Load-dependent Losses Research Articles

Tooth friction in spur gear transmission. From local to mean tooth friction loss

In a gear transmission, power losses come from a variety of sources, classified as load-dependent and no-load-dependent losses. No-load-dependent losses are the ones that remain constant regardless of the applied load, such as losses due to drag in rolling element bearings, seals, churning and/or windage for gears. Load-dependent losses include friction losses due to sliding and rolling between gear teeth. These losses are particularly important in some gear transmissions because of their direct impact on overall efficiency and thermal behaviour. Consequently, knowledge of the friction coefficient associated to this loss is of major interest for optimising gears (geometry, surface finish, lubrication, etc.). In this article, a new method is proposed for predicting the mechanical efficiency losses associated with the mean coefficient of friction for pairs of cylindrical gears. It is based on a model developed previously to estimate the instantaneous tooth friction along the plane of action in gears. This model takes into account the lubricant shear and the friction on contacting asperities. The proposed mean friction coefficient is deduced from the instantaneous friction coefficient using specific calculations, particularly at the pitch point. To verify the method, the estimated results are compared with those in the literature calculated for gears and operating conditions common on FZG test rigs.

Prediction of mechanical efficiency of spur gear pairs based on tribo-dynamics model of multi-tooth meshing

The prediction of load-dependent losses of gear pairs is a topic of constant concern, which depends largely on the modelling of friction coefficient in tooth meshing. Although the current load-sharing based models can handle the friction coefficient in mixed elastohydrodynamic lubrication regimes, dynamics behaviour of each tooth pair or the time variation of direction of normal contact load is not taken into consideration. This study proposes a new method for modelling efficiency of spur gear pairs in transient operating conditions by coupling the multi-tooth meshing model with the friction coefficient model. The friction coefficient is modelled through load-sharing function, and the gear dynamics model is established with regard to alternate meshing of single-double tooth pair and time variation of direction of normal load and mesh stiffness. The model is validated by comparing the calculated results of friction coefficients and load-dependent losses with experimental data in published literatures, showing good agreement. At the end, the efficiency model is applied to two types of gear pairs to investigate the influence of tooth shapes and operating parameters on the load-dependent losses of gear pairs.

Stochastic microcontact model for the prediction of gear mechanical power loss

Gears serve as the primary power transmission element in many industrial and automotive applications. Power loss in the form of heat generation contributes both to reduced fuel economy and elevated transmission operating temperatures which can lead to premature failure of components. The power loss is made up of both load independent losses and load dependent losses. Gear designers need engineering tools to estimate both components to determine overall system efficiency. This research seeks to utilize stochastic descriptions of surface asperity profiles with simplified Elastohydrodynamic lubrication (EHL) metrics to estimate the effective friction coefficient in mixed lubrication gear contacts. Power loss experiments are performed to measure load dependent gear losses and compare them to the model results.

Energy Loss Savings Using Direct Current Distribution in a Residential Building with Solar Photovoltaic and Battery Storage

This work presents a comparison of alternating current (AC) and direct current (DC) distribution systems for a residential building equipped with solar photovoltaic (PV) generation and battery storage. Using measured PV and load data from a residential building in Sweden, the study evaluated the annual losses, PV utilization, and energy savings of the two topologies. The analysis considered the load-dependent efficiency characteristics of power electronic converters (PECs) and battery storage to account for variations in operating conditions. The results show that DC distribution, coupled with PV generation and battery storage, offered significant loss savings due to lower conversion losses than the AC case. Assuming fixed efficiency for conversion gave a 34% yearly loss discrepancy compared with the case of implementing load-dependent losses. The results also highlight the effect on annual system losses of adding PV and battery storage of varying sizes. A yearly loss reduction of 15.8% was achieved with DC operation for the studied residential building when adding PV and battery storage. Additionally, the analysis of daily and seasonal variations in performance revealed under what circumstances DC could outperform AC and how the magnitude of the savings could vary with time.

A multi‐layer framework for energy efficiency assessment of shore‐to‐ship fast charging systems including onshore batteries

This paper proposes a three-layer framework for energy efficiency evaluation of Shore-to-Ship Charging (S2SC) systems using load-dependent loss models of the components. The considered S2SC system is supplied by the grid but is also supported by On-Shore Batteries (OSB). The presented approach is then used to investigate the impact of the specific design and operational parameters on energy efficiency. Power system architectures for three general S2SC solutions for ac, dc, and inductive charging are defined and compared in terms of energy efficiency. Operational parameters are also considered in the analysis, namely, the grid power ratio, determining the load sharing between the grid and the OSB, as well as the OSB charging profile. A case study is performed with peak charging power of 1 MW, and the most efficient S2SC solutions are identified for both ac- and dc-based onboard power systems. Moreover, it is shown that charging OSB with the highest available power from the grid between the charging breaks would often lead to higher energy efficiency than the maximum utilization of the available charging time. Field data from a real S2SC system is used to verify the estimated energy efficiency by the proposed framework. The analysis of the real case S2SC is then extended to include and verify a projected OSB.

Gear and bearing power losses: from dip to minimum quantity lubrication

PurposeThis paper aims to address the influence of lubrication methods on operational characteristics, power losses and temperature behavior of gears and bearings. It contributes to the improvement of resource and energy efficiency of geared transmissions.Design/methodology/approachExperimental investigations were performed at a gear and bearing power loss test rig. Thereby, dip lubrication, injection lubrication with injection volumes from 0.05 to 2.00 l/min and minimum quantity (MQ) lubrication with an injection volume as little as 28 ml/h were considered. Measurements were evaluated in terms of no-load and load-dependent power loss, bulk temperatures and mean gear coefficients of friction.FindingsResults show strongly reduced no-load gear and bearing losses for lubrication methods with low lubricant quantities. Load-dependent losses are similar to conventional lubrication methods and tend to be lower at high speed. This is related to higher bulk temperatures, as the heat dissipation of lubrication methods with low oil quantities is limited. Limited thermal load limits were shown to be extended by LowLoss gears.Originality/valueSystematic investigations were conducted to evaluate the influence of dip, injection and MQ lubrication on power loss and temperature behavior of gears and bearings. The results of this study support further research on needs-based lubrication methods for gearboxes.

Acceleration, Drive Cycle Efficiency, and Cost Tradeoffs for Scaled Electric Vehicle Drive System

This article investigates and quantifies, for varying drive system ratings (0.5–2.0 times the rating of a small and large reference system), the tradeoff relations between the electric vehicle acceleration performance and energy consumption during a wide range of drive cycles, using detailed load-dependent loss models. Additionally, the results are related to estimated drive system cost by transparently determined scalable electric motor and inverter cost models. When reducing the system rating to half, the cost is 83% of the small reference system and 76% of the large. The acceleration time (0–100 km/h) decreases nonlinearly with increasing system rating. Interestingly, the drive cycle energy consumption generally decreases with decreasing drive system rating, and most cycles show a minimum consumption with a downscaled drive system. For the small system, the strongest impact was noted for the HWFET cycle where the energy consumption is reduced 2% when downscaling the drive system by 0.5 relative to the reference system. For the large system, NYCC shows the largest reduction in energy consumption: 4% when scaled by 1.6 relative to the reference system.

Bearing Power Losses with Water-Containing Gear Fluids

Lubricants have a large influence on gearbox power losses. Recent investigations at a gear efficiency test rig have shown the high potential of water-containing gear fluids in drastically reducing load-dependent gear losses and temperatures. In this study, the bearing power losses with water-containing gear fluids were evaluated at a specific bearing power loss test rig explicitly and compared with mineral and polyalphaolefine oils. For all investigated lubricants, a Stribeck curve behavior of the load-dependent losses is observed. The water-containing gear fluids demonstrate lower no-load bearing losses and higher load-dependent bearing losses at higher rotational speeds. The comparison of measured bearing losses with typical calculation procedures showe partially large differences. The results underline the importance of having detailed knowledge of bearing losses when evaluating gear losses in gearboxes.

Experimental investigation of churning power loss of single start worm gear drive through optimization technique

Worm gears have very high total power losses due to high sliding motion and strong reduction ratio resulting in low efficiency. It is currently assumed that the total power loss (TPL) is caused by the load dependent losses; it is not caused by any non-load dependent losses. To verify this hypothesis, a specific gear test rig for worm gear pair was designed to measure the total power loss and churning power loss (CPL) simultaneously by using direct torque measurement technique. Many experiments were performed using different speed of worm gear, immersion depth of lubricant and temperature of lubricant inside the gear box. Taguchi L27 orthogonal array was used for designing the series of experiments. The empirical equation for churning power loss and total power loss with process parameters was modelled by using standard regression technique. The adequacy of the developed mathematical models was checked by Analysis of Variance (ANOVA). The problem was formulated as multi-objective optimization based on statistical analysis. It was found that the churning power loss (CPL), a kind of no-load dependent loss, has significant contribution in total power loss for splash lubrication. The immersion depth and temperature of lubricant are adequately influential parameters for churning power loss. The confirmation test result demonstrates that the optimization technique is one of the best available techniques to predict the optimal input variables for better output responses.

Power Loss Shifted Design of Inductive Energy Transfer Systems

This article proposes a design procedure for power loss shifted inductive energy transfer systems. Based on adequately simplified mathematical circuit models for four different compensation topologies, the load dependent losses of the respective resonant circuits are presented. Power loss shifting is achieved for transfer coils and their compensation capacitors by adjusting the design operating area of the transfer system. As a result, this leads to asymmetrical reactive power and loss distribution on primary and secondary side. Design equations for coil systems and compensation capacitors with predictable transfer and loss behavior are provided. Strategies and equations for the determination of the operating area are given. The procedure can be adapted to many kinds of applications where power losses on either primary or secondary side of an inductive energy transfer system are key to be avoided and further miniaturization needs to be achieved. This strategy offers an additional degree of freedom that can be taken into advantage regarding the reduction of thermal heating or miniaturization efforts. A comparative metrological validation for the application of transcutaneous energy transfer shows that the losses of the secondary implanted components can be drastically reduced with the drawback of a decreased efficiency of the overall system.

Hybrid analytical-experimental method to map power losses of automotive transmissions over their operating range

Abstract This work presents a hybrid analytical-experimental method for determining overall power losses of automotive transmissions. The method consists of measuring load-independent losses and calculating load-dependent losses. Measurements and calculations are done at selected combinations of torque and rotational speed. The results are used for computing the coefficients of a quadratic equation that describes a best-fit surface. The equation is used for predicting the transmission power losses over the operating range defining a transmission efficiency map. The method was verified against power loss measurements of a light-duty six-speed automotive transmission showing a strong correlation between predictions and measurements. The proposed method can be used as an engineering tool to help drive improvements in transmission efficiency and in fuel economy.

Determination of load dependent gear loss factor on asymmetric spur gear

This paper shows the prediction of coefficient of friction and load dependent loss factor for spur gear drives with asymmetric tooth. An accurate evaluation of gear loss factor is important to exactly calculate the power loss and the corresponding mechanical efficiency of the asymmetric spur gear drive. In the present investigative research work, a formulation to accurately estimate the gear loss factor on asymmetric gear has been developed. The tooth load and the corresponding contact stress that develops at the symmetric and asymmetric gear contact surfaces are also evaluated through finite element method in order to deduce the friction coefficient and loss factor. The suitability of three distinct models is studied and compared in this paper. The asymmetric gear pair is analyzed and the loss factor is predicted for influence over the major drive parameters. It is revealed that the approach employed facilitate substantial enhancement in the efficiency which is confined by the detailed parametric study.

Torque loss in FZG-A10 gears lubricated with axle oils

Abstract FZG type A spur gears, lubricated with axle gear oils with high EP properties, were tested in an FZG back-to-back test rig, and their torque loss was measured for wide ranges of the input torque and speed. Several models of the load-independent and load-dependent losses of the gearbox components (gears, rolling bearings and seals), were combined into a global power loss model for the prediction of the gearbox efficiency. The average friction coefficient of the meshing gears was derived from the experimental results. A satisfactory correlation between experimental power loss measurements and the generated simulation results is observed under different operating conditions. Several aspects are discussed such as gear loss factor, friction coefficient and the influence of oil formulations.

Experimental and Numerical Investigation on Windage Power Losses in High Speed Gears

Enhancing the efficiency of gearing systems is an important topic for the development of future aero-engines with low specific fuel consumption. An evaluation of its structure and performance is mandatory in order to optimize the design as well as maximize its efficiency. Mechanical power losses are usually distinguished into two main categories: load-dependent and load-independent losses. The former are all those associated with the transmission of torque, while the latter are tied to the fluid dynamics of the environment, which surrounds the gears. The relative magnitude of these phenomena is dependent on the operative conditions of the transmission: load-dependent losses are predominant at slow speeds and high torque conditions, load-independent mechanisms become prevailing in high speed applications, like in turbomachinery. A new test rig was designed for investigating windage power losses resulting by a single spur gear rotating in a free oil environment. The test rig allows the gear to rotate at high speed within a box where pressure and temperature conditions can be set and monitored. An electric spindle, which drives the system, is connected to the gear through a high accuracy torque meter, equipped with a speedometer providing the rotating velocity. The test box is fitted with optical accesses in order to perform particle image velocimetry (PIV) measurements for investigating the flow field surrounding the rotating gear. The experiment has been computationally replicated, performing Reynolds-averaged Navier–Stokes (RANS) simulations in the context of conventional eddy viscosity models, achieving good agreement for all of the speed of rotations.

Modeling and design of an energy-efficient dual-motor actuation unit with a planetary differential and holding brakes

By connecting two drivetrains to a single load, a redundant degree of freedom is created. In this work, we investigate how the redundancy of such a system can be exploited in order to make it more energy efficient. The system under study consists of two drivetrains coupled to a planetary differential. Both drivetrains are composed of a geared DC motor and a holding brake. First, we derive an accurate semi-empirical model of this system and prove its validity on a test setup. Based on this model, which includes nonlinear friction terms, we analyze how the power flows and energy losses depend on the redundant degree of freedom. Furthermore, we discuss how the design of the actuator can be optimized for energy efficiency. This strategy is applied to a case study, where a 250 W geared DC motor is replaced by a more efficient dual-motor actuator. Experiments confirm that a dual-motor actuator succeeds in reducing the energy consumption at various loads and speeds. We also show that the results are very sensitive to friction and other speed- and load-dependent losses.

Improved calculation method for load-dependent gear losses

The topic of this study is to investigate the load-dependent losses of practical spur gears, for which the existing calculation method is analyzed in detail and improved. In drive technology, spur gears are frequently used for the transformation of torque and speed. Power transmission always involves power losses. Thereby, particular interest has to be given to the load-dependent gear loss as it often accounts for a large share of the total loss. According to the state of the art, the calculation of load-dependent gear loss is mainly based on (i) gear loss factors derived from simplified load distributions and (ii) a mean coefficient of friction derived from empirical equations based on spur gears without flank modifications. In practice, however, helical gears for improved NVH (Noise-Vibration-Harshness) behavior and flank modifications for uniform contact patterns are used. The modified mesh and contact conditions of modified helical gears affect the load-dependent gear losses significantly. Hence, significant deviations compared to the state of the art can occur. Comprehensive experimental investigations at the FZG efficiency test rig and FZG Bearing power loss test rig have been carried out to investigate the load-dependent gear losses of modified helical gears. The results are used to improve an existing calculation method that distinguishes between geometrical and tribological influence factors. Thereby, the local mesh and contact conditions along the plane of action are considered by the gear loss factor HVL according to Wimmer, whereas the calculation of the mean coefficient of friction µmz has been enhanced by regression analyses. A comparison of the improved calculation method to the state of the art shows improved accuracy for determining the load-dependent gear losses and hence the efficiency of gear boxes.

Energy Consumption of Geared DC Motors in Dynamic Applications: Comparing Modeling Approaches

In recent years, many works have appeared, which present novel mechanical designs, control strategies, or trajectory planning algorithms for improved energy efficiency. The actuator model is an essential part of these works, since the optimization of energy consumption strongly depends of the accuracy of this model. Nevertheless, various authors follow very different approaches, often neglecting speed- and load-dependent losses and inertias of components such as the motor and the gearbox. Furthermore, there is no consensus on how negative power affects power consumption. Some authors calculate energy consumption by integrating the electrical power entirely, by integrating its absolute value, or by integrating only positive power. This letter assesses how well commonly used models succeed in predicting the energy consumption of an 80 W geared DC motor performing a dynamic task, by comparing the results they produce to experimental baseline measurements.