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spindle design1
Machine Tool Spindles The key to improve
productivity
and
performance
spindle design2
Performance featuresTo increase productivity and performance of spindles, certain features that are to considered are as follows :
•Desired spindle power both peak and continuous.
•Maximum spindle load both axial and radial.
•Minimum size and weight
•Maximum torque over a broad range of speeds
•Speed allowed
•Tooling style
•Belt driven or integral motor-spindle design
spindle design3
Factors considered for spindles design
Besides the above-mentioned performance features, other factors that will affect the ultimate
spindle design are as follows :
Amount of available space in the head
Complexity
Purpose and application
Cost considerations
Market demands
spindle design4
Benefits of spindlesCertain benefits of spindles are as follows :
Machine tool spindles reduce the number of cuts in mfg by half.
Spindles provide position and transmit power to a tool
They hold a rotating workpiece .
They hold cutting tools and spin them at high torque and speed.
Spindles support many key machining tasks.
Allow flexibility in cutting a variety of materials.
spindle design5
Uses of spindles
Spindles are used to perform variety of tasks like as follows :
Grinding Milling Engraving Drilling Boring Turning
6
Machine Tool SpindleFunction of machine spindle
The function of the main spindle of metal cutting machine tools are:
1. The guiding of tool and/or work at the cutting point with adequate kinematic accuracy.
2. The absorption of externally applied forces such as the weight of the work and cutting forces with minimum static, dynamic and thermal distortion.
Other Factors
The dimensional accuracy and surface finish of the work being machined, as well as the rate of metal removal of a machine tool, are among other factors directly governed by the static, dynamic and thermal behavior of the spindle bearing unit.
In this way, spindle deflection strongly affects the production accuracy of the machine tool, and for this reason, it must be designed to be stiff enough
The deformation of the a spindle depends not only on its own stiffness, but also upon the stiffness of its bearing and that of the housing.
spindle design
7
Spindle Mounting
Forces acting on a machine tool spindle
1. Cutting force F acts at the spindle nose. This force has a radial Fcr and axial Fa, respectively.
2. Driving force Fd, acts radially, between bearings
Fixed (locating) bearing: is the bearing that takes the axial force component. It should prevent the spindle from moving axially in both directions. (source of heat generation).
Floating (Non locating) bearing: takes a radial force component only. It can not prevent spindle from moving axially.
The reaction of the radial component at each spindle bearing can be calculated simply.
The axial component is taken only by one bearing, either he front or rear bearing.
Spindle-bearing arrangement with front fixed point is commonly used in machine tools. It leads to:
Higher nose stiffness Lower thermal expansion Higher machining accuracy
spindle design
8
Spindle DesignDesign Criteria1. Static Criteria: stiffness – strength
2. Dynamic criteria: Natural frequency - Damping – Mode Shape – dyn. Amplitude
Machine spindle may be classified into two categories:
1. Hollow of stepped cross section: Ex. Horizontal milling machine, vertical milling machine, lathe, turret lathe.
2. Solid of uniform cross section: Ex. Boring machine, Drilling machine, Grinding machine.
In the following analysis, for simplicity, it will be be assumed that:
1. the spindle has a uniform cross section (hollow or solid).
2. The effect of the driving force is neglected.
3. The reactive moment of the fixed bearing is neglected
spindle design
9
The accuracy of the work accuracy produced by the main spindle is governed by the total deflection of the spindle at the point of force application in the radial direction.
The total nose deflection at the spindle nose is:
Y = y1 + y2 + y3
Where:
y 1 : the contribution due to shaft deflection
y2 : the contribution due to bearing deflection
y3 : the contribution due to housing deflection
Because of the series connection of the individual contributions to the total flexure, the total flexibility at the point of force application is given by:
1/k = 1/k1 + 1/k2 + 1/k3
= y1/F + y2/F + y3/F
= (y1 + y2 + y3)/F = y/F
Spindle design on the stiffness criterion
spindle design
10
Spindle nose deflection y1
For an infinity stiff bearing, the spindle nose deflection y1 is given by:
Where:
Fcr : radial cutting force at spindle nose
E :Modulus of elasticity of spindle material
I : Area moment of inertia of spindle
cross section
l : spindle span (distance bet. bearings)
c : spindle overhang length
Spindle nose deflection y1
).(.3
21 clc
EIFy cr
spindle design
11
Nose deflection y2 due bearing deflectionFor an infinity rigid spindle, the nose deflection y2 due to bearing can be derived as follows.
First : calculate bearing reactions
Rf = Fc (l+c)/l & Rr = Fc.c/l
Second: bearing deflections
yf = Rf /kf = Fcr (l+c)/l .kf
yr = Rr /kr = Fcr.c/l.Kr
Third: From triangle similarity in the lower figure
Spindle deflection y2
Derivation of spindle deflection y2lcl
yyyy
rf
r
)()( 2
rrf ylclyyy
)(2
spindle design
12
rcr
rcr
fcr
r
r
r
r
f
f
klcF
lcl
klcF
klclFy
kR
lcl
kR
kR
y
..).
..
..(
).(
2
2
})(.{
.)(.
..)(.)(.
22
22
2
2
2
2
2
22
2
2
rf
cr
r
cr
f
cr
r
cr
r
cr
f
cr
kc
kcl
lFy
lc
kF
lcl
kFy
lkcF
lclc
kF
lcl
kFy
The contribution of the total nose deflection by the deflection of the frame (bearing housing) y3 is difficult to calculate by the normal method, but the finite element method may by
applied.spindle design
13
It is clear from the previous equations that the total spindle nose deflection and also the total spindle –bearing system depends upon the combined effect of:
The bearing stiffness,
The span; the center distance between bearings l,
The length of the overhang length c and
The geometry of the spindle.
The experiment studies showed that :
1.The front bearing stiffness kf has great effect on the total flexibility of a particular spindle-bearing system
2.Also, a bearing stiffness kf >750 N/m
Note that the frame stiffness is not presented in this curves
spindle design
14
Optimum span length
The optimum span length that gives minimum deflection at the point of force application, (given that all other parameters are unchanged) can be derived from the equation of the total deflection.
If this equation is differentiated with respect to the bearing span l, and equating to zero (maximum or minimum), then a cubic expression is obtained for the span l. the solution for l. with minimum computer, the value of the optimum span length l can be obtained.
In general, the span length l should be greater than three times the overhang length, i.e., l 3c
spindle design
15
Recommended Values of Spindle Nose Stiffness
spindle design
16
Spindle Design Guidelines1. Higher spindle stiffness is achieved by choosing
higher bearing stiffness and higher cross section
2. Dimensions C and l have direct influence on the accuracy of machine tool
3. Dimension C should be as small as possible
4. Optimum dimension of the the length l should be
calculated l / C >3
5. Spindle with large diameter is recommended
6. Hollow spindle gives higher spindle stiffness.spindle design
spindle design17
spindle design18
19 spindle design
20 spindle design
spindle design21
SHAFTING, Hollow vs. Solid Sect .
“When comparing a solid shaft with a hollow shaft of equal section modulus, both will transmit the torque with equal stress levels, but the hollow shaft will be stiffer, or rather will deflect less under the same overhung moment”. The following is an engineering analysis to support this statement :
Section modulus = I /c Where I = Moment of Inertia c= Distance to extreme fiber = D/2
Hollow Shaft : O.D.= 6.625”, I.D. = 5.761 ”Moment of inertia for hollow shaft I = 0.049087 x (OD4 − ID4 ) = 40.4904 Section modulus for hollow shaft = I / c = 12.2
4.99 ”dia. Solid Shaft :Moment of inertia for 4.99” solid shaft =0.785398 x R4 = 30.4349Section modulus for 4.99” solid shaft = I / c = I / R = 12.2
spindle design22
spindle design23
Exercise
1.Go to the machining workshop
2.Select any machine tool
3.Draw its spindle mounting
4.Represent the bearing mounting
5.Represent a part of housing
6.Use a suitable scale