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14 September 2020 Tablets & Capsules L = length of column in millimeters. Use the length of the punch tip. The resulting number will be higher than needed in reality for tablet tooling for several reasons: the for- mula assumes a longer column ratio than microtip tool- ing requires; the load (axial) is applied directly over the punch tip's center; no side loading occurs; and the for- mula doesn't consider crushing strength. The Euler-Bernoulli formula is useful in two ways: 1) you can later use the result to calculate a more accu- rate result for the Rankine formula, and 2) by using the punch-tip length in the calculation, you can determine how much you can increase tool strength by reducing the punch-tip length. Shortening the punch tip by using a tip support shoulder can increase the rating. Empirical Rankine-Gordon formula. The Ran- kine-Gordon formula provides a good quick approxima- tion of the amount you need to reduce the TSM force rating for microtip applications. The Rankine-Gordon formula is: 1 = 1 + 1 F max F e F c where F max = maximum allowable load F e = theoretical allowable load from the Eul- er-Bernoulli formula versus bending F c = maximum compression force per the TSM formula For a precise answer, you must use the secant formula or FEA because they consider additional factors, such as side loading, eccentricity, and torque. Understanding these factors can help you to minimize tool damage. Side loading. In practice, a side load develops due to the relative sideways motion or sliding between the tablet press' pressure roll and the punch head, which applies the load to the punch tip during compression. The side load's magnitude is equal to the compression force times the coefficient of friction between the punch head and the pressure roll. The free body diagram in Figure 3 illustrates how side loading is distributed. To protect microtip tooling, ensure that the punch heads are well lubricated by manually applying grease. The coefficient of friction is 0.16 for a well-lubricated steel punch, so the side load will equal 0.16 times the applied compression force. The punch barrel takes up most of the side load, but about 4 percent of the compression force ends up being applied to the punch tip. You can protect upper punch tips a bit more from side loads by increasing upper- punch penetration. Eccentricity In practice, the pressure roll doesn't apply the com- pression load directly to the center of the punch head at first but rather to the edge of the head flat. The larger the head flat in comparison to the punch tip diameter, the more off-center (or eccentric) the load and the lower the fit the shoulder, as shown in Figure 2. The lower punch pulldown determines how much tip support you can use. Some tablet presses are well suited to accommodat- ing minitablet tooling because the tablet press doesn't pull down the lower punch further than the fill cam. On other machines, lower punch pulldown is a fixed feature, and you must either install a shim or lengthen the lower punch tip to match the press' pulldown requirements. Flight control is especially important for minitablet tool- ing. Be sure to perform proper maintenance and adjust- ment of lower punch retainers. Calculating force ratings for microtip tooling Traditional punch-tip force ratings, such as those based on formulas in the TSM, are often higher than what you can safely apply to microtip tooling because the for- mulas don't consider bending or buckling as possible fail- ure modes. A number of methods are available to calcu- late the force ratings for microtip tooling. They include the Euler-Bernoulli formula and Rankine-Gordon formula, which I will discuss here, as well as the secant formula and finite element analysis (FEA), which are beyond the scope of this article. Euler-Bernoulli formula. Classic beam theory, as introduced by Leonhard Euler and Jacob Bernoulli, can be a helpful place to begin calculating microtip force ratings. The formula is: F = EIπ 2 (KL) 2 where F = theoretical allowable load (N). E = modulus of elasticity (N/mm 2 ). Use 207,000 for tool steels. I = area moment of inertia (mm 4 ). Round tips use: I = D 4 π 64 where D = round-tip diameter in millimeters. K = column effective length factor (dimensionless). Recommended: Use a K value of 1, so it drops out of the equation. Figure 2 Lower punch with punch-tip support shoulder and matching die with counterbore Punch tip Support shoulder Die Counterbore