
<PAGE>   1
                                                                 Exhibit 4.13


                          Form of Senior Notes due 2008


                       (FORM OF FACE OF 2008 SENIOR NOTES)

                  [IF THE NOTE IS TO BE A GLOBAL NOTE, INSERT - This Note is a
Global Note within the meaning of the Indenture hereinafter referred to and is
registered in the name of the Depositary or a nominee of the Depositary. This
2008 Note is exchangeable for 2008 Notes registered in the name of a person
other than the Depositary or its nominee only in the limited circumstances
described in the Indenture, and no transfer of this Note (other than a transfer
of this Note as a whole by the Depositary to a nominee of the Depositary or by a
nominee of the Depositary to the Depositary or another nominee of the
Depositary) may be registered except in limited circumstances.

                  Unless this Note is presented by an authorized representative
of The Depository Trust Company (55 Water Street, New York, New York) to the
issuer or its agent for registration of transfer, exchange or payment, and any
Note issued is registered in the name of Cede & Co. or such other name as
requested by an authorized representative of The Depository Trust Company and
any payment hereon is made to Cede & Co., ANY TRANSFER, PLEDGE OR OTHER USE
HEREOF FOR VALUE OR OTHERWISE BY A PERSON IS WRONGFUL since the registered owner
hereof, Cede & Co., has an interest herein.]

No. _________________________                    $____________________________
CUSIP No.____________________


<PAGE>   2





                                 KENNAMETAL INC.
                            __% Senior Notes due 2008

                  KENNAMETAL INC., a corporation duly organized and existing
under the laws of the Commonwealth of Pennsylvania (the "Company", which term
includes any successor corporation under the Indenture hereinafter referred to),
for value received, hereby promises to pay to Cede & Co., or registered assigns,
the principal sum of _______________ ($______________) on _______ __, 2008 (such
date is hereinafter referred to as the "Maturity Date"), and to pay interest on
said principal sum from January __, 1998, or from the most recent interest
payment date (each such date, an "Interest Payment Date") to which interest has
been paid or duly provided for, semi-annually in arrears on _______ __ and
_______ __ of each year, commencing on _______ __, 1998, at the rate of __% per
annum until the principal hereof shall have become due and payable. The interest
so payable, and punctually paid or duly provided for, on any Interest Payment
Date will, as provided in the Indenture, be paid to the person in whose name
this Note (or one or more Predecessor Securities, as defined in said Indenture)
is registered at the close of business on the regular record date for such
interest which shall be the close of business on the _______ __ or _______ __,
as the case may be, preceding such Interest Payment Date. Any such interest not
punctually paid or duly provided for shall forthwith cease to be payable to the
registered Holders on such regular record date and may be paid to the Person in
whose name this Note (or one or more Predecessor Securities) is registered at
the close of business on a special record date to be fixed by the Trustee for
the payment of such defaulted interest to be fixed by the Trustee, notice
whereof shall be given to the registered Holders of this series of Notes not
less than 10 days prior to such special record date, or may be paid at any time
in any other lawful manner not inconsistent with the requirements of any
securities exchange on which the Notes may be listed, and upon such notice as
may be required by such exchange all as more fully provided in the Indenture.
The principal of, and premium, if any, and the interest on this Note shall be
payable at the office or agency of the Trustee maintained for that purpose in
the Borough of Manhattan, The City of New York, in any coin or currency of the
United States of America that at the time of payment is legal tender for payment
of public and private debts; provided, however, that payment of interest may be
made at the option of the Company by check mailed to the registered Holder at
such address as shall appear in the Security Register.

                  The indebtedness evidenced by this Note is, to the extent
provided in the Indenture, senior and unsecured and will rank in right of
payment on parity with all other senior unsecured obligations of the Company.
Each Holder of this Note by accepting the same, (a) agrees to and shall be bound
by such provisions, (b) authorizes and directs the Trustee on his or her behalf
to take such action as may be necessary or appropriate to acknowledge or
effectuate the subordination so provided and (c) appoints the Trustee his or her
attorney-in-fact for any and all such purposes.

                  This Note shall not be entitled to any benefit under the
Indenture hereinafter referred to, be valid or become obligatory for any purpose
until the Certificate of Authentication hereon shall have been signed by or on
behalf of the Trustee.



<PAGE>   3


                                                                            2



                  The provisions of this Note are continued on the reverse side
hereof and such continued provisions shall for all purposes have the same effect
as though fully set forth at this place.

                  IN WITNESS WHEREOF, the Company has caused this instrument to
be executed.

Dated

                                             KENNAMETAL INC.


                                             By:______________________________
                                                 Name:
                                                 Title:

Attest:


By:______________________________
    Name:
    Title:



<PAGE>   4










                     (FORM OF CERTIFICATE OF AUTHENTICATION)

                          CERTIFICATE OF AUTHENTICATION

                  This is one of the Notes of the series of Notes described in
the within-mentioned Indenture.

Dated___________________________

THE FIRST NATIONAL BANK OF
CHICAGO, as Trustee

By______________________________
   Authorized Signatory


                            (FORM OF REVERSE OF NOTE)
                                 KENNAMETAL INC.
                            __% Senior Notes due 2008

                  This Note is one of a duly authorized series of Securities of
the Company (herein sometimes referred to as the "Securities"), specified in the
Indenture, all issued or to be issued in one or more series under and pursuant
to an Indenture dated as of January __, 1998 (the "Base Indenture"), duly
executed and delivered between the Company and The First National Bank of
Chicago, as Trustee (the "Trustee") (as supplemented by a Second Supplemental
Indenture, dated January __, 1998), (the Base Indenture as so supplemented, the
"Indenture"), to which Indenture and all indentures supplemental thereto
reference is hereby made for a description of the rights, limitations of rights,
obligations, duties and immunities thereunder of the Trustee, the Company and
the Holders of the Securities. By the terms of the Indenture, the Securities are
issuable in series that may vary as to amount, date of maturity, rate of
interest and in other respects as provided in the Indenture. This series of
Securities is limited in aggregate principal amount as specified in said Second
Supplemental Indenture.

                  The Notes are not entitled to the benefit of any sinking fund.

                  The Notes may be redeemed at any time at the option of the
Company, in whole or from time to time in part, upon not less than 30 and not
more than 60 days' notice to the Holders thereof, on any date prior to maturity
(the "Redemption Date") at a price (the "Redemption Price") equal to (i) 100% of
the principal amount of the Notes, plus (ii) accrued interest to the Redemption
Date (subject to the right of Holders of record of such Notes on the relevant
record date to receive interest due on an Interest Payment Date that is on or
prior to the Redemption Date) plus (iii) a Make-Whole Premium (as defined
below), if any. In no event will the Redemption Price of the Notes be less than
100% of the principal amount of the applicable series of Notes being redeemed,
respectively, plus accrued interest to the applicable Redemption Date.



<PAGE>   5


                                                                            2



                  As used herein:

                  "Make-Whole Premium," means an amount equal to the excess, if
         any, of:

                  (i) the sum of the present values, calculated as of the
         applicable Redemption Date, of:

                           (A) each interest payment that, but for such
                  redemption, would have been payable on any such Note (or
                  portion thereof) being redeemed on each Interest Payment Date
                  occurring after the Redemption Date (excluding any accrued
                  interest for the period prior to the Redemption Date); and

                           (B) the principal amount that, but for such
                  redemption, would have been payable at the final maturity of
                  any such Note (or portion thereof) being redeemed; over

                  (ii) the principal amount of such Note (or portion thereof)
         being redeemed.

The present values of interest and principal payments referred to in clause (i)
above will be determined in accordance with generally accepted principles of
financial analysis. Such present values will be calculated by discounting the
amount of each payment of interest or principal from the date that each such
payment would have been payable, but for the redemption, to the applicable
Redemption Date at a discount rate equal to the applicable Treasury Yield (as
defined herein) plus __ basis points.

                  "Treasury Yield" means a rate of interest per annum equal to
the weekly average yield to maturity of United States Treasury securities that
have a constant maturity that corresponds to the remaining term to maturity of
the Notes, calculated to the nearest 1/12th of a year (the "Remaining Term").
The Treasury Yield will be determined as of the third business day immediately
preceding the applicable Redemption Date.

                  The weekly average yields to maturity of United States
Treasury securities will be determined by reference to the most recent
statistical release published by the Federal Reserve Bank of New York and
designated "H.15(519) Selected Interest Rates" or any successor release (the
"H.15 Statistical Release"). If the H.15 Statistical Release sets forth a weekly
average yield to maturity for United States Treasury securities having a
constant maturity that is the same as the Remaining Term, then the Treasury
Yield will be equal to such weekly average yield to maturity. In all other
cases, the Treasury Yield will be calculated by interpolation, on a
straight-line basis, between the weekly average yields to maturity on the United
States Treasury securities that have a constant maturity closest to and greater
than the Remaining Term and the United States Treasury securities that have a
constant maturity closest to and less than the Remaining Term (in each case as
set forth in the H.15 Statistical Release). Any weekly average yields to
maturity as calculated by interpolation will be rounded to the nearest 1/100th
of 1%, with any figure of 1/200th of 1% or above being rounded upward. If weekly
average yields to maturity for United States Treasury securities are not
available in the H.15 Statistical Release or otherwise, then the


<PAGE>   6


                                                                            3



Treasury Yield will be calculated by interpolation of comparable rates selected
by the Independent Investment Banker.

                  If less than all of the Notes of a series are to be redeemed,
the Trustee will select the Notes to be redeemed by such method as the Trustee
shall deem fair and appropriate. The Trustee may select for redemption Notes and
portions of Notes in amounts of whole multiples of $1,000.

                  The Indenture contains provisions for defeasance of (a) the
entire indebtedness of this Note and (b) certain restrictive covenants upon
compliance by the Company with certain conditions set forth therein.

                  In case an Event of Default, as defined in the Indenture,
shall have occurred and be continuing, the principal of all of the Notes may be
declared, and upon such declaration shall become, due and payable, in the
manner, with the effect and subject to the conditions provided in the Indenture.

                  The Indenture contains provisions permitting the Company and
the Trustee, with the consent of the Holders of not less than a majority in
aggregate principal amount of the Notes of each series affected at the time
outstanding, as defined in the Indenture, to execute supplemental indentures for
the purpose of, among other things, adding any provisions to or changing or
eliminating any of the provisions of the Indenture or of any supplemental
indenture or of modifying the rights of the Holders of the Notes; provided,
however, that, among other things, no such supplemental indenture shall (i)
reduce the principal amount thereof, or reduce the rate or extend the time of
payment of interest thereon (subject to the Company's right to defer such
payments in the manner set forth herein), or reduce any premium payable upon the
redemption thereof, without the consent of the Holder of each Note so affected,
or (ii) reduce the aforesaid percentage of Notes, the Holders of which are
required to consent to any such supplemental indenture, without the consent of
the Holders of each Note then outstanding and affected thereby. The Indenture
also contains provisions permitting the Holders of a majority in aggregate
principal amount of the Securities of any series at the time outstanding
affected thereby, on behalf of all of the Holders of the Notes of such series,
to waive a Default or Event of Default with respect to such series, and its
consequences, except a Default or Event of Default in the payment of the
principal of or premium, if any, or interest on any of the Securities of such
series. Any such consent or waiver by the registered Holder of this Note (unless
revoked as provided in the Indenture) shall be conclusive and binding upon such
Holder and upon all future Holders and owners of this Note and of any Note
issued in exchange for or in place hereof (whether by registration of transfer
or otherwise), irrespective of whether or not any notation of such consent or
waiver is made upon this Note.

                  No reference herein to the Indenture and no provision of this
Note or of the Indenture shall alter or impair the obligation of the Company,
which is absolute and unconditional, to pay the principal of and premium, if
any, and interest on this Note at the time and place and at the rate and in the
money herein prescribed.



<PAGE>   7


                                                                            4



                  As provided in the Indenture and subject to certain
limitations therein set forth, this Note is transferable by the registered
Holder hereof on the Security Register of the Company, upon surrender of this
Note for registration of transfer at the office or agency of the Trustee in The
City of New York accompanied by a written instrument or instruments of transfer
in form satisfactory to the Company or the Trustee duly executed by the
registered Holder hereof or his attorney duly authorized in writing, and
thereupon one or more new Notes of authorized denominations and for the same
aggregate principal amount and series will be issued to the designated
transferee or transferees. No service charge will be made for any such transfer,
but the Company may require payment of a sum sufficient to cover any tax or
other governmental charge payable in relation thereto.

                  Prior to due presentment for registration of transfer of this
Note, the Company, the Trustee, any Paying Agent and the Security Registrar may
deem and treat the registered holder hereof as the absolute owner hereof
(whether or not this Note shall be overdue and notwithstanding any notice of
ownership or writing hereon made by anyone other than the Security Registrar)
for the purpose of receiving payment of or on account of the principal hereof
and premium, if any, and interest due hereon and for all other purposes, and
neither the Company nor the Trustee nor any Paying Agent nor any Security
Registrar shall be affected by any notice to the contrary.

                  No recourse shall be had for the payment of the principal of
or the interest on this Note, or for any claim based hereon, or otherwise in
respect hereof, or based on or in respect of the Indenture, against any
incorporator, shareholder, officer or director, past, present or future, as
such, of the Company or of any predecessor or successor corporation, whether by
virtue of any constitution, statute or rule of law, or by the enforcement of any
assessment or penalty or otherwise, and such liability being, by the acceptance
hereof and as part of the consideration for the issuance hereof, expressly
waived and released.

                  The Indenture imposes certain limitations on the ability of
the Company to, among other things, merge or consolidate with any other Person,
sell, assign, transfer or lease all or substantially all of its properties or
assets or create or incur liens on certain of its property. All such covenants
and limitations are subject to a number of important qualifications and
exceptions. The Company must report periodically to the Trustee on compliance
with the covenants in the Indenture.

                  The Notes of this series are issuable only in fully registered
book-entry form without coupons in denominations of $1,000 and any integral
multiple thereof. This Global Note is exchangeable for Notes in definitive form
only under certain limited circumstances set forth in the Indenture. As provided
in the Indenture and subject to certain limitations therein set forth, Notes of
this series so issued are exchangeable for a like aggregate principal amount of
Notes of this series of a different authorized denomination, as requested by the
Holder surrendering the same.

                  This Note shall be governed by and construed in accordance
with the laws of the State of New York.



<PAGE>   8


                                                                            5



                  All terms used in this Note that are defined in the Indenture
shall have the meanings assigned to them in the Indenture.



<PAGE>   9


                                                                            6


                            ------------------------
                                   ASSIGNMENT


                  FOR VALUE RECEIVED, the undersigned assigns and transfers this
Note to:



        (Insert assignee's social security or tax identification number)




                    (Insert address and zip code of assignee)

and irrevocably appoints



agent to transfer this Note on the books of the Trustee. The agent may
substitute another to act for him or her.

Date:___________________________________

                                   Signature:_________________________________

                                   Signature Guarantee:________________________





       (Sign exactly as your name appears on the other side of this Note)



