TCA technology is a pure mathematical method, which assumes that the gear teeth are rigid, and TCA technology only analyzes the contact condition of a pair of gear teeth, that is, it does not consider the elastic deformation of gear teeth after bearing and the possible situation that multiple pairs of teeth are in mesh at the same time, so it cannot accurately reflect the contact condition of gear pairs after actual loading.
In the 1980s, kerenzer of Gleason company of the United States proposed the gear tooth load-bearing contact analysis (LTCA) technology, which broke the hypothesis of rigid gear teeth in TCA, and established the solution methods of contact marks, transmission error curves, the number of teeth simultaneously engaged at a certain instant, load distribution between meshing tooth pairs, load sensitivity of gear pairs and stress process of bevel gears and hypoid gears under load. LTCA method reveals the meshing mechanism of gear pair under load. It is an important gear design technology. It can carry out high-precision computer simulation of the meshing process of gear teeth under load conditions before the trial production of gear products, so as to obtain the working performance of gears under simulated real working conditions. It is of great significance to shorten the production cycle, reduce costs and design high-quality gear products.
LTCA technology has attracted extensive attention at home and abroad. Litvin and Gosselin can not only get the load transmission error curve, but also calculate the actual coincidence degree of the gear pair by LTCA with the help of the finite element method. Bibel calculated the load-bearing transmission error curve of spiral bevel gear pair through LTCA. Falah [et al. Used LTCA to calculate the actual coincidence degree of spiral bevel gear pair. Zheng Changqi established a set of tooth LTCA model of local conjugate gear pair by introducing the concepts of load equivalent installation adjustment value and transmission angle displacement coordination principle. Fang Zongde proposed the finite element flexibility coefficient method and applied it to the tooth LTCA of modified helical gear. Through the geometric and mechanical calculation of single tooth pair, the meshing of multiple pairs of teeth was carried out Contact analysis avoids multiple division of finite element mesh and repeated solution of finite element equation; Fang Zongde also proposed LTCA method based on finite element method, flexibility matrix method and mathematical programming method, which can obtain complete load-bearing transmission error curve and load-bearing contact mark, and more accurately describe the meshing process of gear pair. Based on this, he proposed a new idea and method of constructing closed-loop feedback optimization design loop based on local synthesis method, machining parameter design, TCA technology and LTCA technology; Fang Zongde successfully solved the load-bearing contact problem on the edge of spiral bevel gears by using mathematical programming method, which provides a method for the numerical simulation of the whole process of load-bearing meshing of spiral bevel gears. Based on the finite element analysis and calculation method, Tang Jinyuan studied the variation laws of the transmission performance parameters, the contact stress of the tooth surface and the bending stress of the gear teeth of the orthogonal face gear mesh under the loading condition, and accurately obtained the transmission performance parameters of the face gear transmission, such as the coincidence degree, transmission error, load distribution coefficient, and the influence law of the load on these transmission performance parameters. Zhao Ning studied the LTCA of spur gear under the condition of tooth profile modification. The results show that the tooth profile modification can tilt the contact path of spur gear, increase the effective coincidence of gear pair, improve the load distribution of tooth surface and improve the stability of transmission while avoiding edge contact. Pu Taiping studied the LTCA analysis method of Spiral Bevel Gear Considering machining error, installation error, shaft deformation and bearing stiffness. Using the finite element contact calculation method, the contact stress of spiral bevel gear surface, tooth root bending stress and tooth surface contact resultant force were calculated, and the tooth surface contact trace and transmission error curve were obtained. The coincidence degree and load distribution coefficient were calculated according to the contact change curve, The calculation method of each parameter and the influence law of load on each parameter are given. Based on the local synthesis method, Deng Xiaozhong analyzed the TCA, LTCA and stress process of high coincidence spiral bevel gear in detail, which provided an effective tool for designing spiral bevel gear transmission with good meshing performance, high strength and low noise. Shen Yunbo analyzed the meshing performance of curved teeth and spur gears under load. Wang Cheng superimposed the calculated tooth surface flexibility matrix and shaft deformation through the finite element method, and obtained the tooth surface normal flexibility matrix of herringbone gear. Based on this, he proposed the LTCA method of herringbone gear.
At present, there are few literatures on cycloid tooth LTCA. Based on the light load contact analysis of Cycloid Bevel gear, Liu Zhifeng and others have established a set of LTCA methods of Cycloid Bevel Gear Pair considering errors under load, which can solve the real contact area, motion error curve Load distribution, etc.