Session: 02-09-01: Session #1: Variation Simulation and Design for Assembly Description

Paper Number: 95641

95641 - Assembly for Enhanced Repeatability Under Planar Constraints 

A die has two halves which approach each other along the smaller dimension which is often in the vertical direction. In dies used to cure preformed material, the top die is actuated to significant force levels. In such cases the actuation axis cannot be simultaneously controlled in position and force and the press position is established by points of contact on the mating surfaces. To ensure repeatability, three external V-grooves are often used to guide so that the two halves are located accurately in the plane perpendicular to the designed approach direction. For a contact perspective, the engagement is effectively a cylinder on surface contact. This paper presents an exact constraint analysis using the theory of screws and a method to optimise the design of the V-grooves for such dies.

 

Infinitesimal screw theory describing the instantaneous motion, or the velocity and the corresponding reciprocal space, that of the possible force system are used to describe the motion of a rigid body. The contact between cylinder on plane constrains motion normal to the plane and rotation in the plane containing the cylinder axis and the normal to the plane. To achieve precision placement, the actuation force on the top die has been treated as the nesting force and the sliding surfaces (V-grooves) have been designed to avoid friction locking. A force input is specified along the approach axis. Starting with the moving die half having a random initial perturbation about the five kinematic degrees of freedom other than the translation axis of actuation, equations governing the local trajectory of the top die as it progressively engages with the grooves is established. Simulation of the trajectories of the top die has been done using generalised dynamics algorithms.

 

The V-grooves have plane surfaces that are nominally radial, as are the axis of the cylinders in contact. Manufacturing and assembly tolerances must be allowed for. The axis of these lines coinciding at a single point when projected in a plane perpendicular to the actuation axis is in fact a special case, or a singularity. The system is analysed to establish a design which breaks the singularity and hence ensures repeatability, trading off accuracy. We record the excursion of the top die in the plane normal to the nominal approach direction in the vicinity of a specified separation when approaching from one side. We show that on reassembly from randomly perturbed initial conditions, repeatability is achieved. As the engagement of the two mating planes uniquely establishes the alignment in translation along the force axis and two orthogonal rotations, complete alignment repeatability is achieved.

Presenting Author: Sudipto Mukherjee Indian Institute of Technology Delhi

Presenting Author Biography: Dr. S. Mukherjee obtained his B.Tech degree from IIT Kanpur in 1985 and his MS and Ph.D. degrees from Ohio State University in USA in 1992. He started teaching at IIT Kanpur in 1992 and has been at the Dept. of Mechanical Engineering at IIT Delhi since 1997 where he is the Henry Ford Chair Professor in the Department of Mechanical Engineering.

Authors:

Jishnu Bordoloi Indian Institute of Technology Delhi
Jitendra P Khatait IIT Delhi
Sudipto Mukherjee Indian Institute of Technology Delhi