Method of manufacturing a collet with optimized gripping action

A method for manufacturing a collet having optimum gripping strength of the type having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws, said method comprising the steps of:

• calculating the total torque generated on a bar passing through the collet for a given collet configuration having predetermined design parameters, the total torque including torque generated just prior to toggle condition between the gripping jaws and the bar and the maximum moment force generated between the gripping jaws and the bar at toggle condition;
• varying one of the design parameters of gripping jaw number, gripping jaw thickness, and gripping jaw material and recalculating the total torque generated until the total torque generated reaches a maximum value for the selected varied parameter thereby defining an optimized value for the selected parameter;
• and
• manufacturing the collet to include the optimized value of the selected parameter producing maximum total torque in combination with the values of the other parameters producing the optimized value of the selected parameter.

A method for producing a collet having enhanced gripping strength, comprising the steps of:

• calculating the maximum number of gripping jaws which can be disposed around the inner radius of the collet;
• defining the thread geometry of the collet nut;
• calculating the axial force per gripping jaw imparted from the collet nut being tightened onto the collet holder using the collet nut thread geometry;
• deriving the radial force per gripping jaw from the axial force per gripping jaw;
• calculating the total torque due to frictional force between the gripping jaws and a bar disposed through the collet without slippage between the jaws and bar, the total torque due to frictional force being dependent upon the radial force per gripping jaw, the coefficient of friction, and the number of gripping jaws;
• determining if slip occurs between the gripping jaws and the bar based upon the geometry of the gripping jaws and the coefficient of friction between the gripping jaws and the bar;
• calculating the total torque developed between the gripping jaws and the bar just prior to a toggle condition between the gripping jaws and the bar, comprising the following steps:
• determining the engagement length between a gripping jaw and the bar;
• dividing the gripping jaw into a number of segments along the engagement length thereof;
• determining the torque per segment by summing the forces generated in the radial and tangential direction and summing moments about the center of the bar for each segment;
• determining the torque per gripping jaw by summing the torques per segment;
• and
• multiplying the torque per gripping jaw by the number of gripping jaws in the collet;
• calculating the total torque developed between the gripping jaws and bar at toggle condition between the gripping jaws and the bar at a first incremental toggle angle, comprising following steps;
• dividing a gripping jaw into a number of segments along the length thereof;
• calculating the moment generated for each segment due to the degree of elastic deformation of each section of the gripping jaw, and summing the moments for the segments along the gripping jaw;
• calculating the moment generated for each segment due to the Coulomb friction force between the segment of gripping jaw and bar, and summing the moments for the segments along the gripping jaw;
• summing the total moment due to elastic deformation and total moment due to Coulomb friction force for the gripping jaw to give total torque at toggle for the gripping jaw;
• and
• calculating the total torque at toggle for all gripping jaws by multiplying the total torque at toggle for the one gripping jaw by the number of gripping jaws in the collet;
• repetitively incrementing the toggle angle and recalculating the total torque at toggle for all gripping jaws until the total torque at toggle reaches a maximum value;
• summing the maximum total torque at toggle with the total torque developed just prior to toggle to give a value of total torque with toggle;
• varying one of the design parameters of gripping jaw number, gripping jaw thickness, and gripping jaw material and recalculating total torque with toggle until an optimum value of the selected varied parameter is reached;
• and
• manufacturing the collet to include the optimum value of the selected parameter in combination with the values of the other parameters producing the optimum value of the selected parameter.