experimental results. Finally, the mechanism of soft layers adjusting the load distribution ratio of the composite pre-tightened tooth joints was investigated by the finite-element model. The following conclusions were drawn: (1) the application of soft layers can achieve a uniform load distribution among the teeth in the multi-tooth joint and improve the bearing capacity of the composite pre-tightened multi-tooth joint; (2) the elastic modulus and thickness of the soft layers significantly affected the load distribution ratio of the joint. When the elastic modulus of the soft layer varies, the thickness of soft layers required for reaching the optimal load distribution ratio for each tooth of the multi-tooth joint changes.

Competing mechanism between vertical stiffness and anti-slip safety in double-cable multi-span suspension bridges

Double-cable multi-span suspension bridges (double-cable bridges) have great development prospects in long-span bridge engineering. The vertical stiffness of the bridge and the anti-slip safety between the cable and saddle are the two primary competing factors governing the preliminary design of double-cable bridges. It is essential to study the competing mechanism between these two factors to determine reasonable parameters for designing sustainable double-cable bridges. In this study, the deflection-span ratio and anti-slip safety coefficient were adopted as indices to evaluate the vertical stiffness and anti-slip safety, respectively. Finite-element analysis was performed to investigate the influence of the main design parameters on the relationship between the deflection-span ratio and anti-slip safety coefficient and to clarify the competing mechanism between these two factors. Finally, we propose some recommendations for the preliminary design of double-cable bridges. The results of our study reveal that increasing the bending stiffness of the middle tower, increasing the constant load distribution ratio, or installing vertical friction plates in the top sub-saddle are useful in expanding the application scope of double-cable bridges. This study provides new insights into the competing mechanism between the vertical stiffness and anti-slip safety of double-cable bridges.

A bi-block sleeper dynamic strain monitoring method based on embedded FRP-OF sensor

The traditional surface contact monitoring, in which sensors and wires are exposed outside, has a great risk on long-term monitoring at high-speed railway (HSR). This paper proposed a method that embedding the Fiber Reinforced Polymer-Optical Fiber (FRP-OF) sensor into the bi-block sleeper, which was designed for long-term monitoring of sleeper dynamic strain at high-speed railway. Sleeper is the key component of bi-block ballastless track that bears and transmits the load from wheel. Its internal dynamic strain somehow reflects the wheel/rail force under the high-speed train load. Considering the symmetry of bi-block sleeper, a single block of sleeper was selected for this research. To validate the feasibility of monitoring sleeper strain by embedding FRP-OF sensor in sleeper, both laboratory static test and field dynamic test have been conducted. The results showed that there was a linear relationship between the sensor response and the applied load in the laboratory static test. The wheel load ratio assigned to each sleeper and the mechanical behavior is verified theoretically and experimentally. The single wheel load is mainly borne by five sleepers below the rail, which bearing 8%, 22%, 32%, 22%, 8%. Then, the load of different train can be sensed by the sensors in the field dynamic test, which clearly identified the process of wheel action and showed good repeatability. The dynamic strain in sleeper was about 3-7με with 150kN axle load at 350 km/h, which was converted to rail seat force of 33-35kN, and 7-18με with 230kN axle load at 160 km/h which was converted to rail seat force of 89-96kN. The impact factors on the track are different since the difference of the vechicles load. In general, the vertical transient strain level of sleeper is low, but the trend of strain variation is obvious and accords with the characteristics of wheel load distribution ratio. It can be seen that the sensors had good performance on dynamic strain monitoring of bi-block sleeper, which will be used as the important supplementary means of the future wheel/rail force monitoring.

Multi-tier delay-aware load balancing strategy for 5G HC-RAN architecture

The fifth-generation (5G) cellular network aim to provide ultra-low latency and enhance data rate service to its associated users. The centralized baseband processing of incoming traffic increases the computational complexity and end-to-end delays in a conventional C-RAN architecture. This paper proposes a multi-tier HC-RAN architecture using the edge computing concept at the Remote Radio Head (RRH) to overcome the above limitations. Further, to reduce load at the C-BBU and fronthaul, we have proposed a multi-tier delay-aware load balancing (MDALB) algorithm. The proposed algorithm is run over the EO to strategically distribute incoming flow between eRRH and C-BBU based on a load distribution ratio. The efficiency of the proposed strategy is analyzed through mathematical models and simulations based on various performance matrices. The performance parameters’ results show that the use of multi-tier processing in HC-RAN minimizes end-to-end delay and packet loss whereas increases the system throughput and packet delivery ratio.

Dynamic characteristics of a straight bevel gear drive system considering multi-state meshing and time-varying parameters

In order to investigate the dynamic characteristics of the straight bevel gear drive system, its torsional-bending-axial dynamics model considered the multi-state meshing characteristics is established. The time-varying load distribution ratio and meshing stiffness of the system are calculated by micro element method according to the performance of the straight bevel gear. Three different Poincaré sections are defined to study the dynamic characteristics of the system. The mechanism of tooth disengagement and back-side contacting is studied according to the time history diagram of the total normal force. The nonlinear dynamics equation of the system is solved by the variable step fourth-order Runge-Kutta method when the bevel gear drive system in automobile reducer is taken as the research object. The transition process of system dynamic characteristics and the influences of the meshing frequency, load coefficient and the comprehensive transmission error are studied by using the time history diagram of the total normal force, phase portraits, Poincaré maps, bifurcation diagrams and the corresponded top Lyapunov exponent (TLE). The chaotic motion found in the research is unfavorable from a practical point of view which can be avoided by adjusting the value of parameters or the initial value of state variables in engineering. The research can provide a theoretical basis for the parameter design and dynamic characteristic control of straight bevel gear drive system.

Prediction of tribological and dynamical behaviors of spur gear pair considering tooth root crack

Variations in gear tooth meshing stiffness and tribological characteristics caused by tooth root cracks seriously affect the dynamic performance of gears, limiting the development of durable high strength gears. Therefore, the potential energy method was applied to obtain the time-varying meshing stiffness of the spur gear pair, and the finite element method was applied to verify the calculation results. Secondly, the load distribution of the gear with the cracked tooth root was derived using coordinated deformation conditions, and the effect of the tooth root crack on the tribological characteristics of the tooth surface was obtained based on the elastohydrodynamic lubrication (EHL) model. Finally, the tribo-dynamic behaviors of the gear under the action of the root cracks were investigated. The results indicated that root cracks change the load distribution ratio in the double-tooth meshing zone, which leads to corresponding changes in the tooth surface film thickness and friction coefficient. In addition, when the cracked teeth are engaged in meshing, the reduction in meshing stiffness causes vibration and shock, which causes the appearance of sidebands near the main meshing frequency. The amplitude of the dynamic meshing force increased with the increase in the degree of root cracks.

Intelligent ballast control system with active load-transfer for electric tractors

For agricultural tractors fixed ballast cannot provide high-efficiency traction under time-varying resistance in the field. Combining the characteristics of electric tractors with high-weight battery packs, this paper develops an intelligent ballast control system including a battery position adjustment (BPA) mechanism and an active ballasting control method. A tractor traction performance prediction model was developed to predict traction performance parameters and load-transfer in real time. The movement of the battery pack enables load-transfer based on the BPA. To ensure the lowest sliding rate of optimal tractive efficiency, an active ballasting control method based on a particle swarm optimisation algorithm was proposed that enabled control of the optimal battery position. The results of MATLAB/Simulink simulation indicate that the traction resistance after grading and pre-treatment not only reduced the frequency of change in the resistance signal but also retain the original trend. The results of a hardware in the loop test showed that the average tractive efficiency in the mode of active ballasting mode higher than that of the no ballasting mode (increased by 6.6%) and fixed ballasting mode (increased by 4.7%). The mean wheel slip in active ballasting mode was lower than that of the no ballasting mode (decreased by 10.3%) and the fixed ballasting mode (decreased by 4.9%). In addition, the front axle dynamic load distribution ratio in active ballasting mode was always greater than 0.2, which ensured the operational stability of the tractor. This study provides theoretical support and technical reference for optimising the traction performance of electric tractors. • An intelligent ballast control system with active load-transfer is developed. • The concept of batteries instead of ballasts. • Battery position adjustment mechanism (BPA) is designed. • Active ballasting control method based on traction performance prediction model. • The maximum average tractive efficiency is increased by 6.6%.

Bearing strength and failure behaviour of composite pre-tightened multi-tooth joint

The bearing strength and failure behaviour of a new composite pre-tightened multi-tooth joint was studied experimentally and numerically. Four groups of different types of specimens were fabricated by varying key design variables including the pre-tightening force, tooth depth, tooth length, and number of teeth. Axial tensile tests were performed to determine the bearing capacity, failure modes, and load distribution law of the specimens. Furthermore, a three-dimensional continuum damage mechanics (CDM) model was established based on the Pinho theory and nonlinear shear constitutive model. Finally, the corresponding numerical results were compared with the experimental results and demonstrated good agreement. The results indicated that in a certain range, the bearing capacity of the joints increased with an increase in the pre-tightening force, tooth depth, tooth length, and number of teeth. The designed multi-tooth joint has four typical failure modes: crushing failure, shear failure, longitudinal splitting failure, and fibre breakage. The load distribution ratio of each tooth of the joint is non-uniform, and it is significantly affected by the number of teeth and failure mode. The comparisons among the experimental and numerical results indicated that the CDM model is effective for predicting the bearing strength and failure behaviour of the multi-tooth joints.

Study on load distribution ratio of composite pre-tightened tooth joint by shear nonlinearity

Load distribution has a great influence on the mechanical properties of composite pre-tightened multi-tooth connection. To obtain the load distribution mechanism of composite pre-tightened multi-tooth joints, the multi-tooth joints were studied by experimental and theoretical methods. First, an experimental study was conducted on three-tooth specimens with different tooth depths and tooth lengths, and the failure mode, bearing capacity and load distribution mechanism of the specimens were obtained. Then, based on the nonlinear constitutive of interlaminar shear, an analytical model for load distribution of composite pre-tightened multi-tooth joint was proposed to research the multi-tooth load distribution mechanism. Finally, the theoretical and experimental results were compared. The research showed: (1) The theoretical results of the multi-tooth load distribution ratio were in good agreement with that of the experimental results, the maximum error between the theoretical value and the experimental value of the three-tooth joint was 17.44%, and the minimum error was only 2.35%; (2) The load distribution ratio of composite pre-tightened multi-tooth was uneven, for three-tooth joints, the values of load distribution ratio from large to small were: the first tooth, the third tooth and the second tooth.; (3) Multi-tooth load distribution ratio changed with the change of external load. The change of load distribution ratio was obvious in the early stage of loading, and tended to be gentle in the later stage of loading.

The effect of age, birth weight and milk suction time on some carcass characteristics and load distribution ratio (LDR): Eastern Anatolian red cattle example in Turkey

The aim of this research is to evaluate the current situation and create a model for some countries involved in animal production. Eastern Anatolian Red (EAR) breed that adapts to arid and barren areas has been raised in Turkey. The experimental animals comprised 31 head of EAR cows of different ages, fed on pastures and in the barn. This study determined the effects of age, birth weight and suction time on carcass characteristics of EAR cows. The animals were divided into 6 groups based on birth weight, 4 groups based on age and 6 groups based on milk suction time. They were reared under a conventional system that was based on grazing during summer and a semi-intensive system during winter. Carcass length, fat thickness over longissimus dorsi, marbling score, and LDR were significantly (P< 0.05) affected by age group. Significant (P< 0.05) differences were noted for carcass length, fat thickness over LD, and marbling score among animals with different birth weights. The milk suction time had a significant (P< 0.05) effect on all the parameters measured. In this research, the 4th age group was seen advantageous based on carcass characteristics and LDR and resembled other groups. As indicated in the study, the carcass characteristic output from the 2nd birth weight group shows that carcass length was a far more important output than other carcass portions or carcass quality parameters. Similarly, the 1st group based on milk suction time came to the forefront for some carcass characteristic, although it indicated partial similarity with other groups.

Modeling and dynamics analyzing of a torsional-bending-pendular face-gear drive system considering multi-state engagements

A face-gear drive system has been extensively used in important transmission devices with strict requirements for size and weight such as helicopter reducer and so on. Its dynamic characteristics directly affect the stability and reliability of the equipment. A piecewise torsional-bending-pendular nonlinear dynamics model of the face-gear drive system is established to study its nonlinear dynamics and dynamic characteristics. The multi-state engagements including drive-side teeth engaging, teeth disengagement, back-side teeth engaging, and alternate engaging between single-teeth pair and double-teeth pairs caused by the couple of the backlash and the contact ratio being greater than 1.0 is considered. The change of the dynamic engaging force and load distribution ratio for the system is analyzed by numerical results under three different states engagement. The effects of the load coefficient, meshing frequency and the comprehensive transmission error on the dynamic characteristics and nonlinear dynamics of the system are studied based on three different Poincaré mappings defined by bifurcation diagrams, top Lyapunov exponent diagrams, phase portraits and variation curve of the dynamic engaging force. Results show that the complex phenomena such as teeth disengagement, drive-side and back-side impact occur with alternating meshing of the single and double pair teeth via the change of studied parameters. The research is helpful for the optimization of the face-gear drives.

Theoretical analysis of cylindrical roller bearing with flexible rings mounted in groove elastic support

Based on the structural mechanics and rolling bearing dynamics, this paper presented a dynamics model of cylindrical roller bearing with flexible outer ring and a novel elastic support named groove elastic support(GES), and then the load distribution and cage slip ratio of cylindrical roller bearing with GES(BES) were analyzed. The findings are as following: (1) The number of loaded rollers of BES is more than that of cylindrical roller bearing with rigid support(BRS), and the largest contact load between roller and ring of BES is lower than that of BRS. (2) The number of loaded rollers of BES decreases with the groove number, arc beam thickness and outer ring’s thickness. The smaller radial load, ranging from 500N to 1400N in this paper, has no obvious effect on the number of loaded roller for BES and BRS; (3) Under the same condition, cage slip ratio of BES is much lower than that of BRS. Cage slip ratio of BES increases with the groove number, arc beam thickness and outer ring’s thickness. All results reveal that the GES has a large impact on the load distribution and cage slip ratio in cylindrical roller bearing, and will be beneficial to extend the bearing service life under the condition of high-speed and light-load.