1213E_MSD_EXCO 1/11/06 10:06 AM Page 37 SIZEWISE Edited by Colleen Telling Sizing and applying ROLLER SCREWS Gary Shelton Roller screw shaft Principal Design Engineer Ground shaft Exlar Corp. Timing gear planetary Chanhassen, Minn. Roller screw nut roller screw How it works Roller screws convert ro- tary motion into linear mo- Roller screws’ tion just like acme and numerous ballscrews. Comparably contact points sized roller screws, however, vs. ballscrews’, have better efficiency than lengthen their acme screws and can carry lives and Spacer larger loads than ballscrews. washer increase load In addition, they can cycle Roller timing gear capacity and more often and turn signifi- stiffness. They Roller cantly faster than either, contain ground suiting them to precise, con- Retaining clip leadscrews for high- tinuous-duty applications. Roller journal precision applications Radiused flanks on the and come in tolerance rollers deliver point contact classes G1, G3, G4, and G5. like balls on a raceway, and only the radius is part of the profile. Therefore, a larger radius transversely and a precision- and additional contact points can ground spacer is inserted be- be packed into the available tween the front and back halves. space, thus lowering stress. In ad- The double nut is another alter- dition, the rolling contact be- native. As the name suggests, it tween components has low fric- uses two nuts preloaded against tion, yielding high efficiency. Be- each other on one screw. There is cause the rolling members are no sacrifice of life for its de- fixed relative to each other and creased backlash, but the double never touch adjacent rollers, nut costs more than standard sin- roller screws can turn at speeds gle-nut arrangements. up to 5,000 rpm. And, compared Roller screws are sealed to to similarly sized ballscrews, gle nut, ideal for maximum life varying degrees. Like other lead roller screws can have a load ca- with backlash less than 0.001 in. screws, roller screws must be well pacity up to 15 times greater. Another design is the split nut; lubricated and able to tolerate Nut options let users choose although it virtually eliminates contaminants such as nonlubri- among backlash, load capacity, backlash, it also reduces the dy- cating fluids, metal chips, and and cost trade-offs. The most namic load rating by about 38%. abrasives. The first level of pro- common configuration is a sin- In this design, the nut is split tection is adding wipers to the Courtesy of Steven Engineering, Inc. - 230 Ryan Way, South San Francisco, CA 94080-5370 - Main Office: (650) 588-9200 - Outside Local Area: (800) 258-9200 - www.stevenengineering.com 1213E_MSD_EXCO 1/11/06 10:06 AM Page 38 Sizewise fect critical speed. In particular, Double and split nuts compressive axial loads reduce The double nut preloads two nuts critical speeds, while tensile loads against each other on one screw, tend to increase them. A roller whereas the split nut is divided screw’s rotational speed should transversely and includes always be below the critical a precision ground speed, defined as: spacer. Where: ncrit = Critical rotational speed un- der zero axial load (rpm) do = Screw diameter, in. (mm) fs = Support bearing factor l = Screw’s length, in. (mm) Trunnion stud nut Additionally, roller-screw nut Trunnion studs allow a load speeds must not exceed their me- riding on slides to translate and can chanical speed limit. This depends interface with slotted links or yolk actuation. on screw diameter and lubrica- tion method. Specifically, oil should not surpass 140,000/do front or back of the nut. Wipers some basic questions must be an- and grease should not be more scrape particulates from the swered. What is the: than 90,000/do. threads as the screw cycles back ... budget? Another design factor is buck- and forth. This configuration re- ... maximum required linear ling force. Buckling occurs when quires maintenance of adequate speed? the compressive load on a screw’s lubrication to load-bearing parts ... maximum required load? shaft is too great for its diameter. of the nut. Another sealing op- ... maximum required stroke? Like critical speed, buckling tion is force tubes, which enclose In addition, how will the com- force is based on screw length, di- roller screws in a housing to keep ponents be protected from con- ameter, and the type of bearing lubricants in and foreign particles taminants and what level of pre- supporting the screw. When siz- out. Force tubes can be made for cision is needed? ing roller screws, the application’s IP67 ratings and mount in many Certain calculations must be maximum applied compressive arrangements. performed when selecting roller load must be less than the buck- screws. For instance, with the ling force, calculated as: high-speed capacity of a roller General sizing screw, the shaft tends to set up procedures natural frequency vibrations, Roller screws provide shock- which must be considered by cal- load resistance and handle loads culating its critical speed. Screw di- up to 779,000 lbf. To select the ameter, length, loading direction, Where: best diameter, lead, and sealing, and bearing arrangement all af- Fb = Buckling force, kN fb = Buckling force bearing factor Nut Buckling support When sizing a motor, engi- neers must also calculate the re- Nut fb=1.0 quired torque and compare it against predetermined ratings of Support Screw the motor and drive to control bearing the roller screw’s velocity and po- sition. Load and acceleration This schematic shows installation with a bearing on one end of the screw torques must not exceed the pro- and supports to the nut, which prevent it from moving transversely. posed motor’s torque rating. If an application requires a specific Courtesy of Steven Engineering, Inc. - 230 Ryan Way, South San Francisco, CA 94080-5370 - Main Office: (650) 588-9200 - Outside Local Area: (800) 258-9200 - www.stevenengineering.com 1213E_MSD_EXCO 1/11/06 10:06 AM Page 39 motor, engineers should try a while static load ratings range motion software and load, allow- roller screw with a lower lead or a from 1,461 to 794,670 lbf. ing for programmed positioning, belt or gear reduction in be- velocity, and thrust. tween. Here are some helpful Common Industries and applications uti- equations: applications lizing planetary roller screws in- Roller screw actuators can be clude: Under load: ␭ = (SF) used in place of hydraulics or • Medical — artificial hearts, (2 ␲␩) pneumatics for high loads and patient positioning tables, and Where: fast cycles. Advantages include automated high-force syringes ␭ = Torque, lbf-in. (Nm) eliminating a complex system of (for example, high-force syringes F = Applied load, lbf (N) valves, pumps, filters, and sen- require a very slow, non-pulsing S = Screw lead, in. (mm) sors; decreasing space; lengthen- extension) ␩ = Motor efficiency (usually 71 ing working lives; and reducing • Machine tool — presses, to 90%) maintenance. The absence of broaching, grinding, dressing, high-pressure fluid also means and cutting (broaching opera- Under acceleration: ␭ = (Il + Im)␣ that leaks do not exist and noise tions need high force at moderate Where: levels diminish significantly. speeds) Adding servo control to electro- • Military — weapons posi- Il = Reflected inertia due to load, in.-lb-sec2 (N-m-sec2) mechanical actuators offers a tioning, door control, and artil- stronger connection between the lery handling (military systems Im = Inertia of proposed motor’s armature; obtain from motor specs, EXAMPLE SIZING PROBLEM 2 2 lbf-in.-sec (N-m-sec ) SAMPLE CALCULATION PROPOSED ROLLER SCREW ␣ = Acceleration of motor, rad/sec2 Application information Diameter = 0.79 in. (20 mm) Cubic mean load = 500 lbf (2,225 N) Lead = 0.1969 in. (5 mm) (S/2␲)2m or Il = Max speed = 6 in./sec Dynamic load rating = 7,120 lb g (152 mm/sec) (31.7 kN) Where: Min time to max speed = 0.1 sec Non-preloaded m = Mass of applied load, lb (g) Stroke length = 18 in. Screw supported by two bearings g = Gravitational constant, (457 mm) on one side; none on the other 2 2 384 in./sec (9.75 m/sec ) Required lifetime = 5 million in. Nut performs no Another sizing parameter is (127 million mm) guidance function the follower’s (nut) linear speed, 3 Lifetime: L10 = (7,120/500) ϫ 0.1969 = 568 million in. of travel which relies on the shaft’s rota- Critical speed: The application’s rotational speed must be less than the critical and tional speed (S) and the roller mechanical speed limits. Rotational speed is determined from the linear speed equation: screw’s lead. This is found using n = (152/5) ϫ 60 = 1,824 rpm. V = nS Using fs = 0.32, the critical speed is: ϫ 6 ϫ ϫ 2 Where: ncrit = 86.4 10 20 0.32/(457 ) = 2,648 rpm. The mechanical speed limit with oil cooling is: 140,000/20 = 7,000 rpm. V = Linear velocity, in./sec (mm/sec) Buckling force: The applied load, 500 lbf, must be below the force required to buckle the screw. In this case fb = 0.25: n = Follower rotational 81.3 ϫ 0.25 ϫ (204) speed, rev/sec Fb = = 15.6 kN = 3,500 lb (4572) An important roller screw siz- Torque: Under load, the required torque is (0.1969 ϫ 500) ing parameter is diameter, which l = ϫ ϫ = 20.89 lbf-in. usually ranges from about 0.14 (2 3.14 0.75) to 5.91 in.; leads are approxi- A motor whose continuous-torque rating is 30 lbf-in. may be appropriate. To determine if this accommodates the inertial load under acceleration (assume Im for a mately 0.04 to 1.18 in. For split servomotor is 0.00058 lbf-in.-sec2; ␣ = 1,884 rad/sec2), one must use the reflected nuts, the dynamic load rating inertia equation: can be as little as 832 lbf or as 2 (0.1969/2π) ϫ 500 2 Il = = 0.0013 lbf-in.-sec ; then great as 40,286 lbf; static load 384 rating, on the other hand, is ␭ = (0.00058+0.0013) ϫ 1,884 = 3.54 lb-in.