| The constantly no clearance precision steel ball transmission is a new type of small teeth difference planetary transmission, which has advantages of construction compact, no backlash, high transmission efficiency and so on. So it is widely used in precision mechanical area. The accuracy requirement of precision transmission for precision mechanical is higher and higher. The drive accuracy is measured by backlash, so deep analysis of return difference has some practical engineering significance.The transmission working principle is analyzed. The cycloid equation of tooth profile is derived based on machining tool path. The theoretical tooth shape and the practical tooth profile equation for hypocycloid and epicycloid are established through analyzing the relationship between machining tool and steel ball. The practical tooth profile universal equation for hypocycloid and epicycloid are deduced by changing cutter parameter.The influences of eccentricity, steel ball radius, groove angle and cutter position circle error on the tooth profile error of structural parameter on deceleration engagement pairs are analyzed, and the mathematical model on the tooth profile comprehensive error is deduced. The formula for calculating geometric lost motion of reducing mechanism is derived. And then the influence of machining error and installation error for geometric lost motion is obtained by analyzing dates. According to Hertz theory, the mathematical model on the elasticity backlash of reducing mechanism and its change law is studied.By using the equivalent mechanism method, the mathematical model on the transmission error of equi-speed mechanism is established, and the influence of the four equivalent rod length on the output angle is obtained. The formula for calculating geometric lost motion on equi-speed mechanism is derived. According to Hertz theory, the mathematical model on the elasticity backlash of equi-speed mechanism is analyzed, and its change law is drawn.The force arm of the transmission mechanism is analyzed when actual processing of tooth profile and the ball meshing. And the curve of the coupling backlash of reducing mechanism is drawn. By changing the geometric parameters of the arm, the influence curves of geometric parameters on the coupling backlash of reducing mechanism are analyzed. The arm model of actual processing output mechanism is established by researching the force of non parallelogram shaped double crank mechanism. Furthermore, the mathematical model on coupling backlash of equi-speed mechanism is obtained. The influence curves of the length error of each rod on coupling backlash of equi-speed mechanism are drawn and studied. The mathematical model on coupling backlash of transmission mechanism is obtained by the synthesis of coupling backlash of reducing mechanism and the equi-speed mechanism. |
PDF Full Text Request