various embodiments of the presently disclosed acme screw / nut set are described in detail with reference to the figures , in which like reference numerals identify corresponding elements throughout the several views . the abbreviation “ e . g .” in the figures stands for “ for example ” indicating that the dimensions and angles shown in the figures are exemplary dimensions and angles . in the context of drive mechanisms and other mechanical devices , a high load application commonly creates a high amount of friction and , consequently , a high temperature condition . the modification of an acme nut in accordance with the present disclosure minimizes noise generation , excessive friction and motion seizure in a high load condition for acme screws . a method of calculating the radial clearance required on the major thread diameter , in an effort to minimize loss of performance and motion is also disclosed . referring now to fig1 , a screw / nut set 10 in accordance with the present disclosure is shown . screw / nut set 10 includes an acme screw 15 and a nut 20 . nut 20 is illustrated mounted within nut housing 25 . screw 15 may be an acme screw class c , and acme nut 20 shown in fig1 may include a modified internal thread in accordance with the present disclosure . screw / nut set 10 illustrated in fig1 is representative of a 1½ - 5 screw having a diameter ( x ) equal to 1 . 50 inches . the diameter ( y ) of nut 20 is equal to 2 . 125 inches . these dimensions are provided as examples only and not provided to , nor intended to , limit the scope of this disclosure . it is contemplated that this disclosure is not directed to any one particular size screw and / or nut . rather , the present disclosure may be applied to a plurality of screws and nuts having a plurality of different dimensions . the following formula is applied to determine the minimum required clearance as a function of a predetermined temperature rise ( δt ) above the ambient temperature . the minimum required clearance is defined as the clearance necessary to essentially prevent seizure of the motion of the mechanical components at the elevated temperatures encountered during normal working conditions . since nut 20 is restrained on its outer periphery by housing 25 , as the temperature of nut 20 increases , nut 20 will expand radially inward . an assumption is being made that there will be no outward expansion of nut 20 due to the restraining force exerted by nut housing 25 . the amount of thermal expansion of nut 20 is calculated by the following equation where rn is representative of the amount of thermal expansion . cten represents the coefficient of thermal expansion of the nut material , δt represents the raise in temperature from the ambient temperature , and d represents the major diameter of nut 20 . similarly , screw 15 is a solid mass and , therefore , will expand radially outward as its temperature increases . the amount of thermal expansion of screw 15 is calculated by the following equation where rs is representative of the amount of thermal expansion of screw 15 . ctes represents the coefficient of thermal expansion of the screw material , δt represents the raise in temperature from the ambient temperature , and d represents the major diameter of acme screw 15 . the material of nut housing 25 will also expand radially outward as its temperature increases . the amount of thermal expansion of the housing 25 is calculated by the following equation where rh is representative of the amount of thermal expansion of nut housing 25 . nut 20 is able to expand radially outward in an amount which is proportional to the amount of expansion of nut housing 25 . cteh represents the coefficient of thermal expansion of the housing material , δt represents the raise in temperature from the ambient temperature , and the variable b represents the diameter of the bore of nut housing 25 . the required clearance on the major diameter due to the thermal expansion may be calculated by the following equation : utilizing the values in the example described above , the following results are obtained : thus , the total radial clearance required on the major diameter of the thread including a factor of safety ( g ) is calculated as follows : the factor of safety contemplates , for example , extra radial clearance on the major diameter of the thread for grease retention and a misalignment accommodation . applying the values of the example given above with a temperature rising from 70 ° f . to 200 ° f . ( δt = 130 ° f .) and factor of safety of g = 0 . 004 ″ the total clearance will be as follows : since there will be an axial backlash increase due to the radial clearance increase , the width of the internal thread of nut 20 is adjusted to achieve a minimum axial clearance , in the design of the modified centralized acmesscrew / nut set 10 in accordance with the present disclosure . referring now to fig2 , a modified acme thread configuration on major diameter in accordance with the present disclosure is illustrated . width x 1 of screw thread 30 on major diameter and width x 2 of thread groove 35 of nut 20 also on the major diameter are shown as per ansi b1 . 8 standard without any modification . thread 30 of screw 15 remains unchanged . screw 15 is shown crowded to the one side of the thread 35 of nut 20 . the axial clearance expanded from amin .= 0 . 0025 ″ to 0 . 0058 ″ based on the relationship between radial and axial clearances shown in fig3 . referring to fig3 , an acme thread modified on major diameter in accordance with the above - described example is illustrated . the detail views in fig3 illustrate the relationship between radial and axial clearances in the thread . the increase in axial clearance ( backlash ) is governed by the following equations : therefore , the total backlash δar due to an increase in radial clearance and an initial minimum axial backlash is a sum of δa and amin . in accordance with an embodiment of the present disclosure , groove 35 of nut 20 is widened to accommodate an axial thermal expansion difference between the material of screw 15 and the material of nut 20 . the expansion of nut 20 in the axial direction is calculated in accordance with the following equation : next , the expansion of screw 15 in the axial direction for the length of nut 20 is calculated in accordance with the following equation : thus , the total required axial backlash due to the thermal expansion may be calculated in accordance with the following equation : the value derived from this calculation represents the minimum backlash at the pitch diameter . groove 35 of nut 20 may be physically enlarged to provide this backlash . as determined above , the backlash is equal to δar and is due to the increase of clearance in the radial direction . consequently , groove 35 of nut 20 may be widened based on the difference between total thermal expansion requirement at and an existing backlash δar as shown in the following equation to determine afin : afin = δt * l *( cten − ctes )−[( δ t { d ( cten + ctes )− 0 . 3 * cteh * b }+ g − rmin ]* tg 14 . 5 °− amin after applying the values from the example described above , the following value afin can be derived from the above formula : this afin value is the dimension value which has to be added to the existing width of groove 35 of nut 20 . in the example described herein , the minimum width for the top of groove 35 is 0 . 0738 ″ based on ansi b 1 . 8 ( see fig2 ). after adding 0 . 00546 ( afin ) to that dimension the final groove width wg is : the additional axial clearance may be added to the wg dimension if necessary . in this case , due to the flexibility of the plastic nut material with an unobstructed expansion flow in the axial direction , no additional clearance was implemented other than the positive tolerance . as illustrated in fig4 , nut 20 of the drawing calls for 0 . 079 ″+ 0 . 003 /− 0 . 000 . fig4 shows the acme nut drawing in cross - section detail with the circled dimension 0 . 079 + 0 . 003 /− 0 . 000 . while the above description contains many specifics , these specifics should not be construed as limitations on the scope of the present disclosure , but merely as illustrations of various embodiments thereof . for example , although the above embodiments are described with reference to one particular configuration of a screw / nut set , the present disclosure may find application in conjunction with screw / nut sets having many different configurations and dimensions . accordingly , it is contemplated that the disclosure is not limited to such an application and may be applied to various screw / nut sets . those skilled in the art will envision many other possible variations that are within the scope and spirit of the present disclosure .