Z Axis Motor selection

The force of gravity multiplied by the mass of the Z-Axis is equal to downwards force. The motor needs to be able to hold this and lift this on a 20mm (Minor diameter: 16.5) screw with a 5mm pitch. If the force of cutting is greater than the force generated by the weight of the gantry and the need to accelerate the gantry in an upwards then this will be used in the calculations.

Force generated by Z axis = 37.12KG (2.D.P) * 9.81 = 364.1472N


http://www.esc-ltd.co.uk/Drilling%20Formulas.pdf

Fr=0.63* ((0.305*10*500)/2)= 480.375

480.375-364.1472 = 116.2278

As force is acting down upon the cutting tool from the relationship of the gantry and gravity.


L= 37.12*(2*9.81) = 728.2944N (Note: Two times gravity to allow equal acceleration in both Z directions)

Angle of  lifting plane = α
= tan^-1(Pitch/Screw minor diameter*π)
= tan^-1(5/16.5*π)
= 5.51 degree (2.D.P)

μ = 0.01 (http://www.kssballscrew.com/us/pdf/qa/Q-BS-12.pdf)

Friction Angle = β
 = tan^-1 * μ
 = tan^-1 * 0.01
= 0.57 degrees(2.D.P)

F =L tan (β + α)

   = 728.2944 * tan (0.57+5.51)
   = 77.56N (2.D.P)
  
T = F x radius
   = 77.56*0.00825 = 0.63987 Nm

The motor will require a holding force of at least 0.63987 Nm

http://www.ebay.co.uk/itm/DMM-AC-Servo-Motor-Drive-4Axis-750W-for-CNC-Router-Plasma-Mill-kit-/161346672390?pt=LH_DefaultDomain_2&hash=item259102d706

If none of the other servo motors required within the machine require more than 2nm continuous torque this should provide a good solution as it incorporates other required components.

Conceptual Designs

Design 1

This design uses a steel box section base clad with sheet steel, there are two ball screws each side driving the x axis, these are linked with a motor in the center and a pulley on either side and a timing belt. Tension on the belt is supplied by the motor sliding in its mount. The motor on the z axis is a direct drive onto a ball screw. much the same as the Y axis. The Y axis has two rails both supported round rails. The X axis has four to provide support when the X axis tries to rotate around the top rail on either side. This means that rigidity is not contained to the relationship at the top of the gantry. The whole gantry is rotated backwards to center the cutter between the carriages on the rails for the x axis in the Z direction.

The force when cutting in the X axis will be directed into X axis through a rotation of the Y axis and some force applied to the screws thus being controlled by the Y axis motor. This will create a force around the top of the gantry and the carriages on the Y axis. The only resistance to this load is the Aluminum plates that create the side of the gantry.

Out of the four designs this design scores Medium for cutting performance, Medium for ease of construction and medium in the cost category.

 Design 2

This design is primarily the same as design one however it is constructed with  aluminum frame rail for ease of construction and aluminum plates. It holds the same inherent issues as design one however is marginally weaker across the bed of the machine due to the material being aluminum as opposed to steel.

Out of the four designs this design scores Low for cutting performance, Medium-High for ease of construction and medium in the cost category.

Design 3

This design is very different from the other two, it has a single arm supported on one side. It used a singular profile rail. The intention of this design is to drastically reduce the complexity and component count thus reducing cost. It is constructed using aluminum frame rail with aluminum plates as required. However it is the weakest of all the designs. It is the easiest to construct and will be the cheapest due to the low component count.

Out of the four designs this design scores Low for cutting performance, High for ease of construction and High in the cost category.

Design 4

This design is primarily designed from square steel section that will be welded together. The tubes can be filled with an epoxy granite mix if resonance of the machine becomes a problem. The angular sections at the side are to provide support for the forces generated when cutting in the Y axis. This design will use profile rails sitting on the top of the of the frame work. This is to remove the cutting tendency for forces to rotate around the axis of the linear rail as per design one and two. Another change to this design is to fully encapsulate the spindle so it is help essentially between two gantries. These gantries will be 2 off 100x100x5mm steel box section welded together. Aluminum plate will be bolted to these to provide a fixing mechanism for rails and screws. Any welded component will be leveled off with epoxy resin to remove the effect of warping created by the heat of the welding. Although not shown there will be a removable section in the center of lower section. This will allow taller workpieces to be positioned within the machine. In this lowered section will be location stops to push the section up to. The bottom of this section will also be leveled with epoxy resin. The bed of the machine will be a thick aluminum sheet with tapped holes on a 50x50mm grid to allow mechanical fixing of components.

Out of the four designs this design scores High for cutting performance, Low for ease of construction and Low in the cost category.

Scoring Table

               

	Design 1	Design 2	Design 3	Design 4
Cost  (Weighted by a factor of 2)	2	2	3	1
Ease of constuction  (Weighted by a factor of 1)	2	2	3	1
Cutting performance (Weighted by a factor of 4)	2	1	1	3
Total points	14	10	13	15

               
Design one is a very well rounded machine with reasonable performance, reasonably easy to manufacture and put together and reasonable cost.

Design two has poor cutting performance but is well rounded in other aspects

Design three has poor cutting performance however is very cost effective and very easy to manufacture and produce.

Design four, will cost the most, will be hardest to manufacture however will have have by far the best cutting performance.

Product Design Specification

Expected product quality standards and requirements

Comparable products range in quality. Quality is not always dependent on price. Many of the lesser quality products utilise good quality mechanical components however lack a good design to utilise those components fully. However higher quality products utilise marginally substandard parts however generally have a good design lacking only in some minor areas.

This product shall use high quality products and utilise well thought out design principles to allow for highly accurate results that are repeatable and efficient.

The machine shall be finished to a high standard.

Expected product size and weight

The external dimensions of this machine shall be no larger than 2000x2000x1800mm

Weight of the machine must not weigh more than 4 tonnes.

Expected product aesthetics

The product has no aesthetics constraints, other than the machine needing to be presentable and finished to a high standard.

Expected product ergonomic requirements

 
The product will need to be designed with considerations to the ergonomics of work holding and loading of materials.

Expected product performance requirements

The machine has no service life considerations as it will be overbuilt beyond requirement to ensure accuracy and repeatability is suitable. It will be constructed with components with quality that in many cases exceeds that of rival commercial machines.

The machine will be required to be run from a 240v 30A domestic single phase electrical supply.

The product should be able to remove 300cc/minute of material MDF and 100cc/minute of 6061 T6 Aluminum. 

It should be able to achieve an accuracy and repeatability of +/- 0.1mm or better.

Have a working area of at least 1250x1250x200mm

Expected product reliability standards and requirements

The machine should be built with a design and standard that requires only minor maintenance tasks throughout its lifetime. Routine maintenance should be limited to re oiling components and tasks of such magnitude as regular tasks this should happen once a month. Other tasks such as aligning components should be much less frequent, once every 6 months.



Potential operator hazards

Around the machine the operator should wear safety glasses, a sign will be fixed to the machine to remind the operator of this requirement. The machine will also have emergency stop buttons, limit switched and other items to ensure the safety of the operator. 

Potential manufacturing and assembly hazards

All safety hazards resulting from manufacturing and assembly will be covered by the workshop risk assessment 

Potential for misuse/abuse

The machine will have the ability to stop in the event that loads become too high. With loads that are two high this indicates a problem. This will protect both the machine and the operator.

Expected product service environment

The machine shall have to operate in a temperature environment between -10 degree Celsius and +30 degree Celsius.

The machine shall have to operate in a humidity range of 30%-75%

The machine shall produce no more than 85dB of noise at a distance of 1m.

Expected product maintenance requirements

The machine will have to be oiled around once a month where required. Adjustments such as alignments and removing backlash from the machine will be performed every 6 months or as required.

Possible off the shelf component parts

All mechanical components and electrical components should be purchased as opposed to made.

Material requirements

The product must be made out of a combination of materials that allow the machine to be outside the resonance range of 800-975hz.

The machine should not deflect with a cutting load of 80N more than 50micron.

Expected product recycling potential and expected disposal

The machine should be easily recyclable or the materials used be re purposed.

Manufacturing process requirements and limitations

The machine needs to be designed so it can be produced in a “standard” machine shop. Most modern machine shops have at least 3 Axis CNC milling capability, manual lathes and manual universal milling machines.

Product packaging requirements

The machine will not need to be packaged as it is a “one off” that is not being sold

Marketing requirements and compatibility issues

As the machine will not be sold externally it has no marketing requirements.

The machine will only need to be compatible with current electrical regulations.

Spindle selection

The main types of spindle available are:

Cartridge type spindles


These require a separate motor for drive, as a result the whole assembly becomes very bulky and cumbersome however does enable the motor to be changed for varying applications or multiple motors to be added to increase torque at given RPM values.

All in one spindles



These spindles are all in one units that require power inputs, positional inputs (If acceptable) and water feeds if water cooled. This will be the type of milling spindle I will be selecting due to its compact nature and the aims and objectives of the machine. The machine will be run within a very narrow RPM range as a result a lower speed and higher torque motor for milling other materials will not be required.

The criteria set for the spindle selection are:

Must have a minimum power output of 1kw @ 19500 rpm
Must be water cooled to allow long duty cycles
Ideally should have function to facilitate automatic tool changes.

This spindle sold by JiaLing FeiLong Automation Equipments Co. LTD satisfies all the requirements other than the speed requirement. This is a maximum of 1800rpm. However I can slow the feed of the machine to compensate and increase the depth of cut to maintain material removal rate.

http://www.aliexpress.com/item/EN030-Motor-Spindle-for-CNC-milling-with-ATC/620661845.html


The cost is £2233 delivered from China.


Run out is stated at less than 3 micron

The main issue with this item is the cost.

A 2.2kw all in one spindle motor can be bought for £205

This also contains part of the electronics system to run the spindle.

http://www.ebay.co.uk/itm/200687842858

As this machine is not a production machine with the increase in price to utilize an automatic tool changer it just does not make it a viable option and a manual tool changer type spindle will have to be used.

Ballscrew accuracy and considerations

As with all components there is an accuracy value involved. Ball screws have accuracy issues with the pitch of the screw and the variance of accuracy of the central point of the channel over a length as a result of this, ball screws are rolled or ground to a specification set out my the international standards organization.



https://tech.thk.com/en/products/pdf/en_a15_011.pdf


Here is a table stating those tolerances, its probable this machine will use a 1600mm screw in both X and Y direction due to the cutting area required. This results in an error of 16 micron over the total length in regards to screw pitch. With a total travel error with a maximum of 35 micron over the full length. However it is likely that this will be less.

C3 Ball screws will be chosen from a company called true systems. In 20mm diameter and 5mm pitch these screws can withstand a force of 1130kgf. This will be more than suitable for the application of this machine. Being 20mm and hardened to the core wear characteristics will allow the life of the ball screw and nut to outlive the life of the machine.

http://www.trusystems.co.uk/wp-content/uploads/2011/03/Tru-Systems-12pp-A4-Ball-Screw-Brochure-lr.pdf

With a 2400 line rotary encoder on the servo motors should allow for a 2.01 micron resolution on a 5mm pitch screw.

Ball screw whip

The required speed on a 5mm pitch screw = 2000

Ballscrews will "whip" when at or above a certain speed, this speed can be calculated with the formula


http://www2.steinmeyer.com/content/cnt_cnt/docid_961/iso_en

n_k  Critical speed [rpm]
d_N  Nominal diameter [mm]
l_s   Unsupported length [mm]
k   Support bearing factor

Support type

Fixed = contained in place (A motor could be a fixed support, or a support that allows no rotary movement)
Supported = supported on a bearing or similar
Free = no support

fixed - fixed: 25,5
fixed - supported: 17,7
supported - supported: 11,5
fixed - free: 3,9

d_N  Nominal diameter [mm] = 16.5 (http://www.mooreinternational.co.uk/carry-ball-screw/screw20x5.html)
l_s   Unsupported length [mm] =1550 (25mm each end for support)
fixed - supported arrangement (motor one end bearing on the other)



=17.7*16.5*(1/1550^2)*10^7
=1215(3SF) RPM (Not suitable for application)

A rotating nut as opposed to a rotating ball screw would enable a fixed-fixed arrangement

=1751=137 (4SF) RPM (Not suitable)

Increasing the diameter to a 25mm screw will raise the critical speed

http://www.mooreinternational.co.uk/carry-ball-screw/screw25x5.html

d<sub>N=21.5mm

nk=2282 RPM (4.S.F) This is suitable and will allow for a maximum travel speed on a 5mm pitch screw of 11.41 meters/minute without the screw whipping.</sub> 

Analysis of existing solotions

Linear motion system:

The two main drive systems are either servo motors or stepper motors.

Therefore I will compare stepper motors with servo motors subjectively to attain the best type of motor for the application.

Stepper motors vs Servo Motors:

Stepper motors

http://zone.ni.com/cms/images/devzone/ph/81947a871576.gif

This diagram shows the stator and coil arrangement within a stepper motor. A stepper motor does at the name suggests and steps by a given amount. The diagram above shows a stepper motor with a single step consisting of 30 degrees. The stepper motors suitable for this application have many more stator and coils resulting in a single step angle of 1.8 degrees. The positioning of the rotor is relative to the coil current arrangement at that point in time. This can thus be manipulated to rotate the motor to the required position. This requires no feedback loop at the position will be dictated by the coil current arrangement.

However due to having no feed back loop if the torque supplied by the motor is less than is being resisted by whatever the motor is driving it will cause the motor to loose position. This could cause issues with part accuracy and the machine being damaged due to torque continuing to be applied despite the machine being stalled at the cutter tip.

Another issue with stepper motors is their speed torque characteristics.


http://www.anaheimautomation.com/images/stepper/torque/17Y402S%20Torque%20Curve%20%28400x293%29.png


The bottom of the graph shows the speed of the motor and the torque of the motor, the vertical axis on the left shows the maximum torque of the motor at that speed. As the speed of the motor increases the torque curve drops off dramatically. With a 200 step/rev motor on a 5mm pitch screw will result in a machine resolution of 0.025mm per step. At a cutting speed of 10 meters/minute this equals 400000 steps/min 6666 & 2/3 steps per second or 33 & 1/3 revolutions per second. This will result in minimal torque at cutting speeds.

Servo Motors

Servo motors are constructed in a very similar way to stepper motors, however they have many less stator poles and poles on the rotor its self. They are rotated in the same way however due to the huge angles between potential positions generated by the stator holes they require a closed loop feedback position. Between stator poles there is an infinitely variable number of positions. This position is controlled by the current supplied to varying stator poles. This allows very fine positioning where as a stepper motor is limited to stepped positions.

http://www.anaheimautomation.com/images/brushless/torquecurve/BLZ362S-24V-3500%20Torque%20Curve%20%28400x321%29.png

This graph shows the torque/speed characteristics of a servo motor. Although as speed increases the torque decreases the curve is much flatter across the rpm range in comparison to the stepper motor.

One benefit of the stepper motor over the servo motor is the cost, generally servo motors cost more.

https://www.damencnc.com/en/components/motors-and-drivers/steppermotor/197

This is a NEMA 23 2nm stepper motor at a cost of €41.99

https://www.damencnc.com/en/components/motors-and-drivers/delta-ac-servo-motors/932

This is a servo motor that can ran at 2NM continuous load at a cost of €400


Although stepper motors are certainly less expensive, the servo motors do have the ability to stop in the event of an issue and provide better speed torque characteristics. Thus Servo motors have been chosen as opposed to stepper motors.
Guide system:
Upon analysis of the three machines 3 linear guide systems were apparent.

Round rails

http://www.zappautomation.co.uk/mechanical-products/precision-round-rail-385/sfc25-precision-round-rail.html

Cost: £36/1000mm

Supported round rails

http://www.zappautomation.co.uk/mechanical-products/precision-supported-round-rail-386/tbr20-supported-roaund-rail-32343.html

Cost: £46.20/1000mm
Profile rails

http://www.zappautomation.co.uk/mechanical-products/isel-linear-guide-rail-systems-384/linear-guid-rail-systems/lfs-8-1-linear-guide-rails-31198.html

£82.31

Round rails without support will provide little support in suitable dimensions resulting in deflection values that will affect the accuracy of the machine. Supported round rails the carriage will rotate around the axis of the rail. This will result in them not being able to suitably transmit force into the support structure they will be bolted too. A profile rail system will provide suitable support however they are the highest cost item, despite this they will be chosen as the linear guide system.

Drive mechanisms

The two main drive mechanisms are ball screws and rack and pinion from analysis of the three commercial machines.

Ball screwsBall screws have a round profile cut in a pitch along the axis of the screw, ball bearings then run in in this profile. A nut with the same profile is used. The ball bearings are then placed within the two profiles and circulated throughout the ball screw. By loading two ball screws against each other its possible to eliminate the backlash within the machine. Ballscrews are also generally very smooth along the axis, this will therefore improve surface finish and accuracy over other drive mechanisms. However ball screws do have some short comings. These include:

Requirement for design to ensure ball screws don't become contaminated.
Precision alignment during assembly



http://valuablemechanisms.files.wordpress.com/2010/05/ball-screw.gif

Rack and pinionRack and pinion is constructed as the name suggests, by running a toothed pinion and a toothed rack its possible to convert rotary motion to linear motion. There are a few ways of eliminating backlash on the rack and pinion setup. One way is to force the pinion deeper into the rack, however, this results in excess load on the motor driving the pinion and increased wear on both the rack and pinion. Another way is to run another pinion on the rack and gently apply force in the opposing direction. However, this adds complexity to the design of the machine. Also due to the increased friction other other drive mechanisms they are inefficient.



http://img.directindustry.com/images_di/photo-g/racks-pinions-20096-2786531.jpg

http://www.cntmotion.com/before_you_buy.html

Construction

One of the machines used aluminum profile as the main material used within the construction of the machine, others are using steel and or cast iron as the main construction material.

There are four main criteria to consider when selecting a material for a machine such as this.

Tensile strength and compressive strength
Mass and frequency damping properties  
Young modulus
Cost

As this machine is a one off machine and not a production machine, casting is not really a viable option on a one off due to the cost involved of creating tooling. Cast iron is also not readily available in sheet format for machining also much like steel it is a fairly heavy material.

Aluminum alloy is a fairly light material. Its also readily available and each to process. The machine will require all moving assemblies to be fairly light weight due to available and cost of motors. However, a structure could be created that is strong enough to withstand the forces from aluminum and transmits resonance to non moving components such as the base of the machine. The base of the machine will be made from steel as its easy to fabricate, cost effective and readily available.

Other aspects:

One of the machines has a dust extraction system, as this machine will mostly be used to machine MDF this would improve safety of use of this machine and improve the cutting operation due to less re cutting of machined material being left from the previous cutting operation or pass.

All machines seem to move the spindle and tool as opposed to the workpiece. This is to maximize the available work area within the footprint of the machine. However a fixed spindle style machine would increase strength and allow the frame to be much more substantial resulting in less resonance.

Due to the space constraints the moving spindle type machine will be required.

Existing market solotions

First solutionCompany name: Marchant Dice Ltd

Machine model: 4' x 4' Rack and Pinion

Machine work area (mm): 1250x1250x75

Price: £5,994

Link: http://www.worldofcnc.com/collections/cnc-router-packages/products/4-x-4-rack-and-pinion-desktop-cnc-router-package

Work area: 4'x4'x100mm

Relevant Features:
Driven by rack and pinion using stepper motors
20mm HIWIN Profile rails to allow linear motion
Aluminum profile rail construction
1900mm x 1900mm foot print
240v single phase power requirement
Dust extraction considered in design
3KW Spindle




Second solution:
Company name: signstech ltd

Machine model: 4.2ftx4.2ft CNC Router Engraver Miller

Machine work area (mm): 1300x1300x90mm
Price: £2990

Link: http://www.worldofcnc.com/collections/cnc-router-packages/products/4-x-4-rack-and-pinion-desktop-cnc-router-package

Work area: 1300x2500x90mm

Relevant Features:
Driven by ball screws ran by stepper motors
X,Z axis Round guide rail, Y axis Linear rail
Cast iron constuction
1900mm x 1900mm foot print
240v single phase power requirement
2.2KW Spindle



Third solution
Company name: Mantech UK Ltd
Machine model: JDM 25
Price: £14298
Link: http://www.ebay.co.uk/itm/CNC-Router-Engraving-Cutter-Model-M25-1300-x-2500mm-4ft-x-8ft-/170986281281?_trksid=p2054897.l4275

Work area: 1300mm x 2500mm x 200mm

Relevant Features:
1,480x3,000mm table size
0.05mm resolution
4.5KW water cooled spindle
6.34KW Total maximum power
0-24,000RPM spindle speed
Driven by stepper motors
Linear motion provided by profile rails
380v 50Hz/60HZ supply
Vacuum table holding mechanism
Dust extraction capabilities
Steel framework and steel plate construction

Tool Deflection values

The cutting strategy dictates that the finishing cut should be a full depth pass of 20mm with a small step over value. This value shall be 0.5mm. A large value for a finishing pass however it simulates a worse case scenario.

6061 T6 Aluminum alloy finishing pass data

                                            6061 T6 Aluminum alloy roughing pass data

 
                                                              MDF finishing pass data

                                                               MDF roughing pass data

                                         All four data sets were calculated using this tool:
                                                  http://zero-divide.net/?page=fswizard

Cutting strategy

To continue calculating and obtaining data for the parameters of this machine I need to define a method for tool paths (The paths the cutter will pass along)

The machine will need to be capable of high speeds and high feeds to machine MDF. These characteristics can be used to machine aluminum providing the correct tooling is selected.

Traditional CNC cutting strategies generally cut in small depths across the whole area when cutting a pocket or profile and then finish the outside or inside profile with a small cut width. They also incorporate what is known as a step over value where each cut is a given value of thickness. An example of this is a slot will be cut 10mm wide with a 10mm cutter the cutter will then move over 5mm and cut the slot width to 15mm this would be a 50% cross over or 5mm.

HSM (High speed machining) strategies are generally very different. Cutting a pocket will start with a circular pocket that then cuts in an axial pattern towards full depth. When at full depth it will then machine outwards with a step over value and finish the profile in the same manner as traditional CNC would. There are other aspects of variations within HSM that improve things further such as Waveform from EDGECAM.

The advantage of high speed machining is that it can dramatically increase MRR values. Heat produced within the cutting process is mostly ejected with the chip. Tool life increases as the tool is generally not cutting on just the end section of the tool and is cutting on the full flute length of the cutting flutes.

However there are some drawbacks to HSM. It increases the volume of each chip resulting in more aggressive chip clearance methods such as high pressure coolant being directed at the cutter. It also increases cutting force dramatically. This is something that needs to be avoided.

The cutting strategy that will be employed within this machine is a more traditional approach. However using tooling designed for HSM. This will allow shallow cuts with high spindle speed and high feed speed whilst steel keeping a suitable MRR value. It will also mean that less force is applied to the cutter and machine. Resulting in less deflection affecting accuracy and less magnitude of resonance.

Theoretical surface finish

Surface finish is dictated by the following equation

http://www.harrisonep.com/electropolishing-ra.html

Ra value is a measurement of surface finish, its the average of measurements taken from the peaks and valleys of a surface due to the cutting operation relative to a mean line.

http://www.rubert.co.uk/Ra.htm

This graph above shows a graphical representation of this data.

6061 T6 Surface finish calculation

Using the 6061 T6 aluminum speeds and feeds dictated in a previous post and the equation below its possible to estimate the surface finish of the cutting operation.








http://www.kanabco.com/vms/eng_surface/eng_surface_04.html

Tool data from
http://www.niagaracutter.com/solidcarbide/metric/nc_metric_catalog.pdf
3 flute 10mm solid carbide end mill

r = tool tip radius (Inches) 0.02 inches (2.D.P)
f = feed rate per tooth (Inches) = 0.003 inches (3.D.P)

Ra=((0.02-sqrt(0.02^2-(0.003/2)^2))*1000000)/2
     =((0.02-sqrt(0.0004-(0.00000225)))*1000000)/2
     =((0.02-sqrt(0.00039775))*1000000)/2
     =((0.02-0.01994367067517913062473309999688)*1000000)/2
     =(0.00005632932482086937526690000312*1000000)/2
     =(56.32932482086937526690000312)/2
     =28μin    
1 Microinch = 0.000001 inches therefore 28μin = 0.000028 inches
                                                                             = 0.0007112 mm
                                                                        Ra = 0.7112 µm

MDF theoretical surface finish calculation




r = tool tip radius (Inches) 0.02 inches (2.D.P)
f = feed rate per tooth (Inches) = 0.0079 inches (4.D.P)

Ra=((0.02-sqrt(0.02^2-(0.0079/2)^2))*1000000)/2
    = 196μin (3.S.F)
    = 4.9784µm

     

Axis movement required

Z axis height from the bottom of the workpiece should be material thickness + tool length + 50mm clearance for holding mechanisms.

The machine should be able to machine the full depth of a material with a cutter. As the maximum material thickness is 100mm the Z axis travel should be 250mm minimum.

The maximum material size in X direction is 1220mm. Allowing 40mm either side for clamping this should brings the required travel in X to 1300mm

Y direction will be 1220mm + 80mm for clamping + allowance for tool changer.


According to this image below an ISO20 tool holder is 30mm wide. Allowing a generous 100mm for the tool change brings the total Y axis movement to 1400mm.

http://www.spindel-shop.de/Shop/images/product_images/info_images/iso20-er16.jpg

Maximum electrical power and general requirements

The machine needs to be run from the electrical system within the workshop. This is a 240v 30A supply. However there is also a 2.25 KW compressor on the same circuit.

total power = 240*30= 7200w

This leaves 4950W available for the machine in its entirety.

The machine should be an automatic tool changing mechanism. The simplest way of performing this would be to add a stationary rack at the end of the table. The machine would then center over the top of the tool in a suitable holder. The Z axis come down to the tool holder and draw the tool holder and tool into a spindle. This will thus require pneumatics or hydraulics of some description.

Maximum tool size required in diameter: 13mm shank. This is partially dictated by the high spindle speeds as a result of MDF being the primary material being worked. But also as a function of the machine. Parts will be nested into a sheet and multiple parts cut at the same time. Therefore having a large cutter will be wasteful of material.

The machine needs to provide storage of some description of items like the compressor due to its foot print within the workshop.

The machine needs to be of a horizontal orientation despite the fact the this requires a larger foot print. However it does provide a lower center of gravity and thus is safer. It also allows materials to be easily loaded and positioned for clamping.

As this machine will be horizontal table height should be comfortable to lean across and position fixtures and other items. Work benches are around the correct height for this.

Many work benches are 900mm from top surface to floor. This will make for a suitable height.

http://www.bigdug.co.uk/shelving-c2/garage-shelving-c1248/rac-boltless-garage-workbench-pp13240?utm_source=google&utm_medium=cpc&utm_term=rac-professional-garage-workbench-2-levels-900h-x-1205w-x-605d-mm-30-load-kg-300-height-900-width-1205-depth-605-506-0134-387335&utm_campaign=product+listing+ads

The machine should have an accuracy of +/- 0.5mm in MDF and +/- 0.1mm in 6061 T6 Aluminum.

Smaller tolerance and repeatability would be beneficial. These are maximum theoretical values.

Work area criteria

The maximum work area in X and Y will be a compromise between my maximum machine size and available materials.

The maximum machine size will be dictated by a the size of a typical small single car garage with some room to move around the machine. A typical small garage could be considered to be 2400 x 4900 mm.

http://en.wikipedia.org/wiki/Garage_%28residential%29

The machine is being situated within a four car garage. With one quarter being dedicated to the a workshop area situating this machine as well as a work bench and other tools/equipment.

Thus the machine should have a maximum foot print of 2000x2000mm. Floor to ceiling height in this area is 2600mm. Thus the machine should be no more than 2000mm tall to not block the lights within the workshop.

With MDF being the primary material being machined the available sizes dictate the working area to some extent. MDF is readily available in sizes of 1220x1220mm in thicknesses up to 25mm.

However for this machine it needs to be able to machine tooling foam this is readily available in sheets up to 100mm in thickness with width and length small then that of MDF.

(Cutting power and force calculations are not going to be considered for this material as it requires the same cutter speed as MDF and is much easier to machine due to its low density)

Resonence from cutting operation and concequences

Some resonance from the cutting operation will occur within the machine.

This will be a result of the cutting teeth impacting the work.

Using the example cutting conditions its possible to attain the frequency of the resonance created by the cutting operation.

                                     
                                    
This image shows a climb milling pass on the edge of a workpiece. The circle with a gradient shows the magnitude of the cutting force with relation to its cutting path relative to one tooth.

As the load is at peak (The start of chip formation) is where the force is the highest dictated by dark red. As the cutter cuts the chip the force decreases with relation to the cross sectional area of the chip decreasing. This is depicted by the fading gradient where finally all force is released and thus the force circle turns white.

This creates a resonance in the machine that transmits through the machine. If there is much backlash within the machine this will transmit back to the cutter and thus into the workpiece causing an undesirable surface finish.

Backlash is considered the clearance between components that is taken up upon movement.  Within climb milling the force generated by the cutter will be in the same direction as the workpiece direction.

Thus, this will cause the clearance between components to open and close as the cutter takes a cut on one of its teeth opening the clearance then the clearance being closed as a result of the feed mechanism in the time between cuts of each tooth. This will happen in a frequency relative to the amount of times per second the cutter impacts the workpiece. Using the speeds and feeds parameters set out in the "More criteria" post its possible to calculate this frequency.

induced frequency = (Spindle speed in rpm/60)*cutter teeth

6061 T3: 19385/60 * 3 = 969.25Hz
     MDF: 24000/60 * 2 = 800Hz

Backlash when conventional milling is less of a problem because of how the force is applied. With climb milling the peak force is on the initial section of the cut and tapers off. With conventional milling it tapers up to peak force. The force is on a radial motion at a tangent to the cutter with force being applied in an opposing direction to the cutter direction when the cutter face reaches a perpendicular tangent to the feed direction. Thus the clearance is kept closed reducing resonance.

Although climb milling will increase the issue of resonance being transmitted back to the workpiece finish. It does provide a multitude of benefits these include:

Better surface finish due to less material being in shear at end of cut, resulting in less deflection nearing material surface.

Increased tool wear due to the tools cutting rather than rubbing and then digging into the workpiece,  tools rubbing causes dulling of tool edges and increase in heat throughout the workpiece and cutter due to friction.

Less re cutting of chips as the cutter leaves chips behind the cutter relative to the feed direction rather than conventional milling where it will place the chips in front of the cutter causing it to drag the chips through the cut wedges between the cutter and the workpiece causing gouges to the workpiece.

Force is directed down into the workpiece as opposed to up resulting in less clamping force required of thin components when machining. This is evident when climb milling. The chips are tall and thin as they are ejected from the cutter. This means the force of the chips is in an upward direction and therefore any force in in the z axis must be directed downwards. This also results in the heat of the cut being spread over a larger area of the cutter.

The only real downside of climb milling as opposed to conventional milling (other than backlash issues as described above) is that in very hard materials it can cause a great deal of shock to the cutter causing micro fractures ultimately resulting in tool failure due to the chip load being highest at the start of the cut resulting in a higher impact. However this machine is only designed to cut materials as hard as aluminum and as a result this is not really a consideration.

As a result of this the machine must be designed in such a way to eliminate backlash as much as possible in as many areas as possible.

Attaining force direction from cutting operation.

This machine will perform three main modes of cutting. These are:

Climb milling

 Climb milling in this image the cutter is rotating in a clockwise direction and the arrow dictates the workpiece direction.

Characteristics of climb milling:

Generally a better finish on the surface. This is because less force is applied to the material at the end of each chip formation. I.e each touch that passes through the material.

Chips are ejected behind the cutter resulting in chips not being drawn into the cutter.

As the chip formed from thick to thin as the tooth passes through the material this causes peak force to be perpendicular to the feed direction. Tangential force calculated in the previous post is where chip formation is at its thickest dictated by incorporating face area of chip. Thus in climb milling this will be at the start of the cut. So if using the example force as dictated in previous posts for aluminum this will apply 86N when the tooth of the cutter is perpendicular to the cutting surface. This direction will be perpendicular to the force. Thus if a climb milling cut is performed in the Y direction it will apply force to the Z Axis.

This image dictates conventional milling. The rotational direction of the cutter is the same as climb milling. The arrow also dictates work feed direction.

The thickest chip will occur at the end of the cut. It will apply force perpendicular to the cutting face at that point. Thus again like climb milling the force will be perpendicular to the feed direction.

A slot will have the same force direction.

Its worth noting that climb milling although causing perpendicular forces will in fact be in opposing directions to each other. With climb milling the cut is likely to deflect the cutter away from the workpiece where as conventional milling the cutter will deflect towards the workpiece due to it essentially creating a reaction force as it "scoops" out the chip towards the end of the cut.

Calculating tangential cutting force

Tangential cutting force for aluminum.

F_t = σ × A × Z_c × E_f × T_f

http://www.ctemag.com/aa_pages/2012/120512-Milling.html

• Ultimate tensile strength (σ) = 310mpa

• Cross-sectional area of the uncut chip (A) =  2*0.0762 = 0.1524mm

• Number of teeth engaged with a workpiece (Z_c) 3/(360/180)=1.5

• Engagement factor of a workpiece material (E_f) = 1.1 from previous post and website link

• Cutting tool wear factor (T_f) = 1.1 from table on web page.

 F_t = 310 * 0.1524 * 1.5 * 1.1 * 1.1  = 86 N 2SF

 

Tangential cutting force for MDF.

F_t = σ × A × Z_c × E_f × T_f

http://www.ctemag.com/aa_pages/2012/120512-Milling.html

• Ultimate tensile strength (σ) = 18mpa

• Cross-sectional area of the uncut chip (A) =  3.125*0.2 = 0.625mm

• Number of teeth engaged with a workpiece (Z_c) 2/(360/180)=1

• Engagement factor of a workpiece material (E_f) = 1.1 from previous post and website link

• Cutting tool wear factor (T_f) = 1.2 from table on web page.

 F_t = 18 * 0.625 * 1 * 1.1 * 1.2  = 15 N 2SF

spindle power required calculations

Spindle power calculation in 6063 T6 Aluminum alloy


http://www.mitsubishicarbide.net/contents/mhg/ru/html/product/technical_information/information/formula4.html

Pc (kW) Actual Cutting Power

ap (mm) Depth of Cut = 2mm

ae (mm) Cutting Width = 10mm

vf (mm/min) Table Feed per Min = 4431

Kc (MPa) Specific Cutting Force = 580 (Taken from table)

η (Machine Coefficient) = 0.9 (Presumed efficiency)

Pc=(2x10x4431x580)/(60*10^6*0.9) =   51399600/54000000 = 0.95kw (2D.P)

Spindle power calculation in MDF



http://www.mitsubishicarbide.net/contents/mhg/ru/html/product/technical_information/information/formula4.html

Pc (kW) Actual Cutting Power

ap (mm) Depth of Cut = 2mm

ae (mm) Cutting Width = 10mm

vf (mm/min) Table Feed per Min = 9600

Kc (MPa) Specific Cutting Force = 56 (Derived from Kc of Aluminum alloy/tensile strength, then figure multiplied against tensile strength of MDF)

η (Machine Coefficient) = 0.9 (Presumed efficiency)

Pc=(3.125x10x9600x56)/(60*10^6*0.9) =   16800000/54000000 = 0.31kw (2D.P)

Cutting speeds and feeds criteria

Guide speeds to allow calculation in 6063 T6 Aluminum alloy.

MRR value: 100cc/minute

Cutter size: 10mm
Cutter material: Carbide TiCN coating
3 flutes.

Feed per tooth or chipload: 0.003" (0.0762mm)
(http://www.cobracarbide.com/catalog/technical_information_endmills.html

Using 3/8" cutter as reference as its closest to 10mm


Cutter speed = surface speed/cutter circumference
                      = 609000/(pi*10)= 19385 rpm (5sf)

Feed rate= (19385*0.0762)*3= 4431 mm/minute. (3sf)

Thus cut depth = mrr/cutter diameter/feed rate = 100 000/10/4431= 2.26mm (3.D.P)

Guide speeds to allow calculation in MDF

The settings in the last post for MDF were incorrect as they were for a single flute cutter

http://www.trend-uk.com/en/UK/productlist/2/36/spiral_cutters.html

according this this manufacture their spiral end mills designed for wood are suitable for speeds up to 24,000 rpm.

There is no information in regards to feed per tooth. However, MDF requires a high feed per tooth as it easily turns to dust rather than cut chips. Thus a large cut is required to prevent this from happening. The dust is very abrasive and reduces tool life. A 0.2mm chip load per revolution per tooth should be suitable. Due to this high chip load the number of flutes need to be reduced to allow time for chips to clear as not to load up the cutter so a 2 flute cutter will be used in this example.

RPM
Feed rate = (24,000*0.2)*2 = 9600 mm/minute.

Cup depth=mrr/cutter diameter/feed rate = 300000/10/9600 = 3.125mm