Spline Standards And Spline Calculation.pdf
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Interpolate the data using spline and plot the results. Specify the second input with two extra values [0 y 0] to signify that the endpoint slopes are both zero. Use ppval to evaluate the spline fit over 101 points in the interpolation interval.
Compare the interpolation results on sample data that connects flat regions. Create vectors of x values, function values at those points y, and query points xq. Compute interpolations at the query points using spline, pchip, and makima. Plot the interpolated function values at the query points for comparison.
You also can perform spline interpolation using the interp1 function with the command interp1(x,y,xq,'spline').While spline performs interpolation on rows ofan input matrix, interp1 performs interpolationon columns of an input matrix.
This Spline Design Data is based on ISO 5480. ISO 5480 standard applies to splined connections with involute splines based on reference diameters for connecting hubs and shafts either with a removable connection, a sliding fit or a permanent fit. It lays down the following fundamental principles:
In the formulae given in table A, the signs for the number of teeth and addendum modification factors of internal gear splines as defined in DIN 3960 have been introduced in order to facilitate the use of computers for all calculations in respect of fitted splined connections. These lead to negative signs for all hub diameters and dimensions (see DIN 3960). In the tables of dimensions given in DIN 5480-2, only the absolute values of diameters and inspection dimensions are listed, i. e. the values are to be understood as absolute values in order to avoid any misunderstanding.
The tooth interlock of a shaft and hub splined connection is determined by the basic rack profile, the reference diameter, the module and the number of teeth. The selection of nominal dimensions is essentially determined by the following condition: the shaft cross section remaining available for transmitting torques shall not be reduced more than is necessary to permit easy slip-fitting of components such as, for instance, ball or roller bearings. In connections centred on any reference diameter, this condition is met by making the reference diameter equal to the bore of the bearing and then modifying the profiles of the teeth of the hub and the shaft accordingly.
This month, we will focus on calculating and sizing DIN 5481 type spline serrations for any application. The latest document is a 2009 update to the original 1956 standard. However, the document is not available in the U.S. due to publishing restrictions. As far as I know, it is only printed in German. Nevertheless, the procedure for designing with these straight-sided serrations is straightforward. The splines themselves make for connections that are simple, elegant, easily calculated, and strong. They can be manufactured by milling cutter, hob, broach, and rolling. Net shape molding is easily done with tooling readily made by many suppliers.
The DIN standard fixes spline serrations both internal and external with a constant space angle of 60° for numbers of teeth between, 28 to 42 and pitch diameters from 7.0 mm up to 60.0 mm. For larger splines,, a constant space angle of 55° is specified for numbers of teeth between, 41 to 81 and pitch diameters of 60.0 to 120.0 mm.
DIN 5481 includes standard tables for internal and external spline fits. This design data is tried and true. However, the document is in German and equations for the table data are not provided. For net shape gearing, this type of serration can be applied to any custom application requirements. Unique spline sizes and fits that are not found in the tabled data can be developed just by using the same geometric logic. Custom sizes are easily calculated by understanding the underlying basic geometry.The spline geometry, illustrated in Figure 1, is as follows:
For ease of assembly, a net shape molded tapered spline, as illustrated in Figure 3, can be designed. These are more complicated to execute and measure, but they are developed exactly the same way as single straight splines. Pick two locations along the spline length, determine the taper angle desired, and then determine the measure over wires or pins to suit your taper. Design of the internal member is done by off-setting the external member (via an increase in the distance between pins), then rotating it one tooth space. Once done, the model is ready for virtual assembly.
The difference between the measure to the center of the (external) pin and the measure to the center of the (internal) pin will result in a total space clearance between two mating splines (an example of which is seen in Figure 4) of the same amount or one-half the amount per side when assembled. For example: if the center to the external pin is 10 mm and the center to the internal pin is 11 mm; then the total clearance will be 1 mm or 0.5 mm on the side of each spline. This can be readily verified by modeling.
Determining the strength of the spline connections is reasonably easy with finite element programs. The geometry is symmetrical. Therefore, a small portion of the component and number of the teeth are only needed for the analysis. The strength will be determined by the number of teeth and portions of teeth in contact (see Figure 5). The load sharing is predicated on the physical tooth alignments. Plastics tend to deliver surprisingly good results especially in unfilled materials. The compliance of the teeth may result in complete load sharing, whereas in hardened steel splines compliant load sharing can be significantly limited. In these cases, the precision of the analysis will be predicated on accuracy of the components and assembly alignments in addition to experience and good engineering judgment regarding loaded tooth contacts within the application. The key to load sharing is deflection. FEA will give a theoretical result. But if axis alignments, pitch and lead variations can be discerned and modeled, virtual contact can be evaluated to derate the theoretical result accordingly and lead to a more accurate analysis.
A drawback to measuring internal splines is verifying the between-pin distance. This can be especially difficult when the component is non-metallic. As long as the pins are firmly held in place without causing deflection of the teeth, a particular concern with plastics, a CMM can take measurements between the exposed wires. A cylindrical wedge can be helpful to hold the pins in place, as illustrated in Figure 6. However, with smaller modules even this technique becomes more difficult. In these cases and for high volume components GO / NOGO gages are recommended. For modules of 0.7 and smaller, the gage may be the only reasonable choice. (Figure 7)
BALL SPLINE The NB ball spline is a linear motion mechanism utilizing the rotational motion of ball elements that can sustain loads and at the same time can transfer torque. It can be used in a wide variety of applications including robotics and transport type equipment. The NB ball spline consists of a spline shaft with raceway grooves and a spline nut. The spline nut consists of an outer cylinder (main body), retainer, side rings, and ball elements that is designed and manufactured to achieve a reliably smooth motion. High Load Capacity and Long Travel Life The raceway grooves are...
ALLOWABLE ROTATIONAL SPEED OF SPLINE SHAFT When the rotational speed is increased and approaches the spline shaft resonant frequency, the spline shaft is disabled from further operation. This speed is called the critical speed and can be obtained by the following equations. In order to leave a sufficient safety margin, the allowable operating speed should be set at about 80% of the calculated value. Using the following equations, select the size of ball spline shaft. First, calculate Id and A by equation (8) and (9) then, substitute the values into equation (7). Figure B-6 Mounting Method...
The spline nut is prelubricated with lithium soap based grease prior to shipment for immediate use. Please relubricate with a similar type of grease periodically depending on the operating conditions. Low dust generation grease is available from NB standard grease, (refer to page Eng-39) The NB spline nut has seals as standard. The seals work well to contain the grease inside the nut especially for the ground shaft, since the seal shape approximates the spline shaft profile. Figure B-9 Example of Lubrication Mechanism SPECIAL REQUIREMENTS Based on customer drawings and requirements NB does...
Examples of installing the SSP type are shown in Figures B-13 and B-14. Figure B-13 Using a Retaining Ring Figure B-14 Using a Push Plate The SSP type spline nut comes with a key shown in Table B-14 Major Dimensions of Key BALL SPLINE Mounting of SSPM Type Examples of installing the SSPM type are shown in Figures B-16 to B-19. Figure B-16 Using F Type Lock Plates Figure B-17 Using LP Type Lock Plates
F Type Lock Plate (Standard Plate) The lock plate shown in Figure B-20 is provided with the SSPM spline nut. Table B-15 F Type Lock Plate Figure B-20 F Type Lock Plate LP Type Lock Plate (Optional Plate) The LP type lock plate is also available for purchase with the SSPM spline nut. Figure B-21 LP Type Lock Plate When using the LP type lock plate, please machine the housing as shown above. Table B-16 LP Type Lock Plate BALL SPLINE Mounting of SSPF Type Examples of installing the SSPF type are shown in Figure B-22. Figure B-22 Examples of installing SSPF Type Mounting of SSPT Type Examples...
part number structure example t^mn.H-En-tstiiB-ig/raii SSPS: anti- nominal diameter blank: standard number of nuts attached with special accuracy grade blank: high spline shaft total length preload symbol blank: standard When two spline nuts are used in close contact. Note: retainer material is resin. BALL SPLINE
SSPM TYPE part number structure SSPM type nominal diameter number of nuts attached with special accuracy grade blank: high spline shaft total length preload symbol blank: standard Note: retainer material is resin. When two spline nuts are used in close contact. BALL SPLINE 2b1af7f3a8