Servomech滚珠丝杠

INDEX 1. DESIGN 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 1 1.2 Ball track profi le . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 1 1.3 Ball recirculating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 2 1.4 Backlash or preload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 3 1.5 Accuracy grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5 1.6 Thread lead accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 5 2. SELECTION OF BALL SCREWS 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 8 2.2 Basic rating life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 10 2.3 Basic dynamic axial load rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 10 2.4 Basic static axial load rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 11 2.5 Max. allowed rotating speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 11 2.6 Max. allowed buckling load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 12 2.7 Effi ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 12 2.8 Torque and power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 13 2.9 Axial stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 15 2.10 Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 15 3. SERVOMECH PRODUCT RANGE 3.1 Production capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17 3.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17 3.3 Geometry inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 17 3.4 Mounting suggestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 21 3.5 Working temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 21 3.6 Ball nut types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 21 3.7 Questionary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 22 3.8 Designation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 24 BALL SCREWS AND NUTS © Copyright SERVOMECH 2010 This catalogue contents is under publisher copyright and may not be reproduced unless permission is agreed. Every care has been taken to ensure the accuracy of the information contained in this catalogue, but no liability can be accepted for any errors or omissions. 中国官方总代理 电话：010-67716353 传真：010-67748659 1 BALL SCREWS AND NUTS BALL SCREW SHAFT WIPER BALL NUT BODY BALL RECIRCULATION ELEMENT WIPER BALLS One of the main ball screw features is a high effi ciency obtained by rolling of balls between the screw shaft and the nut body. Where ball contacts shaft and nut body, the rolling friction occurs. This feature is one of main advantages compared to alternative solutions like an acme screws, where the screw thread surface slides directly on the nut thread surface, so the sliding friction occurs in the contact zone. Ball screws can be classifi ed as follows (in accordance with Standards ISO 3408 and DIN 69051): ▪ positioning ball screws, ▪ transport ball screws. The difference between the two typologies is related to application requirements, where an accuracy and a position repeatability are the most important. The positioning ball screw is used where high stiffness, high positioning accuracy and high repeatability is required. Ball screws with preloaded nut are mainly used in these applications. The transport ball screw is used for moving a load where stiffness, accuracy and/or repeatability is not required. The above mentioned standards ISO 3408 and DIN 6905 also defi ne all ball screw constructive param- eters. 1.2 Ball track profi le There are two thread track profi les: ▪ profi le with a round groove - two fl anks of the groove make a part of the same arch (both fl anks centres coincide with the ball centre), ▪ profi le with a gothic (ogival) groove - two fl anks of the groove are two arches, their centres are moved respect to the ball centre, in order to obtain a required contact angle. Generally, a small variation of thread profi le geometry strongly infl uences performances of the ball screw system. 1. DESIGN 1.1 Introduction A ball screw is a mechanical system capable of converting rotary motion to linear motion or vice versa. An example of such a system, shown in Figure 1, is composed of a ball screw threaded shaft, a ball nut body, balls, ball recirculation elements and wipers (when present). Fig. 1 - Ball screw assembly 中国官方总代理 电话：010-67716353 传真：010-67748659 2 Dw R s Dw R sR s α α 2 w s D R = 2 w s D R < BALL SCREWS AND NUTS Dw - ball diameter Rs - ball track radius α - contact angle The round profi le (see Figure 2.a): the zone of contact between the ball and the ball track, where signifi - cant effects of sliding are present, is quite wide; consequences of sliding are a high wear of bodies in contact, a relatively high power losses (heating), a relatively low effi ciency and life. The round profi le is used in applications with a high load and a very low linear speed. The gothic profi le (see Figure 2.b): the zone of contact between the ball and the ball track, where sig- nifi cant effects of sliding are present, is very reduced; it helps lower wear of bodies in contact, lower power losses (heating), smaller thermal deformation (and, as consequence, higher accuracy and better repeatability of the system during positioning), higher effi ciency and longer life. SERVOMECH designs and manufactures ball screws, whose thread has got the gothic profi le. 1.3 Ball recirculation The continuous ball recirculation inside the thread is achieved by ball recirculating elements (called also liners or defl ectors) fi tted into the ball nut body. a) round groove b) gothic groove Fig. 2 - Ball track profi le a) nut with RADIAL liner b) nut with FRONTAL defl ector Fig. 3 - Ball recirculation A solution used to obtain the ball recirculation affects: ▪ max. rotating speed of ball screw threaded shaft or ball nut, ▪ the system load capacity, ▪ ball nut axial stiffness. 中国官方总代理 电话：010-67716353 传真：010-67748659 3 F Δl a FaxS Δl Fax Δl F FaxΔl FprΔl FprΔl 2 1 F F F F F ax 2 pr 1 lim BALL SCREWS AND NUTS A solution with the RADIAL liner (see Figure 3.a) is usually used in ball screws with lead not greater then 20 mm; the liner is fi t in the groove present in the ball nut body and restricts a ball trajectory at one single revolution around the ball screw shaft. A solution with the FRONTAL defl ector (see Figure 3.b) is usually used in ball screws with lead greater then 10 mm and in all multiple-start ball screws. The recirculation of balls is obtained by defl ectors fi tted on ends of the ball nut body and joined with an axial hole (passing through the body); the defl ectors deviate ball trajectory from the ball track to the axial hole or vice versa. SERVOMECH designs and manufactures ball screws realizing various ball recirculating solutions, suit- able for specifi c, concrete application and its conditions and requirements. 1.4 Backlash or preload Depending on type of the ball nut used (preloaded or not preloaded ball nut), applying an axial, centric load to the ball screw shaft or nut, two effects may occur: ▪ backlash, ▪ elastic deformation. The backlash is an axial displacement which nut or threaded shaft makes, without any relative rotation between them; it can be caused by inversion of nut or threaded shaft motion direction or by inversion of applied load direction. The elastic deformation coincides to axial defl ection of parts in contact, under the action of an unidirec- tional axial force applied. In case of the ball screw with backlash, applying an axial force, both effects occur. The diagram in Figure 4.a shows the total axial displacement Δl of ball screw assembly related to the applied force F. In the left part of the diagram, where F = 0, the displacement Sa indicates the ball screw backlash, while in the right part of the diagram, where F > 0, the displacement ΔlFax indicates the elastic deformation corresponding to force Fax. a) single nut, with backlash b) double nut, preloaded Fig. 4 - Ball screw assembly: axial load - axial displacement diagram The preload is an axial force, generated different ways inside the ball screw assembly. Its purpose is to eliminate backlash and increase assembly stiffness. This force must be determined accurately, in order to avoid ball screw life reduction (when the preload is too high) or, otherwise, positioning errors caused by backlash generated under working load (when the preload is too small). The preload depends on the applied axial load: 中国官方总代理 电话：010-67716353 传真：010-67748659 4 832. FF maxaxpr P P P P - ΔP Fpr P P + ΔP Fpr BALL SCREWS AND NUTS where: Fpr - preload force Fax max - max. working load The diagram on Figure 4.b shows the total ball track elastic deformation along the axis related to the level of the load applied on a preloaded ball screw. The two curves (1 and 2) represent two semi-nuts of the same assembly. The intersection point repre- sents the preload force Fpr operating on both semi-nuts without external axial load. After the external load Fax is applied, the force acting to the semi-nut 1 changes from Fpr to F1, while the force acting to semi-nut 2 changes from Fpr to F2, in order to keep a ratio F1 = F2 + Fax. The force Flim represents the max. load, which will not cause detachment of balls and ball tracks. This force is 2.83 × Fpr. Generally, for preloaded nuts, SERVOMECH recommends a preload force of Fpr = 0.08 × Ca; in a partic- ular condition, this value can be reduced or increased, but in any case the max. value must not exceed Fpr = 0.12 × Ca. There are three methods of preloading: ▪ preload with four contact points (see Figure 5), ▪ compression preload (see Figure 6), ▪ traction preload (see Figure 7). The fi rst preloading method is valid for single nuts only and it is suitable for applications with low linear speed. This method requires use of balls with effective di- ameter greater then nominal; this way, there will be four contact points for each ball, two between ball and nut and two between ball and threaded shaft, and the backlash will be eliminated (see Figure 5). This solution doesn’t allow an optimal rolling of balls because sliding between surfaces in contact may oc- cur. In this case, the preload force must not exceed Fpr = 0.04 × Ca, in order to prevent ball screw overheating and consequently life reduction. Fig. 5 - Preload with 4 contact points Fig. 6 - Compression preload SEMI-NUTS BALL SCREW SHAFT NUT BALL SCREW SHAFT Fig. 7 - Traction preload SEMI-NUTS BALL SCREW SHAFT 中国官方总代理 电话：010-67716353 传真：010-67748659 5 BALL SCREWS AND NUTS The second and the third preloading method can applied either to ball screws with single nut or to ball screws with double nut, giving them an optimal effi ciency. There are only two contact points for each ball, one between ball and nut and one between ball and threaded shaft, so a sliding between surfaces in contact may not occur. In case of ball screws with single nut, the preload force is obtained by thread lead variation (called shift) during the fi nishing of the internal thread. In case of ball screws with double preloaded nut - compression preload, the contact points have “X- confi guration”. The preload force tries to make two semi-nuts less distant and compresses the part of threaded shaft between them. This solution is applied to cylindrical preloaded nuts, fi t into a housing and preloaded by means of locknut or cover and bolts. In case of ball screws with double preloaded nut - traction preload, the contact points have “O-confi gu- ration”. The preload force tries to make two semi-nuts more distant and pulls the part of threaded shaft between them. This solution is applied to preloaded nuts with fl ange or cylindrical, where the preloading force is obtained by interposing a spacer ring with calibrated thickness between the two semi-nuts. The actual preload force depends on the distance ΔP, so this distance must be determined very care- fully, in order to avoid overloading or overheating of ball screw, with consequent reduction of its per- formances and life. 1.5 Accuracy grade The accuracy grade is the quality level reached during the manufacturing of ball screws, which identifi es relevant geometrical and dimensional parameters and defi nes specifi c tolerances. SERVOMECH applies ISO 3408 and DIN 69051 regulations as reference standards for own production. Depending on the ball screw application typology, different accuracy grades are recommended: Application typology Accuracy grade recommended positioning 1, 3, 5 transport 1, 3, 5, 7, 10 SERVOMECH manufactures ball screws in accordance with accuracy grade 3, 5, 7, 10. 1.6 Thread lead accuracy Main parameters which contribute to determine the thread lead accuracy are: l - threaded length of the shaft lu - threaded length of the shaft, subjected to the specifi ed accuracy le - threaded length of the shaft, not subjected to the specifi ed accuracy (SERVOMECH considers its length equal to the thread nominal diameter) l0 - nominal threaded length of the shaft ls - specifi ed threaded length of the shaft ep - tolerance of the mean error, referred to lu thread portion e0a - actual mean travel deviation, referred to nominal thread portion l0 C - linear compensation, valid for l0 thread portion (possibly required by customer) esa - actual mean travel deviation, referred to specifi ed thread portion ls vup - permissible travel variation, referred to lu thread portion v300p - permissible travel variation, referred to 300 mm long thread portion v300a - actual travel variation, measured over 300 mm long thread portion v2πp - permissible travel variation, referred to a thread portion equivalent to 2π radian (1 shaft revolution) v2πa - actual travel variation, measured over a thread portion equivalent to 2π radian (1 shaft revolution) 中国官方总代理 电话：010-67716353 传真：010-67748659 6 e p ulel el l e p e 0 aC upV 2π 2πaV 2πpV 300 mm 300pV 300aV 00 l ulel el l s0 l 2π 2πaV 2πpV 300 mm 300pV 300aV e p e p e s a BALL SCREWS AND NUTS Fig. 8.a - Travel deviation in relation to nominal travel Fig. 8.b - Travel deviation in relation to specifi ed travel Diagrams Figure 8.a and 8.b illustrate the graphical method of travel deviation evaluation. 中国官方总代理 电话：010-67716353 传真：010-67748659 7 lu [mm] vup [μm] > U 1 3 5 7 10 0 315 6 12 23 – – 315 400 6 12 25 – – 400 500 7 13 26 – – 500 630 7 14 29 – – 630 800 8 16 31 – – 800 1 000 9 17 34 – – 1 000 1 250 10 19 39 – – 1 250 1 600 11 22 44 – – 1 600 2 000 13 25 51 – – 2 000 2 500 15 29 59 – – 2 500 3 150 17 34 69 – – 3 150 4 000 21 41 82 – – 4 000 5 000 – 49 99 – – 5 000 6 300 – – 119 – – lu [mm] ep [μm] > U 1 3 5 7 10 0 315 6 12 23 52 210 315 400 7 13 25 57 230 400 500 8 15 27 63 250 500 630 9 16 32 70 280 630 800 10 18 36 80 320 800 1 000 11 21 40 90 360 1 000 1 250 13 24 47 105 420 1 250 1 600 15 29 55 125 500 1 600 2 000 18 35 65 150 600 2 000 2 500 22 41 78 175 700 2 500 3 150 26 50 96 210 860 3 150 4 000 32* 62* 115* 260* 1 050* 4 000 5 000 39* 76* 140* 320* 1 300* 5 000 6 300 48* 92* 170* 390* 1 550* v300p [μm] 1 3 5 7 10 6 12 23 52 210 v2πp [μm] 1 3 5 7 10 4 6 8 – – ep [μm] 1 3 5 7 10 p u p V le 300300 2 uu BALL SCREWS AND NUTS Thread length Travel variation allowed refered to lu STANDARD TOLERANCE GRADE Thread length Tolerance of mean error, refered to lu STANDARD TOLERANCE GRADE Positioning ball screws Positioning ball screws Positioning and transport ball screws Positioning ball screws Transport ball screws * - values calculated by linear extrapolation STD. TOLERANCE GRADE STD. TOLERANCE GRADE STD. TOLERANCE GRADE 中国官方总代理 电话：010-67716353 传真：010-67748659 8 n vPh 3 2 21 FFFm u� i Fi [N] Fm [N] 1 5 000 8 3342 10 000 F = 8 334m F [N] F = 5 000 F = 10 0002 1 s s21 BALL SCREWS AND NUTS 2. SELECTION OF BALL SCREWS 2.1 Introduction Elements that affect the functioning of the ball screw, as well as guidelines for proper sizing of ball screws, are indicated below. In order to allow correct sizing of ball screws, the following points must be known: ▪ required life, ▪ detailed working cycle (all load levels, relative speed and working period of time), ▪ mounting conditions, ▪ environmental conditions, ▪ lubrication conditions. During work, the load applied to the ball screw must be coaxial with a screw itself. It is essential for proper functioning of the ball screw and achievement of the required life. Any load not coaxial to the screw, caused by misalignment and/or other reasons, signifi cantly reduces its life. In addition, it must be supported by guides or external support systems. Step 1: determinate the thread helix lead (Ph) where: Ph [mm] - thread helix lead v [mm/min] - linear speed (of threaded shaft or nut) n [rpm] - rotating speed (of nut or threaded shaft) As a fi rst approximation, the rotating speed can be considered equal to the max. working speed. Step 2: determinate the equivalent axial dynamic load (Fm) The equivalent axial dynamic load is defi ned as that hypothetical axial load, constant in magnitude and direction, acting axially and centrically on a ball screw, which, if applied, would have the same infl u- ence on ball screw life as the actual loads to which the ball screw is subjected. It must be determined by dividing the working cycle at separate, distinct subcycles, each of them identifi ed with the proper load level, rotation speed and time period. The equivalent axial dynamic should be determined considering actual working conditions: ▪ case 1: linearly variable axial load at constant speed example: current position s where: F1 - axial load at the beginning of displacement (current position s1) F2 - axial load at the end of displacement (current position s2) 中国官方总代理 电话：010-67716353 传真：010-67748659 9 i ti [s] Fi